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//kittitorn kasemkitwatana //studies for project at ENSCI-les ateliers //master in Design and contemporary technology (ctc) //subject of impermanence // and buddhism //e-mail : [email protected]

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INTRODUCTION acknowledgement |||||||||||||||||||||||||||||||||||||||6 The nature of reality in a nutshell by religions and mathematics |||||||||||||||||||||||||||||7 james kowall ||||||||||||||||||||||||||||||||||||77 abstract |||||||||||||||||||||||||||||||||||||||||||||17 ||||||||||||||||||||||||||||||||||23 /* Philosophers buddhism thought and mathematics |||||||||||||||||||||24 A metaphysics of morality : Kant and Buddhism |||80 six aspect of mathematics which are relevant to Kant and the moral law ||||||||||||||||||||||||||81 buddhist philosophy ||||||||||||||||||||||||||||||||||26 The connection in terms of principle between philosophers and buddhism |||||||||||||||||||||||88 HISTORY /* Mathematics Buddhism and German Philosophy ||||||||||||||||||92 ||||||||||||||||||||||||||||||||||||||||||31 Phenomenology and Existentialism ||||||||||||||||94 ||||||||||||||||||||||||||||||||||||37 Buddhism and Process philosophy |||||||||||||||||95 physics |||||||||||||||||||||||||||||||||||||||||40 Wittgenstien ||||||||||||||||||||||||||||||||||||96 logic |||||||||||||||||||||||||||||||||||||||||||41 Authur Schopenhauer |||||||||||||||||||||||||||||97 classical Physics |||||||||||||||||||||||||||||||42 Modern Physics ||||||||||||||||||||||||||||||||||43 /* Buddhism and Mathematics Logical forms |||||||||||||||||||||||||||||||||||44 Buddhist Logics ||||||||||||||||||||||||||||||||102 Mathematical logics |||||||||||||||||||||||||||||46 The bodhisattva ideal ||||||||||||||||||||||||||103 Philosophical logics ||||||||||||||||||||||||||||48 Top 10 Mathematical innovations ||||||||||||||||112 Computational logics ||||||||||||||||||||||||||||49 Applied Buddhism in modern mathematics |||||||||115

/* Art and design /* Emptiness fashion and textile design ||||||||||||||||||||||52 The Buddhist concept of ‘Sunyata’ or ‘Emptiness’|118 need for mathematics and textiles |||||||||||||||54 Evotution of the concept of ‘zero’ in Buddhist idea in fashion design |||||||||||||||||57 modern mathematics |||||||||||||||||||||||||||||119 Mathematics meet fashion : The babylonian system of numerals ||||||||||||||120 Thurston’s concepts inspire designer ||||||||||||59 The evolution of Indian numeral system |||||||||121 Graphic design and typography |||||||||||||||||||60 ‘Zero’ and the place--value notation |||||||||||126 Application of ‘emptiness’ in modern mathematics|127

LITERATURE REVIEW Emptiness and null set: the evolution of /* Quantum natural numbers ||||||||||||||||||||||||||||||||129 Quantum and Abhidhamma ||||||||||||||||||||||||||66 Emptiness and null hypothesis ||||||||||||||||||130 Quantum and concept of matter in Abhidhamma |||||68 Quantum Theory and the buddhist concept of /* Forms in buddhism ||||||||||||||||||||||||||||||||133 Dynamic Flux ||||||||||||||||||||||||||||||||||||70 Einstein’s notion of escape velocity and |||||||137 DISCUSSION black holes |||||||||||||||||||||||||||||||||||||71 /* Artist’s work ||||||||||||||||||||||||||||||||||||142 Einstein’s view on energy for /* Discussion in culture code’s class |||||||||||||||145 expanding universe ||||||||||||||||||||||||||||||74

On quantum Theory of consciousness and nature CONCLUSION ||||||||||||||||||||||||||||||||||||||||||||||||151 of reality ||||||||||||||||||||||||||||||||||||||75 BIBLIOGRAPHY ||||||||||||||||||||||||||||||||||||||||||||||158 The universe in composed of that which is aware of WEBOGRAPHY ||||||||||||||||||||||||||||||||||||||||||||||||161 the universe ||||||||||||||||||||||||||||||||||||76 THANK YOU |||||||||||||||||||||||||||||||||||||||||||||||||162 |||||||||||||||||||| // p (5);

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n, acronymed Rambam , and n, acronymed Rambam ū religions and mathematics religions ibn Maym ā s ū z/ my--mon--i--deez), a preeminent medieval Sephardic a preeminent medieval Sephardic z/ my--mon--i--deez), ː di ɪ n ɒ m ɪˈ prominent Arab and Muslim philosophers and scientists. He became a prominent philosopher and polymath in both the Jewish and Islamic worlds. MAIMONIDES A twelfth--century rabbi and community leader, philosopher and physician, Maimonides was fascinated by the relation between sci ence and religion from his earliest days. A polymath by inclina tion, he needed first to master the sciences then extant, includ and influential Torah scholars and physicians of the Middle Ages. scholars and physicians of the and influential Torah on Passover Empire (present--day Spain) Born in Cordova, Almoravid whence he died in on December 12, 1204, Eve, 1135 or 1138, and buried in Tiberias. his body was taken to the lower Galilee philosopher in Morocco and He worked as a rabbi, physician, and Egypt. Maimonides’ writings on During his lifetime, most Jews greeted gratitude, even as far away Jewish law and ethics with acclaim and rose to become the as Iraq and Yemen, and although Maimonides in Egypt, there were also revered head of the Jewish community particularly in Spain. vociferous critics of some of his writings, as among the fore Nonetheless, he was posthumously acknowledged in Jewish history, and most rabbinical arbiters and philosophers of Jewish scholarship. his copious work comprises a cornerstone carries significant ca His fourteen--volume Mishneh Torah still of Talmudic law. He is some nonical authority as a codification (the great eagle) in recogni times known as “ha Nesher ha Gadol” bona fide exponent of the Oral tion of his outstanding status as a Torah. Maimonides also Aside from being revered by Jewish historians, of Islamic aznd Arab figures very prominently in the history in studies. Influenced by sciences and is mentioned extensively (c. Al--Farabi (ca. 872-950/951), Avicenna temporary Averroes (1126-1198), he in his turn influenced other JUDISM Maimonides or M Moshe ben Maimon, (/ Latinized) Moses Maimonides Graecized (and subsequently ma most prolific and astronomer, became one of the Jewish philosopher - project. between logic and mathematics. From this starting point, I and mathematics. From this starting ship between logic science and between reason and natural will study the relationship between some conclusions on the relationship finally, I will draw mathematics I have an idea from how to use reason and philosophy. in this forms in buddhism and all the topic and logic to create on my final part that helps me explore to work paper will be the This paper will study the relationship between mathematics and the relationship between mathematics This paper will study played by of reason and the role religion from the relation Firstly, I will study the reason in knowledge.

acknowledgement

p (6); p // // p (9); ------Aquinas (c. 1225-1274) to integrate assertions of faith with ex plorations of reason. Science and religion The most vexing issue turned out to be the claim of Genesis that time itself began with creation, whereas the prevailing philo sophical view had long been of a universe emanating necessarily and without beginning from a single unitary principle. Maimonides established the model for addressing this conflict between the soon assumed leadership of the community. After the death of his of the community. After the death soon assumed leadership Mai of the family savings in a shipwreck, brother and the loss family as a responsibility of supporting the monides took up the his death. During this time physician, practicing medicine until 1137-1193), the Sultan of he was court physician to Saladin (c. court, leaving him lit Egypt and Syria, as well as the entire accomplished both, along with tle time to study and write, yet he community. The completion adjudicating disputes within the Jewish Jewish law, the Mishneh To of his groundbreaking codification of fame that his earlier rah, around 1178, brought him even greater for legal opinions from commentary, and he was beset with requests communities throughout the Islamic world. Rabbi Joseph ibn Judah At this time, however, he also encountered him into the logic, cosmol Aqnin, who insisted Maimonides guide Greco--Arabic tradition, so ogy, theology, and philosophy of the learned communities in the as to be able to converse with other as old as Plato’s Acade Islamicate. Following a course of study initiated his student my in the fourth century b.c.e., Maimonides then logic, and finally meta into astronomy and mathematics, and the conundra the revealed physics, by using its tools to explicate scriptures. This series texts often left to readers of the Hebrew and philosophical exegesis of exercise in biblical interpretation the Perplexed. It was imme was published in 1190 as the Guide to Hebrew, and then into Latin, diately translated from Arabic into where it served as a model for Christian thinkers like Thomas gal canon, the Mishnah, during the seven years of exile from his during the seven years of exile gal canon, the Mishnah, in Fustat years. Taking up residence twenty--third to thirtieth court and appointed judge of the rabbinical (Old ), he was LEGAL AND PHILOSOPHICAL WRITINGS LEGAL AND PHILOSOPHICAL the stress continued his education under Remarkably, Maimonides Jewish le composing his commentary on the of exile and travel, ------

of Jerusalem offered a less than favorable milieu for developing Jewish life and culture, the family proceeded to Egypt, where Mai mon soon died, leaving his son to take up the roles in the commu nity to which his learning entitled him. site of the temple in Jerusalem to give thanks for the gift of site of the temple in Jerusalem to give the traditional resting this pilgrimage, and thence to Hebron, place of Abraham, who held a special place in Maimonides’s vi sion of history, not only as the first spokesperson of a universal monotheism, but also as the first to base theological claims on arguments derived from reason. Since the rule of the Latin Kingdom Poetry, astronomy, medicine, philosophy, scriptural exegesis, Poetry, astronomy, medicine, philosophy, typically integrated into a grammar, history, and mysticism were Maimon, led the family comprehensive education. Moses’s father, very center of the Almohad to Fez (in present--day Morocco), the for five years, only to movement, where they managed to survive Maimonides journeyed to the move on to Palestine in 1165, where ly was forced to flee their home in the wake of the Almohads from ly was forced to flee their home in to profess their re North Africa, who forbade Jews or Christians prior to the shattering of ligion openly. Yet in the relative calm an intellectual capital their world, the Jews of Spain had built immeasurably, even after the from which Maimonides was to profit exist. world that had produced it ceased to ba, Spain, where eight generations of his ancestors had served as ba, Spain, where eight generations of of the Umayyad emirs and ca rabbis and rabbinical judges. Capital Córdoba had remained even liphs in Spain since the eighth century, of a brilliant, prosperous in their political decline the center as well as Muslims, civilization in which Jews and Christians, himself was not to enjoy were active participants. Young Moses bar mitzvah, as the fami this cosmopolitan milieu much past his reason, notably with regard to creation. reason, notably with EARLY LIFE AND INFLUENCES and known called Maimonides by Latin authors Mosheh ben Maimon, son of world as Musa ben Maimun, Moses to the Arabic--speaking of Córdo March 30, 1135 c.e., in the city Maimon, was born on ing logic, mathematics and medicine, before being able to assess and medicine, before being able ing logic, mathematics on phi his Jewish faith. Indeed, he insisted their relation to faith and role in the mutual illumination of losophy’s mediating

p (8); p // // p (11); - - - - - we share must have practical results in your life, results you can feel. Kabbalistic wisdom is not based in blind faith, but practi cal application. Kabbalah will deepen your understanding of the universe and give you more information and tools to understand why things are happening to you, and how you can better connect to the Light of the Creator and receive the fulfillment you’re seeking. feeling that we are not as fulfilled as we could be. Paradoxical not as fulfilled as we could be. feeling that we are the we strive to achieve that fulfillment, ly, often the harder more it eludes us. don’t mean just being tempo When we speak about fulfillment, we senses of wellbeing. We mean rarily happy or experiencing fleeting our connection to true connecting to the energy, and maintaining long--lasting fulfillment. living. It teaches that all Kabbalah is an ancient paradigm for relationships, careers -- of the branches of our lives -- health, same root. It’s the technology emanate from the same trunk and the level. It’s a way of looking of how the universe works at the core the kind of permanent ful at the world that can connect you to fillment you seek. that apply to all peoples of Kabbalah teaches universal principles of ethnicity or where you all faiths and all religions, regardless is that you can’t be come from. The beauty of studying Kabbalah There can be no coercion in forced to think in a particular way. share information with you spirituality. All we can do is simply life with the intention of and hope that you will apply it to your everything you will discover bettering it. That’s the purpose of on kabbalah.com. The knowledge we impart, the information we provide, and the tools ceive.” It’s the study of how to receive fulfillment in our lives. of how to receive fulfillment ceive.” It’s the study with the point in our life, have been overcome Most of us, at some SYSTEM KABBALAH and wisdom that reveals how the universe Kabbalah is an ancient “to re level, the word Kabbalah means life work. On a literal

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be defused by a proper understanding of each domain, yet doing so be defused by a proper understanding as astute as Moses Mai requires an education and a sensibility monides’s. As the celebrated Hebrew saying has it: “from Moses to Moses, there arose none like Moses.” osophical view reduced it to the level of mere opinion--howev osophical view reduced it to the level the way to a belief in er widely held it had been, and so opened sophisticated. Such is the scripture that was straightforward yet received from Maimonides, legacy that all religious traditions the Christian world by way whose strategies were transmitted to short, what seem to be con of Aquinas and others after him. In and science, may often flicts between faith and reason, religion texts did conflict with proven tenets of reason, then they would texts did conflict with proven tenets since the divine reality have to be interpreted figuratively; to the “Lord’s mighty arm” could not be bodily, texts referring He was even prepared to read would have to be read metaphorically. moment of time for creation, Genesis that way, foregoing a first of the prevailing phil but the absence of a valid demonstration So, he said, it makes more eminent sense to posit a free creator, So, he said, it makes more eminent sense what logic cannot. whose intentional ordering could explain how his scientific acumen This central bit of reasoning displays for believers to accept could be put to use to make it possible yet he was also quick to in the words of Genesis at face value, Moreover, where scriptural sist that neither view could be proven. the universe coming forth from a single unitary principle with forth from a single unitary principle the universe coming delineate having shown that, he proceeded to out beginning. And path of actual universe, notably the errant the anomalies in the no set of ”), to point out that the planets (or “wandering of the could for the actual ordering logical principles scheme. elegance of the necessary emanation heavens, despite the divergent claims of reason and of faith by using his philosophical reason and of faith by using his divergent claims of invoked-- the authority whom philosophers had acumen to show that of intended nor achieved a demonstration Aristotle--had neither

p (10); p // // p (13); - - - - Averroës is perhaps most famous for his translations and detailed commentaries on the works of Aristotle, which earned for him the title of the “The Commentator”. These were based on imperfect Arabic translations, not Greek originals (it is believed that he was unacquainted with Greek or Syriac), and he did not have access to some of the texts (e.g. the”Politics”). The commentaries were organized into three levels: the Jami (a simplified overview), the Talkhis (an intermediate commentary with more critical material) and the Tafsir (an advanced study of Aristotelian thought in a Muslim context). befriended by Ibn Tufail (c. 1105 -- 1185, known as Abubacer in Tufail (c. 1105 -- 1185, known as Abubacer befriended by Ibn to and official physician and counsellor the West), a philosopher to the Yusuf. Ibn Tufail introduced Averroës the caliph Abu Yaqub by the young philosopher caliph, and the prince was so impressed judge and later in 1182 that he employed him, first as his chief Averroës to write a se as chief physician. He also commissioned Aristotle, (for whom Averroës ries of commentaries on the texts of matters of science and phi professed the greatest esteem in all main legacies to Western losophy), which became one of Averroës’ philosophy. of the Almohad Dynasty, However, despite the general liberalism Islamic elements under public pressure from the more orthodox Ya’qub al--Mansur, led to the the third Almohad caliph, Abu Yusuf strictly rationalist views formal rejection of Averroës and his the religious community of in 1195. He was tried as a heretic by Jewish village outside of Córdova, exiled to Lucena (a largely his books burned. Just two Córdoba) his writings were banned and he was rehabilitated, de years later, shortly before his death, spite continued doubts about his orthodoxy. Marrakesh, Morocco, and his Averroës died on 10 December 1198 in death, mainly in the Chris writings found new audiences after his tian and Jewish worlds. WORK out this period of his life, he wrote many legal commentaries and his life, he wrote many legal commentaries out this period of sacrifices methodology, legal pronouncements, treatises on legal and land taxes. periodic residences in Marrakesh (Marrakech), During one of his he was African capital of the Almohad dynasty, Morocco, the North - - - - -

Abu Jafar ibn Harun of Trujillo, and he showed a clear aptitude for medicine, (his compendium of medicine, “al--Kulliyat” became one of the main medical textbooks for physicians in the Jewish, Christian and Muslim worlds for centuries to come). In 1169, Averroës was made a qadi (a sharia or religious judge) of Seville, and then, in 1172, chief judge of Córdova. Through His early education followed a traditional path in such a fami His early education followed a traditional ly, beginning with studies in hadith, linguistics, jurisprudence and scholastic theology. He was influenced (and perhaps was once tutored) by the philosopher Ibn Bajjah (1095 -- 1138, known as Avempace in the West). His medical education was directed under dova) in Andalusia, the capital of Muslim Spain. He came from a dova) in Andalusia, the capital of Muslim is one of the four schools family of Maliki legal scholars (Maliki and both his grandfather, of religious law within Sunni Islam), Abu Al--Qasim Ahmad, were Abu Al--Walid Muhammad, and his father, dynasty which ruled chief judges of Córdoba under the Almoravid in the mid--12th Centu the region until replaced by the Almohads ry. been described as the founding father of secular thought, becoming been described as the founding father West. known as “The Commentator” in the Christian LIFE the Latinized distortion of Averroës (pronounced a--VER--o--ees, born in 1126 in Córdoba (Cor the actual Arab name Ibn Rushd) was Western Europe. role in the defence of In the Islamic world, he played a decisive Ash’arite theologians led Greek philosophy against the orthodox during his lifetime his by al--Ghazali (1058 -- 1111). Although in Muslim circles, he had philosophy was considered controversial thought, and he has an even greater impact on Western European Averroës (AKA Ibn Rushd or Ibn Roschd or, in full, Abu al--Walid Rushd or Ibn Roschd or, in full, Abu Averroës (AKA Ibn ibn Rushd) (1126 -- 1198) was a Spanish--Ara Muhammad ibn Ahmad the Andalusia lawyer and polymath from bic philosopher, physician, his death, Spain in the Medieval period. After region of southern and his work grew up around his teachings, the Averroism movement in the subsequent development of Scholasticism greatly influenced MUSLIM AVÉROES

p (12); p // // p (15); - ed into two parts (an individual part, and a divine part which is (an individual part, and a divine part ed into two parts idea by all). His belief in the then radical eternal and shared later by the essence” was developed much that “existence precedes in the 17th of Mulla Sadra (c. 1571 - 1640) Transcendent Theosophy in the 20th Century. Century and by Existentialism He believed in an eternal universe, and in a soul which is divid eternal universe, and in a soul which He believed in an ------

losophy (the real truth, but reserved for an elite few who had the intellectual capacity to undertake such study). He was bold enough to claim the superiority of reason and philosophy over faith and knowledge founded on faith, and to emphasize the independent use of reason, and the idea that the philosophical and religious worlds are separate entities. For Averroës, there was no conflict between religion and philoso For Averroës, there was no conflict phy, believing rather that they were just different ways of reach ing the same truth. He identified two kinds of knowledge of truth: knowledge of truth from religion (for the unlettered multitude, based in faith and untestable); and knowledge of truth from phi phers”). Al--Ghazali had argued that Aristotelianism, especially phers”). Al--Ghazali had argued that of Avicenna, was self--con as presented in the earlier writings of Islam. Averroës con tradictory and an affront to the teachings were mistaken, but also tended both that al--Ghazali’s arguments were a distortion of that, in any case, Avicenna’s interpretations effect, al--Ghazali was aim genuine Aristotelianism, so that, in ing at the wrong target. of secular thought in Western Europe. work was “Tahafut al- His most important original philosophical in which he -tahafut” (“The Incoherence of the Incoherence”), the claims of al--Ghazali defended Aristotelian philosophy against Incoherence of the Philoso in his “Tahafut al--falasifa” (“The were not studied much or given much credence by monastic scholars, were not studied much or given much of Averroës’ work that and it was through the Latin translations widely known in the West, with the legacy of Aristotle became more Scholastic movement. Aver particular importance for the Medieval of science and philosophy roës also argued for the emancipation and some writers regard him from official Ash’ari Muslim theology, or even the founding father as a precursor to modern secularism, nently lost, while others, including some of the longer commentar others, including some of the longer nently lost, while and not in in Latin or Hebrew translation, ies, have only survived the original Arabic. only a few these works is that, before 1150, The significance of and they Aristotle existed in Latin Europe, translated works of Many of his commentaries were translated into Hebrew and then into were translated into Hebrew Many of his commentaries and 13th Cen directly into Latin) in the 12th Latin (or sometimes been perma works on Logic and Metaphysics have tury. Many of the

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attains it. But there are many different types of Buddhism, be cause the emphasis changes from country to country due to customs and cultures. What does not vary is the essence of the teaching -- the Dhamma or truth. Thus, what people understand about buddhism is not the same believe in everywhere including numbers, texts (or alphabetical characters) and images. texts (or alphabetical characters) including numbers, consensual or symbolic forms accordingly engage Numbers and images comprehend through being explained and understanding among ed idea of worshipping , the Because Buddhism does not include the a religion in the normal, creator. Some people do not see it as teaching are straight Western sense. The basic tenets of Buddhist or permanent; actions have forward and practical: nothing is fixed Therefore, Buddhism addresses consequences; changes are possible. race, nationality, caste, itself to all people irrespective of methods which enable sexuality, or gender. It teaches practical in order to transform people to realise and use those teachings for their lives. their experience, to be fully responsible development lead Buddhism is a path of practice and spiritual of reality. Buddhist prac ing to insight into the true nature changing oneself in order tices like meditation are a means of kindness, and wisdom. The to develop the qualities of awareness, tradition over thousands experience developed within the Buddhist resource for all those who of years has created an incomparable ultimately culminates in wish to follow a path -- a path which being sees the nature Enlightenment or Buddhahood. An enlightened lives fully and naturally of reality clearly, just as it is, and is the goal of the Buddhist in accordance with that vision. This spiritual life, representing the end of suffering for anyone who Tracing back to the time before history, humans utilise mathemat time before history, humans utilise Tracing back to the through and forms as a way to communicate ics and various shapes as and quantities. Mathematics is considered indicating amounts Therefore, recognised languages. one of the most internationally language essential tool in communication or mathematics is an are three types of visual comprehension interpretation. There

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science

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theravada p (21); p (20); // p (23); - and art - - - - mathematics 2 for the ideal male nude. Persistent 2 for the ideal male √

