The Story About Stephen Wolfram

Total Page:16

File Type:pdf, Size:1020Kb

The Story About Stephen Wolfram The Physicist Turned a Successful Entrepreneur THE STORY ABOUT STEPHEN WOLFRAM by Gennaro Cuofano FourWeekMBA.com Wolfram Alpha: The Physicist Turned a Successful Entrepreneur - The Four-Week MBA Wolfram Alpha: The Physicist Turned a Successful Entrepreneur Why Wolfram Alpha? Among my passions, I love to check financial data about companies I like. Recently I was looking for a quick way to get reliable financial information for comparative analyses. At the same time, I was looking for shortcuts to perform that analysis. I was researching for myself. I thought why waste so much time on scraping financial reports? While surfing the web, I was looking for a solution and a term popped to my eyes “computational engine.” Wolfram Alpha! That search opened me a universe I wasn’t aware of. Yet that universe wasn’t only about a fantastic tool I learned to use in several ways. I found out the most amazing entrepreneurial story. That is how I jumped in and researched as much as I could about this topic! Why is this story so remarkable? Imagine a kid that as many others, is struggling at arithmetic. Imagine that same kid at 12 years old building a physics dictionary and by the age of 14 drafting three books about particle physics. A few years later at 23, that kid, now a man gets awarded as a prodigious physicist. We could stop this story here, and it would be already one of the most incredible stories you’ll ever hear. Yet this is only the beginning. In fact, what if I told you, that same person turned into a successful entrepreneur, which built several companies and a whole new science from scratch! (Let’s save some details for later) That isn’t only the story of Wolfram Alpha, a tool that I learned to use and cherish. That is the story of one of the smartest people of our century, a shrewd entrepreneur, and polymath, which turned to influence and being influenced by people like Steve Jobs and Benoit Mandelbrot. This is the story of Stephen Wolfram. Writing this post for me has been a pleasure and torture. On the one hand, I jumped into Stephen Wolfram‘s videos, books, and articles. The more I found out, the more I wanted to know. It was an endless loop. However, the unbounded intelligence of Stephen Wolfram is such that trying to circumscribe it in one post, it is like trying to close the universe in a box. Yet more than a post this is an e-book, and I hope you’ll enjoy reading it as much as I enjoyed writing it! Before we get to the practical matters related to Wolfram Alpha, I deconstructed his life and ideas. The Quest to Unfold Complexity: who is Stephen Wolfram? Because, after all that’s what technology is all about: setting up systems to achieve human purposes Stephen Wolfram in Computation and the Future of the Human Condition Stephen Wolfram is the founder of Wolfram Alpha, a powerful computational engine (more about what a computational engine is later on). Yet the path that brought Stephen Wolfram to the launch of its latest creature looked more like a life-long quest. Born in London in 1959. Stephen Wolfram showed incredible qualities since a young age. In fact, by age 15 he had drafted three physics books and his first scientific paper. By the age of 21, he had received an important fellowship, which launched him on a life-long quest: understanding complex systems by stripping out their complexity. Yet Stephen Wolfram approach was unique for a couple of reasons, I believe. First, he understood that computation was the most compelling discovery of the past century. Therefore, he focused since the beginning of using machines to enhance human abilities. Second, he believed that to understand complexity he had to look at natural processes to find the most essential programs that mother nature used by time to time to run the show of life. Yet Stephen Wolfram didn’t spend his life as a hermit (except when, for practical purposes, he had to put together a book, which would become a New Kind of Science) or isolated from the world. Instead, he understood the importance of more practical matters, such as managing people. The quest to complexity started from the study of cellular automata, which launched him to formulating a computing theory of everything. So, what are cellular automata? Computing a theory of everything So I want to talk today about an idea. It’s a big idea. Actually, I think it’ll eventually be seen as probably the single biggest idea that’s emerged in the past century. It’s the idea of computation. Now, of course, that idea has brought us all of the computer technology we have today and so on. But there’s actually a lot more to computation than that. It’s really a very deep, very powerful, very fundamental idea, whose effects we’ve only just begun to see. Stephen Wolfram TED Talk Cellular automata are programs that follow simple deterministic rules but show complex behaviors, the more steps they take along their evolution. What does that mean and what makes them so valuable from a scientific standpoint? Imagine starting playing a game with fundamental and straightforward rules. Chances are you’ll start projecting yourself at the end of the game, foreseeing a particular scenario. However, as much as you would love to imagine, even if you had Albert Einstein‘s or Salvador Dali’s ability to day-dream you will never manage to foresee