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The Grammar of the Elements

Did the Sanskrit alphabet influence Mendeleev’s periodic table?

Abhik Ghosh and Paul Kiparsky

mitri Ivanovich Mendeleev might have led Mendeleev to reference was not the first to recog- Sanskrit in this way. nize the periodicity of the In general terms, the origin of Men- chemical elements or even deleev’s periodic table is fairly well- Dto construct a primitive periodic table. known. As a freshly tenured profes- He did go much further than his peers, sor at Saint Petersburg University in however, in conceptualizing periodic- Russia in 1867, Mendeleev found him- ity as a fundamental law governing self responsible for teaching inorganic­ the nature of the elements. Based on chemistry with no suitable textbook at that insight, whenever the properties hand. Characteristically, he set about of a given element didn’t fit the over- writing his own—Osnovy Khimii [Prin- all pattern, he famously left an empty ciples of Chemistry]—between 1868 spot in his table for an as yet undiscov- and 1870. During this period, while ered element. He used the prefixes eka, searching for a sensible order for dis- dvi, and tri, Sanskrit for the numbers cussing the chemistry of the approxi- es such as Sanskrit, and there is strong one, two, and three, to name these hypo- mately 65 elements known at the time, evidence that Mendeleev cultivated thetical elements, referring to the num- he hit upon the idea of the “periodic friends in that milieu. Further, the San- ber of places they were from a known, table.” His insight transformed chem- skrit alphabet is a two-dimensional­ pe- lighter element in the same group. istry from a trackless wilderness of dis- riodic array and, assuming Mendeleev Let that sink in. Not Greek. Not Lat- parate facts to something approaching saw it (an eventuality that we con- in. Not even German, the lingua franca a well laid-out garden. sider probable, as explained below), of science in continental Europe at the Less is known about Mendeleev’s it would have been an obvious source time. But Sanskrit, an ancient Indian exact eureka moment, which came of inspiration for the construction of language that few Europeans outside shortly before March 1, 1869. In one other periodic systems. certain rarefied circles had even heard popular account, the idea of the pe- Taking a longer view of things, it’s about. This unique decision led us, a riodic table occurred to Mendeleev fair to say that Mendeleev’s periodic chemist and a linguist, to explore what while playing solitaire using a set of system grew out of a larger project cards printed with the symbols and on possible chemical compounds, atomic weights of the elements. In an- which he had articulated in his 1861 Abhik Ghosh is a professor of inorganic and mate- other story, most likely apocryphal, “Essai d’une théorie sur les limites rials chemistry at the University of Tromsø–The the idea of the periodic table came des combinaisons organiques [Essay Arctic University of Norway and is fluent in San- to him in a dream, much as the cor- of a theory on the limits of organic skrit. His earlier forays into science education and rect structure of benzene supposedly combinations].” He called the communication include the popular science book came to August Kekulé in a dream (see project chemical mechanics in his 1861 Letters to a Young Chemist, which he edited, “The Many Guises of Aromaticity” in the book Organic Chemistry, in which he and Arrow Pushing in Inorganic Chemistry, January–February­ 2015 issue). credited the chemist Antoine-Laurent which he wrote with his former student Steffen To us, a third source of inspiration de Lavoisier with initiating the line Berg. Paul Kiparsky is a professor of linguistics at Stanford University and is a Sanskrit scholar. His seems plausible, one that would also of thinking. Lavoisier’s work also book P ini as a Variationist uncovered a major explain Mendeleev’s enigmatic use of had a linguistic vein, as though by dimension of Pāṇini’s grammar that was not the Sanskrit prefixes. Saint Petersburg constructing a nomenclature that knownāṇ even to the earliest commentators. Email at the time was a preeminent center of systematically reflected the chemical for Ghosh: [email protected] research on classical Oriental languag- composition of a substance (for © 2019 Sigma Xi, The Scientific Research Honor Society. 350 American Scientist, Volume 107 Reproduction with permission only. Contact [email protected]. Ti = 50 Zr = 90 ? = 180 V = 51 Nb = 94 Ta = 182 Cr = 52 Mo = 96 W = 186 Mn = 55 Rh = 104.4 Pt = 197.1 Fe = 56 Ru = 104.4 Ir = 198 Ni = Co = 59 Pd = 106.6 Os = 199 H = 1 Cu = 63.4 Ag = 108 Hg = 200 Be = 9.4 Mg = 24 Zn = 65.2 Cd = 112 B = 11 Al = 27.3 ? = 68 Ur = 116 Au = 197? C = 12 Si = 28 ? = 70 Sn = 118 N = 14 P = 31 As = 75 Sb = 122 Bi = 210? O = 16 S = 32 Se= 79.4 Te = 128? F = 19 Cl = 35.5 Br = 80 I = 127 Li = 7 Na = 23 K = 39 Rb = 85.4 Cs = 133 Tl = 204 Ca = 40 Sr = 87.6 Ba = 137 Pb = 207 ? = 45 Ce = 92 ?Er = 56 La = 94 ?Yt = 60 Di = 95 In = 75.6 Th = 118?