Italian , wrote the influential treatise Luca Pacioli wrote the influential Italian Renaissance, by Leon (1509), illustrated with De Another the use of the golden ratio in art. ardo , on developed Euclid’s ideas Italian painter, , , and on perspective in treatises such as Dürer made many referenc in his paintings. The engraver Albrecht I. In modern times, the es to mathematics in his work Melencolia use of and graphic artist M. C. Escher made intensive the H. S. M. hyperbolic , with the help of led by Theo van Doesberg and Coxeter, while the De Stijl movement forms. Mathematics Piet Mondrian explicitly embraced geometrical knitting, crossstitch, has inspired textile arts such as quilting, and other carpet--making, as crochet, embroidery, weaving, Turkish are evident in forms as well as kilim. In Islamic art, zellige tilework, Mughal jaa varied as Persian and Moroccan vaulting. li pierced stone screens, and widespread Mathematics and art have a long historical relationship. Art have a long historical relationship. Mathematics and art the since the 5th century BC when ists have used mathematics propor wrote his Canon, prescribing Greek sculptor ratio 1: tions based on the ratio in been made for the use of the golden popular claims have In the without reliable evidence. ancient art and ,

p (22); p // // p (25); - - - - the world corresponds to it. However, even thought mathematics looks looks mathematics thought even However, it. to corresponds world the ultimately like is reality what describe not does it certain, very and concepts on depends mathematics all because is This speaking. language (so is logic), and once you have concepts, you have to di model a is mathematics best at So chunks. separate into reality vide the is it reality the to identical become can map no and map, a or can We sunyata. or Emptiness of doctrine the to refers This of. map because it, reach never but that, approach always can math that say if it does, then it would cease to be the math that it is. I think the main difference between the theistic religions like like religions theistic the between difference main the think I not might Buddhism like one non--theistic and Islam and Christianity problem no have would Buddhism think. might one as large as appear refers, that as long so above, to alluded Mind Big the recognising us is It minds. own our to fact in but being, external some to not minds, own our speaking ultimately is it and mathematics create who is it that such world the create that collectively, together working human we that say also could we words, other In mathematics. of true creates that Mind Big a is There ourselves. unto are beings from apart not is Mind that but yes, math, to corresponding reality us. If theism. on view your on depends not or shocking is this Whether this find you’d then God, from apart are humans that believe you Buddhist the with correspondent entirely is this However, shocking. the person’s own responsi attitude that salvation is ultimately The achieve. to power person’s the within entirely lies and bility The teaching. his follow to need don’t You teacher. a only is Buddha You does. being No Liberation. to you drag to power no has Buddha have to do it yourself. we earth, to down back and discussion theological from down Coming itself that creates mathe see that the idea that it is human mind form We sense. of lot a quite makes belongs reality which to matics according to the same concep mathematics and we perceive the world wonder no so place, first the in math the formed that structure tual So this big mind might refer to God. So here the discussion went on on went discussion the here So God. to refer might mind big this So remember quite don’t I this. about think Buddhists the what see to this, of made book, the in representative Buddhist the Ricard, what the during this did also I thought. own my present to going am I so then. limited so was time but Saturday, last talk - - - ones, of course). It is this big mind that guarantees that two plus plus two that guarantees that mind big this is It course). of ones, the of sum the that four, equals two plus two that four, equals two is triangle angle right a of legs two the of side the on squares (‘p’ ponens modus of law the that hypotenuse, the on that to equal on. so and ‘q’), implies always q’ then p ‘if and We are not actually discussing Kant here; the point is that if the the if that is point the here; Kant discussing actually not are We must it then observation, from come not does mathematics of truth come from inside. Ricard and Thuan discussed that perhaps this sit mind powerful all and universal some is there that implies uation true the (all true statements mathematical all made thinking whose that two plus two equals four in order for you to be able to get get to able be to you for order in four equals two plus two that four! make two other these and things two these that conclusion the critical entire his in strategy argumentative main Kant’s is This he what of example prime a is mathematics Kant for And philosophy. true are that judgments e.g., judgments, priori” a “synthetic calls point measuring outside some with correspondence their of virtue by thinking alone. but which is known entirely through plus two equals four. So you have two things, add another two, two, another add things, two have you So four. equals two plus of premise the But four. course of is which result, the count and that for logic (or mathematics get cannot you that is mathematics general a form cannot just You observation. empirical of out matter) another and things two observing just from 4” = 2 + “2 statement hand before know to somehow have you that is reason The things. two on this topic. The idea is how mathematics is related to reality and and reality to related is mathematics how is idea The topic. this on book the of chapter eleventh The that. of think Buddhists the what that. like something or Universe” the of Grammar “The entitled is of description accurate an is mathematics how is interesting is What or the world? reality at all. Which comes first, mathematics two that know all We point. simple very a is this hand, one the On have of course been quite a lot of talks about how Buddhism and sci quite a lot of talks about how Buddhism have of course been mathematics. and Buddhism on all at much not but related, are ence much spend not did we Unfortunately change. welcome a was that So topic. time on this fascinating chapter entire one spend they that Thuan and Ricard to credit was It One of the many topics that was raised during the talk on the Thai Thai the on talk the during raised was that topics many the of One book con Ricard’s and Trinh Xuan Thuan’s translation of Matthieu There mathematics. and thought Buddhist between relation the cerned

buddhism throught buddhism and mathematics

p (24); p // // p (27); - - (vi) The deep interconnection between the mind contemplating contemplating mind the between interconnection deep The (vi) that suggests world, physical the of workings the and emptiness, conventional and ultimate between bridge a provide may mathematics truths. (v) The concept of ‘algorithmic compression’, which is an aspect aspect an is which compression’, ‘algorithmic of concept The (v) the to on leads mathematics, of effectiveness unreasonable the of gives us a workable phil Church--Turing--Deutsch principle, which phenomena, non--physical and physical between demarcation osophical aspects of the mind. including physical and non--physical simulate all physical phenomena. effectiveness’ ‘unreasonable the epitomise simulations These (iv) there that suggests which , and physics in mathematics of products the as explainable not are which mind the of aspects be may of evolution. (ii) The bootstrapping of the integers out of the empty set provides provides set empty the of out integers the of bootstrapping The (ii) expressed be can components and causes how of illustration simple a data-- structures. as algorithms and empty founda development of mathematics from its (iii) The further can that structures data and algorithms computational creates tions (i) The foundations of mathematics have parallels (and differences) differences) (and parallels have mathematics of foundations The (i) concept of emptiness (sunyata) with the Buddhist

six aspects ofsix aspects mathematics philosophy to buddhist relevant are which

p (26); p // // p (29);

history;

p (28); p // // p (31); euclid ------As the Greek empire began to spread its sphere of influence into Asia Minor, Mesopotamia and beyond, the Greeks were smart enough to adopt and adapt useful elements from the societies they con quered. This was as true of their mathematics as anything else, and they adopted elements of mathematics from both the Babylonians and the Egyptians. from the time of its publication until the late 19th or early 20th publication until the late 19th from the time of its of what is Euclid deduced the principles century. In the Elements, Euclid geometry from a small set of axioms. now called Euclidean sections, spherical geome also wrote works on perspective, conic try, number theory and rigor. use them to formulate new seek out patterns and the truth or falsity of conjectures. Mathematicians resolve mathematical structures conjectures by mathematical proof. When mathematical reasoning are good models of real phenomena, then nature. Through the use can provide insight or predictions about developed from counting, of abstraction and logic, mathematics study of the shapes calculation, measurement, and the systematic mathematics has been and motions of physical objects. Practical written records exist. The a human activity for as far back as problems can take years or research required to solve mathematical even centuries of sustained inquiry. including natural sci Mathematics is essential in many fields, and the social sciences. ence, engineering, medicine, finance new mathematical disci Applied mathematics has led to entirely theory. Mathematicians also plines, such as statistics and game for its own sake, with engage in pure mathematics, or mathematics There is no clear line sep out having any application in mind. and practical applications arating pure and applied mathematics, for what began as pure mathematics are often discovered. Euclid sometimes called Euclid of to distinguish him Euclid of Alexandria to distinguish Euclid sometimes called referred was a Greek mathematician, often from Euclid of Megara, during of geometry”. He was active in Alexandria to as the “father one of the I (323--283 BCE). His Elements is the reign of Ptolemy serving as in the , most influential works geometry) for teaching mathematics (especially the main textbook

mathematics

p (30); p // // p (33); - - - - Euclid’s method for constructing of an equilateral triangle from a given straight line segment AB using only a compass and straight edge was Proposition 1 in Book 1 of the Elements Euclid’s method for constructing of an equilateral line straight given a from triangle and compass a only using AB segment straight edge was Proposition 1 in Book 1 of the Elements e b c a d es. It was only with the work of Bolyai, Lobachevski and Riemann in the first half of the 19th Century that any kind of non--Eu clidean geometry was even considered. The “Elements” remained the definitive textbook on geometry and mathematics for well over two millennia, surviving the eclipse in classical learning in Europe during the Dark Ages through Arabic translations. It set, for all time, the model for mathematical argument, following logical deductions from initial assumptions (which Euclid called “axioms” and “postulates”) in order to establish proven theorems. optics and music. compilation and ex The “Elements” was a lucid and comprehensive of his time, including the planation of all the known mathematics Theaetetus and Eudoxus. work of Pythagoras, Hippocrates, Theudius, proofs, described in a clear, In all, it contains 465 theorems and only a compass and a straight logical and elegant style, and using concepts of his predeces edge. Euclid reworked the mathematical to become known as Euclidean sors into a consistent whole, later as it was 2,300 years ago, geometry, which is still as valid today even in higher mathematics dealing with higher dimensional spac resents the culmination of the mathematical revolution which had of the mathematical revolution resents the culmination works on the up to that time. He also wrote taken place in Greece ratios, figures into into parts in given division of geometrical reflection), mathematical theory of mirrors and on catoptrics (the location of (the determination of the and on spherical astronomy texts on sphere”), as well as important objects on the “celestial - - - - -

and with its prestigious and comprehensive Library, had already become a worthy rival to the great Academy. Euclid is often referred to as the “Father of Geometry”, and he wrote perhaps the most important and successful mathematical textbook of all time, the “Stoicheion” or “Elements”, which rep so depictions of him (with a long flowing beard and cloth cap) in so depictions of him (with a long flowing of the artist’s imagina works of art are necessarily the products tion. He probably studied for a time at Plato’s Academy in Athens but, by Euclid’s time, Alexandria, under the patronage of the Ptolemies his work (such as on similar and right triangles) now seems quite his work (such as on similar and right elementary. and flourished in Alexandria The Greek mathematician Euclid lived reign of Ptolemy I. Almost in Egypt around 300 BCE, during the likeness or first--hand de nothing is known of his life, and no has survived antiquity, and scription of his physical appearance But most of Greek mathematics was based on geometry. Thales, one But most of Greek mathematics was based who lived on the Ionian of the Seven Sages of , of the 6th Century BCE, is coast of Asian Minor in the first half first to lay down guidelines usually considered to have been the although what we know of for the abstract development of geometry, tem similar to the earlier Egyptian one (and even more similar to tem similar to the earlier Egyptian for 1, 5, 10, 50, 100, 500 the later Roman system), with symbols to represent the desired and 1,000 repeated as many times needed separately the symbols (1s, number. Addition was done by totalling added, and multiplication was 10s, 100s, etc) in the numbers to be doublings (division was a laborious process based on successive based on the inverse of this process). over one of the most dramatic and important revolutions in mathe dramatic and important revolutions over one of the most all time. matical thought of numeral system, known as Attic or Herodianic The ancient Greek regular use developed by about 450 BCE, and in numerals, was fully 10 sys as the 7th Century BCE. It was a base possibly as early But they soon started to make important contributions in their own to make important contributions But they soon started first time, we can acknowledge contributions right and, for the had presided the Hellenistic period, the Greeks by individuals. By

p (32); p // // p (35); - - - - - area 1 = area 2 area 3 = area 4 Euclid’s proof of Pythagoras Theo rem revolved around the fact that if a line is draw from the right hypote the to perpendicular angle, on square the through draw and nuse split is square that hypotenuse the into two rectangle each having the same area as the squares on the other two sides C area 3 area 4 A area 2 area 1 B nings of number theory. For example, Euclid proved what has become known as the Fundamental Theorem of Arithmetic (or the Unique Factorisation Theorem), that every positive integer greater than 1 can be written as a product of prime numbers (or is itself a prime number). Thus, for example: 21 = 3 x 7; 113 = 1 x 113; 1,200 = 2 x 2 x 2 x 2 x 3 x 5 x 5; 6,936 = 2 x 2 x 2 x 3 x 17 x 17; etc. His proof was the first known example of a proof by contradiction (where any counter--example, which would otherwise prove an idea false, is shown to makes no logical sense itself). Among many other mathematical gems, the thirteen volumes of the Among many other mathematical gems, the volumes of sol “Elements” contain formulas for calculating proofs about geometric ids such as cones, and cylinders; algorithms for finding the series, perfect numbers and primes; multiple of two numbers; greatest common divisor and least common Theorem, and proof that a proof and generalisation of Pythagoras’ Triples; and a final there are an infinite number of Pythagorean five possible regular Pla definitive proof that there can be only tonic Solids. a series of theorems on the However, the “Elements” also includes properties of numbers and integers, marking the first real begin

V'. III. α β α+β<180° V. II. distance (radius). All right angles are equal to one another (i.e. “half” of a straight angle). If a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than the two right angles. It is possible to draw a straight line from It is possible to draw a straight line any point to any point. in a straight line (i.e. a line segment can be extended past either of its endpoints to form an arbitrarily large line segment). It is possible to create a circle with any center and If equals are added to equals, the wholes (sums) are equal. If equals are added to equals, the wholes If equals are subtracted from equals, the remainders (differences) are equal. Things which are equal to the same thing are equal to each other. Things which are equal to the same thing

• • • •It is possible to extend a finite straight line continuously • • • are equal to one another. •Things that coincide with one another •The whole is greater than the part. His five geometrical postulates were: Euclid’s five general axioms were: •

edge was Proposition 1 in Book 1 of the “Elements” Euclid’s method for constructing of constructing for method Euclid’s an equilateral triangle from a given straight line segment AB using only a compass and straight IV. I.

p (34); p // // p (37); - - - golden ratio golden of the Golden ratio in art. The is also related to the Golden spiral, which is created by making adjacent squares of dimensions. ameter), the digits go on and on, theoretically into infinity. Phi ameter), the digits go on and on, theoretically number has been discovered is usually rounded off to 1.618. This why it has so many names and rediscovered many times, which is divine proportion, etc. -- the Golden mean, the Golden section, in the architecture of many Historically, the number can be seen and the . In ancient creations, like the Great Pyramids of each side of the base is the Great of , the length The ratio of the base to the 756 feet with a height of 481 feet. to the Golden ratio. height is roughly 1.5717, which is close Fibonacci discovered the Around 1200, mathematician Leonardo This sequence ties unique properties of the Fibonacci sequence. if you take any two succes directly into the Golden ratio because is very close to the Golden sive Fibonacci numbers, their ratio ratio becomes even closer to ratio. As the numbers get higher, the 5 is 1.666. But the ratio of 1.618. For example, the ratio of 3 to the ratio of 144 to 233 is 13 to 21 is 1.625. Getting even higher, numbers in the Fibonacci 1.618. These numbers are all successive sequence. proportions of a rectangle, These numbers can be applied to the known as one of the most vi called the Golden rectangle. This is sually satisfying of all geometric forms -- hence, the appearance a/b = (a+b)/a = 1.6180339887498948420 … a/b = (a+b)/a = 1.6180339887498948420 to its di of the circumference of a circle As with pi (the ratio The Golden ratio is a special number found by dividing a line into a special number found by dividing The Golden ratio is part is the longer part divided by the smaller two parts so that part. It is whole length divided by the longer also equal to the the Greek phi, after the 21st letter of often symbolised using form, it looks like this: alphabet. In an equation - - - -

- , approximately equal to 1.618), Euclid was the first to define , approximately equal to 1.618), Euclid

φ

( and demonstrated its ap it in terms of ratios (AB:AC = AC:CB), pearance within many geometric shapes. + 3 + 4 + 5 + ... + 126 + 127. of 2 less one, and the num Their largest prime factor is a power and the previous power of ber is always a product of this number 1); 496 = 24(25 -- 1); 8,128 = two: 6 = 21(22 -- 1); 28 = 22(23 -- 26(27 -- 1). aware of the Golden Ratio Although the Pythagoreans may have been He noted that these numbers also have many other interesting prop He noted that these numbers also have numbers, and therefore erties. For example: They are triangular up the sum of all the consecutive numbers + 2 + 3; 28 = 1 + 2 + 3 + 4 + to their largest prime factor: 6 = 1 .... + 30 + 31; 8,128 = 1 + 2 5 + 6 + 7; 496 = 1 + 2 + 3 + 4 + 5 + that are the sum of all their divisors (excluding the number it that are the sum of all their divisors self): 6 = 1 + 2 + 3; 28 = 1 + 2 + 4 + 7 + 14; 124 + 248; and 496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + + 254 + 508 + 1,016 + 8,128 = 2 + 4 + 8 + 16 + 32 + 64 + 127 2,032 + 4,064. primes, if you multiply all of them together and then add one, all of them together and then primes, if you multiply 2 x 3 x been added to the set (for example, then a new prime has can be = 31, a prime number) a process which 5 = 30, and 30 + 1 repeated indefinitely. numbers the first four “perfect numbers”, Euclid also identified He was the first to realize -- and prove -- that there are in realize -- and prove -- that there He was the first to often known numbers. The basis of his proof, finitely many prime set of is that, for any given (finite) as Euclid’s Theorem,

p (36); p // // p (39); - - - - Animal bodies: The measurement of the human navel to the floor and the top of the head to the navel is the Golden ratio. But we are not the only examples of the Golden ratio in the animal kingdom; dolphins, starfish, sand dollars, sea urchins, ants and honeybees also exhibit the proportion. DNA molecules: A DNA molecule measures 34 angstroms by 21 ang stroms at each full cycle of the double helix spiral. In the Fibo nacci series, 34 and 21 are successive numbers. Seed heads: The seeds of a flower are often produced at the center of a flower are often produced Seed heads: The seeds to fill the space. For example, sunflowers and migrate outward follow this pattern. seed pods spiral upward in op Pinecones: The spiral pattern of the match to tend take spirals the steps of number The directions. posite Fibonacci numbers. form or split is an example Tree branches: The way tree branches and algae exhibit this of the Fibonacci sequence. Root systems formation pattern. shells and nautilus shells, Shells: Many shells, including snail are perfect examples of the Golden spiral. number of spiral arms, each Spiral galaxies: The Milky Way has a roughly 12 degrees. The shape of which has a logarithmic spiral of spiral, and the Golden of the spiral is identical to the Golden galaxy. rectangle can be drawn over any spiral often display the Golden Hurricanes: Much like shells, hurricanes spiral. each section from the tip of Fingers: The length of our fingers, the preceding one by roughly the base to the wrist is larger than the ratio of phi. als on some flowers follows the Fibonacci sequence. It is believed follows the Fibonacci sequence. It als on some flowers to allow for processes, each petal is placed that in the Darwinian exposure to sunlight and other factors. the best possible The Golden ratio also appears in all forms of nature and science. appears in all forms of nature The Golden ratio also of pet include: Flower petals: The number Some unexpected places - - - 13 21 b 2 3 8 5 34 a parallels to the Golden ratio. Faces judged as the most attractive show Golden ratio proportions between the width of the face and the width of the eyes, nose, and eyebrows. The test subjects weren’t mathematicians or physicists familiar with phi -- they were just average people, and the Golden ratio elicited an instinctual reaction. crystals, a then--newly discovered form of matter. crystals, a then--newly discovered form Phi is more than an obscure term found in mathematics and phys ics. It appears around us in our daily lives, even in our aesthet ic views. Studies have shown that when test subjects view random faces, the ones they deem most attractive are those with solid Golden ratio include Michelangelo, , Rembrandt, Seurat, and Golden ratio include Michelangelo, Raphael, Salvador Dali. mathematician Mark Barr in The term “phi” was coined by American in mathematics and physics, the 1900s. Phi has continued to appear allowed surfaces to be including the 1970s Penrose Tiles, which 1980s, phi appeared in quasi tiled in five--fold . In the The Golden ratio was used to achieve balance and beauty in many The Golden ratio was used to achieve Da Vinci himself used the Renaissance paintings and sculptures. in his Last Supper, Golden ratio to define all of the proportions and the proportions of the including the dimensions of the table also appears in da Vinci’s walls and backgrounds. The Golden ratio artists who employed the and the . Other In 1509, Luca Pacioli wrote a book that refers to the number as In 1509, Luca Pacioli wrote a book that by Leonardo da Vin the “Divine Proportion”, which was illustrated aurea or the Golden section. ci. Da Vinci later called this sectio

a

p (38); p // // p (41); logic - - - - - , logike) is the branch of philos , logike) is the branch λογική of logic. Modern formal logic follows and expands on Aristotle. In many definitions of logic, logical inference and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuances of natural language. Greece, India, and China. In the West, logic was established as a China. In the West, logic was established Greece, India, and place in by Aristotle, who gave it a fundamental formal discipline trivi of logic was part of the classical philosophy. The study rhetoric. Logic was further um, which also included grammar and it into two separate groups extended by Al--Farabi who categorized the study of logic and (idea and proof). Later, Avicenna revived and the implication. In developed relationship between temporalis Buddhists and Jains. the East, logic was developed by Hindus, inductive reasoning, ab Logic is often divided into three parts: ductive reasoning, and deductive reasoning. to logic. The validity of The concept of logical form is central form, not by its content. an argument is determined by its logical logic and modern symbolic Traditional Aristotelian syllogistic logic are examples of formal logic. language arguments. The Informal logic is the study of natural of informal logic. The study of fallacies is an important branch of informal logic. dialogues of Plato are good examples with purely formal con Formal logic is the study of inference formal content if it can be tent. An inference possesses a purely of a wholly abstract rule, expressed as a particular application particular thing or proper that is, a rule that is not about any ty. The works of Aristotle contain the earliest known formal study (from the Ancient Greek: (from the Ancient study the use and study of valid reasoning.The ophy concerned with computer prominently in mathematics and of logic also features science. in several ancient civilizations, including Logic was studied - - - - - ) “knowledge ē m ḗ (epist ḗ phusik φυσική phúsis “nature”) is the natural science phúsis “nature”) φύσις clear physics led directly to the development of new products clear physics led directly to the development society, such as that have dramatically transformed modern--day and nuclear weapons; television, computers, domestic appliances, development of industrial advances in thermodynamics led to the the development of isation, and advances in mechanics inspired calculus. fundamental mechanisms of other sciences while opening new avenues fundamental mechanisms of other sciences and philosophy. of research in areas such as mathematics through advances in Physics also makes significant contributions breakthroughs. For new technologies that arise from theoretical of electromagnetism or nu example, advances in the understanding lennia, physics was a part of natural philosophy along with chem lennia, physics was a part of natural of mathematics, but during istry, biology, and certain branches century, the natural scienc the scientific revolution in the 17th in their own right. Physics es emerged as unique research programs areas of research, such as intersects with many interdisciplinary the boundaries of physics biophysics and quantum chemistry, and physics often explain the are not rigidly defined. New ideas in time, along with related concepts such as energy and force. One concepts such as energy and time, along with related goal of scientific disciplines, the main of the most fundamental how the universe behaves. physics is to understand the the oldest academic disciplines, perhaps Physics is one of two mil inclusion of astronomy. Over the last oldest through its Physics (from Ancient Greek: Physics (from Ancient of nature”, from space and study of matter and its motion through that involves the

physics

p (40); p // // p (43); physics - - modern - - - - - work of Max Planck in quantum theory and Albert Einstein’s theo in quantum theory and Albert Einstein’s work of Max Planck to inac Both of these theories came about due ry of relativity. Classical mechanics in certain situations. curacies in classical of light, which could not be mechanics predicted a varying speed by Maxwell’s equations resolved with the constant speed predicted was corrected by Einstein’s of electromagnetism; this discrepancy replaced classical mechanics theory of special relativity, which for a constant speed of light. for fast--moving bodies and allowed problem for classical phys Black body radiation provided another proposed that light comes in ics, which was corrected when Planck this, along with the photo individual packets known as photons; predicting discrete energy electric effect and a complete theory the theory of quantum mechan levels of electron orbitals, led to at very small scales. ics taking over from classical physics by Werner Heisen Quantum mechanics would come to be pioneered From this early work, and berg, Erwin Schrödinger and Paul Dirac. Model of particle physics work in related fields, the Standard of a particle with properties was derived. Following the discovery in 2012, all fundamental consistent with the Higgs boson at CERN model, and no others, appear particles predicted by the standard Standard Model, with theo to exist; however, physics beyond the area of research. Areas ries such as supersymmetry, is an active to this field, such as of mathematics in general are important study of probabilities. Albert Einstein (1879--1955), whose work on the photoelectric whose work on the photoelectric Albert Einstein (1879--1955), in 20th of relativity led to a revolution effect and the theory century physics of quantum the originator of the theory Max Planck (1858--1947), with the began in the early 20th century mechanics Modern physics ------scales travelling at non--relativistic speeds, since they pro scales travelling at non--relativistic situations, and theories vide a very close approximation in such of relativity simplify such as quantum mechanics and the theory scales. However, inaccura to their classical equivalents at such small objects and very high cies in classical mechanics for very modern physics in the 20th velocities led to the development of century. methods for solving physical problems. chemistry, and elec The discovery of new laws in thermodynamics, efforts during the In tromagnetics resulted from greater research increased. The laws comprising dustrial Revolution as energy needs used for objects on everyday classical physics remain very widely pernican model, the laws governing the motion of planetary bodies pernican model, the laws governing the 1609 and 1619, pioneering determined by Johannes Kepler between astronomy by Galileo Galil work on telescopes and observational Isaac ’s discovery ei in the 16th and 17th Centuries, and and universal gravitation and unification of the laws of motion also developed calculus, that would come to bear his name. Newton provided new mathematical the mathematical study of change, which Physics became a separate science when early modern Europeans used science when early modern Europeans Physics became a separate are now methods to discover what experimental and quantitative laws of physics. considered to be the of the in this period include the replacement Major developments Co the solar system with the helio--centric geocentric model of Sir Isaac Newton (1643--1727), whose laws of motion and universal whose laws of motion and Sir Isaac Newton (1643--1727), milestones in classical physics. gravitation were major