the complex behaviors that will arise along the way from those trivial programs. How is that possible that from such simple programs spring up so much complexity of behavior? The answer lies in rule number 30! Let’s dive a bit into it to see how it works. Rule Number 30: simplicity as the mother of all creations The weather has a mind of its own” isn’t such a primitive thing to say: the fluid dynamics of the weather is just as sophisticated as something like a brain Stephen Wolfram, on blogs.scientificamerican.com It probably was the summer of 1985 – as recalled in Idea Makers – when Steve Wolfram stumbled upon something that would leave a mark on his life and guide him toward a life-long quest. What was that? It all started from rule number 30. As someone that found computation as the most important discovery of the past century Stephen Wolfram didn’t waste time doing calculations. Rather he let computers run all the possible programs that could be found in nature, as simple cellular automata and look at what behaviors they would show. That is what happened that summer in 1985. Cellular automata are self- replicating systems showed as a grid of changing cells. Each cell in the grid reacts based on the neighboring cells. In other words, you start from a grid like the one below A simple rule determines whether a cell will be on or off in the next generation based on the configuration of its neighborhood. For instance, if a cell is white, and the one on its left and right are white, then the cell stays white. Instead, if a white cell falls in-between two black cells, then it turns black. And so on for all the possible arrangements. The possible configurations on a grid comprised of three cells as you can see from the red rectangle above are eight. But the possible combinations, given the fact that each cell can be either black or white (in a binary state) can be 256 – 2 ^ 8 (therefore the two possible states, black or white, at the power of the eight possible combinations). We start by letting the cellular automaton take 20 steps, We can see already a more complex behavior so far. Yet nothing exciting. When we start taking additional steps, the more steps we take, the more complexity arises. That is what we get after 100 steps. As you can see the patterns created by a simple cellular automaton starts to become kind of interesting. Source: blog.stephenwolfram.com When in the 1980s Stephen Wolfram observed this kind of behavior he was shocked. That kind of shock that changes your life, the aha moment! In fact, the more steps he let rule 30 take, the more complexity arose out of simple deterministic rules! The fact that simple rules could replicate nature is pretty counter-intuitive, yet quite effective. Cone Snail, Photographer: Richard Ling Cellular Automata Rule 30 Source: artfail.com The most powerful part is that to build such complexity you don’t need a super powerful computer, but only a three-digit number grid that follows super simple rules. Rule number 30 above all, was the beginning of a quest that would lead Stephen Wolfram to formulate a New Kind of Science. It also opens up a new way of thinking, where intelligence isn’t solely a human thing, but it can be found anywhere in nature. Therefore, the complexity arising from our brain isn’t different from what happens in nature. Both are described well by computations. Before we dive more into what would become the principles of Stephen Wolfram‘s book, A New Kind of Science, let’s dive more into his life. Before Wolfram Alpha If you’ve been using the iPhone, chances are you’ve also been using Wolfram Alpha all along. In fact, you may not know it, but your built-in intelligent assistant, Siri, uses Wolfram Alpha‘s API to provide answers to any question.
Recommended publications
  • Jet Development in Leading Log QCD.Pdf
    17 CALT-68-740 DoE RESEARCH AND DEVELOPMENT REPORT Jet Development in Leading Log QCD * by STEPHEN WOLFRAM California Institute of Technology, Pasadena. California 91125 ABSTRACT A simple picture of jet development in QCD is described. Various appli- cations are treated, including transverse spreading of jets, hadroproduced y* pT distributions, lepton energy spectra from heavy quark decays, soft parton multiplicities and hadron cluster formation. *Work supported in part by the U.S. Department of Energy under Contract No. DE-AC-03-79ER0068 and by a Feynman Fellowship. 18 According to QCD, high-energy e+- e annihilation into hadrons is initiated by the production from the decaying virtual photon of a quark and an antiquark, ,- +- each with invariant masses up to the c.m. energy vs in the original e e collision. The q and q then travel outwards radiating gluons which serve to spread their energy and color into a jet of finite angle. After a time ~ 1/IS, the rate of gluon emissions presumably decreases roughly inversely with time, except for the logarithmic rise associated with the effective coupling con­ 2 stant, (a (t) ~ l/log(t/A ), where It is the invariant mass of the radiating s . quark). Finally, when emissions have degraded the energies of the partons produced until their invariant masses fall below some critical ~ (probably c a few times h), the system of quarks and gluons begins to condense into the observed hadrons. The probability for a gluon to be emitted at times of 0(--)1 is small IS and may be est~mated from the leading terms of a perturbation series in a (s).
