Reading the early Christian theology of arithmetic: methods of research and the search for a method

Joel Kalvesmaki

Part of the Theology of Arithmetic website.

This lecture was presented 19 November 2002 at Catholic University of America. Works cited can be found under the last name of the author in my bibliography.

Just over two years ago, I first encountered the writings of Iamblichus, a fourth century philosopher who transformed the philosophical heritage of Plotinus, giving it a markedly theurgic character. My reading of his Pythagorean Way of Life challenged a notion I once held dearly. Until that point I had assumed that the philosophy of late antiquity was markedly Platonic, and that Plato was held by all neoplatonists to be the greatest of philosophers. Hence, I was shocked to find Iamblichus, one of these so-called neoplatonists, giving ultimate homage not to Plato, but to Pythagoras, whom I vaguely recognized at the time as one of the anonymous crowd of pre-Socratic philosophers. In his biography of Pythagoras, Iamblichus presented a view of philosophy that encompassed much more than the neoplatonism I knew. It included a reverence for the mathematical sciences, and saw within arithmetic, geometry, music, and astronomy disciplines that were capable of leading a person to the metaphysical heights, even union with the One.

Around the same time I was reading Iamblichus, I was cutting my teeth on the writings of the fourth century monastic theologian, Evagrius of Pontus, who spent the last two decades of his life in Palestine and Egypt. In his famous treatise On Prayer, Evagrius explains why he composed 153 sententiae on prayer. He cites John 21.11 and explains the significance of the number 153 as a composition of 100, 25, and 28, each of which had its own special meaning: 100 is a square number; 25, a circular; and 28, a triangular.

I struggled hard to find out what Evagrius could have meant by this cryptic explanation, since there weren't many references on the matter, and the English translation I was using was mistaken in a critical place. I struggled even harder to make some sense of Iamblichus's penchant for arithmetic and its role in theurgic union. As I worked on these problems and continued to read other Christian authors from late antiquity, I found many others instances of arithmetic and numbers being used to illustrate symbolically the world of the body, of nature, and of God. Invariably, there was not much secondary literature to explain this phenomenon, and before long, it seemed as if I had found myself with a live, kicking, screaming, dissertation topic.

In the course of reading for comprehensive exams for my Ph.D., and in preparation for assembling a dissertation proposal, I have, among other things, read through dozens of books and articles that purport to treat certain aspects of number symbolism in Greek and Latin—sometimes Hebrew—literature. What I intend to present here is a critical synopsis of that secondary literature. In this serial book review, I shall argue that there is not enough scholarship on early Christian number symbolism, and that what we have is frequently beset by factual errors and methodological problems. Ultimately, I would like to suggest that we have yet to discover a method of research that fully comprehends and penetrates the phenomenon of Christian arithmology.

I shall briefly present some examples of the early Christian theology of arithmetic, just to make certain we understand the phenomenon with which we're dealing. Next I shall present the various approaches various scholars have taken to address the study of number symbolism. This romp through the bibliographical orchard will begin with what I think are the rotten apples, and proceed to the healthier, more vibrant fruits of scholarship. In summary I shall present a number of observations and questions that remain with me.


Some of you, reading the title of tonight's talk, may have wondered, What kind of animal is the "early Christian theology of arithmetic"? This is illustrated by the examples in Iamblichus and Evagrius to which I have already referred, as well as those on this handout. [Handout included excerpts from the New Testament, Barnabas, the Sibylline Oracles, Origen, Anatolius, Jerome, and Eusebius (the fifth/sixth century author of an isopsephic inscription in Shnan).]

These are but a few of the many, many examples of early Christian number symbolism, and the Christian use of numbers is only one of the many kinds from this period. If time and interest permit I'd be happy to introduce us to species of this genre, inside, outside, or somewhere on the borders of the Christian realm.

Now, a few notes about terminology. When I refer to "early" I generally mean texts from the time of Jesus (on the earliest end) to that of Ss. Isidore of Seville and Maximus the Confessor. Naturally, these borders are porous, since the entire tradition, both prior and subsequent to this era, must be included to understand any part of it.