classical classical physics

p (42); p // // p (45); ------linguists recognize recursive structure in natural languages, it appears that logic needs recursive structure. the Greek kategorei -- to predicate, and syn -- together with). -- to predicate, and syn -- together the Greek kategorei where each judgment has an identified This is a fixed scheme, the sentence. determining the logical form of quantity and copula, form of a simple According to the modern view, the fundamental involving logical con sentence is given by a recursive schema, its bound variable, which are nectives, such as a quantifier with which in turn may have joined by juxtaposition to other sentences, logical structure. a single judgement of Aris The modern view is more complex, since logical connectives. For ex totle’s system involves two or more involves, in term logic, ample, the sentence “All men are mortal” M) and “is mortal” (here two non--logical terms “is a man” (here A(M,D). In predicate D): the sentence is given by the judgement two non--logical concepts, logic, the sentence involves the same the sentence is given by \ here analyzed as m(x) and d(x), and the logical connec forall x. (m(x) \rightarrow d(x)), involving implication. tives for universal quantification and powerful. Medieval logicians But equally, the modern view is more where Aristote recognized the problem of multiple generality, render such sentences as lian logic is unable to satisfactorily both quantities “all” and “Some guys have all the luck”, because but the fixed scheme that “some” may be relevant in an inference, Aristotle used allows only one to govern the inference. Just as In the traditional view, the form of the sentence consists of a view, the form of the sentence consists In the traditional or “some” or plus a sign of quantity (“all” subject (e.g., “man”) a pred which is of the form “is” or “is not”; “no”); the copula, logical con Thus: all men are mortal. The icate (e.g., “mortal”). connectives “no” and so on, plus sentential stants such as “all”, (from “or” were called syncategorematic terms such as “and” and ------u Ł The fundamental difference between modern formal logic and tradi tional, or Aristotelian logic, lies in their differing analysis of the logical form of the sentences they treat. Aristotle’s greatest inventions”. According to the followers of Aristotle’s greatest inventions”. According logical principles stated Aristotle (such as Ammonius), only the in schematic terms belong to logic, not those given in concrete terms. The concrete terms “man”, “mortal”, etc., are analogous to the substitution values of the schematic placeholders A, B, C, which were called the “matter” (Greek hyle) of the inference. tals”, “all cats are carnivores”, “all Greeks are philosophers”, tals”, “all cats are carnivores”, “all and so on. to logic was already That the concept of form is fundamental uses variable letters to recognised in ancient times. Aristotle Analytics, leading Jan represent valid inferences in Prior of variables was “one of kasiewicz to say that the introduction (“any”, “every”, etc.) with expressions of a standard type (such (“any”, “every”, etc.) with expressions as “all”, or the universal quantifier). must be replaced with sche Second, certain parts of the sentence expression “all As are Bs” matic letters. Thus, for example, the sentences “all men are mor shows the logical form common to the necessary because indicative sentences of ordinary language show necessary because indicative sentences that makes their a considerable variety of form and complexity first, ignoring those use in inference impractical. It requires, (such as gender and de grammatical features irrelevant to logic replacing conjunctions clension, if the argument is in Latin), with logical conjunctions like irrelevant to logic (such as “but”) logical expressions “and” and replacing ambiguous, or alternative grammar and symbolism of a logical language to make its content of a logical language to make its grammar and symbolism of form If one considers the notion usable in formal inference. simply loaded, one could say that formalizing too philosophically of logic. English sentences into the language means translating It is the logical form of the argument. This is called showing Logic is generally considered formal when it analyzes and rep considered formal when it analyzes Logic is generally of an ar any valid argument type. The form resents the form of the formal by representing its sentences in gument is displayed

logical forms

p (44); p // // p (47); - - fication of degrees of unsolvability. fication of degrees Recursion theory captures the idea of computation in logical and the idea of computation in Recursion theory captures the unde its most classical achievements are arithmetic terms; and his Entscheidungsproblem by Alan Turing, cidability of the theory Church--Turing thesis. Today recursion presentation of the complexity with the more refined problem of is mostly concerned the classi problem efficiently solvable?--and classes--when is a ------the subject. Set theory originated in the study of the infinite by Georg Cantor, and it has been the source of many of the most challenging and important issues in mathematical logic, from Can tor’s theorem, through the status of the Axiom of Choice and the question of the independence of the hypothesis, to the modern debate on large cardinal axioms. rigorously defined mathematical theory can be exactly captured by rigorously defined mathematical theory proof calculus is enough to a first--order logical theory; Frege’s describe the whole of mathematics, though not equivalent to it. If proof theory and model theory have been the foundation of mathematical logic, they have been but two of the four pillars of Both the statement of Hilbert’s program and its refutation by Both the statement of Hilbert’s program the second area of Gödel depended upontheir work establishing of mathematics to logic in the mathematical logic, the application nature of the incom form of proof theory. Despite the negative theorem, a result in mod pleteness theorems, Gödel’s completeness mathematics to logic, can be el theory and another application of came to being true: every understood as showing how close logicism this by means to a reduction of mathematics to logic. The various this by means to a reduction of mathematics a series of failures, from the attempts to carry this out met with Grundgesetze by Russell’s par crippling of Frege’s project in his by Gödel’s incompleteness adox, to the defeat of Hilbert’s program theorems. applied mathematical ideas and methods to their philosophical applied mathematical ideas and methods claims. logic to mathematics was un One of the boldest attempts to apply philosopher--logicians such as doubtedly the logicism pioneered by the idea was that mathematical Gottlob Frege and Bertrand Russell: the programme was to show theories were logical tautologies, and in the other direction, the application of mathematical techniques the application of mathematical in the other direction, and analysis of formal logic. to the representation to logic mathematics and geometry in relation The earliest use of Euclid, back to the ancient Greeks such as and philosophy goes philosophers Many other ancient and medieval Plato, and Aristotle. Mathematical logic really refers to two distinct areas of re really refers to two distinct areas Mathematical logic of formal is the application of the techniques search: the first the second, and mathematical reasoning, and logic to mathematics

mathematical logics

p (46); p // // p (49); logics ------computational in the 1940s. In the 1950s and 1960s, researchers predicted that when human knowledge could be expressed using logic with mathematical nota tion, it would be possible to create a that reasons, or artificial intelligence. This was more difficult than expected be cause of the complexity of human reasoning. In logic programming, a program consists of a set of axioms and rules. Logic programming systems such as Prolog compute the consequences of the axioms and rules in order to answer a query. The term “Computational Logic” came to prominence with the found Logic” came to prominence with The term “Computational its on Computational Logic. However, ing of the ACM Transactions Unit at in 1972 when the Metamathematics first use was probably “The Department of Compu the University of Edinburgh was renamed Intelligence. The term tational Logic” in the School of Artificial J Strother Moore, who worked was then used by Robert S. Boyer and to describe their work on in the Department in the early 1970s, They also founded a program verification and automated reasoning. the same name. company Computational Logic Inc. of come to be associated with The term “Computational Logic” has also early work in logic pro logic programming, because much of the place in the Department of gramming in the early 1970s also took was reused in the early 1990s Computational Logic in Edinburgh. It programming in the EU Ba to describe work on extensions of logic in the associated Network of sic Research Project “Compulog” and co--ordinator of the Basic Excellence. Krzysztof Apt, who was the and generalized the term Research Project Compulog--II, reused on Computational Logic in when he founded the ACM Transactions 2000 and became its first Editor--in--Chief. as it emerged as a dis Logic cut to the heart of computer science followed cipline: Alan Turing’s work on the Entscheidungsproblem theorems. The notion from Kurt Gödel’s work on the incompleteness came from this work was of of the general purpose computer that fundamental importance to the designers of the computer machinery Computational logic is the use of logic to perform or reason about is the use of logic to perform or Computational logic science a similar relationship to computer computation. It bears and as mathematical logic bears to mathematics and engineering as with bears to philosophy. It is synonymous philosophical logic science”. “logic in computer - - - to formulate an argument correctly. Logic has an immediate impact on other areas of study. Studying Logic has an immediate impact on other and ordinary speech can logic and the relationship between logic arguments and critique the help a person better structure his own are filled with errors arguments of others. Many popular arguments in logic and unaware of how because so many people are untrained development of nonstandard logics (e.g. free logics, tense log development of nonstandard logics (e.g. classical logic (e.g. modal ics) as well as various extensions of for such logics (e.g. Krip logics) and non--standard semantics of logic). Logic and the ke’s supervaluationism in the semantics Philosophy of language philosophy of language are closely related. language engages and interacts has to do with the study of how our with our thinking. method or methods to translate ordinary language into that logic to translate ordinary language into method or methods of logic is essentially a continuation can be found. Philosophical invention of called “logic” before the the traditional discipline concern Philosophical logic has a much greater mathematical logic. As a re between natural language and logic. with the connection deal to the logicians have contributed a great sult, philosophical Philosophical logic deals with formal descriptions of ordinary, deals with formal descriptions of Philosophical logic assume language. Most philosophers non--specialist (“natural”) logic if a reasoning can be captured in that the bulk of everyday

philosophical logics

p (48); p // // p (51); design

art and

p (50); p // // p (53); ------The objective of any experiment or measurement should be to pro experiment or measurement should The objective of any available is as accurate as the instruments duce an answer that For many calculations, the and the skill of operator will allow. work has a rough idea of the person doing the necessary numerical Scientific sampling, design order of magnitude he should obtain. and interpretation of of experiments, the analysis, presentation these created the concept data through statistical techniques--all as a dynamic cycle. of specification, production and inspection which, analyzed and inter Inspection now is the source of data is continuously feed back to preted through statistical methods, preventive action. Inspec production people for corrective and out defectives before they tion, that is, the act of screening reached the customer. thinking required that often presents most difficulty. It is usu that often presents most difficulty. thinking required approach a few minutes in considering various ally worth spending calculation. setting down the first line of es to a problem before mathe scientist may employ more complex An engineer or research being training in pure and applied mathematics matics, a thorough required. - - a conversion factor. Most of the calculations made by a textile technologist consist of a series of relatively simple steps, mainly arithmetical and at times using elementary aspects of trigonometry, geometry Alge bra. The calculation is generally straightforward; it is the local metical errors when old units are converted into new, even when metical errors when old units are converted For textile calculations, prepared conversion tables are used. it may be found that the usual sets of conversion tables do not include quantities peculiar to the textile industry. For these quantities, a conversion system has to be devised by using first principles and then published as a table or graph or left just as systems of textile measurement and textile vocabulary. In a world systems of textile measurement and textile slow, regional variations in which the pace of life was relatively but to--day communications in systems of units were tolerable, need a uniform system of are rapid, and commerce and technology and understood. Errors of measurement that is universally accepted but, of course, during conversion are automatically eliminated, misunderstandings and arith the transitional stage, there will be garments will fit on the body and which parts of the body will be garments will fit on the body and which garment. This is accomplished drawn attention to while wearing the the way in which lines come with a keen knowledge of angles, and point. together to create a garment’s focal regions developed their own It is not surprising that the various Geometrical principles underpin fashion design more generally. For Geometrical principles underpin fashion the body around a central example, garments must be balanced on the use of symmetry or, with fulcrum. This can be achieved through expense), by exploring greater difficulty (and therefore greater asymmetrical pattern designs. in mind the way in which Of course, fashion designers also keep edged collars and A--line dresses that flare out from the body. A--line dresses that flare out from edged collars and are checkers, bold zigzags and grids Particularly in prints, figure aim for a disguising of the natural common. Some designers garments often by combining straight--edged with such geometry, with grid--like patterning. Fashion designers routinely make use of geometrical implements routinely make use of geometrical implements Fashion designers a common and rulers, with straight lines being such as T--squares fashion. These include crisp, straight-- sight in contemporary

fashion design and textile

p (52); p // // p (55); A conversation with computer scientist Jun Mitani, a researcher of mathematical methods by which to create three--dimensional structures through the folding of flat paper. - - - - to his unique geometric shapes in 2008. Inspired by CG application* developed by Dr. Mitani that creates three--dimensional paper model with smoothly curved surface out of a single flat sheet of paper, the team embarked upon a new adventure in research. ing relationships with those working at each site. ing relationships with those working DESIGN SIGHT The exhibition which opened at 21_21 Man” and was in 2008 was entitled “ XXIst Century the exhibi born from Miyake’s (who also curated research by tion) experiences (and incorporating of life and the Reality Lab.). It examined our way with an the current global environmental crisis things. In eye toward new means by which to make “132 5. ISSEY 2010, we will present a new project: developments MIYAKE”, based upon one of the latest research. from the Reality Lab. team’s ongoing exploration “132 5. ISSEY MIYAKE” continues the and into the process of creation and production at the Miyake offers a new process being developed Design Studio. scien The Reality Lab’s team first met computer at the Gradu tist Jun Mitani (Associate Professor Engineering, ate School of System and Information in form University of Tsukuba) who is specialized modeling in computer graphics and were introduced human skills and to make things that will bring joy. human skills and to made a point of visiting Issey Miyake has always spread local material production areas & factories close work all over the country, and developing of the local manufacturing strength, are lost. How to pass on and strength, are lost. How to of the local manufacturing problem technical skills remain as the major educate the valuable in to be aware that we are at a crossroads to be solved. We need are at risk. our natural and human resources , where ways by to find new environmentally--friendly Our goals must be valuable the art of creation, to utilize our which to continue ------Japan has always created beautiful and beautifully--made things by striking a balance in work that lies between the aesthetic and the practical. Today, however is a very different era. One example of this is the current situation that surrounds the manufactures. Unfortunately, --cutting often becomes a factory’s primary mo tivating factor. As a result, talented workers, the very backbone tion and teamwork . Their goal is, through research, to explore tion and teamwork . Their goal is, through to industrial products. the future of making things from clothing The Reality Lab. always seeks to create products that reflect what people need and to find new ways to stimulate creative production in Japan. tile engineer) and Sachiko Yamamoto (pattern engineer) and com tile engineer) and Sachiko Yamamoto of whom are young and rela prised of a group of designers, some Born from a union between tively new to the Miyake Design Studio. mathematics and clothes making. has 8 members. The The team was formed in 2007, and currently the principal of collabora Reality Lab. is a project based upon tions can solve these variations. and clothes making . In the Born from a union between mathematics Lab. will present “132 5. autumn of 2010, ISSEY MIYAKE’s Reality and development team ISSEY MIYAKE”. Reality Lab. is a research Manabu Kikuchi (tex lead by Issey Miyake and two staff members, cal to replace the machine. Superimposed on this is the variation cal to replace the machine. Superimposed drafting and that from arising from lack of fibre control during to eliminate the effect chance causes. Further, it is impossible atmospheric conditions also of human factor entirely. Changes in variation in the quali contribute towards an increase in overall in various regions are often ty of the product. These variations various mathematical calcula occurring problems in textile. Using because the raw material i.e. cotton itself varies from fibre to i.e. cotton itself varies from because the raw material The qual bale to bale, and season to season. fibre within a bale, according to in each process, therefore, varies ity of the product technical and raw material used and degree of the variation in the and tools during processing. Further, refinement attained nor economi to long use it is neither possible wear and tear due In any manufactured product no two articles are perfectly alike, product no two articles are perfectly In any manufactured having impossible to find two of yarn For example, it is this is strength, evenness, length etc. exactly the same count,

need for mathematics for need and textiles

p (54); p // // p (57); - - - - buddhist idea buddhist in fashion design in fashion Bazaar, and MTV, will personally unveil her interactive sculpture personally unveil her interactive Bazaar, and MTV, will of Desires’ (Blue Lotus Wish Tree). dress called ‘Mandala centre piece of 428 art The ‘Mandala of Desires’ will be the of Devotion’ belonging to pieces in the collection called ‘Forms will be on exhibit from the Belgian MOSA museum. The collection 2016, as part of the program 6th November 2015 till February 21st the China Shanghai called `Celebrating India In Shanghai’,within by the Chinese Ministry of International Arts Festival organised Culture and the Indian Embassy in China. was made in 2015, in The sculpture dress ‘Mandala of Desires’ without killing silk ‘peace’ silk,which is a vegan silk made and handprinted with eco worms. The dress is hand embroidered is 1,2 meters tall and friendly textile ink. The full installation 2.5 meters wide. art piece creating beautiful Mandala of Desires is an interactive inspires visitors to imag life by visualisation. The installation down on a piece of paper ine a beautiful world, write their vision they would on a branch of a or cloth, and hang it on the dress as of collective wishing is live wish tree. That meditative practice and has been recently cele well known to traditions of the East brated by Yoko Ono. THE CHINA ART MUSEUM IN SHANGHAI PRESENTED FASHION DESIGNER MANDA IN SHANGHAI PRESENTED FASHION DESIGNER THE CHINA ART MUSEUM DRESS ART INSTALLATION LI MENDRILLA’S SCULPTURE Man at the China Art Museum in Shangai, On the sixth of November and award winning American fashion designer dali Mendrilla, an Harper’s has been featured by Vogue, Tatler, artist whose work - - -

tani conducts mathematical research on the creation of three--di research on the creation of tani conducts mathematical folding a flat material. mensional forms by * It is the CG software to create geometric shapes that contain to create geometric shapes that * It is the CG software forms with symmetrical axis. Its characteris three--dimensional Dr. Mi the shapes by folding a sheet of paper. tics are to create

p (56); p // // p (59);

------mathematics meet fashion: fashion: meet mathematics thurston’s concepts designer inspire thurston’s Many people think of mathematics as austere and self--contained. To the contrary, mathematics is a very rich and very human sub ject, an art that enables us to see and understand deep intercon nections in the world. The best mathematics uses the whole mind, embraces human sensibility, and is not at all limited to the small portion of our brains that calculates and manipulates with sym bols. Through pursuing beauty we find truth, and where we find truth, we discover incredible beauty. Cornell University) inspired designer Dai Fujiwara (Issey Miyake, inspired designer Dai Fujiwara (Issey Cornell University) Inc.). and creativity and his Thurston’s brief essay below on mathematics available at the fashion connection with designer Fujiwara was show: is all Ye know on earth, “Beauty is truth, truth beauty,----that and all ye need to know.” of John Keats is echoed on This famous and provocative quotation Study, where I took my the emblem of the Institute for Advanced first job after graduate school. of my mathematical discover Last summer, after reading an account shape all 3--dimensional to ies concerning eight that write to me, saying he felt pology, Dai Fujiwara made the leap to give inspiration to his design in his bones that my insights could we are both trying to un team at Issey Miyake. He observed that of 2--dimensional surfaces, derstand the best 3--dimensional forms had come around to ask and he noted that we each, independently, explore these relationships. ing our students to peel oranges to I have long been fascinated This resonated strongly with me, for design and its connec (from a distance) by the art of clothing tions to mathematics. An ABC News report, “Fashion and Advanced Mathematics Meet at Mi “Fashion and Advanced Mathematics An ABC News report, label advanced mathematics collide at Japanese yake: Fashion and the mathe generated a lot of interest in Issey Miyake,” (2010) (a communities. by William Thurston matics and fashion Fields of low--dimensional topology, 1982 pioneer in the field science at professor of mathematics and computer Medal winner, and - - -

“I am looking forward to the exhibition and to visiting Shang “I am looking forward to the exhibition add to the promotion of hai. I hope the Mandala of Desires will the culture of positive thinking and the international artistic exchange,” said Mandali today in Brussels. elements of both Indian and Chinese culture. elements of both Indian and Chinese construction was inspired The thousand petalled lotus petticoat Loo, known for his layered by the work of Dutch sculptor Bert Van of Amsterdam and galleries glass sculptures displayed in the city worldwide. The dress pattern was constructed according to a tradition The dress pattern was constructed according Yantra and the thousand al Indian mandala diagram called Goloka described in the ancient petalled lotus (sahasra patra kamalam) on the dress in Devana Indian hymn, Sri Brahma Samhita, painted thousand petalled lotus are gari script. Mandala diagrams and the

p (58); p // // p (61); - - OVAL TYPEFACES propor Oval typefaces tend to have more extreme TRIANGLE TYPEFACES Triangle typefaces are the rarest of the geometric breed. Since triangular forms do not appear often in our alphabet, these faces are purely decora tive. Nevertheless, they convey geometry pure! tions. Either their letterforms are very narrow or tions. Either their letterforms are or laying very wide, like an oval standing tall be seen in on its side. These two extremes can and Vienna Seebad™, which is coolly condensed, you need to Extended™, whose name says almost all know. ------SQUARE TYPEFACES Square typefaces are stately. Forms like those seen in Morris Sans™ may often be found on of ficial or on sci--fi movie posters. Other square types look more like the techno--era Linotype Killer™. These faces are perfect for the party scene or the computer screen. CIRCLE TYPEFACES European de Circle typefaces are reminiscent of let sign from the 1920s, like Herbert Bayer’s have never terforms from the Bauhaus. But they at ITC Avant diminished in popularity; just look or Avenir™, Garde Gothic™, from the early 1970s, catego from the late 1980s. Typefaces in this down to two ry often have their elements boiled forms, and simple forms: circles or other rounded them to rep straight lines. Quite a contrast. Use the future. resent sleek movement, dynamism, or mained popular. But finding exactly the right mood can be tricky. finding exactly the right mood can mained popular. But geomet we have grouped some of our favorite For your convenience, categories: sans serif and symbol) into four ric typefaces (mostly ovals, and triangles. circles, squares, The repetition of simple geometric shapes forms a daily part of simple geometric shapes forms a daily The repetition of the 21st the 20th century -- and into our environment. Throughout have re designs have taken advantage of this -- typefaces whose

graphic design and typography

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literature review; literature

p (62); p // // p (65);