    [Show full text]
  • PARTON and HADRON PRODUCTION in E+E- ANNIHILATION Stephen Wolfram California Institute of Technology, Pasadena, California 91125
    549 * PARTON AND HADRON PRODUCTION IN e+e- ANNIHILATION Stephen Wolfram California Institute of Technology, Pasadena, California 91125 Ab stract: The production of showers of partons in e+e- annihilation final states is described according to QCD , and the formation of hadrons is dis­ cussed. Resume : On y decrit la production d'averses d� partons dans la theorie QCD qui forment l'etat final de !'annihilation e+ e , ainsi que leur transform­ ation en hadrons. *Work supported in part by the U.S. Department of Energy under contract no. DE-AC-03-79ER0068. SSt1 Introduction In these notes , I discuss some attemp ts e ri the cl!evellope1!1t of - to d s c be hadron final states in e e annihilation events ll>Sing. QCD. few featm11res A (barely visible at available+ energies} of this deve l"'P"1'ent amenab lle· are lt<J a precise and formal analysis in QCD by means of pe·rturbatirnc• the<J ry. lfor the mos t part, however, existing are quite inadle<!i""' lte! theoretical mett:l�ods one must therefore simply try to identify dl-iimam;t physical p.l:ten<0melilla tt:he to be expected from QCD, and make estll!att:es of dne:i.r effects , vi.th the hop·e that results so obtained will provide a good appro�::illliatimn to eventllLal'c ex­ act calculations . In so far as such estllma�es r necessa�y� pre�ise �r..uan- a e titative tests of QCD are precluded . On the ott:her handl , if QC!Ji is ass11l!med correct, then existing experimental data to inve•stigate its be­ may \JJ:SE•«f havior in regions not yet explored by theoreticalbe llJleaums .
    [Show full text]
  • The Problem of Distributed Consensus: a Survey Stephen Wolfram*
    The Problem of Distributed Consensus: A Survey Stephen Wolfram* A survey is given of approaches to the problem of distributed consensus, focusing particularly on methods based on cellular automata and related systems. A variety of new results are given, as well as a history of the field and an extensive bibliography. Distributed consensus is of current relevance in a new generation of blockchain-related systems. In preparation for a conference entitled “Distributed Consensus with Cellular Automata and Related Systems” that we’re organizing with NKN (= “New Kind of Network”) I decided to explore the problem of distributed consensus using methods from A New Kind of Science (yes, NKN “rhymes” with NKS) as well as from the Wolfram Physics Project. A Simple Example Consider a collection of “nodes”, each one of two possible colors. We want to determine the majority or “consensus” color of the nodes, i.e. which color is the more common among the nodes. A version of this document with immediately executable code is available at writings.stephenwolfram.com/2021/05/the-problem-of-distributed-consensus Originally published May 17, 2021 *Email: [email protected] 2 | Stephen Wolfram One obvious method to find this “majority” color is just sequentially to visit each node, and tally up all the colors. But it’s potentially much more efficient if we can use a distributed algorithm, where we’re running computations in parallel across the various nodes. One possible algorithm works as follows. First connect each node to some number of neighbors. For now, we’ll just pick the neighbors according to the spatial layout of the nodes: The algorithm works in a sequence of steps, at each step updating the color of each node to be whatever the “majority color” of its neighbors is.