Group I Group II Group III Group IV Group V Group VI Group VII Group VIII – – – RH4 RH3 RH2 RH –

Series R2O RO R2O3 RO2 R2O5 RO3 R2O7 RO4 1 H = 1 2 Li = 7 Be = 9.4 B = 11 C = 12 N = 14 O = 16 F = 19 3 Na = 23 Mg = 24 Al = 27.3 Si = 28 P = 31 S = 32 Cl = 35.5 4 K = 39 Ca = 40 — = 44 Ti = 48 V = 51 Cr = 52 Mn = 55 Fe = 56, Co = 59 Ni = 59, Cu = 63 5 (Cu = 63) Zn = 65 — = 68 — = 72 As = 75 Se = 78 Br = 80 6 Rb = 85 Sr = 87 ?Yt = 88 Zr = 90 Nb = 94 Mo = 96 — = 100 Ru = 104, Rh = 104 Pd = 106, Ag = 108 7 (Ag = 108) Cd = 112 In = 113 Sn = 118 Sb = 122 Te = 125 I = 127 8 Cs = 133 Ba = 137 ?Di = 138 ?Ce = 140 — — — — — — — 9 (—) — — — — — — 10 — — ?Er = 178 ?La = 180 Ta = 182 W = 184 — Os = 195, Ir = 197 Pt = 198, Au = 199 11 (Au = 199) Hg = 200 Tl = 204 Pb = 207 Bi = 208 — — 12 — — — Th = 231 — U = 240 — — — — —

De Agostini Picture Library/Bridgeman Images; Science History Images/Alamy Stock Photo; Abhik Ghosh The 1869 version of chemist Dmitri Ivanovich Mendeleev’s periodic table (top) shows his Böhtlingk interacted­ on a daily basis early attempts to organize the elements. Within a couple of years, he rotated the table by 90 is unknown. But we do know that the degrees and brought it into a form that is relatively recognizable to a modern audience (bot- two men shared an interest in Siberia tom). Note the use of question marks to indicate a missing element. Note also the absence of (Mendeleev’s birthplace) and pro- noble gases; the entire group of these elements was unknown at the time. moted research on the Arctic. Indeed Böhtlingk composed a remarkable example, sulfuric/sulfurous, sulfate/​ we first need to consider how he may grammar of the Siberian language Ya- sulfite, and so on), the theory of have learned about a language that few kut (also known as Sakha), in which he chemical compounds could be reduced Europeans knew about at that time. applied the principles of Sanskrit gram- to a kind of grammar. Mendeleev It turns out that in the middle of the mar to extraordinary effect. Böhtlingk took this approach to a new level by 19th century Saint Petersburg Univer- also supported Mendeleev’s nomina- formulating generalizations about sity consisted of only four faculties tion for the Academy’s prestigious chemical formulas. (branches of learning), one of which Demidov Prize, which the chemist won Mendeleev’s search for a unifying was dedicated entirely to Oriental lan- for his first textbook, Organic Chemistry. language of chemistry may have led guages. Perhaps of greater significance The importance of Sanskrit to the him to linguistics, and ultimately he was Mendeleev’s friendship with the study of linguistics and European lan- may have been inspired by Sanskrit. eminent Indologist and philologist Otto guages was already well-known to Because of our familiarity with this von Böhtlingk, who worked at the Saint European philologists and linguists at ancient Indian language, we can see Petersburg Academy of Sciences during that time. They knew that Sanskrit is parallels that may have been over- the first decade of Mendeleev’s career. linguistically related to the great ma- looked in the past—parallels that may Böhtlingk is best known for his mag- jority of modern European languages indicate why Mendeleev paid homage num opus, a seven-volume Sanskrit-­ (with the exception of Finnish, Basque, to it in his life’s greatest work. German dictionary that he compiled and a handful of others) as well as over the course of 23 years (1853–1875), Farsi (but not Turkish and Arabic). In- Mendeleev’s Sanskrit Connection but he also translated and edited a deed, the recognition of this linguis- To understand why Mendeleev used whole raft of other major Sanskrit tic kinship—as­ famously expressed Sanskrit words in his periodic table, works. To what extent Mendeleev and by English philologist and judge Sir © 2019 Sigma Xi, The Scientific Research Honor Society. www.americanscientist.org Reproduction with permission only. Contact [email protected]. 