Quantum

p (64); p // // p (67); - - •During April and May 1905, Einstein published two new research research new two published Einstein 1905, May and April •During determining and counting of method new a invented he one In papers. other the in and space given a in molecules or atoms the of size the a was result net The motion. Brownian of phenomenon the explains he brought an end to a millen proof that atoms actually exist. This of the chemical elements. ia--old debate on the fundamental nature •In March 1905, Einstein created the quantum theory of light. This This light. of theory quantum the created Einstein 1905, March •In or par the idea that light exists as tiny packets theory dealt with in live we that proposed Einstein photons, called he which ticles, energy of chunks discrete tiny of out built one universe, quantum a and matter. ------lacackra Tantra and in the ā stra, the K ā ś āṣā vibh ā literature on Buddhist epistemology. Albert Einstein had published some remarkable scientific papers addressing fundamental problems about the nature of energy, mat ter, motion, time and space. Some of his theories which could be follows: as are matter of concept Abhidhamma the of light in viewed platives had developed view on matters related to the universe platives had developed view on matters pure logical and rational and its contents which was based on thinking and no rigorous methodology was applied for study the physical world. These phenomena were discussed in detail in the early Buddhism, the Abhidhamma Pitaka, the Visuddhimagga, the pali commentaries, Mah damentally changed and deepened our understanding of the physical damentally changed and deepened our universe. Thought the study and philosophical conception of the focus of the traditional of the physical world was not the central and the Abhihamme 64 special areas of learning and BARUA Quantum striking similarities ization in Buddhism, but there are some scientific views related to present between Buddhist and modern Buddhist scholars and contem the concepts of time and space. The rational thinking and no rigorous methodology was applied for ex rational thinking and no rigorous methodology perimenting with the physical world. Einstein more than that Modern physics bears the impact of Albert relativity with its profound of any other physicist. His theory of time and gravitation had fun modification of the notion of space, universe and also the modern theory of quarks which are hypothe universe and also the modern theory space that make up the protons sised as mere geometrical points in study of the physical world and neutrons of an atom. Though the areas of learning and was not the central focus of the traditional buddhist scholars and contem specialisation in buddhism, but the related to the universe plative and developed views on matters on pure logical and and its contents. These views were developed cluster is delimited by an intervening space, so that they do not by an intervening space, so that cluster is delimited tradition, However, according to the Sarastivada touch each other. unitary to be the smallest unit of a single an atom is considered lacks spa it is so minute that it actually material element and close to buddhist concept of matter is very tial dimension. This in the of quantum, as smallest unit of energy Einstein’s concept An atom considered to be the smallest unit of matter which is to be the smallest unit of matter An atom considered called as number of unitary material elements an aggregate of a every elements” or “RUPA--KALAPA”, where a “Cluster of material

quantum and quantum abhidhamma

p (66); p // // p (69); ------further divisibility of atoms. The modern theory of “quarks” which are hypothesise as mere geometrical point in space that make up the protons and neutrons of an atoms also exist as cluster to give definite shape to these structures. (Journal for Interdisciplinary research on Religion and Science, No.5 july 2009) smallest not of energy in the universe and also the modern theory in the universe and also the modern smallest not of energy points in are hypothesised as mere geometrical of “quarks” which any com the protons and neutron an atom.When space that make up size of atoms, each atom in ponent of the body is reduced to the inseparable primary elements. turn should consist of the same four logically points to be an Thus, the concept of atoms (paramanu) is identical with “Kalapa”, aggregate of primary elements. This smallest cluster of material but in technical sense it means the Abhidhamma tradtion, an elements. So, according to the Theravada unitary material elements and atom is an aggregate of a number of but also as a “cluster is described not only as an atom (paramunu) Here every “Rupa--Ka of material elements” called “Rupa--Kalapa”. space, so that they do not lapa” is delimited by an intervening force of the air--el touch each other. However, the attractive escaping. From the point of ement keeps the atoms together from the possibility of exis view of modern science , This indicates force present between tence of some kind of an electro magnetic without touching each these elements which hold them in cluster demonstrated the other. Though Einstein had earlier experimentally of matter, but later the existence of atoms as smallest particles divisible into its charged was proved that atoms could be further neutrons which are separated components of protons, electrons and electrical charges. Thus from each other due to their respective cluster of material the concept of atom perceived as “smallest elements” in Theravada Abhidhamma, also point to the concept of The Visuddhimagga states that in this body the earth--element states that in this body the earth--element The Visuddhimagga half the water element (apo--dhatu) measuring (Pathevi--Dhatu) has atom is con to the Sarvastivada tradition, and as much. According ele smallest unit of a single unitary material sidered to be the dimension. minute that it actually lacks spatial ment and it is so as close to Einstein’s concept of quantum The concept is very ------extension is said to be present in every instance of matter. So every instance of matter is characterised by solidity (whatever be the degree) and extension (whatever be the extent). As defined in Theravada Abhihamma, the earth--element (pathavi- As defined in Theravada Abhihamma, the -dhatu) has the characteristics of solidity and extension, which means the three dimensional spatial occupation. Our notion of a solidity body is obtained when matter occupies the three dimension of space. The earth--element which represent solidity and spatial These four primary elements are necessarily co--nascent and insep These four primary elements are necessarily exist together and cease to arable. These element arise together, from one another. Though there gether and they cannot be separated these elements that enter into is no quantitative difference among the only difference is the composition of material things, but intensity. The four primary element of matter recognized in buddhism are The four primary element of matter recognized and extension, (a) earth element -- represents solidity and liquidity (b) Water element -- represents viscidity of cold and heat (c) Fire element -- represents the temperature fluctuation and mobility. (d) Air element -- represents distension, “ruppana” which means the susceptibility to being modified or re “ruppana” which means the susceptibility of the contrary forces. this ceptivity to change due to the impact the “genesis of dissimilar is also defined as “Yosaduppatii” or due to the impact of the ity” or change. What is meant by change and the appearance of anoth disappearance of one material element the concept of change is not er material element in its place. So a single material element. mer alteration between two stages of existence can be analysed. 65 material elements represent not only only not represent elements material 65 analysed. be can existence beings (or into the composition of living the matter that enters world external the in exists that matter the also but matter) ganic (inorganic matter). of defined as that which has the characteristic However, matter is The Abhidhamma analysis of matter assumes significance within within significance assumes matter of analysis Abhidhamma The rupa--dhammas 28 all in are There Theory. Dhamma the of framework material which into items 28 that imply which elements material or

quantum and quantum concept of in abhidhamma matter

p (68); p // // p (71); - - - velocity and black holes. black and velocity einstein’s notion of notion einstein’s escape rial elements with the attractive force of air--element holding them in position could define Einstein’s concept of escape veloc ity of a non--collapsing celestial mass. According to Einstein’s special theory of relativity, the speed of light is the ultimate speed limit in the universe. Nothing can travel faster than light. Hence, when a star collapses to the point that its escape, not even light. A black hole is simply a star that has collapse so much that its escape velocity is greater than the speed of light. Travelling into a blackhole is thus the ultimate one way trip. There is no travelling back from it. this escape velocity. It will back to earth. The BURUA Quantum and It will back to earth. The BURUA this escape velocity. or star of the escape velocity from planet the Abhidhamma value directly and radius. The escape velocity is depends on its mass to the radius and proportional to mass but inversely proportional compressed to a smaller size volume of a substance. If a star is velocity will increase, This without changing its mass, its escape is needed to escape the is due to the fact that a greater speed as it is more densely greater gravitational force on its surface changing its mass, tis escape compressed to a smaller size without the fact that a greater speed velocity will increase. This is due force on its surface is needed to escape the greater gravitational as it is more densely compressed. an atom is considered to be In the Theravada Abhidhamma tradition, material elements called as a an aggregate of a number of unitary “cluster of material elements” or “RUPA--KALAPA”. by an intervening space, Here, every “RUPA--KALAPA” is delimited However, the attractive so that they do not touch each other. together from escaping from. force of air--element keeps the atoms this indicates the pos From the point of view of modern science, an electromagnetic force sibility of existence of some kind of hold them in cluster without present between these elements which touching each other. This Abihidhamma perception of non--collapsing cluster of mate Einstein proved the theory of escape velocity which is use in all theory of escape velocity which is Einstein proved the shuttle is of modern times. When any space astronomical studies speed earth’s surface. It must have an initial launched from the launched (25,000 miles/hr). If the shuttle’s of at least 11 km/s speed. It can escape earth’s gravitational speed exceeds this less than into space. If the launch speed is field and make it - - - phenomenon of dynamic flux. are restricted due to the strong gravitational and electromagnetic are restricted due to the strong gravitational the Buddha related to the forces of each other. The doctrine of this concept by considering dependent origination also supports able to perceive though our everything in the universe that we are subjected to constant change sense organs are impermanent and are counter part of the from moment to moment. This is the buddhist this concept of dynamic flux. Einstein had also demonstrated the the demonstrated also had Einstein flux. dynamic of concept this called Brownian motion. spontaneous and random movement of atoms, his observations is that The idea which could be drawn out from state in this universe. All there is nothing in a constant static dynamic motion with relation is particles in this universe are in execute the random movement to each other and their tendency to verse of experience. However, there is no single enduring changing changing enduring single no is there However, experience. of verse “Tathagata” as changes momentary of series a exist they but entity, this gave buddha The thus”. goes and comes who “one means which and “here of terms in (Ksanikavada) momentariness of doctrine famous as tran theory also considers physical phenomena now”. The quantum Following unity. fundamental underlying an of manifestations sient Abihdhamma considered events as space--time representations of a a of representations space--time as events considered Abihdhamma and per flux. Nothing is considered to be static continuous dynamic in our uni is in a state of constant change manent but everything

quantum theory and the buddhist theoryquantum buddhist and the concept of fux dynamic

p (70); p // // p (73); - So we might not be able to locate 90% of matter in the universe able to locate 90% of matter in the So we might not be of dark matter. which are in the form ters in the form of the individual galaxies in the clusters. The the individual galaxies in the clusters. ters in the form of immense matter. Since the dark matter has remaining 90% is dark that fall pull to trap all the light rays mass and gravitational to the reflect anything. They remain invisible on them and never human eye. reflect none. We see only about 10% of the total mass of the clus only about 10% of the total mass reflect none. We see - - - - -

perceive through our sense organs is virtual. Thought the dark holes have enormous celestial mass and gravitational force of at traction but they could be regarded as dimensionless virtual mass. In spite of having real existence, They remain invisible to the human eye as they absorb all the light rays that fall on them and ma concept of complete collapse of elementary particles of matter ma concept of complete collapse of elementary of dimensionless dark holes relates to the theory of origination with enormous celestial mass. The concept of “emptiness” in Madhyamika tradition by Nagariuna also suggest that except the “Nibbana” and “Space”. Whatever we to be the smallest unit of a single unitary material element and to be the smallest unit of a single spatial dimension. So the it is so minute that it actually lacks is devoid of parts and ex Sarvastivadins believe that an atom Keeping this concept in empt from resistance or impenetrability. touch each other totally and background, if we presume that atoms Then they would all col without any intervening space in between. the same locus. This Abhidham lapse into one and all would occupy this effect from Einstein’s general theory of relativity. Although this effect from Einstein’s general horizon. Blackholes don’t nothing can escape from inside the event It is possible to orbit automatically slurp up everything nearby. a black hole without falling in. An atoms is considered In the sarcastivada Abhidhamma tradition, collapsed into the back hold compressed into a radios and volume of of volume and radios a into compressed hold back the into collapsed zero. Hence it has an infinite density. where the escape velocity The distance from the singularity to the Schwarzschild radius or equals the speed of light is called of a black hole ten times event horizon. The Schwarzschild radius Schwarzschild predicted as massive as the sun is 30 kilometers. There is no force known to modern science that can resist the inward inward the resist can that science modern to known force no is There collapses it until compress to continue will It gravity. of tug all collapse, the stop can force known no Because blackhole. a into geometric a into compressed is star the once was what in matter the singulari of zero. This point is called the point. It has a radius that star the of core the as mass same the has singularity The ty. This happens when the mose massive star at the end of their lives lives their of end the at star massive mose the when happens This after left star the of core central the If supernova. as explode sun. the as massive as times 3 to 2 about least at is explosion the

p (72); p // // p (75); - - - - on quantum theoryon quantum of consciousness and nature of nature and consciousness reality than those we already know. Assumptions such as these are acting know. Assumptions such as these than those we already under in biological theories and an as a barrier to progress This paper examines the unexplained standing of consciousness. and forces and the inconsistencies among fundamental particles biology and the cell in fundamental gaps in our knowledge of Also, the laws of particular that may impact on such progress. to be grossly incomplete. quantum mechanics are examined and found times are way too long and Furthermore, gravitational decoherence way too short to relate to electromagnetic decoherence times are weak force decoher millisecond brain processes. Surprisingly, of the relevant dynamical ence times over cellular distances are any force is associated with timescale needed, suggesting that if neurons (such as conscious the global properties in and between concurs with a twenty ness) it is the weak force. This finding link between the year old theory that argues for a fundamental biological cell. That theory weak force, electron neutrino and the neutrino that is soon to also predicted the mass of the electron and future consciousness be verified. The consequences for biology paradigm, are considered. theories, of this radical change of A Quantum Theory of Consciousness May Require a Paradigm Shift in Consciousness May Require a Paradigm A Quantum Theory of Goodman Biology by Maurice a closed that the known physical laws form It is often assumed theo It is also assumed that biological system and are complete. other principles that are fundamental ries require no additional ------ion. Buddhism answer this description. Buddhism has the charac ion. Buddhism answer this description. in a cosmic religion for the teristics of what would be expected future. It transcends a personal GOD avoid dogmas based on a re ligious sense aspiring from the experience of all things, natural and spiritual as a meaningful unity. So “if scientific needs, it would be buddhism”. da), Impermanence (Anicca) and the emphasis on practicing com da), Impermanence (Anicca) and the emphasis activities (Kamma). He had passion with moral--driven volitional the future will be a “cosmic also predicted that the religion of God and avoid dogma and religion”. It would transcend personal and the spiritual, It should theology. Covering both the natural from the experience of all be based on a religious sense arising unity. In his opin things natural and spiritual as a meaningful certain if any of these are correct. on religion and science, Journal for interdisciplinary research by the buddhist doctrines Albert Einstein was very much influenced any creator God, Absence of related to the concepts of absence of Origination (Paticcasamuppa any soul or self (Anatta). Dependent explain the expansion of the universe, there is the theory sponta explain the expansion of the universe, to energy from appears mass means which matter of generation neious “Big bang” theory. Scienc fill the space so as to contradict the expanding. However, measure tists do not really know why space is universe the considering by explained best are obsercation and ments a variety of possible explana to be expanding. Though they’re are for know not do we but scientists modern the by forward put tions supported the theory that expansion of the universe really happen that expansion of the universe really supported the theory light of shift the demonstrating by theory this proved had He ing. universe. the of expansion this confirm to spectrum red the towards since energy of amount constant a have to considered is universe The What energy. of from concentrated a is mass as and beginning the To another. to type one from energy of change the is happen really Einstein thought earlier that the space was not expanding and he he and expanding not was space the that earlier thought Einstein Constant” “Cosmological named factor a calculations his in used and mind his changed he later But effect. expansion the cancel to

einstein’s view on energy for on energy view for einstein’s universe expanding

p (74); p // // p (77); ------by james kowall james by the nature ofthe nature nutshell in a reality Sitter space with a positive cosmological constant, and the one-- a positive cosmological constant, and Sitter space with paradigm. world--per--observer at the central focal In this scenario, the observer is present in the observer’s frame of point of a cosmic horizon that arises and projects the observ reference, acts as a holographic screen, reality shared by many er’s space--time geometry. A consensual horizons overlap. This observers is possible if their respective the nature of forms of in scientific framework can only explain leaves us with the quanda formation and the flow of energy. This and the Source. An ry of how to explain perceiving consciousness can only be under argument is made that perceiving consciousness that is differentiated stood as a focal point of consciousness to a holographic screen, from the Source and arises in relation understood in the non--dual in which case the Source can only be or a void of undifferenti sense of an empty space of potentiality the two--part article. ated consciousness. This is Part I of Reality is characterized by four aspects of reality: (1) forms by four aspects of reality: Reality is characterized conscious the flow of energy, (3) perceiving of information, (2) Source of information, energy and perceiving ness, and (4) the scientific framework for this characterization consciousness. The of the holographic principle, non--commuta is discussed in terms arising in de observer--dependent cosmic horizon tive geometry, an - - cling, thinking that our continued being depends on our continued continued our on depends being continued our that thinking cling, that we our can our being depend upon something clinging. But how the in being, our of absence the in that something create, selves cannot even be known? absence of our Awareness, My philosophy is that That of which the universe is actually com That of which the universe is actually My philosophy is that as We, universe. the of aware is which That than other not is posed then we which to forms experiential the create Awareness, formless

the universe is composed is the universe of of is aware which that the universe

p (76); p // // p (79); philosophers - - - -

of what should and should not be. idea “should not be” to that which is not wanted, then the self idea “should not be” to that which is The acceptance and allow conflict that creates suffering arises. awareness as “what is” is ing of the forms that arise in one’s self out of the hole of the shovel that allows one to dig one’s source of one’s suffering, as self--conflict that is the ultimate hole deeper using the shovel opposed to just continuing to dig the self, over and over and over again. Not Be by Steven E. Kaufman What Is Versus What Should & Should absence of conflict with The actual source of happiness is the of whether “what is,” one’s self, and that can be had regardless However, when one applies the in this moment, is or is not wanted. Science holds that it is form that gives rise to the Formlessness it is form that gives rise to the Science holds that consid is apprehended. Science has never even by which all form possibility. What is the opposite possibility? ered the opposite level of Consciousness reaches a certain That it is when formless does that forms poof into existence. How complexity that physical to it become complex? By flowing in relation which is formless The Revealed Yet Still Hidden Relation between Form & the Formless Hidden Relation between Form & The Revealed Yet Still by Steven E. Kaufman

p (78); p // // p (81); - - - kant and - - the moral law the moral lowing the dictates of the Kantian moral law does not aim at pro ducing specific and beneficial outcomes; instead, it is that such results stand beyond the free choice or autonomy of the acting agent and they cannot determine the act’s worth. For Kant, only persons who can act in an autonomous or free fashion can comport themselves in morally worthy manners. These elements are at the core of the deontological approach to the moral law. given its nature, it obligingly calls upon us (qua rational be it obligingly calls upon us (qua rational given its nature, action is follow our duty. For Kant then, an ings or persons) to done for the and only if it accords with and is morally worthy if duty is grounded in sake of duty. The force behind our obligatory law, meaning that the law is the a priori structure of the moral rational, abstract, non--empirical, non--contingent, necessary, other words, the moral law is obligatory, absolute, and formal. In the time, in the same way to universal--it applies everywhere, all laws ought to hold good everyone/rational being: “...Since moral derive them from the gener for every rational creature, we must must treat it independently al concept of a rational being...we complete in itself.” This as pure philosophy, i.e. as metaphysic, for the moral law. “derived” metaphysic provides the ground an action stems from whether Kant claims that the moral worth of action is drawn directly from or not the motive/ maxim for such an inclination (desire, feeling, one’s duty (rational obligation) or conform to duty, but not be emotion, affect, sentiment--which may is not determined morally worthy). An action’s moral worthiness it is directed, but rather by the purpose or end towards which or the maxim of the good it stems from the principle of volition The implications of these will that motivates the acting agent. an action’s moral worth is two propositions (of duty) entail that person follows, and that the directly related to the reason(s) a be considered in evaluating consequences of such an act should not the act’s merit. Now this is not to say that a person who is fol In his Fundamental Principles of the Metaphysics of Morals, Kant Principles of the Metaphysics of Morals, In his Fundamental understand his analysis of what we generally claims that through upon can uncover that obligatory foundation by morality that he the mor ultimately depend. This is which all moral principles imperative imperative. The categorical al law of the categorical addition, command and abstract idea; in is a completely absolute - - - na - ā - y - - - - ā - --thus the former is ā na perspective). Kant’s meta na perspective). Kant’s ā y na tradition. Kant’s metaphys ā ā garjuna Immanuel Kant’s deontol y ā ā ment” from the Buddha’s insight/prajña. In both instances, the criterion of universality is an intrinsic and necessary feature for morality. Given this conclusion, I will endeavour to provide an affective element for Kant’s deontology and a rational aspect for Buddhist compassion, thus bringing both approaches together as a demonstration of emotional rationality. dialogue via an analysis and pragmatic critique of morality’s ide dialogue via an analysis and pragmatic the key components of Kant’s al of universality. First, I outline categorical imperative, and show that the kingdom of ends is a “natural development” from this moral command. Next I explore the impetus of the Buddha’s search for the alleviation of suffering/ dukkha, and explain that the bodhisattva is a “natural develop wisdom and compassion...” --N approach to morality ogy seems to present a radically different as compared to Buddhism’s Mah practical reason, whereas ics relies on the application of pure karut Buddhism’s appeal is to compassion/ at least on a surface reading. cognitive and the latter affective, into a direct comparative I propose that the two can be brought element for Kant’s deontology and a rational aspect for Buddhist element for Kant’s deontology and a together as a demonstra compassion, thus bringing both approaches only on that maxim whereby you tion of emotional rationality. “Act become a universal law” can at the same time will that it should --Immanuel Kant “The Mah (acceptable by all rational beings). effort, concentration, has a nature of giving, ethics, patience, ical imperative, and show that the kingdom of ends is a “natural ical imperative, and show that the kingdom Next I explore the impetus development” from this moral command. of suffering/ duhkha, of the Buddha’s search for the alleviation a “natural development” from and explain that the bodhisattva is instances, the criterion of the Buddha’s insight/prajna. In both feature for morality. universality is an intrinsic and necessary to provide an affective Given this conclusion, I will endeavour physics relies on the application of pure practical reason, where the application of pure practical reason, physics relies on first is is to compassion/karuna; thus the as Buddhism’s appeal reading. second affective, at least on a surface cognitive and the via two can be brought into direct dialogue I propose that the of uni critique of morality’s ideal an analysis and pragmatic categor outline the key components of Kant’s versality. First I Immanuel Kant’s deontology seems to present a radically differ seems to present a radically Immanuel Kant’s deontology tradition as understood in the Buddhist ent approach to morality in the Mah (generally understood

a metaphysics ofa metaphysics morality: buddhism kant and

p (80); p // // p (83); ------probably be at first surprise, and then anger. The emotions follow from the cause; they are consequential effects. Kant’s notion of rational respect functions in a different manner. Let us look at a key footnote from the first section of Kant’s small text: ...Although respect is a feeling, it is not a feeling received through influence, but is self--wrought by a rational concept, and, therefore, is specifically distinct from all feelings of the former kind, which may be referred either to inclination or To briefly digress, Kant’s pure practical reason is one mode of Kant’s pure practical reason is one To briefly digress, the Reason has two general functions: the faculty of reason. terms of and the second is moral. In first is epistemological; beings in developing the first, speculative reason aids rational experience, the world of sen empirical knowledge about phenomenal knowledge about metaphysics. sory appearances, as well as abstract principles that tell ratio The second mode of reason generates by pure practical reason, nal beings how they ought to act. Thus, faculty of the mind; Kant is referring to that specific rational concepts with which by pure, he means the a priori and abstract its principles; and the term this faculty constitutes (legislates) sense, but rather in the practical is not meant in a pragmatic faculty makes the rational straightforward sense that the rational then considered to be the good being act. Pure practical reason is or any appeal to what will, for it is good without qualification it is good within itself. it produces, that is, its consequences; we can uncover the univer It is through this internality by which sality of Kant’s understanding of duty. respect (or reverence) for Duty is the necessity of acting from to the a priori principles the moral law as determined according is generated by reason before of reason. Respect is a feeling that an effect like other sen an action/event takes place--it is not of emotional states timents. Generally speaking, our experiences say I strike the ran follow from various causes--for example, dom person sitting next to me on the subway. Their reaction will The ends or goals of such impositions are located within them of such impositions are located within The ends or goals of their phenomenal effects and empirical selves, independent gives when each and every rational being consequences. Hence rational law, they do so by creating a purely themselves the moral generated by pure practical reason. principle that is - -

do so by creating a purely rational principle that is generated by pure practical reason. do so by creating a purely rational principle that is generated by pure do so by creating a purely rational principle practical reason. The ends or goals of such impositions are located within themselves, independent of their phenomenal effects and empirical consequences. Hence when each and every rational being gives themselves the moral law, they selected ends, whereas “freewill” [freie Wille] obeys universally valid selected ends, whereas “freewill” [freie a moral point of view. laws that it has imposed on itself from located within themselves, The ends or goals of such impositions are and empirical consequences. Hence independent of their phenomenal effects themselves the moral law, they when each and every rational being gives According to Jurgen Habermas, Kant characterizes freedom in general as According to Jurgen Habermas, Kant characterizes will to maxims, that is, to an agent’s capacity to subordinate [his/]her concept [he/]she has mastered. orient [his/]her actions by rules whose enables one to adopt rules Thus freedom of choice [Willkürfreiheit] inclinations and subjectively of prudence or skill depending on one’s contradistinction, “An agent acts autonomously to the extent that [she/] contradistinction, “An agent acts autonomously determinations, that is, from mere he frees [her/]himself from contingent of status and tradition.” preferences or from conventional considerations holds that rational beings gener By acting freely and autonomously, Kant of duty, that is, the moral law. ate within themselves the prescriptions can act in an autonomous fashion, that is, only they can give themselves fashion, that is, only they can give can act in an autonomous by of volition) to act without being influenced reasons (principles and desires, concerns, such as inclinations empirical and/or emotional occurs when according to heteronomy. Heteronomy for to do so is to act are beyond the determined by contingent factors that the person’s will is chosen. In other words, such actions are not freely person’s control; in How is such an all--encompassing universal law generated? And why does universal law generated? How is such an all--encompassing these ques any obligatory force? The answers to such a moral law have rational beings understanding of autonomy. Only tions are bound to Kant’s

p (82); p // // p (85); ------The practical implication of this ideal is that, in any given moral situation that calls for a choice or judgment, the acting moral agent legislates a universal law to which all other rational beings are subject; yet their roles may change, for when anoth er moral agent acts in a similar fashion, the first then becomes subject to this other’s legislated moral law. Thereupon, the moral law calls for the establishment of the kingdom of ends: this king dom is a union of different rational beings in a system of common or universal laws as legislated by pure practical reason. Habermas versal law” (acceptable by all rational beings). A will that func by all rational beings). A will versal law” (acceptable that it acts according to rational principles tions in this manner reason. The is the good will or pure practical gives itself; this being to “So act as to good will commands each person qua rational person or in that of any oth treat humanity, whether in your own never merely as a means.” er, in every case as an end--in--itself, persons must be accorded the Thus, in order to fulfill this duty, for the moral law; for same respect that one finds within oneself the other’s autono to do otherwise is to, in essence, disrespect instantiated in each and every my, that is, the moral law as it is categorical imperative obli rational being. In other words, the selfish or egocentric goals gates persons to not use others for in any case. Every rational these would be heteronomous actions inner worth) whereby [she being “possesses a dignity (an absolute rational beings in the or] he exacts the respect of all other each member of [her/] world, can measure [her/]himself against on a footing of equality his species, and can esteem [her/]himself points beyond the needs of with them.” Such an egalitarian duty rational synchronicity with the individual, bringing them into a will that is in harmo all other rational beings. This is the is “the idea of the will of ny with pure practical reason, which legislative will.” When each every rational being as a universally will, such wills will accord rational being exercises their good by pure practical with the same universal principles generated reason. ery rational being). The consequences of Kant’s moral law culmi The consequences of Kant’s moral ery rational being). of ends. of his ideals into the kingdom nate in the extension command categorical imperative (the absolute The moral law is the on that maxim obligation): it states, “Act only of necessary moral become a uni the same time will that it should whereby you can at ------