    [Show full text]
  • Purchase a Nicer, Printable PDF of This Issue. Or Nicest of All, Subscribe To
    Mel says, “This is swell! But it’s not ideal—it’s a free, grainy PDF.” Attain your ideals! Purchase a nicer, printable PDF of this issue. Or nicest of all, subscribe to the paper version of the Annals of Improbable Research (six issues per year, delivered to your doorstep!). To purchase pretty PDFs, or to subscribe to splendid paper, go to http://www.improbable.com/magazine/ ANNALS OF Special Issue THE 2009 IG® NOBEL PRIZES Panda poo spinoff, Tequila-based diamonds, 11> Chernobyl-inspired bra/mask… NOVEMBER|DECEMBER 2009 (volume 15, number 6) $6.50 US|$9.50 CAN 027447088921 The journal of record for inflated research and personalities Annals of © 2009 Annals of Improbable Research Improbable Research ISSN 1079-5146 print / 1935-6862 online AIR, P.O. Box 380853, Cambridge, MA 02238, USA “Improbable Research” and “Ig” and the tumbled thinker logo are all reg. U.S. Pat. & Tm. Off. 617-491-4437 FAX: 617-661-0927 www.improbable.com [email protected] EDITORIAL: [email protected] The journal of record for inflated research and personalities Co-founders Commutative Editor VP, Human Resources Circulation (Counter-clockwise) Marc Abrahams Stanley Eigen Robin Abrahams James Mahoney Alexander Kohn Northeastern U. Research Researchers Webmaster Editor Associative Editor Kristine Danowski, Julia Lunetta Marc Abrahams Mark Dionne Martin Gardiner, Tom Gill, [email protected] Mary Kroner, Wendy Mattson, General Factotum (web) [email protected] Dissociative Editor Katherine Meusey, Srinivasan Jesse Eppers Rose Fox Rajagopalan, Tom Roberts, Admin Tom Ulrich Technical Eminence Grise Lisa Birk Psychology Editor Dave Feldman Robin Abrahams Design and Art European Bureau Geri Sullivan Art Director emerita Kees Moeliker, Bureau Chief Contributing Editors PROmote Communications Peaco Todd Rotterdam Otto Didact, Stephen Drew, Ernest Lois Malone Webmaster emerita [email protected] Ersatz, Emil Filterbag, Karen Rich & Famous Graphics Steve Farrar, Edinburgh Desk Chief Hopkin, Alice Kaswell, Nick Kim, Amy Gorin Erwin J.O.
    [Show full text]
  • Cellular Automation
    John von Neumann Cellular automation A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays.[2] A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. An initial state (time t = 0) is selected by assigning a state for each cell. A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. Typically, the rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously, though exceptions are known, such as the stochastic cellular automaton and asynchronous cellular automaton. The concept was originally discovered in the 1940s by Stanislaw Ulam and John von Neumann while they were contemporaries at Los Alamos National Laboratory. While studied by some throughout the 1950s and 1960s, it was not until the 1970s and Conway's Game of Life, a two-dimensional cellular automaton, that interest in the subject expanded beyond academia.
    [Show full text]
  • A New Kind of Science
    Wolfram|Alpha, A New Kind of Science A New Kind of Science Wolfram|Alpha, A New Kind of Science by Bruce Walters April 18, 2011 Research Paper for Spring 2012 INFSY 556 Data Warehousing Professor Rhoda Joseph, Ph.D. Penn State University at Harrisburg Wolfram|Alpha, A New Kind of Science Page 2 of 8 Abstract The core mission of Wolfram|Alpha is “to take expert-level knowledge, and create a system that can apply it automatically whenever and wherever it’s needed” says Stephen Wolfram, the technologies inventor (Wolfram, 2009-02). This paper examines Wolfram|Alpha in its present form. Introduction As the internet became available to the world mass population, British computer scientist Tim Berners-Lee provided “hypertext” as a means for its general consumption, and coined the phrase World Wide Web. The World Wide Web is often referred to simply as the Web, and Web 1.0 transformed how we communicate. Now, with Web 2.0 firmly entrenched in our being and going with us wherever we go, can 3.0 be far behind? Web 3.0, the semantic web, is a web that endeavors to understand meaning rather than syntactically precise commands (Andersen, 2010). Enter Wolfram|Alpha. Wolfram Alpha, officially launched in May 2009, is a rapidly evolving "computational search engine,” but rather than searching pre‐existing documents, it actually computes the answer, every time (Andersen, 2010). Wolfram|Alpha relies on a knowledgebase of data in order to perform these computations, which despite efforts to date, is still only a fraction of world’s knowledge. Scientist, author, and inventor Stephen Wolfram refers to the world’s knowledge this way: “It’s a sad but true fact that most data that’s generated or collected, even with considerable effort, never gets any kind of serious analysis” (Wolfram, 2009-02).