As for the term "theology of arithmetic," you will find that I use other terms that I regard as synonymous: "arithmology" and "number symbolism." "Arithmology" was a term devised in 1915 by Armand Delatte, who noted the use of ajriqmologiva in a late Byzantine manuscript. Although the word makes its appearance around the era of the cabalistic writings, later than my period, it is not too misleading a term since it highlights the way authors manipulated the arithmetical properties and relations of numbers to unlock the secrets of the universe. "Number symbolism" is also a good term, especially when we keep in mind the meaning of "symbol" in the ancient world—objects that participated in and made present the person or object it symbolized. Those of you familiar with the way iconography was treated in the ancient world should recognize my point clearly. Thus, "number symbolism" refers to the way numbers participated in and made present for the ancient world realities that were not immediately present.

Although both these terms are adequate, I chose the phrase "theology of arithmetic" for my title for several reasons. First, it is the title of at least two ancient Greek works, one of which is an amalgam of Christian and pagan interpretations of each of the numbers from one to ten. This is the Qeologouvmena jAriqmetikh'". The Greek title describes well its contents: scattered observations on the intersection of the realm of theology, cosmology, and anthropology with that of arithmetic. The title also goes a long way to help explain what many people in late antiquity regarded the role of number to be, either a conduit to, or the result of, knowledge of God and, hopefully, union with him.

Although these terms all nicely complement each other, I am reluctant to use certain other terms. "Numerology" has overtones of modern New Age practices, and I would rather avoid this association, even if it is appropriate in some cases. So too with "arithmancy." Numbers were many times used in Late Antiquity in a manner reminiscent of its practice in certain religious movements begun in the twentieth century, but linking the two eras in toto is as problematic as terming everything we find in the Greek magic papyri "magic."

Another word I tend to avoid is "mathematics." For those in Late Antiquity, "mathematics" referred to a set of disciplines that undergirded, but was not identical to, arithmetic, geometry, music, and astronomy--the famous quadrivium--and it included notions such as equality, "greater-than-ness," "less-than-ness," similarity, dissimilarity, quantity, extension, absoluteness, and relation. Thus, although all arithmetic was mathematical, not all mathematics was arithmetical. This distinction was once part of the English language, but in the course of the eighteenth and nineteenth centuries we began to treat "mathematics" and "math" in a much more specialized fashion. Today, this distinction is all but lost. In this presentation I shall attempt to align my terminology with that used in "Late Antiquity," and use the term "mathematics" when referring to the general sciences, not arithmetic.

The State of Research

The bulk of mistakes made by recent scholars clusters into a number of identifiable groups. Although I do not wish to point out every error, I do want to mention some of the most frequent.

As some of you may imagine, there is a recurring temptation to explore ancient number symbolism in the light of modern concerns, especially those found in New Age movements. Sometimes this takes the form of a religious pastiche, sometimes as a modernization of ancient voices. In some studies, especially those exploring the meaning of every number up to ten, Pythagorean and early Christian interpretations are mixed in with interpretations from post-cabalistic, Buddhist, or modern scientific settings. One particular study includes an entry for zero, an inclusion that would have baffled someone like Iamblichus. For the Greeks there was no number beyond the limit of one; there was no zero. The proposition that zero is a number undermines, among other endeavors, the quest for union with the One.

Other studies incorporate Late Antique arithmology as but one way of deciphering the meaning of the numbers in our name, or in our birth date. To detail the directions taken by these books goes beyond the scope of our discussion tonight. I do not wish to discount fully all these approaches, but they mostly detract from the purpose I’ve set out, to understand Christian number symbolism from late antiquity on its own terms. The purpose calls for an answer that has some connection to historical inquiry, among others, and the imposition of modern arithmological practices upon late antique ones can lead to serious mistakes.

Some scholars who take a more historical approach to the phenomenon commit the same fault by reading in not modern practices, but medieval ones. The trophy in this department goes to Biblical scholarship, a discipline that, to this day, invites the use of cabalistic gematria to decipher Biblical texts. In one study, the 153 fish of John 21.11 is read as a code for a Hebrew isopsephy—provided you take the Milesian notation, create an atbash of the alphabet, then find the corresponding abbreviation for 153. Anachronism aside, this is a procedure far more complex than any explicit isopsephic texts we have demonstrate. In another study the census figures of the book of Numbers constitute an elaborate riddle on the numerical value of certain key Hebrew words. The chief problem with such endeavors is that they presume an early, pre-Christian origin for Hebrew isopsephy, without any investigation of the matter. To my knowledge, there is no study critically exploring the origins and lines of influence of Greek, Hebrew, and Latin isopsephy, but what I have studied suggests that the earliest, unquestionable instance of Hebrew isopsephy occurs in the second century CE, associated with Rabbi Judah and his interpretation of Jer. 9.10. It is my working thesis, one not contradicted by evidence that Scholem and Dornseiff produce, that Hebrew isopsephy arises in the wake of a very vibrant Greek one, and the failure of scholars to attend to this matter has led to many dubious "discoveries."