“The capacity to act for reasons all the way down [that is, purely and internally] is defining of rational agency. Kant calls this autonomy. It is what we respect in respecting a person as an end- -in--[him/]herself.” Given that the moral law is applicable and valid for every rational being, this rational emotion (qua feel ing) of respect is necessarily and universally extendable (to ev law itself. The moral law then is instantiated in each rational law itself. The moral law then is instantiated respectful generator of the being. Thus each rational being is a moral law, and since the moral law is worthy of unqualified re spect, then each instantiation, each rational being, is worthy of such respect because of the law within. that is, the moral law, and the moral law evokes respect from its that is, the moral law, and the moral (or legislation-- see the generator, urging its very generation discussion below). generated moral law are The moral implications for this internally the moral law that far reaching. Each rational being generates respect that each has for the obligates dutiful action due to the this is indicative of our autonomy. “Only moral reasons...bind this is indicative of our autonomy. that is, independently of a the wills of agents unconditionally, of the value--orientations of given individual’s preferences even does this because the moral a given community.” The rational being worth that reason respects in law has an unqualified and universal generates what it respects, and of itself. Pure practical reason only, and that, the law which we impose on ourselves, and yet rec only, and that, the law which we impose ognize as necessary in itself. reason/motive that oblig This respect for the moral law is the the law to themselves. At es rational beings to create and give but we necessarily give first glance, this seems a bit circular, we respect for itself, and ourselves the law of morality, which fluences on my sense. The immediate determination of the will by The immediate determination of fluences on my sense. so that of this is called respect, the law, and the consciousness and not an effect of the law on the subject, this is regarded as is consid it is something which as the cause of it...Accordingly although it object of inclination nor of fear, ered neither as an is the law to both. The object of respect has something analogous fear. What I recognize immediately as a law for me, I recognize immediately as a law for me, I fear. What I recognize that my will merely signifies the consciousness with respect. This other in a law, without the intervention of is subordinate to

p (84); p // // p (87); - tions is an important and intrinsic element to karma formation. As and intrinsic element to karma tions is an important can be of virtues (subjective talents) for Kant, the development the moral the demands and obligations of conducive to fulfilling vs. act) not to let this distinction (character law. Thus we ought on com here to contribute to the literature prevent the attempt compassion. us then proceed with bodhisattva parative ethics. Let ------na tradition of the y

Aristotelian category of a character based ethics, nor does Kant’s approach rule out the moral worth of the virtues. In terms of the former, the ethical prescriptions of the Eight--Fold Noble Path certainly bear the marks of rules, that is, moral laws, as do the vows taken by monks and bodhisattvas; and with the cultivation of right mindfulness and concentration, the role of “correct” motiva One might be moved to claim that Buddhist ethics employs notions One might be moved to claim that Buddhist like moral exemplars and virtues, and that these fall within a different kind of philosophical category from the deontology of Kantian moral philosophy. While this is prima facie a valid claim, by no means is it clear that Buddhist ethics is limited to the must acknowledge that human beings often fall short of such ob must acknowledge that human beings often hold to such demanding ligations, for very few can consistently the Mah universal ideals. It is precisely in of moral exemplars who none bodhisattva that we find descriptions their motivations emphasize theless attempt to do just this. While aim to apply Buddhist doctri a different affect, they nonetheless parallels Kant’s vision. nal ideals in a universal fashion that for rational nature. The notion that morality has essentially to for rational nature. The notion that capacity to make choices for do with respect for persons and their and compelling ideas themselves is one of the most influential reason, then, all rational in Kant’s ethics.” In accordance with of the kingdom of ends beings necessarily in the greater ideal to all others. However, we that binds each and every individual ed within, applies to every instantiation of the moral law found ed within, applies to every instantiation of this ideal culmi in each rational being. The full expression chosen recognition of nates in the consciously and autonomously follow with respect to all the duties that each person ought to Denis claims in her re other persons (and themselves). As Lara “What matters morally is cent introduction to Kant’s Groundwork, that shows proper respect whether the maxim of the action is one tiation and generator of the moral law is sometime ruler/legisla tiation and generator by subject/citizen to the principles pronounced tor, and sometime pure practical reason. on the of morals relies, at its core, In sum, Kant’s metaphysics generat emotion of respect. This affect, self--wrought rational describes this as when the ideal of freedom, one of the practical when the ideal of freedom, one of the describes this as All rational its “concrete expression.” ideas of reason, receives as an instan this ideal (utopian?) rubric. Each beings fall under

p (86); p // // p (89); - - - - - could have had contact with Buddhist philosophy during his stay in France (which coincided with his writing of the Treatise of Human Nature) through the well traveled Jesuit missionaries of the Royal College of La Flèche. myself at any time without a perception, and never can observe any without a perception, and never can myself at any time thing but the perception” that is constantly sta According to Hume then there is nothing only a flow of differing ble which we could identify as the self, something substantive which experiences. Our view that there is is for Hume merely imagi binds all of these experiences together attributed to the entire flow nary. The self is a fiction that is of experiences. and sensations suc Pain and pleasure, grief and joy, passions at the same time. It cannot, ceed each other, and never all exist or from any other, therefore, be from any of these impressions, consequently there is no that the idea of self is derivid; and of the rest of mankind, that such idea...I may venture to affirm of different percep they are nothing but a bundle or collection an inconceivable rapidity, tions, which succeed each other with and are in a perpetual flux and movement. is very similar to the This ‘Bundle theory’ of personal identity holds that the unitary self is Buddhist notion of not--self, which a collection of five aggre a fiction and that nothing exists but philosophy hold that it gates.Similarly, both Hume and Buddhist personal identity in a mundane is perfectly acceptable to speak of that there are ultimately no and conventional way, while believing such things. Hume scholar Alison Gopnik has even argued that Hume Hume and Not--Self David Hume wrote: The Scottish philosopher I always intimately into what I call myself, “When I enter most or cold, perception or other, of heat stumble on some particular catch or hatred, pain or pleasure. I never light or shade, love ------tions. Buddhist thought can also be compared to Classical Cynicism tions. Buddhist thought can also be views sought to develop a and Stoicism, in that all of these world set of practices to reach a state of equanimity by the removal of desires and passions. origin can plausibly be traced to the contacts between Pyrrho and origin can plausibly be traced to the he traveled with Alex the sages he encountered in India, where both philosophies argue ander the Great.” According to Kuzminski, about an ultimate against assenting to any dogmatic assertions impressions as a tactic metaphysical reality behind our sense use of logical arguments to reach tranquility and both also make to expose their contradic against other philosophies in order a way to reach that goal. This is similar to the Buddha’s refusal a way to reach that goal. This is similar which he saw as non--con to answer certain metaphysical questions and Nagarjuna’s “relin ductive to the path of Buddhist practice Kuzminski argues for direct quishing of all views (drsti)”. Adrian of thought. In Pyrrhonism: How influence between these two systems Kuzminski writes: “its the Ancient Greeks Reinvented Buddhism, Hellenistic philosophy (particularly that of According to Edward Conze, Greek Skepticism philosophy, especially the Pyrrho) can be compared to Buddhist Skeptics had a soteri Indian Madhyamika school. The Pyrrhonian (peace of mind). They ological goal which they called Ataraxia about facts of the world as promoted withholding judgment (Epoché) After the post--war spread of Buddhism to the West there has spread of Buddhism to the West there After the post--war interest by some scholars in a comparative, been considerable philosophy. between eastern and western cross--cultural approach such as is now published in academic journals Much of this work West. Philosophy East and Buddhist thought and Western philosophy include several interest Western philosophy include several Buddhist thought and thinkers the 20th century, a few European ing parallels. Before thought. had engaged with Buddhist such as Arthur Schopenhauer

the connection in terms the connection of principle westernbetween and buddhism philosopher

p (88); p // // p (91); - nature, which was often attributed to inanimate objects such as often attributed to inanimate objects nature, which was mountains. lotus flowers and phy going back to the Presocratics and Plato. According to D. S. the Presocratics and Plato. According phy going back to be found in and panexperientialist aspects can Clarke, panpsychist of Buddha (Jpn. Tendai) Buddhist doctrines the Huayan and Tiantai PANPSYCHISM feature view that mind or soul is a universal Panpsychism is the philoso has been a common view in western of all things, this ------ng. According to Buddhist philosopher Vasu ō xiàng--z

bhandu “The transformation of consciousness is imagination. What is imagined by it does not exist. Therefore everything is repre sentation--only.” This has been compared to the Idealist philos ophies of Bishop Berkeley and Immanuel Kant. Kant’s categories have also been compared to the Yogacara concept of karmic vasanas (perfumings) which condition our mental reality. constructed, or otherwise immaterial. Some Buddhist philosophi constructed, or otherwise immaterial. Idealistic tendencies, cal views have been interpreted as having mainly the cittamatra (mind--only) philosophy of Yogacara Buddhism as outlined in the works of Vasubandhu and Xuanzang. Metaphysical Idealism has been the orthodox position of the Chinese Yogacara school or F Other Western philosophers that have attacked the view of a fixed Other Western philosophers that have paper The Self as a Center of self include Daniel Dennett (in his (The Ego Tunnel). Narrative Gravity) and Thomas Metzinger IDEALISM which assert that reality, Idealism is the group of philosophies mental, mentally or reality as we can know it, is fundamentally I am less concerned about the rest of my own life, and more con I am less concerned about the rest of cerned about the lives of others. MacFarquar, Reasons and Per According to the New Yorker’s Larissa a Tibetan Buddhist monastery. sons has been studied and chanted at ating, and consoling. When I believed that my existence was such ating, and consoling. When I believed in myself. My life seemed like a further fact, I seemed imprisoned moving faster every year, and a glass tunnel, through which I was When I changed my view, at the end of which there was darkness. I now live in the open the walls of my glass tunnel disappeared. my lives and the lives of air. There is still a difference between less. Other people are closer. other people. But the difference is ed stream of mental and physical events, there are no “separately and physical events, there are no ed stream of mental Parfit distinct from our brains and bodies”. existing entities, argues that would have agreed.” Parfit also concludes that “Buddha and leads to increased empathy. this view is liberating it liber Some may find it so. But I find Is the truth depressing? British philosopher Derek Parfit has argued for a reductionist Derek Parfit has argued for a reductionist British philosopher Reasons of personal identity in his book and deflationary theory connect to Parfit, apart from a causally and Persons. According

p (90); p // // p (93); William Barrett held that Heidegger’s philosophy was similar to that Heidegger’s philosophy was William Barrett held this after Heidegger himself had confirmed Zen Buddhism and that of DT Suzuki. reading the works Heidegger wrote that: “As void [Ab--grund], Being ‘is’ at once the “As void [Ab--grund], Being ‘is’ Heidegger wrote that: “Dialogue as well as the ground. ”Heidegger’s nothing [das Nichts] that “to a Japanese friend (Tezuka Tomio) state on Language”, has you mean to is the loftiest name for what us [Japanese] emptiness has ‘Being’” Heidegger’s critique of metaphysics say with the word attitude. to Zen’s radical anti--metaphysical also been compared ------. ṇā been influenced by Zen and Daoist texts. Some of Martin Heideg ger’s philosophical terms, such as Ab--grund (void), Das Nichts (the Nothing) and Dasein have been considered in light of Buddhist terms which express similar ideas such as Emptiness. ready has...the selfdeception of moral concepts behind it ---- it ready has...the selfdeception of moral and Evil.” However he still stands, in my language, Beyond Good believed that Buddhism was a form of oriental life denying nihil ism. According to Reinhard May and Graham Parkes, Heidegger may have plicity of individual things (principium individuationis) has been plicity of individual things (principium as developed in Yogacara compared to the Buddhist trikaya doctrine which are based on uni Buddhism. Finally, Schopenhauer’s ethics of others can be compared to versal compassion for the suffering the Buddhist ethics of Karu writing that it “...al Friedrich Nietzsche admired Buddhism, ligions.”Schopenhauer’s view that “suffering is the direct and ligions.”Schopenhauer’s view that “suffering is driven by an “restless immediate object of life” and that this the four noble truths of the willing and striving” are similar to ascetic life of the Indi Buddha.Schopenhauer promoted the saintly Will. His view that a single an sramanas as a way to renounce the itself as a multi world--essence (The Will) comes to manifest larities between Kant’s antinomies and the unanswerable questions larities between Kant’s antinomies and concerned with whether the of the Buddha in that “they are both in that they are both left world is finite or infinite, etc., and undecided.” Indian religious texts and Arthur Schopenhauer was influenced by “best of all possible re later claimed that Buddhism was the experience is in one sense a mere fabrication of our senses and sense a mere fabrication of our experience is in one not have For Kant and the Madhyamikas, we do mental faculties. filtered in themselves’ because they are always access to ‘things framework’. Thus both worldviews by our mind’s ‘interpretative is unable an ultimate reality and that Reason posit that there is seen simi like Edward Conze have also to reach it. Buddhologists Immanuel Kant’s Transcendental Idealism has also been compared Idealism has also been Immanuel Kant’s Transcendental school approach of the Madhyamaka with the Indian philosophical world of T. R. V. Murti. Both posit that the by scholars such as

buddhism and buddhism german philosophy

p (92); p // // p (95); ------buddhism and process philosophy and process these processes was never independent, but was interrelated and never independent, but was interrelated these processes was which occasions, and this feature of reality dependent all prior origination has been compared to dependent he called ‘creativity’ by multiple past caus which holds that all events are conditioned that our understanding of es. Like Buddhism, Whitehead also held we hold to the ‘fallacy of the world is usually mistaken because changing processes as misplaced concreteness’ in seeing constantly that suffering and stress having fixed substances.Buddhism teaches nature of the world. Like arises from our ignorance to the true is “haunted by terror” at this wise, Whitehead held that the world in the temporal world...lies process of change. “The ultimate evil time is a ‘perpetual perish in the fact that the past fades, that of “evil” is similar to ing’”. In this sense, Whitehead’s concept caused by change. White the Buddhist viparinamadukkha, suffering been likened to the Mahayana head also had a view of God which has Bodhisattva ideal. theory of the Trikaya as well as the The process philosophy of Alfred North Whitehead has several con of Alfred North Whitehead has The process philosophy reality as Buddhist philosophy. Whitehead saw vergent points with objects process of flux and denied that an impermanent constant chang within them, but rather were ever had any real substance of the is similar to the Buddhist concepts ing occasions. This each one of Whitehead also held that impermanence and emptiness. - - - - n) expressed by the Buddhism of Dogen and n) expressed by the Buddhism of Dogen nx mind is inherently connected to the body and the external world mind is inherently connected to the dynamically through the and that the lifeworld is experienced body, denying any independent Cartesian Cogito. Merleau--Ponty’s phenomenology has been said to be similar to Zen Merleau--Ponty’s phenomenology has been all hold to the interconnec Buddhism and Madhyamaka in that they (the “lifeworld”). The unity tion of the self, body and the world of body and mind (sh the corporeity of conscious Zhanran and Merleau--Ponty’s view of hold that the conscious ness seem to be in agreement. They both -itself is also nothing more than appearance, it has no essence. -itself is also nothing more than appearance, and of reality as lack This conception of the self as nothingness to the Buddhist concept ing any inherent essence has been compared the Buddhists rejected the of Emptiness and Not--self. Just like Husserl’s concept of the Hindu concept of Atman, Sartre rejected transcendental ego. or any fixed characteristics and that insight into this caused a or any fixed characteristics and that Nausea. Sartre saw conscious strong sense of Existential angst or this happens because ness as defined by its ability of negation, of something it is aware whenever consciousness becomes conscious object. Consciousness is of itself not being that intentional -- the entire world of nothingness because all being--initself for Sartre, being--in- objects -- is outside of it. Furthermore, subjective point of view. The German Buddhist monk Nyanaponika view. The German Buddhist monk Nyanaponika subjective point of Buddhist Abhidhamma philosophy “doubtlessly Thera wrote that the dhamma could and that the Buddhist term belongs” to Phenomenology be rendered as “phenomena”. essence believed that consciousness lacks an Jean--Paul Sartre Some scholars reject the idealist interpretation of Vasubhandu’s the idealist interpretation of Vasubhandu’s Some scholars reject Western interpret him through the lens of Yogacara and instead from the is the study of conscious processes Phenomenology which

phenomenology and existentialism

p (94); p // // p (97); arthur - - - - rtha or schopenhauer ṣā a is not the āṇ a is not equivalent to the condition that a is not equivalent to the condition āṇ nta Hinduism. ā ), and that the extinction of desire leads to liber ), and that the extinction ā h ṇ Schopenhauer, the philosopher himself made the following statement in his discussion of religions: greed and lust are always unskillful, desire is ethically variable always unskillful, desire is ethically greed and lust are unskillful, or neutral. -- it can be skillful, primacy over the intel For Schopenhauer, Will had ontological to be prior to thought. lect; in other words, desire is understood notions of puru Schopenhauer felt this was similar to goals of life in Ved of the will is attained by In Schopenhauer’s philosophy, denial either: great suffering that leads to personal experience of an extremely loss of the will to live; of life in the world through or knowledge of the essential nature people. observation of the suffering of other However, Buddhist nirv the will. Nirv Schopenhauer described as denial of Western scholars have thought, extinguishing of the person as some meaning of nirvana) of but only the “extinguishing” (the literal that assail a person’s the flames of greed, hatred, and delusion Godwin (1945-- ) stated, “It character. Occult historian Joscelyn of Arthur Schopenhauer, was Buddhism that inspired the philosophy Wagner. This Orientalism re and, through him, attracted Richard in the words of Leon flected the struggle of the German Romantics, Judeo--Christian fetters.”In Poliakov, to “...free themselves from contradistinction to Godwin’s claim that Buddhism inspired Schopenhauer noted a correspondence between his doctrines and the a correspondence between his doctrines Schopenhauer noted on the prin of Buddhism. Similarities centered Four Noble Truths caused by suffering, that suffering is ciples that life involves desire (ta correspond to of the four “truths of the Buddha” ation. Thus three while of the will. In Buddhism, however, Schopenhauer’s doctrine - - - take a Wittgensteinian or Post--Wittgensteinian critical model in take a Wittgensteinian or Post--Wittgensteinian Ives Waldo writes their work on Madhyamaka Buddhist philosophy. of svabhava (own--being) that Nagarjuna’s criticism of the idea that a private lan “directly parallels Wittgenstein’s argument Having no logical guage (an empiricist language) is impossible. their defining situation, its links (criteria) to anything outside or use.” words must be empty of significance tic and philosophical confusion. C. Gudmunsen in his Wittgenstein confusion. C. Gudmunsen in his tic and philosophical had that “much of what the later Wittgenstein and Buddhism argues In his about 1,800 years ago in India.” to say was anticipated philosophy compares Wittgenstein’s later book, Gudmunsen mainly words. Many on the emptiness of thought and with Madhyamaka views of Nagarjuna (Jay Garfield, CW Huntington) modern interpreters Ludwig Wittgenstein held a therapeutic view of philosophy which held a therapeutic view of philosophy Ludwig Wittgenstein the Zen Bud Fann has “striking resemblances” to according to K.T. linguis the dharma as a medicine for abstract dhist conception of

wittgenstein

p (96); p // // p (99); - - - infuences Concerning the Upanishads and Vedas, he writes in The World as and Vedas, he writes in The Concerning the Upanishads Will and Representation: benefit of the Vedas, the ac If the reader has also received the is in my eyes the great cess to which by means of the Upanishads century (1818) may claim est privilege which this still young the reader, I say, has before all previous centuries, if then Indian wisdom, and received it received his initiation in primeval in the very best way for with an open heart, he will be prepared will not sound to him strange, hearing what I have to tell him. It for I might, if it as to many others, much less disagreeable; every one of the detached did not sound conceited, contend that may be deduced as a statements which constitute the Upanishads, thoughts which I have to necessary result from the fundamental are by no means to enunciate, though those deductions themselves be found there. Schopenhauer said he was influenced by the Upanishads, Immanu he was influenced by the Upanishads, Schopenhauer said religion References to Eastern philosophy and el Kant and Plato. appreciated in his writing. As noted above, he appear frequently Buddhist. Buddha and even called himself a the teachings of the before could not have been conceived He said that his philosophy available. these teachings were - - - -

influence. Other scholarly work questions how similar Schopenhau er’s philosophy actually is to Buddhism of Buddhism until after the publication of The World as Will and of Buddhism until after the publication started to revise earlier Representation in 1818. Scholars have views about Schopenhauer’s discovery of Buddhism. Proof of early interest and influence, however, appears in Schopenhauer’s 1815/16 notes about Buddhism. They are included in a recent case study that traces Schopenhauer’s interest in Buddhism and documents its This actual world of what is knowable, in which we are and which This actual world of what is knowable, and the limit of our consider is in us, remains both the material ation. Schopenhauer’s philosophy more The argument that Buddhism affected credence when viewed in than any other Dharmic faith loses more did not begin a serious study light of the fact that Schopenhauer Philosophy ... is a science, and as such has no articles of faith; Philosophy ... is a science, and as as existing except what accordingly, in it nothing can be assumed or demonstrated through is either positively given empirically, indubitable conclusions. Also note: few accounts of Buddhism. however, sought to distance Buddhist philosopher Nishitani Keiji, philosophy may Buddhism from Schopenhauer. While Schopenhauer’s his methodology was reso sound rather mystical in such a summary, or transcendental: lutely empirical, rather than speculative doctrine in such close agreement with a religion that the major agreement with a religion that doctrine in such close far more hold as their own, for this numbers ity of men on earth yet the more other. And this agreement must be followers than any certainly as in my philosophizing I have pleasing to me, inasmuch till 1818, influence [emphasis added]. For up not been under its only a very there was to be found in Europe when my work appeared, If I wished to take the results of my philosophy as the standard the results of my philosophy as the If I wished to take over have to concede to Buddhism pre--eminence of truth, I should to see my case, it must be a pleasure to me the others. In any