2019 November–December 351 William Jones in a lecture to the press the most powerful rules in Asiatic Society in Calcutta in colo- the briefest possible manner. nial India on February 2, 1786—is The insights emerging from his often thought to mark the begin- analysis first inspired linguists ning of comparative linguistics 200 years ago and continue to and Indo-European studies: serve as an important source of ideas in the field today. For ex- The Sanscrit language, what­ ample, according to legendary ever be its antiquity, is of a Massachusetts Institute of Tech- wonderful structure; more per- nology linguist Noam Chom- fect than the Greek, more copi- sky, the Aṣṭādhyāyī provided ous than the Latin, and more the first “generative grammar” exquisitely refined than either, in the modern sense of the word, yet bearing to both of them a meaning a complete set of rules stronger affinity, both in the for combining morphemes (the roots of verbs and the forms smallest meaningful units of lan- of grammar, than could pos- guage, such as word roots and sibly have been produced by stems, prefixes and suffixes) into accident; so strong indeed, that grammatical sentences. The work no philologer could examine also provided comprehensive them all three, without believ- rules governing other aspects of ing them to have sprung from the Sanskrit language, such as the some common source, which, phonological patterning of San- perhaps, no longer exists. skrit sounds (for example, how The “common source” to sounds change systematically as which Jones referred is now called you slur them in speech), the for- Wikimedia Commons proto-­Indo-European. The semi­ mation of compound words (such Indologist and philologist Otto von Böhtlingk worked at nomadic, horse- or chariot-riding as airplane, headache, or Schaden- the Saint Petersburg Academy of Sciences and was friends Indo-European tribes who called with Mendeleev, who was on the faculty at Saint Peters­ freude), and interconversions themselves ārya (today known burg University. Böhtlingk‘s first major publication in 1839 among different parts of speech as Aryans) settled northern India was a German edition of the Aṣṭādhyāyī, which formalized (for example, kind, kindly, and around 1500 bce and spoke an Sanskrit grammar. Foundational to that grammar is a two- kindliness). One could use these early form of Sanskrit, so-called dimensional, periodic alphabet, which possibly intrigued rules to generate new words as Vedic Sanskrit, which is preserved Mendeleev as he searched for a grammar of the elements. well as novel expressions and in their religious text, the Rigveda sentences. In our view, what (veda means knowledge, and is P ini did for Sanskrit, Men- derived from the verb vid, to know, a enough to make us wonder whether deleev tried to do for chemistry. cognate of Scandinavian vide/vite/veta, the former inspired the latter. P ini’s P ini,āṇ like Mendeleev, did not op- German wissen, and English wisdom). Aṣṭādhyāyī—literally the “eight-­ erate in a vacuum, although his is the A thousand or so years later (ap- chaptered thing”—is an astonishingāṇ earliestāṇ work on Sanskrit grammar proximately 350–500 bce), a Sanskrit achievement. It provided the most that has come down to us in full, un- scholar named P ini—who lived in concise, precise, and complete analysis mutilated form. Vedic scholars who G ndh ra, one of the great intellectual of Sanskrit by rigorously adhering to preceded him had already worked out and artistic hotbedsāṇ of ancient India, a sophisticated theory of phonetics to whichā ānow straddles the Pakistan–­ help fix the pronunciation of sacred Afghanistan border—formalized the texts such as the Rigveda. grammar of the entire language in the They classified speech sounds by Aṣṭādhyāyī. This seminal treatise con- What Pāṇini their place of articulation and degree sists of 3,959 rules organized into eight of aperture of the mouth and larynx, chapters. As it happens, Böhtlingk’s did for Sanskrit, as shown in the diagram on page 354. first major publication in 1839 was Note that from top to bottom in the a German edition of the Aṣṭādhyāyī, Mendeleev tried to “two-dimensional alphabet,” the point which he titled Acht Bücher gramma- of articulation moves outward in the tischer Regeln [Eight Books of Gram- do for chemistry. oral cavity. For example, the first row matical Rules]. And foundational to of stops originates from the throat the Aṣṭādhyāyī was a two-dimensional,­ (the velars or gutturals), the second periodic alphabet, which may have in- what is now called the minimum de- row