Equally problematic is the temptation to take one interpretation of a number found in an ancient author and superimpose that upon another text of roughly the same period. One scholar analyzes the second Dialogue of Gregory the Great and imperfectly squeezes the pericopes into a structural pattern of 5 / 12 / 12 / 5, then argues that this shows Gregory’s intention of highlighting the perfection of charity for one’s neighbor (represented by 25, the product of 5 and 5) and general perfection (12). None of this emerges naturally from the Dialogue, however, and this particular scholar must contort Gregory’s narrative to make it fit his pattern. This interpretation of five and twelve is present in many ancient authors, but it is not immediately obvious in Gregory’s Dialogues. Besides, there were many interpretations of the meaning of five and twelve. So suppose the structure proposed for the Dialogues is correct. Who is to say that Gregory didn’t mean to convey the role of the five senses, and the twelve signs of the zodiac? In the end, we are left to the scholar’s imagination, not Gregory’s. Not surprisingly, our scholar treats none of the other books of the Dialogues.

One more set of mistakes I feel important to mention is a recurring tendency to assess arithmology in light of a very few Latin sources, especially St. Augustine, to the detriment of Greek ones, or to the exclusion of other Latin authors. This is understandable from the vantage point of a medievalist who must deal with an age soaked in Augustine’s afterglow. But it does not do justice to a study of the arithmology of early Christianity. For example, the most ambitious scholarly endeavor to compile all the instances of patristic number symbolism is Meyer and Suntrup’s lexicon, a list of key, theological interpretations of a variety of numbers by important Latin Fathers. But the lexicon excludes any consideration of Greek writings (even when a Latin Father is borrowing directly from a Greek source) and it omits important early Christians who composed in Latin and had a theology of arithmetic, for instance, St. Hilary, Tyconius, and Boethius. Other scholars make Augustine the focus of Christian arithmology in Late Antiquity, and this is, I think, a mistake. True, he alone of the Latin Fathers argues for the importance of numbers and derives a rudimentary theory of how numbers worked in the physical world, but his actual theology of arithmetic is neither more nor less developed than is Ss. Hilary, Ambrose, and Jerome’s. Only hindsight or an acute sense of the power Augustine was to wield over centuries to come could make him a father of number symbolism.

These are a few of the most prominent recurring problems in the secondary literature. There are other studies that are substantially sound—or at least they are missing the more egregious mistakes found in other works. But some of these do not say much more than the primary sources do. In this category belong quite a few articles that examine the use of numbers in a particular author, but they fail to say anything about why the author used them in that fashion, or they fail to put the author into the larger context of Pythagoreanism and other numerate disciplines. This is a category of the secondary literature about which I wish to say no more than this: Readers' time could be used with equal or greater profit by simply reading carefully the primary sources.

The next category of methods I wish to discuss are introductory studies into specific realms of arithmology. These studies distinguish themselves by charting historically the lines of influence of certain ideas upon certain authors. They critically distinguish lines of influence in late antiquity and look for some shape to the arithmological tradition. As such they are good starting points. Let me mention some of the more helpful works.

There are a number of introductions to ancient arithmetic and geometry. But many of these are concerned with "real" arithmetic and tend to skip over late antiquity to the Arab mathematicians, or they make no mention of the philosophical and theological visions of arithmetic that so predominated the study of numbers in the ancient world. Serafina Cuomo has observed this deficiency and has recently written an excellent introduction to mathematics of the fifth century BCE to the sixth century CE. Her work, Ancient Mathematics, ranges over virtually all kinds of ancient social interest in number, be it economic, architectural, scientific, or religious. Also of note is Ifrah’s work, which starts from the prehistory of numerical notation and extends to the age of computers.