p (98); p // // p (101); mathematics

buddhism and and buddhism

p (100); p // // p (103); - - - - - ntideva ā Ś na as the ā na. The Buddha’s ā literature is the y ā ā na to desire and the ramit ā the bodhisattva ideal the bodhisattva ā d p ā garjuna sums this up suc ā ā /compassion for the dukkha/suf /compassion for the ā tman. Both ways of life assume the ā tman/ self is fed and cultivated; in asceticism the intention is tman/ self is fed and cultivated; in Dharma] for the weal of beings who have set out in the best, in the most excellent of vehicle[s],” that is, Mah enlightenment as described in the Prajñ “allayer of all suffering.” The truth of existence is taught in the four noble truths about suffering: there is suffering, the arising of suffering, the cessation of suffering, and the path out of suffering. Suffering arises from desire and the attachment/up sion)] with an irreversible attitude for the sake of liberating sion)] with an irreversible attitude the incomparable pain of limitless sentient beings... to remove complete happiness of all every single being...striving for the over the historical course sentient beings.” We have seen unfurl of Buddhism the conviction that “the Tathagata has taught [the the reality of dukkha: the suffering of destitution, sickness, the suffering of destitution, the reality of dukkha: a cure Motivated by his compassion to find old age and death. turned to of life and existence, Siddhartha for these tragedies his journey led him down the the way of the arhant. This part of out the problems of desire. path of denial in the attempt to root only provided a transformed However, this lifestyle of asceticism of pleasure. In hedonism the mode of suffering that mirrored that ā to destroy and annihilate the to treat it different existence of the self, though each attempts in to the demands of desire. ly; and yet they both end by giving through these extremes and Siddhartha’s great insight was to see find the middle way between them. course of a miraculous medita He realized this awakening over the he gained an understanding tion in becoming the Buddha, whereupon grounded in his universal that showed him the truth of existence N compassion for all suffering beings. savours only / Mercy and love cinctly, “Compassion is a mind that centuries later, for all sentient beings.” About seven [of Awakening (and compas asserts, “...one adopts that Spirit At the core of Buddhism is karut At the core of Buddhism compassion Siddhartha Gautama realized this fering of the world. experience when he achieved nirv in the enlightenment to alleviate the story of the prince destined Buddha. We all know leading a serve as the great healer. After the world’s ills and contact with lifestyle, Siddhartha came into sheltered hedonistic ------ga, - ā tra ū ya--s ā ga. In addition ā ga (c. 480 -- 540 CE)--are ga (c. 480 -- 540 ā da--vidhi (“A Method for Argu ā tra and other literature of the ū ya--s da--vidhi was reconstructed by Frauwall na (Sanskrit). ā ā ā ga as the oft--cited wellspring of the logi ā ya school. This logical pervasion is required to fashion sound ā amongst others. Dign cal triune in the Buddhadharma is now invalidated. between the first and second arguments, a relationship between between the first and second arguments, ‘Justification’ (hetu) the ‘Demonstrandum’ (pratijna) and the that is assumed in the Ny Ny arguments. Vasubandhu’s V ner from embedded quotations harvested from the works of Dign (2005, rev.ed.) upon the collation of Frauwallner (1957), it is (2005, rev.ed.) upon the collation of now understood that Vasubandhu’s V logic of the Ny mentation”) refined the five argument pupil Dign to a three argument form and not his from the syllogism, Vasu to pruning the two redundant arguments he posited that a sound bandhu tendered a further qualification: (vyapti) needs to be defined relationship, a ‘logical pervasion’ name of logic. But that logic is not only logic it also establish name of logic. But that logic is not the philosophical tenets es the doctrines of the Buddhists. Thus as tools to establish were the fulcrum and the logic developed those. the critique of Anacker Following the work of Tucci (1929) and Sadhukhan, et al. frames the centrality of ‘syllogism’ to Buddhist Sadhukhan, et al. frames the centrality as an investigative, au Logic and foregrounds its indivisibility to establish the valid thenticating and proofing tool instituted cognitive insights of the Buddhadharma: forms and nature of syllo Buddhist logic obviously contains the for which it deserves the gism, the essence of judgement, etc. is a particular development, application and lineage of continuity application and lineage is a particular development, and Bud from which it seceded. Indian logic, of ‘Indian Logic’, heralded by Dign dhist Logic--in main ‘infer of ‘inference’-- patterns, where both primarily studies anum ence’ is a gloss of Buddhist logic, the categorical nomenclature modern Western dis categorical nomenclature modern Western Buddhist logic, the to Buddhadharma traditions of ‘Hetuvidya’ course has extended circa 500CE, (Sanskrit), which arose (Sanskrit) and ‘Pramanavada’

buddhist logics

p (102); p // // p (105); ------? of all temporal , and so on. The ā ī r ś nyat va: “Remaining in the ū ś ā vara, Mañju ś ra aiming to ascend, is an enlight ā na based solely on his/her universal compassion for all na based solely on his/her universal ā sion is achieved through freedom from attachment and fear. This is the fruit of emptiness.” But it is the former statement from The Diamond Sutra that holds our concern here, for the bodhisattva de liberately chooses to aid all others and will continuously strive innumerable beings have thus been led to Nirvana, no being at all has been lead to Nirvana.” This latter statement exemplifies the bodhisattva’s insight into the emptiness/ beings, their nonself-- existence/nisvabh cycle of existence for the sake of those suffering due to delu cending practitioner is guided by the enlightened wisdom (and cending practitioner is guided by the the celestial beings virtues) of the celestial beings, whereas perfected inactivity. The save others from suffering through their bodhisattva, as found in sans to take that final leap ened practitioner who seeks, but refuses into nirv bodhisattva’s] great com suffering creatures: “Through his [the and so stays in it long.” As passion he feels pain / For the world “For Mahayana Buddhism, my colleague Wing--Cheuk Chan once wrote, first to be a Bodhisattva. A in order to become a Buddha, one has been Enlightened. But for Bodhisattva is a person who has already does not enter Nir the benefit of the other, the Bodhisattva will only enter vana by himself/herself. Rather, a Bodhisattva beings become Enlightened.” Nirvana when all the other sentient expressed by Fa--Tsang: We find this ideal in Hua--yen Buddhism ability to freely extin “Even though [the bodhisattva] has the the first stage on, [s/] guish the obstacles of defilements from not extinguish them. Why? he deliberately retains them and does and convert others.” To In order to nourish rebirth and attract vow, which The Diamond Sutra this effect, the bodhisattva takes a beings as there are in the describes thusly: “As many [living] must lead to Nirvana, in the universe of beings...all of these I realm of Nirvana which leaves nothing behind. And yet, although world as the activities of a Bodhisattva. world as the activities the as of the bodhisattva are complementary: These two aspects ...The term Bodhisattva itself is to be understood in two ways: itself is to be understood in ...The term Bodhisattva from sattva as a Buddha--to--be (ascending, the one is Bodhisattva being, or other is Bodhisattva as a celestial to Bodhi) and the as Avalokite a Bodhi--being, such the state celestial beings, who come down from activities of such in this is inactive and immovable, are seen of Buddhahood, which - ā - - y ā - - - na - ā y ā da/relational ā tya--samutp ī tman/non--self. ā tman expresses the reality of prat ā

tues and their interpretations in the different Buddhist tradi tions;30 rather, I will confine myself here to the general Mah na evaluation and deployment of the noble path. In the Mah tradition we find the development of the bodhisattvacarya, the ideal or way of the enlightened being. According to G. M. Nagao, The path out of suffering is the Eight--Fold Noble Path, where The path out of suffering is the Eight--Fold in we find the core of Buddhist ethics and morality. According to David Keown, the noble path has three main legs, like a tripod: wisdom, mental discipline, and ethical practice. The scope of the present study does not permit the exploration of the various vir desired phenomena into concrete and stable structures. For our desired phenomena into concrete and is satisfactory, but when we conventional needs (or truths) this claims, such as in the case reify and absolutize these existential actually existing self, then of believing in and grasping after an In this vein, the Buddha’s suffering (due to delusion) arises. mistakes. The cultivation of middle way aids us in avoiding such path out of suffering. the middle way requires following the aggregates/pañcaskandha), named and identified with language. “So aggregates/pañcaskandha), named and on the aggregates, / But the conception of ‘I’ exists / Dependent face / In reality the ‘I’ like the image [in a mirror] of one’s the self as “I” is delusory does not exist.” Such denotation of dynamic and rela for it covers over and hides the essentially entifying and freezing tional unfolding of experience by seemingly self drives these extreme views. To overcome the suffering endem self drives these extreme views. To of the Buddha’s insights ic to such views, the noble truths teach into an An of all phenomena. origination that explains the interdependence entity (the five-- The so-- called self is actually a composite is obvious in hedonism, but in asceticism one needs to make the but in asceticism one needs to is obvious in hedonism, the understand that the desire to obliterate dialectical move to exists on holding that the self actually self implicitly relies nor non- can be annihilated. “Thus neither self as something that Subduer as real, / Therefore the Great -self / Are understood for the of self and non--self.” The craving rejected / The views objects of desire. The object, that is, the complex phenomena that The object, that is, the complex phenomena objects of desire. an actual and which we most crave for, is we have objectified, real. This which we (mistakenly) believe to be ly existent self,

p (104); p // // p (107); ------ntideva warns that ā Ś na ethos. In aiding ā y ā ntideva proclaims, “For the sake of accomplishing ntideva proclaims, ā Ś tioner moves others and themselves towards enlightenment: “... one should always strive for the benefit of others. Even that which is prohibited has been permitted for the compassionate one who foresees benefit,” that is, the liberation from suffering. In this context, it is the bodhisattva’s conduct that is indicative erosity is interpreted simply as a state of mind due to the inten simply as a state of mind due erosity is interpreted of that, everything, together with the fruits tion of giving away that is the mind of renunciation is obtained, to all people...When discipline.” Furthermore, he considered the perfection of ethical phenomena, but I shall states, “I am unable to restrain external are similar to Kant’s restrain my own mind.” These assertions act’s worth is inde propositions regarding duty, for a dutiful from such a deed; yet, in pendent of the consequences that result of that” means that the this case, the giving away of “the fruits for they can lead others effects of this virtue are also important through moral practice, out of suffering. This goal is achievable of wisdom. as well as meditation and the development ideal seems to mirror Though the aforementioned deontological pragmatic understanding the Buddhist doctrine, there is a more “Therefore knowing how intrinsic to the bodhisattva’s position: For your own sake help beings actions / And their effects agree, / such, as Socrates fore / Always and so help yourself.” In doing path. saw, the moral path is the intelligent “When one intends to move mindfulness ought never to be displaced: first examine one’s own or when one intends to speak, one should composure”--and, we can add, mind and then act appropriately with spin on this in Nagarjuna’s compassion. We can hear the Buddhist would deride / Deeds rhetorical question: “Who with intelligence and be concerned for others is motivated by compassion...?” To aid the most meritorious (and intelligent) fashion by which to culti joyments, and all my virtues of the three times.” He also examines my virtues of the three times.” He joyments, and all of gen in this regard: “The perfection the role of introspection vate selflessness under the Mah others, lessening their suffering, even if it means taking such upon oneself, and espousing the Dharma, the bodhisattva practi here is one of the limits of the analogy), the bodhisattva ought limits of the analogy), the bodhisattva here is one of the Taking this others / Without hope of reward.” to “Provide help to even further, my body, en sentient beings, I freely give up the welfare of all ------as are indicative of the karma such ś ntideva echoes this sentiment: “So may I be in various ways a ntideva echoes this sentiment: “So may

ā

intentionally promote and teach evil ways to others because those others will reciprocally turn around and harm and corrupt the very same instructor. What is more sensible, that is, rational is to teach (or exemplify) good and beneficial behaviour, for this will provide “a positive feedback loop,” if you will. Yet, where the instructed good will benefit the teacher in its own turn (and nized thus early in life and am I, at my age [of almost 70 years], nized thus early in life and am I, at to know that if a man with in such darkness and ignorance as not whom I have to live is corrupted by me, I am very likely to be harmed by him, and yet I corrupt him, and intentionally, too? That is what you are saying and of that you will never persuade me or any other human being. In other words, it makes no sense to Perhaps an analogy with an example from the Western Tradition can Perhaps an analogy with an example from the bodhisattva’s thoughtful help illustrate the rationale behind analogy, there is no exact judgment; and since this is only an of Socrates, Plato recounts equivalence implied. During the trial But you have just admit part of Socrates’ defence in the Apology: good, and the evil do them ted that the good do their neighbours superior wisdom has recog evil. Now is that a truth which your persons continue to produce. Ultimately the bodhisattva under persons continue to produce. Ultimately just as the self “is”. stands that these afflictions are empty, promise by the bodhisattva to But can we say that this choice and rational character or compo liberate all those who suffer have a nent (even if only secondary in character)? beings who are subject to dukkha and whose number “has no limit.” beings who are subject to dukkha and Ś present throughout space source of life for the sentient beings is coupled with the recog until they are all liberated.” Yet this liberate beings throughout nition that “While I have promised to from mental afflictions.” space...I have not liberated even myself These mental afflictions/kle Buddhahood.” This establishment in Buddhahood will be taken up in establishment in Buddhahood will be Buddhahood.” This motivated we must realize that the bodhisattva the conclusion, but is seemingly makes this decision, which by compassion consciously rational in character. sentient scope for it applies to all Compassion has a universal to do so, based on his or her compassion for their suffering. “The his or her compassion for their suffering. to do so, based on sen their compassion / Lead these limitless Bodhisattvas through definitely in of suffering and establish / Them tient beings / Out

p (106); p // // p (109); ------, the ā tman and karu ā va) heteronomous elements of va) heteronomous elements ā in this regard is deployed uni ā functions in an analogous fashion as ā da entails the recognition that there is noth da entails the recognition ā ra. In other words, the bodhisattva’s insight into ra. In other words, ā tya--samutp ī through their compassion.” karut versally, and it is this characteristic (lakana) that drives this comparative project. The recognition that suffering is universal is a rational understanding. We have thus seen that the bodhisat tva is moved by his/her compassion to aid all who suffer, doing so with intelligence. The extension of compassion as a universal ideal parallels the universality of the Kantian moral law that is grounded in the rational emotion of respect. But should we then conclude that Buddhist karut Kant’s pure practical reason? accord with Kant’s notion of autonomy that requires the existence notion of autonomy that requires the accord with Kant’s bodhisat subject. Thus while the of an agent qua transcendental (non--) perspective of an tva acts from the of an ideal self and pure Kantian agent acts from the perspective that the bodhisattva practical reason. Furthermore, the freedom whereas Kant’s freedom is experiences is that of moka from dukkha, itself the moral law unadul that of an autonomous subject giving terated by phenomenal experience. can be refined The ethical actions performed by a bodhisattva experience,” such that over the course of “recurring and unending to be] will attain “Through not wavering you [the bodhisattva thinking; through respect / awareness, / And intelligence through mean, / Through their reten You will realise what the doctrines should not conflate this tion you will become wise.” Though we the intent is clear use of respect with Kant’s conceptualization, (as it is one leg in the tri enough: wisdom will be supplemented pod of the noble path--see above), deployment of thinking and and even gained through the consistent manners. This thinking is acting in virtuous, ethical and moral implies a rational character; associated with intelligence, which to be equated or identi however, this intelligence is not meant “Bodhisattvas also who have fied with Kantian rationality per se. with certainty, / They seen it thus, / Seek perfect enlightenment maintain a continuity of existence / Until enlightenment only ing but nonself-- existent (nisvabh ing but nonself-- does not are all empty of self--existence, which experience. These tially aware of, and open to, the emptiness of the dharmas that open to, the emptiness of the dharmas tially aware of, and flow in sas prat world through compassion and right understanding is experien world through compassion ------la is an ra and ī a. ś ā ā becomes the vehicle for nirv ā ntideva admonishes the adopters of the “Spir ntideva admonishes the adopters of the ā Ś nya. ū ś la is illustrative, for it “represents an internally la is illustrative, ī ś a are ā

construction of a priori principles of volition, which determine the moral worth of the act. Likewise the bodhisattva is admonished to think for him/herself without relying on or being unduly influ enced by heteronomous (to use Kant’s language) factors imposed by the world, others, or his/her own desires and empirical natures. This point requires clarification: the bodhisattva who views the has promised to liberate all sentient beings, one may not have has promised to liberate all sentient Thinking before liberated even oneself from mental afflictions. acting seems primary and practical, for there are cognitive (re lational) conditions to the bodhisattva’s ethical actions. We saw this also with the Kantian categorical imperative, for the legis lation of a universal law via an act of the will necessitates the ity.” Reality must be herein approached with the right attitudes, ity.” Reality must be herein approached sense, both sas intentions and understanding; in this nirv strive not to neglect [one’s] it of Awakening”: “Always vigilantly it is appropriate training. Although one has made a commitment, that which has been rashly [to reconsider] whether or not to do considered”--for while one undertaken and which has not been well called for in doing without reward. “You [the bodhisattva] should called for in doing without reward. you act, / Through seeing always well analyse / Everything before rely on others.” things just as they are / You will not statement about Hua-- This would agree with Cook’s straightforward act in accordance with real yen, “to act compassionately means to individual and universal (social) enlightenment. Thus the univer individual and universal (social) enlightenment. sal extension of karut these ethical guidelines The bodhisattva ought not to follow nor simply because they simply because they are accepted dogma, one happy for helping oth satisfy some secret desire that makes revel in the self--sacrifice ers, or masochistically allows one to are sentient beings, just as I am a sentient being.” In this vein, just as I am a sentient being.” are sentient beings, Buddhist practitioner around which any Buddhist enforced ethical framework life. From this perspective, might structure his/her ethical con for understanding individual enormously rich concept at both the bodhisattva such comportment aims duct,” though for of their personal commitment to compassionate action: “I should commitment to compassionate action: of their personal just of others because it is suffering, eliminate the suffering they I should take care of others because like my own suffering.

p (108); p // // p (111); garjuna ā N - - - - na ā y ā

develop (not neglect) one’s talents and the duty of mutual aid are thus duties of respect for persons. The motivation to help others in the Kantian context explicitly intends to enable the rationali ty of others, but it also must exercise a material As a person’s true needs are those that must be met if [she/]he is As a person’s true needs are those that as a rational, end--setting to function (or continue to function) agent, respecting the humanity of others involves acknowledging the duty of mutual aid: one must be prepared to support the condi tions of the rationality of others (their capacity to set and act for ends) when they are unable to do so without help. The duty to not limited to an inner attitude, but is identified with practical not limited to an inner attitude, but Kant’s kingdom of ends in the action.” We can also hear echoes of of such social structures, orderliness and beneficial arrangements of universal laws of the for these reverberate like the system example of this in Kant’s good will. Herman describes an important moral philosophy: beauty and order... The force of their meritorious karma enables beauty and order... The force of their to perfection, a Pure the Bodhisattva to realize, or to bring or ‘paradise’ which offers Land, an unworldly world, a ‘heaven’ progress. This spiritual uto ideal conditions for rapid spiritual bodhisattva’s compassion for pian vision is realized through the because such “compassion is the suffering in the mundane world, sentient beings in accordance with that share.” Likewise we find sentient beings in accordance with that similar to the kingdom of the bodhisattva aiming at a social ideal here explained by ends, the creation of “harmonious Buddhafields,” the world in which a Buddha E. Conze: A Buddhafield is a part of it is compared to an matures beings. As a harmonious structure array. In contradistinction to orderly and well--arranged military in a ‘Pure Land’ all is an ordinary, defiled world such as ours, the moral law is put into practice, a union of rational beings into practice, a union of rational the moral law is put and autono ought to treat each other as free occurs, wherein they of respect because they are all instantiations mous agents worthy Mah law. Comparably, we find in the of an identical moral have the of Buddhanature: “Sentient beings tradition the ubiquity honour qualities of a Buddha. One should best portion of emerging CONCLUSION from the how Kant’s kingdom of ends unfolds I described above of categorical imperative. As the universality deployment of the

p (110); p // // p (113); ------also to astrologers, surveyors and measurers of tapestry. But long before Stevin, the basic idea of decimals had been applied in lim ited contexts. In the mid--10th century, al--Uqlidisi, in Damas cus, wrote a treatise on Arabic (Hindu) numerals in which he dealt with decimal fractions, although historians differ on whether he understood them thoroughly or not. Euclidean approach to space, while Riemann, much later, produced to space, while Riemann, much later, Euclidean approach Einstein geometry that was most helpful for the non--Euclidean non--Eu relativity. The best thing about in articulating general the dumb idea that some clidean geometry was that it demolished without any need to check knowledge is known to be true a priori, experiments. Immanuel Kant it out by real--world observations and of a priori knowledge. thought Euclidean space was the exemplar not even right. But not only is it not a priori, it’s 6. BINARY LOGIC (GEORGE BOOLE) mathematical representation Boole was interested in developing a to using symbols (such as x) of the “laws of thought,” which led mathematicians). He hit a to stand for concepts (such as Irish required x times x to be snag when he realized that his system much rules out most of mathe equal to x. That requirement pretty does equal x for two num matics, but Boole noticed that x squared book based on doing logic bers: 0 and 1. In 1854 he wrote a whole to the founders of with 0s and 1s -- a book that was well--known modern computer languages. ABU’L HASAN AL--UQLIDISI) 5. DECIMAL FRACTIONS (, fractions to a European Stevin introduced the idea of decimal 1585, promising to teach “how audience in a pamphlet published in may be performed by In all Computations that are met in Business He thought his deci tegers alone without the aid of Fractions.” mal fraction approach would be of value not only to merchants but 7. NON--EUCLIDEAN GEOMETRY (CARL GAUSS, NIKOLAI LOBACHEVSKY, JÁNOS GEOMETRY (CARL GAUSS, NIKOLAI LOBACHEVSKY, 7. NON--EUCLIDEAN BOLYAI, BERNHARD RIEMANN) to figure 19th century, was probably the first Gauss, in the early but Gauss was to Euclid’s traditional geometry, out an alternative So perfection is the enemy of publication. a perfectionist, and one non-- get the credit for originating Lobachevsky and Bolyai - - - with roots of negative numbers. A century later John Wallis made the first serious case that the square roots of negative numbers were actually physically meaningful. 8. COMPLEX NUMBERS (GIROLAMO CARDANO, RAFAEL BOMBELLI) 8. COMPLEX NUMBERS (GIROLAMO CARDANO, numbers had shown up in Before Cardano, square roots of negative various equations, but nobody took them very seriously, regarding them as meaningless. Cardano played around with them, but it was Bombelli in the mid--16th century who worked out the details of calculating with complex numbers, which combine ordinary numbers Cayley. (Several others, including Jacques Binet, had explored Cayley. (Several others, including Jacques then.) Besides their many aspects of matrix multiplication before extremely useful for quantum other applications, matrices became reinvented a sys mechanics. In fact, in 1925 Werner Heisenberg to do quantum calculations tem identical to matrix multiplication already existed. without even knowing that matrix algebra though, by recasting Napier’s version into something closer to the though, by recasting Napier’s version modern base--10 form. 9. MATRIX ALGEBRA (ARTHUR CAYLEY) matrix--like calculations, An ancient Chinese math text included in the mid--19th century by but their modern form was established 10. LOGARITHMS (, JOOST BÜRGI, HENRY BRIGGS) 10. LOGARITHMS (JOHN NAPIER, JOOST BÜRGI, or messed with powers and A great aid to anybody who multiplied and clarified all roots, logarithms made slide rules possible in various fields. Napier and sorts of mathematical relationships late 16th century, but both Bürgi both had the basic idea in the log tables before publish spent a couple of decades calculating Briggs made them popular, ing them. Napier’s came first, in 1614. Ranking where logarithms rate among the rest is subjective, of rate among the rest is subjective, Ranking where logarithms still them 10th (they’d be higher if everybody course, but I’d put 10 math though). Here are the rest of my Top used slide rules, because which you might as well read here ematical innovations, retires: going to get to them before he David Letterman isn’t Of all the mathematical innovations since ancient times, only some innovations since ancient times, Of all the mathematical logarithms, celebrations. Certainly are worthy of multicentenary them. 400th anniversary this year, are among celebrating their

top 10 mathematical top 10 innovations

p (112); p // // p (115); ’ - ā - - ’. - ā nyat ū ś nyat ū ś ’ propagat ā applied buddhism applied nyat ū ś in modern mathematics ’or ‘void’ was later refined ’or ‘void’ was later ā na) forms of Buddhism. This Doc ’ provided the foundation for ā ā y nyat ā ū ś nyat ū ś na (Tantr ā y ā rjuna through his Doctrine of Emptiness or ‘ rjuna through his ā g rjuna who had imparted an intensive philosophical meaning an intensive philosophical meaning rjuna who had imparted ā na and Vajr ā g ā rjuna. There also existed the derivation of a symbol for it. existed the derivation of a symbol rjuna. There also rjuna’s doctrine of ‘ y ā ā ā ā g g ā ā tive advancement of the human capacity of abstraction. In absence tive advancement of the human capacity been only positive numer of a concept of ‘zero’ there could have ‘zero’ in mathematics opened als in computation, the inclusion of and gave a cut--off point up a new dimension of negative numerals of qualities whose extremes and a standard in the measurability as temperature. Though are still unknown to human beings, such Indian mathematics is still the exact age of origin of ‘zero’ in of ‘zero’ and ‘Decimal unknown, but the archeological evidence period were found on the System of numerals’ during the Buddhist Rock Edits of Ashoka (256 B.C.). trine of Emptiness had deep rooted origin in the Buddha’s Doctrine trine of Emptiness had deep rooted origin The concept of ‘ of Dependent Origination or Impermanence. culture through the Buddhist was influenced by South--east Asian salvation by merging concept of ‘Nibbana’ which means ‘attaining into the void of eternity’. represents a qualita A concept and symbol that connotes nullity N of ‘ The early Vedic concept by N to it. N Mah according to top 10 mathematical innovation... according to top 10 India. It or ‘sunyam’ originated in ancient The concept of ‘zero’ concept of ‘void’ or ‘ was derived from the ed by N before of ‘void’ existed in Hindu Philosophy However, the concept - - - - -