    [Show full text]
  • Downloadable PDF of the 77500-Word Manuscript
    From left: W. Daniel Hillis, Neil Gershenfeld, Frank Wilczek, David Chalmers, Robert Axelrod, Tom Griffiths, Caroline Jones, Peter Galison, Alison Gopnik, John Brockman, George Dyson, Freeman Dyson, Seth Lloyd, Rod Brooks, Stephen Wolfram, Ian McEwan. In absentia: Andy Clark, George Church, Daniel Kahneman, Alex "Sandy" Pentland (Click to expand photo) INTRODUCTION by Venki Ramakrishnan The field of machine learning and AI is changing at such a rapid pace that we cannot foresee what new technical breakthroughs lie ahead, where the technology will lead us or the ways in which it will completely transform society. So it is appropriate to take a regular look at the landscape to see where we are, what lies ahead, where we should be going and, just as importantly, what we should be avoiding as a society. We want to bring a mix of people with deep expertise in the technology as well as broad 1 thinkers from a variety of disciplines to make regular critical assessments of the state and future of AI. —Venki Ramakrishnan, President of the Royal Society and Nobel Laureate in Chemistry, 2009, is Group Leader & Former Deputy Director, MRC Laboratory of Molecular Biology; Author, Gene Machine: The Race to Decipher the Secrets of the Ribosome. [ED. NOTE: In recent months, Edge has published the fifteen individual talks and discussions from its two-and-a-half-day Possible Minds Conference held in Morris, CT, an update from the field following on from the publication of the group-authored book Possible Minds: Twenty-Five Ways of Looking at AI. As a special event for the long Thanksgiving weekend, we are pleased to publish the complete conference—10 hours plus of audio and video, as well as this downloadable PDF of the 77,500-word manuscript.
    [Show full text]
  • WOLFRAM EDUCATION SOLUTIONS MATHEMATICA® TECHNOLOGIES for TEACHING and RESEARCH About Wolfram Research
    WOLFRAM EDUCATION SOLUTIONS MATHEMATICA® TECHNOLOGIES FOR TEACHING AND RESEARCH About Wolfram Research For over two decades, Wolfram Research has been dedicated to developing tools that inspire exploration and innovation. As we work toward our goal to make the world’s data computable, we have expanded our portfolio to include a variety of products and technologies that, when combined, provide a true campuswide solution. At the center is Mathematica—our ever-advancing core product that has become the ultimate application for computation, visualization, and development. With millions of dedicated users throughout the technical and educational communities, Mathematica is used for everything from teaching simple concepts in the classroom to doing serious research using some of the world’s largest clusters. Wolfram’s commitment to education spans from elementary education to research universities. Through our free educational resources, STEM teacher workshops, and on-campus technical talks, we interact with educators whose feedback we rely on to develop tools that support their changing needs. Just as Mathematica revolutionized technical computing 20 years ago, our ongoing development of Mathematica technology and continued dedication to education are transforming the composition of tomorrow’s classroom. With more added all the time, Wolfram educational resources bolster pedagogy and support technology for classrooms and campuses everywhere. Favorites among educators include: Wolfram|Alpha®, the Wolfram Demonstrations Project™, MathWorld™,
    [Show full text]
  • The Wolfram Physics Project: the First Two Weeks—Stephen Wolfram Writings ≡
    6/21/2020 The Wolfram Physics Project: The First Two Weeks—Stephen Wolfram Writings ≡ RECENT | CATEGORIES | The Wolfram Physics Project: The First Two Weeks April 29, 2020 Project Announcement: Finally We May Have a Path to the Fundamental Theory of Physics… and It’s Beautiful Website: Wolfram Physics Project First, Thank You! We launched the Wolfram Physics Project two weeks ago, on April 14. And, in a word, wow! People might think that interest in fundamental science has waned. But the thousands of messages we’ve received tell a very different story. People really care! They’re excited. They’re enjoying understanding what we’ve figured out. They’re appreciating the elegance of it. They want to support the project. They want to get involved. It’s tremendously encouraging—and motivating. I wanted this project to be something for the world—and something lots of people could participate in. And it’s working. Our livestreams—even very technical ones—have been exceptionally popular. We’ve had lots of physicists, mathematicians, computer scientists and others asking questions, making suggestions and offering help. We’ve had lots of students and others who tell us how eager they are to get into doing research on the project. And we’ve had lots of people who just want to tell us they appreciate what we’re doing. So, thank you! https://writings.stephenwolfram.com/2020/04/the-wolfram-physics-project-the-first-two-weeks/ 1/35 6/21/2020 The Wolfram Physics Project: The First Two Weeks—Stephen Wolfram Writings Real-Time Science Science is usually done behind closed doors.