Beyond the general surveys, there are excellent introductions to certain thinkers or movements. Burkert’s monograph on the question of the historical Pythagoras remains a classic, as attested to by the recent work by Riedweg. On the question of Pythagoreans in the Hellenistic period, two authors stand out: Dillon and Thesleff. Dillon provides an excellent, historically framed, synopsis of the rise of Pythagoreanism in the late Roman Republic and early Roman Empire. Thesleff edited and critically evaluated the pseudepigraphal Pythagorean writings of the Hellenistic period. For our era—late antiquity—there are several scholars who provide a good starting point. O’Meara and Bechtle have written considerably on the philosophy of arithmetic in the fourth through sixth centuries, concentrating on figures such as Alcinous, Iamblichus, and Proclus. Their recent collection of papers on mathematics in late antiquity is an invaluable contribution to the exploration of the philosophical side of numbers, and contributors such as Cleary are correctly attuned to the need to show how arithmetic was, for this tradition of philosophy, a protreptic to theology. Also important to mention are Rappe and Shaw, who have recently written on the role numbers played in the attempt by Plotinus, Iamblichus, and others, to ascend to the One via theurgy. In the area of the intersection of the alphabet, numbers, and magic, the very old work by Dornseiff is surprisingly very rich and fresh. It is the best place to start to get a sense of the importance of the linguistic use of numbers—gematria, magic alphabets, and so forth.

The Jewish use of number symbolism in the Roman Empire is best approached by the works of Scholem, even if his emphasis is on the cabalistic period. Because Scholem’s work concentrates on a later period, there remains much preliminary work to be done on the earlier Jewish use of numbers. In this field there are good introductory studies on Philo (by Staehle) and the Jewish pseudepigrapha (by Collins).

In the area of the early Christian approach to arithmology, there is no adequate introduction. Schimmel’s book is helpful, but is centered on the later arithmological tradition, and is sometimes naïve. Meyer and Suntrup's work, as I have mentioned, has too much a medieval focus. Hopper’s work, referred to repeatedly by medievalists as a classic, is very problematic, though parts of his work may still be read with profit. Although there is no good, general survey, there are introductory studies on specific figures or themes, such as Augustine, Didymus the Blind, Barnabas, and on tropes such as the 30, 60, and 100-fold fruits in the Parable of the Sower (Quacquarelli); or on the 318 Fathers of Nicea (Aubineau). Many of these studies are very helpful, but cannot easily be appreciated or critically read without having first read a broad range of primary sources.

Centuries subsequent to the ones we are now considering have been better studied. The emergence of cabalistic literature in western Europe in the late twelfth century produced a new generation of religious arithmologists, and this new wave of rather flashy Jewish—then Christian—number symbolism is the subject of numerous studies and treatments. Beyond the cabala, much has been done. Scholars of medieval literary treatises have shown how numerical considerations were important to certain poets who timed certain elements in the plot to coincide with line numbers of arithmological significance; surveys of architecture have shown the overt use of number symbolism in the construction of medieval cathedrals and monuments.

This, then, is the sum of research as we now have it. There are some adequate introductions to important parts of the arithmological tradition; there are quite a few important studies; but there is very little on the early Christian use—or even the use by any Mediterranean religion—of numbers.

Methods of Research

The first set of research methods I want to present are those that attempt to create critical distinctions on the basis of an historical account. One of the most popular and influential views is that of Hopper, who sees three kinds of number symbolism, falling neatly into three epochs. The first kind of number symbolism he proposes is "elementary"—symbolism attaching to numbers by virtue of biology or deeply embedded social structures. Thus one is, through a primeval arrangement, a token of loneliness; two is marriage; four is the number of directions; ten, by being the number of fingers, represents perfection. Hopper’s second kind is "astrological." Here the paths of the sun, moon, and stars invest numbers like four and seven with specific meanings that he suggests originated with the Babylonians and were developed by the Hebrews. The third group, "Pythagorean number theory," is a system that examines the arithmetical properties of numbers and assigns these numbers to certain moral or theological meanings. To Hopper, Gnostics mixed all three strands together. This Gnostic concoction cooperated with philosophy to contaminate a hitherto number-free Christianity. Thus, Christian obsession with the Trinity is a Pythagorean corruption of the pure message of Paul and of the New Testament. Hopper suggests that through Augustine’s stamp of approval, arithmology became official and a dominant force in the Middle Ages.