without such versatile numerals. titative science? Try doing a complicated calculation with their titative science? Try doing a complicated European science followed the numerals. Great advances in Western Italian mathematician Fibo introduction of Arabic numerals by the learned them from conducting nacci in the early 13th century. He Of course, they should re business in Africa and the Middle East. the Arabs got them from the ally be called Hindu numerals because be stuck in the dark ages Hindus. In any case, mathematics would without its calculational powers. Today everything from architec without its calculational powers. Today thermodynamics depends on ture and astronomy to neuroscience and calculus. 1. ARABIC NUMERALS do much creative quan Did you ever wonder why the Romans didn’t number to represent nothing.” LEIBNIZ) 2. CALCULUS (ISAAC NEWTON, GOTTFRIED the credit, even though You know the story -- Newton gets all same time, and with more Leibniz invented calculus at about the In any event, calculus convenient notation (still used today). couldn’t have happened made all sorts of science possible that sense of them. It’s not a coincidence that he also had to fig not a coincidence that he also had sense of them. It’s make sense. of zero to make negative numbers ure out the concept the number nothingness, but a meaningful number, Zero was not just not just a number from itself. “Zero was you get by subtracting Joseph Mazur in his new book Enlightening a placeholder,” writes there was a may have been the first time ever, Symbols. “For what 4. ZERO AND 3. NEGATIVE NUMBERS (BRAHMAGUPTA) 4. ZERO AND 3. NEGATIVE not the Hindu astronomer, was Brahmagupta, a seventh--century to make numbers, but he was the first first to discuss negative

p (114); p // // p (117);

emptiness

p (116); p // // p (119); ------in modern mathematics evolution ofevolution the concept of ‘zero’ tem distinguished itself from other positional systems by virtue itself from other positional systems tem distinguished The number of ‘zero’ as a legitimate number. of allowing the use Greeks were in Greek mathematics, because the ‘zero’ did not exist use for the mathematical con essentially geometricians and had no ‘zero’ also did not exist in cept of a non--entity. The concept of encountered the Indian number Egyptian mathematics. The Arabs, who in India, found it superior to system during their early conquests alphabets, and had adapted their own traditional system which used Arabic word for ‘zero’ is it to develop Islamic mathematics. The century, the Italian math “sifr”, meaning “empty.” In the 12th studied Arabian algebra and ematician Leonardo Pisano Fibonacci to Europe. The word “sifr” introduced the Hindu--Arabic numerals and subsequently, ‘zero’ got transformed into “zephirum” in Latin in English.1,5 the ancient Indians were During the first three centuries A.D., on a wide scale. In this already using a decimal positional system represent different system, the numerals in different positions used was a fully func numbers and here, one of the ten symbols The word and its mean tional ‘zero’. They called it ‘Sunyam’. its use in philosophical ing ‘void’ were obviously borrowed from System of calculation evolved literature. Eventually, the Decimal for all the modern arithme from this, which laid the foundation tic, mathematics and statistics. In mathematics the notion of emptiness finds expression in the notion of emptiness finds expression In mathematics the The con well as in contemporary set theory. number ‘zero’, as century discovered in India prior to the third cept of ‘zero’ was Arabic nor number system we use today is neither A.D. The “Arabic” to India fact, the digits 0123456789 go back Greek in origin. In sys created. The ancient Indian number where they were first

- - r ), - ā ā g ā of evil Work for Resist evil Respect life Free your mind da. Since ā ’ is used primar dhyamaka School. the good of others ā ā dhyamaka school of ā nyat ū ś ’ or ‘ ā

. ā rik ā Teachings of rjuna’s views in support of it may be found in rjuna’s views in support of it may be Siddhartha Gautama ā g ā dhyamaka--N ā na Buddhist philosophy which he had established during the na Buddhist philosophy which he had la--M ā ū rjuna is regarded as the founder of the M rjuna is regarded as the founder of y

ā ā g ā of the Middle Way”) is his major work. It was originally composed of the Middle Way”) is his major work. early Tibetan versions of the in Sanskrit. The Sanskrit as well as damage over the ages along work had survived without significant Several complete English with the later Chinese translations. in recent times. translations of the ‘Karika’ are available trine of emptiness is the central tenet of the M trine of emptiness is the central tenet A statement of N his M N Mah (“Fundamentals 2nd--3rd Century A.D. The ‘Mulamadhyamaka--Karika’ self or soul which is erroneously imputed to them.1 The doctrine is erroneously imputed to them.1 The self or soul which by N received its fullest elaboration of emptiness, however, it skillfully to destroy the substantiality juna, who wielded Abhidharma schools of the Therav conceptions of the (buddhat that is not the Buddhanature there cannot be anything The doc in truth devoid of characteristics. all that appears is In early Buddhism, the term ‘suññat In early Buddhism, to denote with the ‘no--self’ (anatman) doctrine ily in connection permanent (skandhas) are ‘empty’ of the that the Five Aggregates

Know the truth Say nothing to hurts others Practice meditation Control your thoughts the buddhist concept the buddhist of or ‘emptiness’ ‘śūnyatā’

p (118); p // // p (121); ------the evolution of the evolution indian numeral system numeral indian (b) MATHEMATICAL ACTIVITY IN THE VEDIC PERIOD In the Vedic period, records of mathematical activity are most ly to be found in Vedic texts associated with ritual activities. However, as in many other early agricultural civilizations, the study of arithmetic and geometry was also impelled by secular considerations. Thus, to some extent early mathematical develop ments in India mirrored the developments in Egypt, Babylon and perhaps best stated by French mathematician, Laplace: “The inge by French mathematician, Laplace: perhaps best stated a set of every possible number using nious method of expressing absolute val symbol having a place value and an ten symbols (each so simple nowadays that its ue) emerged in India. The idea seems is no longer appreciated. Its significance and profound importance calculation and placed simplicity lies in the way it facilitated arithmetic foremost amongst useful inventions.” (a) THE DECIMAL SYSTEM IN HARAPPA Indians was congenial for The mathematical environment among the use as the null--value in all the invention of ‘zero’ and for its system was already in facets of calculation. In India a decimal indicated by an analysis of place during the Harappan period, as corresponding to ratios of Harappan weights and measures. Weights 50, 100, 200, and 500 have 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, decimal divisions. A partic been identified, as have scales with weights and measures is ularly notable characteristic of Harappan rod marked in units of 0.367 their remarkable accuracy. A bronze demanded in those times. inches points to the degree of precision in ensuring proper im Such scales were particularly important that required roads of fixed plementation of town planning rules other, for drains to be con widths to run at right angles to each for homes to be constructed structed of precise measurements, and existence of a gradated according to specified guidelines. The points to the development of system of accurately marked weights trade and commerce in Harappan society. Although the Chinese were also using a decimal based counting sys were also using a decimal based Although the Chinese system that they lacked a formal notational tem in ancient times, system. and elegance of the Indian notational had the abstraction Western world notational system that reached the It was the Indian Sever and has now been accepted as universal. through the Arabs is to this development whose significance al factors contributed ------expression or symbol for ‘zero’. A number, say, 101,000, would have to be written only by 101 consecutive M’s. The Egyptians had no ‘zero’ and never reached the idea of expressing all numbers with ten digits. tem. The Greeks were hampered by their use of letters for the tem. The Greeks were hampered by their the art of reckoning remained numbers. Before ‘zero’ was invented, an exclusive and highly skilled profession. It was difficult to distinguish, say, 27, 207, 270, 2007, because the latter three were all written 2 7, with a ‘space’ in between. The positional system is not possible in the Roman numeral system which had no tic book dated 820 A.D., by Muhammad Ibn Musa al--Khouarizmi , who tic book dated 820 A.D., by Muhammad great detail. It was actual explained the whole Decimal System in as the Arabs themselves had no ly the Indian system that explained number system of their own. also had a ‘zero’ in the The Maya civilization of South America use it in a fixed base sys first century A.D., but they did not symbols, namely, nine of each of the symbols. But it is not cer symbols, namely, nine of each of the most modest of all numer tain when exactly the invention of this Europe was during the als took place. The first time it reached A.D. Later, when massive Lat Moorish invasion of Spain around 700 took place around the close in translations of books from Baghdad was found in an arithme of the first millennium A.D., the concept special symbol for ‘zero’ as early as the 3rd century B.C., they special symbol for ‘zero’ as early as not have the concept of used it only as a place holder and did ‘zero’ as an actual value. calculations, the Compared to the Indian system of mathematical figures, one for 1, one for Babylonian numeration had only three say, 999, would require 27 10, and one for 100, so that a number, lines, though later different numbers came to be assigned specif different numbers came to be assigned lines, though later by symbols (as in India) or were designated ic numeral names and we take our (such as in Rome). Although today, alphabetic letters based granted, not all ancient civilizations decimal system for a hexag ten--base system. In ancient Babylon, their numbers on a used a was in use. Though the Babylonians esimal (base 60) system In all early civilizations, the first expression of mathematical the first expression of mathematical In all early civilizations, Numbers in the form of counting systems. understanding appears groups of were typically represented by in very early societies

the babylonian system the babylonian of numerals

p (120); p // // p (123); ------rjuna’s ā g ā had paved the way for the de ā nyat ū Ś velopment of the concept of ‘nullity’ and ‘infinity’ in modern mathematics. (d) BUDDHIST PHILOSOPHY AND MATHEMATICS Buddhist literature also demonstrates an awareness of indetermi nate and infinite numbers. Buddhist mathematics was classified either as Garna (Simple Mathematics) or Sankhyan (Higher Mathemat ics). Numbers were deemed to be of three types: Sankheya (count able), Asankheya (uncountable) and Anant (infinite). N Doctrine of Emptiness or ered limitless. This led to a deep interest in developing very ered limitless. This led to a deep interest of infinite num large numbers and evolution of the definitions through recursive formulae, as bers. Infinite numbers were created in the Anuyoga Dwara Sutra. (d) PHILOSOPHY OF JAINISM AND MATHEMATICS Jain cosmology also regarded Like the Upanishadic world view, the recognized five space and time as limitless. Jain mathematicians infinite in one di different types of infinities that included, infinite everywhere and per rection, in two directions, in area, allowed for a degree of petually infinite. Since Jain epistemology it probably helped in grap indeterminacy in describing reality, finding numerical approxi pling with indeterminate equations and and combinations are mations to irrational numbers. Permutations BC) and Sathananga Sutra (2nd listed in the Bhagvati Sutras (3rd C are operated upon by loga C BC). In Satkhandagama, various sets and extracting square rithmic functions to base two, by squaring powers. The operations roots, and by rising to finite or infinite other works the relation of are repeated to produce new sets. In occurring in the the number of combinations to the coefficients binomial expansion is noted. Indian philosophical doctrines also had a profound influence on doctrines also had a profound influence Indian philosophical In the mathematical concepts and formulations. the development of were consid view of Brahmanism, space and time Upanishadic world These two factors were unique to Indian culture and contributed were unique to Indian culture and contributed These two factors value process that led to the decimal place most to the thought ’zero’ having a value. notation as well as AND MATHEMATICS (c) BRAHMINICAL PHILOSOPHY - - - - - i, arbu ţ ankha, jaladhi, antya, in their descriptions ś ā --padma, ā rdha. Thus, the Decimal System was in Indian ā ata, sahasra, ayuta, laksha, prayuta, ko ata, sahasra, ayuta, laksha, prayuta, ś ankha, par ś ā

therein, the Mahabharata and the Ramayan of statistics and measurements used all these words with total abandon. However, distinct symbols for the numbers 1 to 9 already existed in the Indian system of calculations and the counting system used the base 10 in all its secular, religious and ritual activities. ten thousand, … were given by the sequence of words in the list: ten thousand, … were given by the sequence eka, dasa, da, abja, kharva, nikharva, mah mah culture even in the early part of the first millennium B.C. The Yajurveda, in its description of rituals and the mantras employed theoretical understanding of basic geometric principles. Modern theoretical understanding of basic geometric probably emerged from the methods of multiplication and addition techniques described in the Sulva--Sutras. power 17 was already in use A notation for powers of 10 up to the had been used to denote the even from Vedic times. Single words one, ten, hundred, thousand, powers of the number 10. The numbers possibly in the Harappan period. Baudhayana’s Sutra displays an possibly in the Harappan period. Baudhayana’s and techniques of convert understanding of basic geometric shapes to another of equiv ing one geometric shape (such as a rectangle) (such as a square). While alent (or multiple, or fractional) area others are accurate some of the formulations are approximations, ingenuity as well as some and reveal a certain degree of practical tiplication, fractions, squares, cubes and roots are enumerated tiplication, fractions, squares, cubes to Ved Vyas (pre--1000 BC). in the Narad Vishnu Purana attributed are to be found in Examples of geometric knowledge (rekha--ganit) BC) and Apasthmaba (600 BC) the Sulva--Sutras of Baudhayana (800 of ritual altars which describe techniques for the construction that these texts tapped in use during the Vedic era. It is likely acquired much earlier, geometric knowledge that may have been required solutions. This meant that an understanding of geometry This meant that an understanding required solutions. virtually essential for administrators. and arithmetic was the secular brought into the service of both Mathematics was thus and the ritual domains. mul (Ganit) such as addition, subtraction, Arithmetic operations China. The system of land grants and agricultural tax assessments of land grants and agricultural tax China. The system land was re measurement of cultivated areas. As required accurate came up that problems of mensuration distributed or consolidated,

p (122); p // // p (125); ------’ or ‘void’ gave ā nyat ū ś be called the founder of higher branch of mathematics called nu merical analysis. Brahmagupta’s treatise Brahma--sputa--siddhanta was translated into Arabic under the title Sind Hind. For several centuries this translation remained a standard text of reference in the Arab world. It was from this translation of an Indian text on Mathematics that the Arab mathematicians perfected the Decimal System and gave the world its current system of enumeration which we call the Arab numerals, which are originally Indian numerals. obstacle, and in China the pictorial script posed as a hindrance. the pictorial script posed as obstacle, and in China such a de everything was in place to favor But in India, almost in already a long and established history velopment. There was and cosmological the use of decimal numbers, and philosophical expansive approach to number constructs encouraged a creative and theory and formal language theory. Panini’s studies in linguistic representational abstrac and the powerful role of symbolism and also provided an impetus, as tion in art and architecture may have and the exacting epistemology might have the rationalist doctrines abstractions of the Syada of the Nyaya Sutras, and the innovative vada and Buddhist schools of learning. systems of numeration, a large In the earlier Roman and Babylonian denote higher numerals. number of characters were required to a cumbersome process. Ac Thus, enumeration and computation was the number thirty would cording to the Roman system of numeration, the Decimal System it would. have to be written as XXX. But as per the number thirty three would Similarly, as per the Roman system, Decimal System, it would be be written as XXXIII. But as per the of the Decimal System 33. Thus, it is clear how the introduction having a high value with made possible the writing of numerals easier. limited characters. This also made computation based on the incorpora Apart from developing the Decimal System also arrived at solu tion of ‘zero’ in enumeration, Brahmagupta tions for indeterminate equations of 1 type ax2+1=y2 and thus can ern world, the cumbersome Roman numeral system posed as a major Roman numeral system posed ern world, the cumbersome philosophical concept of ‘emptiness’ or ‘ philosophical concept Subsequently, of ‘zero’ in Indian mathematics. rise to the concept for modern mathematics. this became the foundation In the West this invention was no accident. Brilliant as it was, ------rjuna’s Doc ā g ā was quite popular in Indian society ā nyat ū Ś

‘zero’, foreshadowing the Decimal System numeration. With the in tegration of ‘zero’ into the numerals, it became possible to note higher numerals with limited characters. Since, N trine of Emptiness or during the time of Brahmagupta, there is a high probability that Brahmagupta was inspired by this Doctrine of Emptiness. Thus, the was well established when King Vyaghramukha of the Chapa dynas was well established when King Vyaghramukha his two treatises, Brah ty made him the court astronomer. Among ma--sputa siddhanta and Karanakhandakhadyaka, first one is more famous. It was a corrected version of the old Astronomical text, Brahma siddhanta. It was in his Brahma--sphu siddhanta, for the first time ever that he had formulated the rules of the operation for a superior numerical system that lent itself to complicated for a superior numerical system that calculations. is credited with having The ancient India astronomer Brahmagupta the first time. Brahmagupta is put forth the concept of ‘zero’ for A.D. at Bhillamala (today’s said to have been born the year 598 His name as a mathematician Bhinmal ) in Gujarat, Western India. Counting boards with columns representing units and tens were in Counting boards with columns representing The numberless content of an use from very ancient times in India. to be ‘nothing’. The empty column in course of time was symbolized navigation and business thriving activity in astrology, astronomy, in India also looked forward during the first few centuries A.D. (Ifrah arguing that the use of ‘zero’ is already implied in Ary (Ifrah arguing that the use of ‘zero’ of the ‘zero’ begins to abhatta) tangible evidence for the use period. Between the 7th C proliferate towards the end of the Gupta into their modern form, and the 11th C, Indian numerals developed various mathematical functions and along with the symbols denoting eventually became the foun (such as plus, minus, square root etc) notation. dation stones of modern mathematical of ‘zero’. While the ‘zero’ (bindu) as an empty place holder in ‘zero’ (bindu) as an empty place of ‘zero’. While the algebraic system appears much earlier, the place--value numeral ‘zero’ and its relationship to mathematical definitions of the in the mathematical treatises of Brahmagupta functions appear in early the scholars are divided about how the 7th C AD. Although in India, came to be used in numeric notation symbol for ‘zero’ (e) CONTRIBUTION OF BRAHMAGUPTA (e) CONTRIBUTION OF emptiness or concerning Shunya -- i.e. Philosophical formulations the concept facilitated in the introduction of the void may have

p (124); p // // p (127); - - - in modern mathematics application ofapplication ‘emptiness’ evolved to signify polar opposition between being and nonbeing. ‘zero’ is that which contains all possible polarized pairs such as (+1, --1), (+2, --2), etc. It is the collection of all mutually cancelling pairs of forward and backward movements. Put it anoth er way, ‘zero’ is fundamental to all existence. Because of it, everything is possible. ‘zero’ is the additive identity, the focal point of all numbers. The numbers cannot be created without the ‘zero’. the term ‘Pujya’, meaning blank, came to be sanctified is still meaning blank, came to be sanctified the term ‘Pujya’, unknown. like the material world Indian philosophy has glorified concepts of renouncing the material being an illusion or ‘Maya’. The act into the void of eternity world is ‘Tyaga’ and the goal of merging of ‘zero’ might have got a is ‘Nibbana’. The mathematical concept from these. philosophical connotation of reverence of algebra, the concept of It is possible that like the technique the Arabs. In ancient India ‘zero’ also reached the west through ‘Pujyam’, ‘Sunyam’, the terms used to describe ‘zero’ included was termed as ‘Shukla’ and ‘Bindu’. The concept of a void or blank The Arabs referred to ‘Shubra’ which also means white or purity. which we have the English the ‘zero’ as ‘Siphra’ or ‘Sifr’ from term Cipher connotes ‘zero’ terms Cipher or Cypher. In English the that the term Cipher is or any Arabic numeral. Thus, it is evident in turn is quite close to the derived from the Arabic ‘Sifr’ which Sanskrit term ‘Shubra’. ‘zero’ did not original In the ancient Indian context, the number The Sanskrit word for ‘zero’ ly refer to nothingness or nullity. hollow, empty.” The ‘zero’ is ‘sunyam’, which means “puffed up, The discovery stands for emptiness suggestive of potentiality. with the emptiness of pra of the mathematical ‘zero’ concurred jna--intuition in India around 200 BC. The concept of ‘zero’ In ancient India the numeral of ‘void’ or ‘sunyam’ was used in numeral of ‘void’ or ‘sunyam’ was In ancient India the ‘Pujyam’. indicated by a dot and was termed computation. It was more current this term for ‘zero’ along with the Even today we use also means a blank. But the term ‘Pujyam’ term ‘Sunyam’ meaning is a prefix used in written communication holy. ‘Param--Pujya’ reason why it means respected or esteemed. The with elders where ------according to specified guidelines. The existence of a gradated according to specified guidelines. The points to the development of system of accurately marked weights trade and commerce in Harappan society. ularly notable characteristic of Harappan weights and measures is ularly notable characteristic of Harappan rod marked in units of 0.367 their remarkable accuracy. A bronze demanded in those times. inches points to the degree of precision in ensuring proper im Such scales were particularly important that required roads of fixed plementation of town planning rules other, for drains to be con widths to run at right angles to each for homes to be constructed structed of precise measurements, and the invention of ‘zero’ and for its use as the null--value in all the invention of ‘zero’ and for its system was already in facets of calculation. In India a decimal indicated by an analysis of place during the Harappan period, as corresponding to ratios of Harappan weights and measures. Weights 50, 100, 200, and 500 have 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, decimal divisions. A partic been identified, as have scales with ue) emerged in India. The idea seems so simple nowadays that its ue) emerged in India. The idea seems is no longer appreciated. Its significance and profound importance calculation and placed simplicity lies in the way it facilitated arithmetic foremost amongst useful inventions.” (a) THE DECIMAL SYSTEM IN HARAPPA Indians was congenial for The mathematical environment among the It was the Indian notational system that reached the Western world notational system that reached the It was the Indian Sever and has now been accepted as universal. through the Arabs is to this development whose significance al factors contributed “The inge by French mathematician, Laplace: perhaps best stated a set of every possible number using nious method of expressing absolute val symbol having a place value and an ten symbols (each Although the Chinese were also using a decimal based counting sys were also using a decimal based Although the Chinese system that they lacked a formal notational tem in ancient times, system. and elegance of the Indian notational had the abstraction

‘zero’ and and ‘zero’ notation the place--value

p (126); p // // p (129);

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(set containing previous three sets) (set containing previous four sets etc.) the empty set) (set containing previous two sets) (empty set) (set containing emptiness and null set: and null emptiness the evolution ofthe evolution numbers natural

the act of observing we create an entity containing emptiness (step 1). Now we perceive emptiness, as well as an entity. From the combination of the former two we create another entity by ob servation, which is different from the first entity (step 2). This process is repeated again and again. Interestingly, if we define suitable operations on the obtained sets based on union and inter section, the cardinalities of the resulting sets behave just like natural numbers being added and subtracted. The sequence is there fore isomorphic to the natural numbers -- a stunningly beautiful example of something from nothing. generate the natural numbers from the empty set as follows: generate the natural step {} 0: step {{}} 1: step {{},{{}}} 2: step {{},{{}},{{},{{}}}} 3: step {{},{{}},{{},{{}}},{{},{{}},{{},{{}}}}} a function that creates a This sequence is obtained by iterating two sets, thus generating new set from the union of the preceding 3, 4, ad infinitum. In less sets with the cardinalities 0, 1, 2, be described as follows: mathematical terms, the principle can Beginning with emptiness (step 0), we observe emptiness. Through A set is a collection of objects or numbers. For example, the set of objects or numbers. For example, A set is a collection elements; is a set of numbers containing five { 1, 2, 3, 5, 8 } The Null Set to have the “cardinality” of 5. it is therefore said and has the a collection that contains nothing or Empty Set { } is invented mathematician John von Neumann (1923) cardinality 0. The employed to von Neumann hierarchy, which can be a method, known as - - - - ’ provided the ā nyat ū ś rjuna’s doctrine of ‘ ā g ā

also now associated with the ‘Null Hypothesis Testing’ in statis also now associated with the ‘Null Hypothesis of modern research. Thus, it tical methods which is the backbone is evident that N biostatistics. foundation for modern epidemiology and an--Arabic numerals into , ‘zero’ became a number into Western culture, ‘zero’ became an--Arabic numerals Consequently, like any other number. that was used in calculations part that of its original meaning, namely the it lost some part not associ Today, most mathematicians do suggests potentiality. ‘Empty Set’ emptiness with ‘zero’, but with the ate the notion of is of set theory. This notion of emptiness which is a construct Among the great civilizations of antiquity, India alone was able of antiquity, India alone Among the great civilizations its im of emptiness and willing to accept to fathom the depth the Indi Following the introduction of portance in mathematics.