from the soft palate (the palatals), trigued Mendeleev as he struggled to scription length principle: the idea that and so on until the fifth row, which create his own periodic array. the best model is one that best com- originates from the lips (the labials). presses a set of information. Maximum Remarkably, the vowels can also be Sanskrit’s Kindred Table compression of the grammatical rules classified by the same system. Along The parallels between P ini’s and was achieved by a rich array of sym- the horizontal axis, the stops are or- Mendeleev’s work are striking bols and abbreviations designed to ex- ganized according to increasing aper- āṇ © 2019 Sigma Xi, The Scientific Research Honor Society. 352 American Scientist, Volume 107 Reproduction with permission only. Contact [email protected]. ture, which correlates with increasing sonority or amplitude. These progres- The Periodic Table’s sions may be likened to the increase in Predecessors atomic weight along both axes of the periodic table. The vertical columns also reflect s early as 1817, merely years phonetic features implemented by after chemist and physi- constricting the larynx and oral cav- Acist John Dalton articulated ity to manipulate the airflow, such his atomic hypothesis, the German as voicing (meaning vibration of the chemist Johann Wolfgang Döberein- vocal cords) and aspiration, which er found he could arrange triads of may be likened to valence and other chemically similar elements (such as chemical commonalities. The distinc- chlorine, bromine, and iodine) with tion between aspirated (breathy) and regular intervals among their atomic unaspirated (unbreathy) consonant weights. pairs may be quite tricky for native In 1862, the French geologist English speakers. Such pairs are actu- Alexandre-­Émile Béguyer de Chan- ally ubiquitous in English. Thus, the courtois arranged the elements by k in skill is unaspirated, but the k in their atomic weights on a spiral on kill is aspirated. Likewise for the t in a cylinder and found that chemi- stop (unaspirated) and top (aspirated). cally similar elements lined up ver- And the same for the j sound in hedge tically (as shown on the right). This (unaspirated) and hedgehog (aspirat- arrangement—which­ he called the vis ed). For readers with some familiarity tellurique, or telluric helix, after tel- with Indian alphabets, we may add lurium, which fell near the center of that the vowels a, i, and u also have the helix—is­ often credited as the first longer variants, denoted in English as genuine periodic table. ā, ī, and ū. The vowels e and o and The English chemist John New- the diphthongs ai and ou, on the other lands reported in 1864 that many hand, are always long. pairs of chemically similar elements Despite being separated by two and differ in atomic weight by a multiple a half millennia, P ini and Mendeleev of eight. Unfortunately, his “law of were uncannily similar in terms of octaves” reminiscent both their goals andāṇ methods. First of of a musical scale all, both required a systematization of was summarily dis- the basic building blocks of their sub- missed as frivolous ject, which in both cases turned out to by his contempo- Li be a periodic system. P ini’s ordering raries. That same Be B of the sounds by place of articulation year, the German and aperture parallelsāṇ Mendeleev’s chemist Julius Lothar C ordering of the elements by their in- Meyer published an creasing atomic weight. On a more early form of the pe- detailed note, just as P ini treated riodic table. the simple stops k, t, p, and so forth These earlier at- as basic, Mendeleev consideredāṇ the tempts to organize Na seven light elements lithium through the elements prob- fluorine as typical (or representative) ably influenced Men- Mg Si elements. (Note that inorganic chem- deleev to some de- Al ists today do not view the first-row gree, although the elements as the most representative of exact extent of that their groups; we would pick chlorine influence remains or bromine rather than fluorine as best unknown. And, as representing the average properties of we argue here, San- the halogens). skrit too may have K Second, as with the periodic table, helped him crack the Ca P ini’s framework for Sanskrit sounds code. Despite others’ wasn’t just