    [Show full text]
  • INFORMATION– CONSCIOUSNESS– REALITY How a New Understanding of the Universe Can Help Answer Age-Old Questions of Existence the FRONTIERS COLLECTION
    THE FRONTIERS COLLECTION James B. Glattfelder INFORMATION– CONSCIOUSNESS– REALITY How a New Understanding of the Universe Can Help Answer Age-Old Questions of Existence THE FRONTIERS COLLECTION Series editors Avshalom C. Elitzur, Iyar, Israel Institute of Advanced Research, Rehovot, Israel Zeeya Merali, Foundational Questions Institute, Decatur, GA, USA Thanu Padmanabhan, Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune, India Maximilian Schlosshauer, Department of Physics, University of Portland, Portland, OR, USA Mark P. Silverman, Department of Physics, Trinity College, Hartford, CT, USA Jack A. Tuszynski, Department of Physics, University of Alberta, Edmonton, AB, Canada Rüdiger Vaas, Redaktion Astronomie, Physik, bild der wissenschaft, Leinfelden-Echterdingen, Germany THE FRONTIERS COLLECTION The books in this collection are devoted to challenging and open problems at the forefront of modern science and scholarship, including related philosophical debates. In contrast to typical research monographs, however, they strive to present their topics in a manner accessible also to scientifically literate non-specialists wishing to gain insight into the deeper implications and fascinating questions involved. Taken as a whole, the series reflects the need for a fundamental and interdisciplinary approach to modern science and research. Furthermore, it is intended to encourage active academics in all fields to ponder over important and perhaps controversial issues beyond their own speciality. Extending from quantum physics and relativity to entropy, conscious- ness, language and complex systems—the Frontiers Collection will inspire readers to push back the frontiers of their own knowledge. More information about this series at http://www.springer.com/series/5342 For a full list of published titles, please see back of book or springer.com/series/5342 James B.
    [Show full text]
  • Complex Systems Theory
    Complex Systems Theory 1988 Some approaches to the study ofc omplex systems are outlined. They are encompassed by an emerging field of science concerned with the general analysis of complexity. Throughout the natural and artificial world one observes phenomena of great com­ plexity. Yet research in physics and to some extent biology and other fields has shown that the basic components of many systems are quite simple. It is now a crucial problem for many areas of science to elucidate the mathematical mechanisms by which large numbers of such simple components, acting together, can produce behaviour of the great complexity observed. One hopes that it will be possible to formulate universal laws that describe such complexity. The second law of thermodynamics is an example of a general principle that governs the overall behaviour of many systems. It implies that initial order is pro­ gressively degraded as a system evolves, so that in the end a state of maximal disorder and maximal entropy is reached. Many natural systems exhibit such behaviour. But there are also many systems that exhibit quite opposite behaviour, transforming ini­ tial simplicity or disorder into great complexity. Many physical phenomena, among them dendritic crystal growth and fluid turbulence are of this kind. Biology provides the most extreme examples of such self-organization. The approach that I have taken over the last couple of years is to study mathemat­ ical models that are as simple as possible in formulation, yet which appear to capture the essential features of complexity generation. My hope is that laws found to govern these particular systems will be sufficiently general to be applicable to a wide range of actual natural systems.
    [Show full text]
  • An Investigation of Complex Systems in 16 Dimensions
    Columbus State University CSU ePress Theses and Dissertations Student Publications 2014 An Investigation of Complex Systems in 16 Dimensions Jordon M. Huffman Columbus State University, [email protected] Follow this and additional works at: https://csuepress.columbusstate.edu/theses_dissertations Part of the Computer Sciences Commons Recommended Citation Huffman, Jordon M., "An Investigation of Complex Systems in 16 Dimensions" (2014). Theses and Dissertations. 140. https://csuepress.columbusstate.edu/theses_dissertations/140 This Thesis is brought to you for free and open access by the Student Publications at CSU ePress. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of CSU ePress. An Examination of Complex Systems in 16 Dimensions by Jordon Huffman A Thesis Submitted in Partial Fulfillment of Requirements of the CSU Honors Program for Honors in the degree of Bachelor of Science in Computer Science TSYS School of Computer Science Columbus State University Thesis Advisor Date 1&£r^> Dr. Rodrigo Obando Committee Member Date (±JZ^ h Y Dr. ChajJes Turnitsa Honors Committee Member Date HhihH r. Rylan Steele Honors Program Directorfcl^jggfe?^^^ ^ Date /yO^Y Dr. Cindy Ticknor —■—..■ l.J.liH.IIHI.UIIUUUHl^lilllJMUJ.IIIHllIl.llH^ Table of Contents Abstract. Introduction 4 Cellular Automata. Investigation 9 Conclusion 13 Future 16 References. .18 An Examination of Complex Systems in 16 Dimensions Description: With the research of Dr. Rodrigo Obando, I have created an application to observe cellular automata rules spaces. The elementary rule space with two hundred and fifty-six rules proves easy enough to study, but the next rule space of 4,294,967,296 rules is much more of a challenge.
    [Show full text]