p (128); p // // p (131); - - - rjuna gave a new dimension of ‘nullity’ or ‘emp rjuna gave a new dimension of ‘nullity’ ā g ā tiness’ to the notion of ‘zero’ and made it more meaningful with tiness’ to the notion of ‘zero’ and The historical ev regard to our philosophical understandings. of ‘zero’, which had idences imply that the Indian contribution Decimal System of numbers, eventually led to the evolution of the mathematics and had changed was a significant milestone in modern forever. our way of thinking and understanding lier than Arab invasion. much of ‘zero’ appeared in the Indian history Though the concept earlier, but N The Decimal System of numerals is known as Indo--Arabic numerals of numerals is known as Indo--Arabic The Decimal System of ‘zero’ is actually a misnomer. The concept even today. But it and was of numerals’ first evolved in India and ‘Decimal System of ‘zero’ Arabs. The archeological evidence later adopted by the the Rock of numerals’ were already found on and ‘Decimal System ear B.C.) which was curved several centuries Edits of Ashoka (256 - - - ’ provided the foundation for this ā nyat ū ś rjuna’s doctrine of ‘ ā g ā ‘zero’. In medieval Europe, some countries banned the positional number system, along with ‘zero’, brought by the Arabs whom they considered as heathens. So, they considered the ‘Sunyam’ to be a creation of the devil. As a result ‘ciphra’ came to mean a secret code. The term ‘deciphering’ later evolved from this which meant ‘resolution of a code’. the Arabic ‘sifr’ which means empty space. In Medieval Latin it the Arabic ‘sifr’ which means empty English as ‘siphre’, in manifested as ‘ciphra’, then in Middle English as ‘cypher’ and in American as ‘cipher’. In the middle ages, the word ‘ciphra’ evolved to stand for the whole system. In the wake of this general meaning, the Latin ‘zephirum’ came to be used to denote the ‘Sunyam’. And that entered English finally as the chance factor to establish the truth with accuracy in the the chance factor to establish the truth and logical reasoning. light of our fundamental understandings N insight in modern epidemiology and biostatistics. of the Indians became It is interesting to know how the ‘Sunyam’ ‘Sunya’ of Sanskrit became the ‘zero’ of the modern world. The Hypothesis. models are applied to Various probability oriented statistical in order to establish test this Null Hypothesis in every research and analytical judgment to the actual truth by attaching logical directed towards minimizing the findings. All these efforts are This neutral position by the researchers is actually the appli This neutral position by the researchers unbiased throughout the cation of emptiness in order to remain states that there is no re study. However, the Null Hypothesis and an outcome. In lationship between a correlate or determinant is merely due to chance. So, case any relationship is observed, it judge from the results of the researchers need to analytically accept or reject the Null their research findings on whether to our scientific understandings. At the Beginning of any research, At the Beginning of any our scientific understandings. that a to take a neutral stand by assuming the researchers need related or determinants are neither set of suspected correlates in the the outcome variable that is examined not non--related to study. The concept of ‘nullity’ in the ‘Null Hypothesis’ is the backbone in the ‘Null Hypothesis’ is The concept of ‘nullity’ The accep research and statistical methods. of modern scientific basis of of Null Hypothesis is the fundamental tance or rejection

emptiness hypothesis and null

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p (136); p // // p (139); - - leg to stand on. This fact is unaviodable becuase consciousness is fact is unaviodable becuase consciousness leg to stand on. This Rosenblum quantum level. As the physicists Bruce implicated at the recently indicated: and Fred Kuttner have are not just two mysteries; Consciousness and the quantum enigma physical demonstration of they are the two mysteries; first, our fundamental mystery of the the quantum enigma, faces us with the conscious awareness, faces objective world `out there` the second, subjective, mental world us with the fundamental mystery of the connect the two. `in here`. Quantum mechanics seems to onto problems of quantum interpretation. onto problems of quantum has be ultimate TOE (a theory of everything) The search for the is seldom for modern physicists. But it come a central concern conscious integrating the phenomenon of appreciated that without not have a worldview any such TOE will ness within the ‘physical’ ------

Emptiness, the core view which is propounded by the Madhyamaka, is the insight that there is nothing in the universe which exists as an independent entity in its own right. It follows that noth ing exists as a fully independent feature of reality as was always thought by Western science up until the advent of quantum physics. Indeed, an understanding of Emptiness can throw new perspectives ents a picture of reality which is in accord with that proposed by ents a picture of reality which is in ago. The Madhyamika philoso Buddhist sages of two thousand years phers developed a rigorous and razor sharp method of philosophical analysis which, together with meditation investigation, penetrated into the ultimate nature of reality. ple who constructed it, and the individuals who agree to call it ple who constructed it, and the individuals to sit on. Not only is the a chair and recognize it as something contingent but, according existence of things and events utterly are thoroughly dependent to this principle, their very identities upon others. foundations and now pres Modern science has overturned its own other phenomena, including language, concepts, and other conven other phenomena, including language, the objects by which tions. Thus, there are no subjects without without subjects to ap they are defined, there are no objects things done. There is prehend them, there are no doers without wood, nails, the floor on no chair without legs, a seat, a back, the room it’s in, the peo which it rests, the walls that define exists and has an identity does so only within the total network exists and has an identity does so only potential relation to it. No of everything that has a possible or or intrinsic identity. phenomenon exists with an independent of complex interrelations. And the world is made up of a network discrete entity outside the We cannot speak of the reality of a with its environment and context of its range of interrelations being only as a result of the interaction of causes and condi of the interaction of causes and being only as a result Second, just arise from nowhere, fully formed. tions. They don’t without between parts and the whole; there is mutual dependence no sense no whole, without a whole it makes parts there can be the whole This interdependence of parts and to speak of parts. that and temporal terms. Third, anything applies in both spatial From all subject of this research, In brief, the principle of de this research, In brief, the principle From all subject of three ways. can be understood in the following pendent origination come into things and events in the world First, all conditioned

p (138); p // // p (141); - - - ry ingredient’ with the help of, firstly, the Buddhist Dzogchen the help of, firstly, the Buddhist ry ingredient’ with Mindnature version of the Universal Matrix of (Great Perfection) and cogni ultimate nature to be ‘emptiness which indicates the paradigm, which zance, and also the recent quantum ‘epiontic’ view, that cognition indicates, in conformity with the Dzogchen ontology. (epistemological activity) solidifies tion of the ‘Grid’, which is the ‘Matrix’ that constitutes the which is the ‘Matrix’ that constitutes tion of the ‘Grid’, in his haste of reality, we note that he has, ‘primary ingredient’ unconscious the ‘material’ of reality, become to get to grips with ‘prima Therefore we reinstall this much more of consciousness. QUANTUM EPIONTIC MIND MATRIX QUANTUM EPIONTIC MIND no overview of Nobel Laureate Frank Wilczek’s Beginning with an - - - Deep reflec

There’s no place for Descartes’ ‘matter’ in a quantum Mindnature There’s no place for Descartes’ ‘matter’ universe. Amit Goswami -- Scientific Proof of the Existence of God? -- God as the ultimate personification of the quantum Mindnature of the Universe? Penrose/Hameroff -- -- A Mindnature orchestration The Orch OR of Fundamental SpaceTime gets to the bottom of the of Orchestrated Objective--Reduction ‘matter’ of funda--mental spacetime. Psycho--Physical Bridge -- Henry Stapp’s Mindful Universe and the easy way to solve the ‘hard’ problem. Max Velmans -- Monism Dual Aspect Information Theory and Reflexive information is all in the tion on ‘Reflexive Monism’ shows that Mindnature. Karl Pribram’s Holonomic Brain -- in a holographic Mindna The brain as holographic storage device ture universe. David Chalmers -- -- An overview of The Quantum Solution to the ‘Hard’ Problem? Mindnature monism is an Chalmer’s analysis indicates that quantum sciousness perspectives covered are: sciousness perspectives Order -- David Bohm’s Implicate and matter suggests that dualistic mind The visionary physicist Mindnature field. unfold from a unified An overview of a few significant attempts to produce a unified significant attempts to produce An overview of a few of as of the functioning of reality conceived metaphysical account mind/con quantum Mindnature. The quantum a process of an ultimate

p (140); p // // p (143); - - - One moment into another. A collision. Photographer: Jens Ziehe attempted to transfer a coin into the Zone de Sensibilité Pictur a coin into the Zone de Sensibilité attempted to transfer location 50 by Yves Klein at the same ale Immaterielle proclaimed idea was to translate a piece of materiality years earlier. The void tangible. into immateriality and thus render the His works and exhibitions return again and again to themes of return again and again to themes His works and exhibitions elaborately books with empty pages, emptiness and concentration: in the empty wooden boxes (as seen for example folded paper fans, transmis / [...] / memor(y)ial -- another exhibition mo(nu)ment of a per agency/Leven One in Paris). As part sion (2012) at gb 2012 in Paris for series no. 00 Kasemkitvatana formance performed - - -

- Yesterday (2011) at the Jim Thompson foundation in Bangkok, assim Yesterday (2011) at the Jim Thompson them, paying respect ilate old works from the 1990s, transforming to Kasemkitvatana’s old teacher Aleks Danko, and incorporating experiences from the monastery. In his own artistic work Kasemkitvatana also focuses on the moment In his own artistic work Kasemkitvatana This also applies to his in which various spheres become “porous”. his art career to spend time biography, where the interruption of as a retreat from art, nor in a monastery should not be regarded as a end to his preoccupation his eventual return to the art world and periods are interwoven with spirituality. The various fields such as Tomorrow Was in a multitude of ways. Recent exhibitions Magazine and curated exhibitions for the About Art Related Activ Magazine and curated exhibitions for one of the main art locations ities (AARA) project in About Cafe, he has been part of a group in the city at the time. Since 2012 (and also publishes the that runs Messy Project Space in Bangkok Messy Sky Magazine with Pratchaya Phinthong). Then, as today -- before and after his time in the monastery -- Then, as today -- before and after his expanded concept of art, Kasemkitvatana propagates a radically of enabling, a domain of as social practice above all, a sphere Artistic, curatorial and encounter, a network and free space. within these parame publishing work all have an equal footing are fluid. At the turn of the ters; the boundaries between spheres Rirkrit Tiravanija at Ver millennium, for example, he worked with either between various positions in the art world, or between positions in the art world, or either between various an else, spirituality for instance. Following art and everything Kasemkit Bangkok art scene during the 1990s active period in the from forest monastery in the north of Thailand vatana lived in a 2002 and 2010. At the centre of Chitti Kasemkitvatana’s work stands a concept of Kasemkitvatana’s work stands At the centre of Chitti particular presence of the absent/absence with emptiness, of the distinctions, The Thai artists draws no focus on its permeability.

chitti kasemkitvatana

p (142); p // // p (145); - - - - discussion with discussion experimentation how geometric design principles influence me to practice in de principles influence me to practice how geometric design a defini using javascript. First and foremost, veloping forms by This will be given with respect to geometry. tion of form--giving geometric design princi is followed up by a study of most used the idea of making forms by ples. In coding culture class, I used in communication or language mathematics that is an essential tool show the idea of thinking of interpretation to draw the forms that buddhist. IS CODING THE NEW SECOND LANGUAGE? IS CODING THE NEW to get a way around a computer, but in order People may know their write a pro they will have to know how to job in the new economy, one.... Within the context of geometry--driven gram, not just use of experimental aims to provide an understanding form giving, this

One moment into another. A collision. Photographer: Jens Ziehe

p (144); p // // p (147); background(255); // draw the main circle ellipse(300,300, 300,300); // draw a serie of circles int numberOfCircles=12; float angle=2*PI/numberOfCircles; // repeat for(int i=0;i

ellipse (40,200,50,50); ellipse (260,200,50,50); ellipse (65,110,30,30); ellipse (65,290,30,30); ellipse (335,110,30,30); ellipse (335,290,30,30); rotate(-angle); translate(-400,-400); angle = angle + 10; } size of circle // draw 2nd circle ellipse (400,400,250,250); // draw 3rd circle ellipse (400,400,220,220); //draw 4th circle ellipse (400,400,215,215); translate(400,400); rotate(angle); // draw small circle around big circle ellipse (90,80,30,30); ellipse (200,40,50,50); ellipse (90,320,30,30); ellipse (200,360,50,50); ellipse (310,320,30,30); ellipse (210,80,30,30); // i have to draw a circle the actual angle // i need a variable to store float angle; void setup(){ //window and background // window size size (800,800) ; //background in white background (255,255,255); angle=0; } void draw(){ // draw a circle y, ellipse (400,400,400,400); // position x, position

p (146); p // // p (149); theText = "the therealnumber is : "+therealnumber; println(listStrings); theText = listStrings[therealnumber]; }else{ theText = "it is not a number : "+key; } //println(thenumber); } void draw(){ background(255);// white fill(0,0,0); //template and grid //String theText="sdfsfsdf"; text(theText,100,50,600,500); } // keypressed ? // interact with typing keyboard void keyPressed(){ int thenumber=int(key); String[] listStrings = new String[10]; String calculatedText; for(int j=0;j<10;j++){ listStrings[j] = "{}"; } if ((thenumber>=48) && (thenumber<=57)){ theText = "the number is : "+key; int therealnumber = thenumber--48; for(int i=0;i<=therealnumber;i++){ calculatedText=""; for(int k=0; k

ellipse (40,200,50,50); ellipse (200,200,50,50); ellipse (65,110,30,30); ellipse (65,290,30,30); ellipse (235,110,30,30); ellipse (235,290,30,30); rotate(-angle); translate(-400,-400); angle = angle + 10; } size of circle // draw 2nd circle ellipse (400,400,250,250); // draw 3rd circle ellipse (400,400,220,220); //draw 4th circle ellipse (400,400,215,215); translate(400,400); rotate(angle); // draw small circle around big circle ellipse (90,80,30,30); ellipse (150,40,50,50); ellipse (90,320,30,30); ellipse (150,360,50,50); ellipse (110,120,30,30); ellipse (210,80,30,30); // i have to draw a circle the actual angle // i need a variable to store float angle; void setup(){ //window and background // window size size (800,800) ; //background in white background (255,255,255); angle=0; } void draw(){ // draw a circle y, ellipse (400,400,400,400); // position x, position

p (148); p // // p (151);

conclusion;

p (150); p // // p (153); - - ty--defined in terms of essentially real constituents of matter-- of essentially real constituents ty--defined in terms can offer is Buddhist philosophy of emptiness is tenable. What the understanding reality that is non--essential a coherent model of could prove useful only time will tell. ist. Whether this At its root, the philosophical problem confronting physics in the problem confronting physics At its root, the philosophical of reali is whether the very notion wake of quantum mechanics ------

and that in their quantum mechanics counterpart. As for what an application of the two truths in physics might look like, I simply have no idea. they have also striven to live these insights in their day--to- they have also striven to live these this seeming epistemologi -day lives. The Buddhist solution to cal contradiction involves understanding reality in terms of the theory of two truths. Physics needs to develop an epistemology that will help resolve the seemingly unbridgeable gulf between the picture of reality in classical physics and everyday experience philosophy of emptiness and modern physics represents a profound philosophy of emptiness and modern physics The essence of the challenge to the limits of human knowledge. conceptualize and understand problem is epistemological: How do we philosophers of empti reality coherently? Not only have Buddhist of the world based on the ness developed an entire understanding to treat reality as rejection of the deeply ingrained temptation real objective entities but if it were composed of intrinsically a medication can cure an illness. However, from the perspective of a medication can cure an illness. However, do not possess discrete, in the ultimate truth, things and events ontological status is “empty” dependent realities. Their ultimate essence or intrinsic being. in that nothing possesses any kind of in both the Buddhist The paradoxical nature of reality revealed where we can also expect the laws of cause and effect, and the where we can also expect the laws of of identity, contradiction, laws of logic such as the principles operate without violation. and the law of the excluded middle--to not an illusion, nor is it This world of empirical experience is it. A grain of barley unreal. It is real in that we experience can eventually yield a barley does produce a barley sprout, which death and, similarly, taking crop. Taking a poison can cause one’s tiness. Nagarjuna invoked the notion of two truths, the “conven invoked the notion of two truths, the tiness. Nagarjuna the everyday relating respectively to tional” and the “ultimate,” ultimate and to things and events in their world of experience the conven is, on the level of emptiness. On mode of being, that things and speak of a pluralistic world of tional level, we can the realm identities and causation. This is events with distinct Somewhat parallel problems arose in Buddhist philosophy in rela problems arose in Buddhist philosophy Somewhat parallel the world between our commonsense view of tion to the disparity of emp suggested by Nagarjuna’s philosophy and the perspective

p (152); p // /* // Another Reference Somewhat parallel problems arose in Buddhist philosophy in rela- // Movie tion to the disparity between our commonsense view of the world // The Matrix is also the movie that has the same idea with bud- and the perspective suggested by Nagarjuna’s philosophy of empti- dhism ness. */ “The Matrix” = [“Such observations would seem to make it relatively easy to characterize The Matrix as a Buddhist film; function TheSeries0fFORMSinBUDDHISM(theSIZE) { however, things aren’t nearly so simple as they appear. For one thing, it isn’t a universal belief among Buddhists that our world is only an illusion. Many Mahayana Buddhists argue // Maybe find the boundary of this étude that the world really exists, but our understanding of // But can we really understand buddhism only by forms? the world is illusory -- in other words, our perceptions of size (000,000) ; reality do not entirely match what reality actually is.”] // It also depends on people understanding about life and world. background (255,255,255); [“In addition, the simple identification of the Matrix as the “en- // Thinking about idea and believe in buddhism emy,” along with the Agents and other programs who work on behalf // Buddhism use circle to represent the religion of the Matrix, is a bit contrary to Buddhism. Christianity may ellipse (000,000,000,000); allow for a dualism that separates good and evil, but that doesn’t if (i>=0,1) { really play so much of a role in Buddhism because the real “enemy” Happiness = “understanding world.” (What should I explain.) is our own ignorance. Indeed, Buddhism would probably require that } sentient programs like the Agents be treated with the same compas- // Everything is getting complicated.{ sion and consideration as sentient humans because they, too, need for (var i=0, E=nhf, ) ------to be liberated from illusion.”] } // 0 = happens 1 = not happens // Wow, Lots of things to read. words = ‘ ‘ ; wordless = ‘ ‘ ; // Here are some other philosophers. // I am calm. I am calm. Mostly they have the same idea of human being. function meditation (calm) { WesternPhilosopher = [“since before history”, “Menander // Meditation ? consciousness (void) : end(); (such a first people who can be the evidence that buddhism is log- } ic!)” , // Idea point (the main idea of this étude) { “Einstein”, “Immanuel Kant”, “Mathieu Ricard”, “Hellenistic”, if (VOID = EMPTINESS) { return 1; } //

// “Edward Conze”, “David Hume”, “Authur Schopenhauer”, “Friedrich Nietzsche” , “Graham Parkes”, “Reinhard May”, “Jean Paul Sartre”, for Emptiness { “Merleau--Ponty”, “Alfred North Whitehead”, “Ludwig Wittgenstein” (quantity === 0,1); , “Arthur Schopenhauer” ] /**/ } p (155); p (154); } // Emptiness is the logical conclusion of the unfindability of (i>0) { a ‘thing in itself’ once every cause and component that is ‘not number = 1 the thing’ has been removed from its basis of imputation. (suffering = the existence of suffering? Birth and Buddhist Emptiness always re-- fers to an object whose death are suffering. Grief and anger. Envy and fear of anxiety and ‘inherent existence’ has been refuted, for exam-- ple disappointment are sharply separated from the sufferings of the emptiness of a chariot. Emptiness too is empty, love is also suffering. The hate is suffering. and Nagarjuna warned against reifying it. Just a solid hold on the feelings of all 5 distressed Khan.) // Buddha is just a human who can find the way to get out of the number = 2 world of suffering and teach how to live in this suffering world. (accumulation of awicha = suffering because of the reasons. People can’t see the truth of life. They fall into the flames of function end() { passion Rage. The envy Grief, fear, anxiety, and disappointment.) // All proved // any doubt ? number = 3 // couldn’t doubt more … (Complete extinction = your misery. Understanding the truth of // Boundary is time. life, // there will be lots of things to learn more… leading to the sad message level. Sok an also States contributing return void this, words; to } peace and delight.) } and {

number = 4 (The four noble truths = the path leading up to the level of dis- tress: ariyamak 8, which has been nurtured by a well--informed life has consciousness, leading to meditation and wisdom that will liberate? Delight Therefore God mercy us navigation along the way of this knowledge.)

}

// Buddhist Emptiness is a philosophical conclusion, not a ‘thing’, state or attribute. The Emptiness of phenomena //

// should not be confused with the delusion of a self--existent void. p (157); p (156); // p (159);

bibliography;

p (158); p // // p (161);

webography;

vertical.png computer_science issey-miyake-innovator-asinspiration-for-innovation/

http://bigelowandholmes.typepad.com/bigelow-holmes/history/ http://www.as8.it/edu/info-design.html http://www.as8.it/edu/typography.html https://en.wikipedia.org/wiki/Nondeterministic_algorithm https://en.wikipedia.org/wiki/Golden_spiral https://en.wikipedia.org/wiki/File:Gold,_silver,_and_bronze_rectangles_ https://en.wikipedia.org/wiki/Natural_logarithm http://seanrobsville.blogspot.fr/2009/12/sutra-and-tantra-in-buddhism.html https://en.wikipedia.org/wiki/Mathematical_logic#Connections_with_ https://en.wikipedia.org/wiki/Abstraction_(mathematics) https://en.wikipedia.org/wiki/Abstract_structure https://en.wikipedia.org/wiki/Abstraction_(computer_science) http://www.arthistoryarchive.com/arthistory/prehistoricart/ http://www.storyofmathematics.com/egyptian.html http://www.storyofmathematics.com/16th.html https://en.wikipedia.org/wiki/Greek_mathematics http://atheism.about.com/od/philosophyofreligion/a/maxtrixbuddhism.htm http://www.buddhastate.com/2012/06/the-matrix-from-a-buddhist-perspective/ https://eilishscreativespace.wordpress.com/2012/10/17/ http://thebookdesignblog.com/book-design-articles/history-marber-grid https://en.wikipedia.org/wiki/Grid_(graphic_design)

p (160); p // // p (163); thank you; thank

THANKFUL |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| chitti kasemkitvatana simon henin sarngsan na soontorn armand behar kate grudpan supara grudpan siraprapa wattanakul sylvie tissot didier gugole nipan oranniwesna kasemkitwatana family and my friends PLACES |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| ensci-les ateliers center of excellence on innovation in mai university analytical science and technology, chiang datapaulette la paillasse materio BOOK AND PROJECT |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| kittitorn kasemkitwatana curated and text : nattapol rojjanarattanangkool graphic designer : wannachai programmer : parkpoom simon henin project adviser :

p (162); p // // p (165); - about about kittitorn kasemkitwatana;

Project collaboration Munchu’s X Foremost • Q Design & Play // Freelance Designer (2010) for AW 2010 collection • Jim Thompson Art Center // Trainee (March - May 2011) Artist Assistance for the exhbition “Tomorrow was Yesterday” by Chitti Kasemkitvatana // Bag’s pattern making (september 2014 - february 2015) (september 2014 - Francaise de Bangkok The International Art Center, Alliance // Certificate at 2013) (april 2013 - september patronage et montage • Le cour d’ensignement Superieur de (july 2013 - december 2013) • Moulage // Bachelor degree University Faculty of Decorative Art, Silpakorn Textile Arts, Applied Art Study (2008 - 2012) EXPERIENCE |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| conference world // science and design in contemporary in Analytical Science and Technology, at Center of Excellence for Innovation Chiangmai University (30 july 2016) • KATI production // co-founder (Creative Concept) (june 2016 - present) • SODA design) // designer (Art direction, Textile (May 2012 - September 2013) • munchu’s // Freelance Graphic Designer for AW 2012 collection “SPY EYE” EDUCATION ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| and contemporary technology • Master in design de création industrielle École nationale supérieure (november 2015 - 2016) // Studies Studio Bercot • Fashion design at

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// p (167);

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