This is a vivid picture of how the theology of arithmetic came about, but I would suggest you not take it seriously. Hopper does not cite many concrete examples to back up his view of primitive arithmology, and there is good evidence to show that there is no archetypal number symbolism unique to all cultures (see, for instance, Burkert’s brief overview of ancient number symbolism from different cultures). Furthermore, Hopper's postulation of the three categories suggests they are exhaustive and mutually exclusive. But this is not the case. Where do we put interpretations of seven as Athena, or assignment of six to the soul, or two to Isis? These associations are neither "elementary," "astrological," nor "Pythagorean." Of course, there is some arithmetical operation that could be performed to associate these deities with these numbers, but the primary sources we have suggest that the associations are more mythological or typological than arithmetical in character. Hopper’s system also leaves no place for isopsephy. It also suggests that the Christian community started from a pure Semitic religion untouched by Greeks or Romans to a corrupted Greek one, a transformation that parallels another corruption he advocates, that of the orientalization of a Roman sense of arithmetic originally interested only in the utilitarian function of numbers. Neither of these paradigms can be squared with the sources. Hopper does make the excellent point that Trinitarian debates, particularly in the second and third centuries, were informed by neopythagorean concerns, but he gives too much credit to a philosophical tradition that was more invented than instantiated, and not enough credit to the numerical sensibility of those who composed the New Testament.

A taxonomy similar to Hopper's is suggested by Butler, who also sees three epochs in arithmology: number symbolism rooted in creation, the allegorical use of numbers, and their magical use. This scheme seems to me to encompass more than Hopper’s but it falls prey to the same problems. For instance, his suggestion that these are three distinct eras of number symbolism falls afoul of chronology. The magical use of numbers seems to be ancient, not late. Think of some events that look suspiciously like the magical use of number: Joshua’s taking of Jericho by circling it seven times on the seventh day, or of Naaman’s cure from leprosy by bathing seven times in the Jordan River, events that do not post-date the epoch of the allegorical use of numbers. Furthermore, Butler argues that the Renaissance was the first age to truly unite all three types of arithmology, a claim that shows the author’s unfamiliarity with ancient authors such as Proclus.

This three-fold division of history is followed yet again by Moehring, who sees the three strands as being "symbolic," "numerological," and "arithmological," which three categories he also presents in a chronological scheme. The use of symbolic numbers precedes that of numerology, which precedes arithmology. In his view, Philo goes beyond the symbolic, but avoids the esotericism and occultism involved in numerological speculation. Moehring correctly observes that Philo engages in no gematria, and in no esoteric use of numbers. Philo’s arithmology (Moehring is reluctant to call it merely "number symbolism") is a result of a tradition’s reflection on the natural, physical cycles of the universe; its use of number is a heuristic device intended to discover interrelations in the world, driven by the belief that the cosmos itself is composed of numbers.

Moehring’s taxonomy is better that Hopper’s or Butler’s. He penetrates more deeply into the meaning of the use of number. By distinguishing between exoteric and esoteric use of numbers, he finds an identifiable feature in the literature. The use of number in the Greek magic papyri, for instance, assumes a knowledge of number not provided by the text, and it has a character different from Philo’s theology of arithmetic. Thus, there may be something to an exoteric versus esoteric distinction. But Moehring’s other distinction between the bare number symbolism of the Chaldeans and Philo’s arithmology doesn’t seem to hold up, or at least the difference does not seem to be bipolar, as he suggests. He does not make a strong case for this distinction between the symbolical and the arithmological use of numbers. Time does not permit me to explain this criticism as I would like, but, to be concise: It seems that much of what Moehring terms an arithmological use is also symbolical.

The best historical texture given to the theology of arithmetic are the narratives provided by Cuomo and Ifrah. Ifrah’s concern is not immediately with the theological features of number, but he keeps an eye on it, and he readily relates aspects of number symbolism to the development of mathematical systems across the centuries. His narrative, however, is too brief to explore the many different kinds of arithmology. He also does not provide his account with enough historical or cultural texture to adequately frame the early Christian theology of arithmetic. Cuomo’s work goes further than Ifrah’s. She ranges over the whole smorgasbord of types of use of number, but she is willing to suggest reasons for their use. "Mathematics gave upper class Romans and Greeks a way of articulating their positions about the state and the individual, power and knowledge." Arithmetic, by Cuomo’s lights, were a way of investigating the self, of achieving happiness, and, for some, union with the One. Christians, she notes, invested a strong ethical component to their interpretation of numbers, especially those found in Scripture. Cuomo is insightful. She correctly does not attempt to put all the different kinds of ancient arithmetic into a single system, and as a result, her account seems as eclectic and thought-provoking as the primary sources. This is, I think, to her credit. But when she focuses on the Christian tradition, for instance, she only begins to penetrate the importance and significance of arithmology. Much of her exposition simply iterates examples from Clement and Augustine, and although she points out the importance of putting their comments into the context of Hellenic institutions and culture, she never shows how this occurred, or why their arithmology had any intellectual clout. Thus, Cuomo makes some provocative points, but never attaches her sources to those points.