organization for organiza- contributions, Men- tion’sāṇ sake. His system allowed the for- deleev’s fame for con- mulation of a variety of generalizations ceiving the periodic table is fair: His about the existing phonological pat- prediction of yet-to-be-discovered el- terning of Sanskrit sounds. Phonology ements indicates a level of apprecia- refers to the patterns of sounds in a lan- tion of periodicity that far surpassed guage (for example, the fact that the se- that of his peers. Aulicino Master and Fellows of St. Catharine’s College, Cambridge; Barbara © 2019 Sigma Xi, The Scientific Research Honor Society. www.americanscientist.org Reproduction with permission only. Contact [email protected]. 2019 November–December 353 velum/ soft hard throat palate palate teeth lips

अ a इ i र r ऌ ḷ उ u ए e ओ o vowels and diphthongs ऐ ai औ au

semivowels (glides and liquids) अ: h भ y र r ल l व v

fricatives श ś ब ṣ स s unaspirated unvoiced क k च c त ṭ त t प p aspirated stops ख kh छ ch ṭh थ th फ ph unaspirated ग g ज j ड ḍ द d ब b voiced aspirated घ gh झ jh ढ ḍh ध dh भ bh nasal ण़ ṅ ञ ñ ण ṇ न n म m Wellcome Collection/CC BY 4.0 Collection/CC BY Wellcome

Pāṇini’s Aṣṭādhyāyī was a terse, maximally concise logical system for the Sanskrit language. Pic­ quence /pf/ is perfectly alright in Ger- tured here is a 1663 birch bark manuscript from Kashmir of Rūpāvatāra, a grammatical textbook man, as in Pfennig, but not in English), by the Ceylonese Buddhist monk Dharmakīrti that was based on the Aṣṭādhyāyī. as opposed to the sounds themselves, their articulation and perception, and their acoustic properties, which are stops covered under phonetics. The P inian alphabet allowed the formulation of ex- unvoiced voiced tensive rules for how Sanskrit āṇsounds change when they follow one another, both in individual words and in sen- vowels and tences and fast speech. Going much diphthongs further, P ini sought and success- unaspirated aspirated unaspirated aspirated nasal fricatives semivowels (glides and liquids) fully formulated the shortest system velum/throat k kh g gh ṅ h a of rules thatāṇ generates all expressions क ख ग घ ङ ह अ in Sanskrit without generating any expressions that are not well formed. palate c ch j jh ñ ś y i e ai च छ ज झ ञ श य इ ए ऐ In an analogous approach, Mendeleev sought a “chemical grammar” that gen- alveolar ridge ṭ ṭh ḍ ḍh ṇ ṣ r ṛ erates all chemical compounds, such as ट ठ ड ढ ण ष र ऋ NaCl and CaCl2, without generating teeth t th d dh n s l ḷ any impossible compounds, such as त थ द ध न स ल ऌ NaCl2 and CaCl, guided by what he lips p ph b bh m v u o au called the principle of isomorphism प फ ब भ म व औ ओ उ (from ancient Greek: isos, “equal” and Barbara Aulicino morphe, “form” or “shape,” in effect, similar molecular formulas). Sanskrit speech sounds written according to the International Alphabet of Sanskrit Trans­ Third, both men encountered oc- literation (IAST) are based on Pāṇini’s organization of the language. From top to bottom in the “two-dimensional alphabet,” the point of articulation moves outward in the oral cavity. The casional problems in reconciling the first row originates from the throat, the second row from the palate, and so on until the fifth physical properties of their building row, which originates from the lips. Along the horizontal axis, the stops are organized accord­ blocks with their combinatoric prop- ing to increasing aperture, which correlates with increasing sonority or amplitude. These pro­ erties. For example, the semimetallic gressions may be likened to the increase in atomic weight along both axes of the periodic table. element tellurium has a higher atomic © 2019 Sigma Xi, The Scientific Research Honor Society. 