There have been other methods of research that have not relied so heavily upon an historical sieve, but have tried other approaches. One such approach is that of Collins, whose examination of the role of numbers in the pseudepigrapha separates the use of numbers according to whether they deal with time or space. Although this differentiation might be problematic in other genres, in the pseudepigraphal literature there appear distinct patterns of association given to certain temporal numbers, meanings not seen in their spatial counterparts. Thus, sevens attached to temporal objects typically suggest a week or the Sabbath rest. But in the spatial realm, the number seven typically recalls the planets, which were normally regarded as seven in number. In the process of her analysis, Collins argues that numbers in the pseudepigrapha prophesying the eschaton are not predictions of a date when the end of the world is due, but a typological stamp upon the text signifying to the reader that God remains sovereign over the events of history, and that the eschaton is a fixed, or impending event.

I doubt whether Collins’s insights could sustain their interpretive force beyond the pseudepigraphal and apocalyptic texts she has chosen. But given this range, she succeeds, building a set of thoughts that penetrate the immediate message of the primary sources to explain why one strand of arithmological texts might have been written. It would be interesting to see how Collins’s theory holds up on the periphery of the genre. For instance, she cites our fourth example, but only as a part of the larger arithmological backdrop to the literature. This is a pity, since the Sibylline Oracles are both pseudepigraphal and apocalyptic, and it seems that this passage falls into neither of Collins’s categories of time and space.

A second approach using a nonhistorical set of distinctions is found in Quacquarelli, whose guiding thesis is that an arithmological tradition must be studied vertically, so to speak, within the chronological extent of the given tradition. In this thesis, he is rejecting the approaches of Kittel, Dölger, Prümm, and Rahner, whom Quacquarelli accuses of interpreting Christian symbols in the light of pagan ones. For Quacquarelli, this is to render a distinct tradition indistinct, and not to understand Christianity on its own terms and symbols. The Christian message was shaped fundamentally by teachings of Jesus Christ, and his death and resurrection, and this historical reality transformed the number symbolism Christians drew from their culture. Quacquarelli’s most important specific example is found in his monograph on the ogdoad in patristic thought. There he argues that the predominance of eight took on a peculiarly Christian meaning, a meaning that cannot be detected in Pythagorean sources. To build his case, he ranges over a variety of evidence—textual, liturgical, architectural, and iconographic. After surveying numerous patristic texts relevant to the theological meaning of eight, he shows how interconnected eight is to the death and resurrection of Christ. He explores the universality of the octagonal baptismal font, the immediacy of eightness in the liturgy (Sunday being the eighth day), and the regular presence of the hand sign for eight in a wide variety of iconography. The meaning of eight is changed in the Christian theology of arithmetic, in the radiance of Christ’s atonement.

Quacquarelli’s argument is strong and compelling. His treatment of the Christian uses of the eight to exemplify the discontinuity between Christianity and paganism is fundamentally sound, and a much-needed antidote to the temptation to understand Christianity in terms it often rejected. His approach to number symbolism in late antiquity, using a religious criterion, appears helpful. Furthermore, Quacquarelli’s sensitivity to the entire tradition of Christianity—all the way up to the modern era—is a strength. I have argued in other settings that it is an act of responsibility to attempt to understand an historical phenomenon in conversation with its successor tradition, and he does this well. But, on the other hand, Quacquarelli’s approach cannot explain an author like St. Anatolius. How could a Christian hero and bishop be the author of arithmology that is fundamentally Pythagorean, i.e., pagan? There are many examples of the Christian use of Pythagorean number symbolism, and Quacquarelli’s approach cannot account for these.

The final method of research I wish to mention is by an anthropologist who has never, to my knowledge, written anything on Christianity in late antiquity or the middle ages. The author is Thomas Crump, who has written extensively on the Japanese practice of seimeiguku, or "full name science." This is a technique used today in Japan, meant to help parents pick names for their children. By calculating a prospective name according to ten different numerical operations, a master of seimeiguku interprets the numbers that attach themselves to the syllables in the name, and suggests how this will affect the person’s life. In the introduction to his general study on the current use of numbers across various human societies, Crump notes how little modern numeracy and its implications have been studied. He emphasizes the point by noting that he is the only author of any scholarly study of seimeiguku in any Western language. Thus, The Anthropology of Number is his attempt to collect, to synthesize, and to promote the modern anthropological study of the function and meaning of arithmetic as practiced today. The work is rich with insights that often suggest exciting new ways of looking at numeracy.