354 American Scientist, Volume 107 Reproduction with permission only. Contact [email protected]. weight than iodine, but their chemi- role in the culture had been likened to language. Mendeleev presumably saw cal properties suggest that tellurium that of Euclid in the West by the late this approach as analogous to his own should precede iodine in the periodic Indologist Johan Frederik (Frits) Staal. quest for a grammar of nature. One of table. Mendeleev’s genius was indeed In another sense, however, P ini’s ul- the most iconic symbols of modern sci- to place tellurium before iodine, in the timate recognition came 2,500 years ence, as it arose in the latter part of the hope that a more accurate determina- āṇ 19th century in Europe, may thus owe tion of their atomic weights would rec- a significant debt to an ancient Eastern tify the discrepancy. In a series of 14 language and culture. verses called the Śivasūtras, allegedly Mendeleev sought a revelation from the Hindu god iva, Bibliography P ini also rearranged the alphabet—­ a “chemical Ghosh, A., and S. Berg. 2014. Arrow Pushing in occasionally in less than intuitiveŚ Inorganic Chemistry: A Logical Approach to the ways—soāṇ that classes of sounds that grammar” that Chemistry of the Main Group Elements. New York: Wiley. combine in the same way with each Gordin, M. D. 2019. A Well-Ordered Thing: other are adjacent. generates all— Dmitrii Mendeleev and the Shadow of the Pe- riodic Table. Revised edition. Princeton, NJ: An Homage to Pāṇini and only the Princeton University Press. In our view, the above parallels are too Kak, S. 2004. Mendeleev and the periodic table extensive to result solely from coinci- possible—chemical of elements. Sandhan 4:115–123. dence. Although Mendeleev probably Kiparsky, P. 1991. Economy and the construction of the Śivasutras. In P inian Studies, Desh- did not know Sanskrit to any apprecia- compounds. pande, M., and S. Bhate. (eds.). Ann Arbor, ble degree, he almost certainly heard MI: University of Michigan.āṇ about P ini and his periodic system later: when his analytical techniques Kiparsky, P. 1996. Mendeleev, Boehtlingk, and of Sanskrit sounds from Böhtlingk. became a cornerstone of modern lin- Panini. INDOLOGY Forum for Classical The latterāṇ perhaps also told him how guistics, minimum description length South Asian Studies. September 30, 1996. he constructed a periodic system of Ya- became recognized as a scientific prin- http://list.indology.info/pipermail/indol ogy_list.indology.info/1996-September kut speech sounds based on P inian ciple, and it was discovered that lin- /005860.html. principles, but with the palatal and guistic rules can live on in daughter Reich, D. 2018. Who We Are and How We Got dental consonants reversed becauseāṇ of languages even after historical chang- Here: Ancient DNA and the New Science of the the way they pattern in Yakut. es have disrupted their phonetic basis. Human Past. New York: Pantheon. To us, it seems likely that Böhtlingk To us, Mendeleev’s remarkable use Scerri, E. R. 2019. The Periodic Table: Its Story was the first to recognize the connec- of the Sanskrit numerals eka-, dvi-, and and Its Significance. 2nd edition. New York: tion between P ini’s and Mendeleev’s tri- in naming as yet undiscovered ele- Oxford University Press. Staal, J. 1965. Euclid and P ini. Philosophy work and advised Mendeleev accord- ments makes the most sense as an hom- East and West 15:99–116. āṇ ingly. On the other hand, we cannot age to P ini, not only to his periodic Stewart, P. J. 2019. Mendeleev’sāṇ predictions: exclude the possibility that Mendeleev alphabet, but also more generally to his Success and failure. Foundations of Chem- knew enough to notice the connection generative,āṇ combinatoric approach to istry 21:3–9. himself, or that he had learned about P ini’s system from Böhtlingk early enough to be inspired by it as he was developingāṇ his system. Either way, the interactions between the two men, which lasted for the better part of a decade, most likely came to an end when Böhtlingk moved to Germany in May of 1868, the year that Mendeleev started writing his Principles of Chemis- try, and nine months before he sent his first write-up of the periodic system to the printer. As for the tellurium-iodine co- nundrum, vindication did come for Mendeleev, but not in his lifetime and not as he had expected. The atomic weights were indeed more or less cor- rect, but it turned out to be the atomic number (the number of protons in an atom’s nucleus), which usually but not always correlates with atomic weight, that fixes an element’s place in the pe- riodic table. As for P ini, he became the model for scholarship in classical India. His āṇ © 2019 Sigma Xi, The Scientific Research Honor Society. www.americanscientist.org Reproduction with permission only. Contact [email protected]. 2019 November–December 355