Crump accepts the distinction commonly made by anthropologists: Societies are either traditional or modern. Numeracy falls into this spectrum according to the degree of abstraction with which a society is able to invest numbers. The greater the quality of notation and the greater the efficiency of calculation, the more arithmetic is enhanced in a society. This itself is linked, in Crump’s view, with the enhancement of linguistic resources. The greater the linguistic complexity of a society, the greater its sophistication of numeracy. A society’s complexity in numeracy is spearheaded by apparently innocuous institutions such as music, games, and art. The game jenken, for instance, known to us as scissors-stone-paper, has a sense of ordinality, but no sense of cardinality, and although it is a game played by children, it represents one of the most complex uses of number in everyday society. Thus, jenken not only pushes on the horizons of a child’s sense of numeracy, but it does this with an odd approach to numeracy as ordinality, or rank, not as number in and of itself. Crump makes similar observations in the areas of music, poetry, dance, and art. We do not have the time to pursue all of these the way we should, but let me mention Crump’s insights on the way we use numbers to describe time, and see how this fits aspects of early Christianity.

Using the modern / traditional distinction, Crump notes that across all human societies share some common features. We all recognize "earlier" in contrast to "later," we all recognize the need to continually recalibrate the present, that peculiar moment that hounds us as we seem to move through time. This need to keep a track of the moving present motivates societies to create structures of time upon which all can agree, and that can reliably predict and regulate future events. Oftentimes, Crump argues, the thing to which societies peg their calendar reflect the difference between modern and traditional societies. To make his point, Crump proposes a distinction evident in Japanese culture, a distinction between "nature" and "cosmos." "Nature" refers to elements in the universe that are earth-bound, such as weather, soil, floods, and other aspects of the ecosystem that can be directly interfered with by people. "Cosmos" refers to elements of the universe beyond our control or interaction—the stars, the planets, the moon, and the sun. The cosmos / nature distinction also coincides with religious patterns in Japan: Buddhism is a religion of the cosmos; Shinto, of nature. Crump then notes that more rural, agricultural societies will tend to mark time by means of nature, not cosmos, since the rhythms of life are guided by the planting and harvesting of crops, events that frequently cannot be planned against the movement of the cosmos. The more numerate a society becomes, however, the greater the tendency to mark time by the cosmos, not nature. Crump argues, in fact, that the encroachment of the modern West on traditional agricultural societies is accompanied by an attempt to superimpose a cosmological reckoning of time upon a natural one.

There is even more to Crump's chapter on numbers in time than I’ve given in this brief sketch. I think that this sampling gives you an idea of the kind of stirring new paradigms he wishes to suggest. To my knowledge, his thesis has not been applied to the early Christian world. I would suggest that such an application would compel us to revise Crump’s theories into a set of insights even more arresting. Think, for instance, of the ancient Christian calendar, which used the numbers of the cosmos to regulate the sense and passage of time. Yet in this same calendar there are also liturgical sets of numbers that Christians synchronized against neither nature, nor the cosmos. The number of psalms to be chanted in the daily service—you may recall the passages of St. John Cassian’s Conferences devoted to this debate amongst the Egyptian monks—was decided by angelic intervention, not the natural world. Presumably it was elders who enforced and maintained a rule given by the heavenly powers. This is an instance where the daily Christian calendar was subdivided into liturgical numbers of angelic origin, and ecclesiastical supervision, without reference to nature or to cosmos. The debates on the dating of Pascha concerned themselves, not only with the integrity of a calendar based on the cosmos, but also with the need to accurately instantiate the numbers found in the passion narratives in the Gospels—the hours of the stations of the Cross. This is a case where the annual Christian calendar was marked by a metatemporal participation in Christ's passion. The present is calibrated according to a heavenly, divine Now that finds its source in the crucifixion and resurrection, that finds its recurrence in the Church gathered at the Paschal feast, and that looks to its entelechy at the eschaton. In all this keeping of Christological and Scriptural time, cosmos and nature fade into the background. This application of ancient Christianity to Crump’s theories threatens to undo his division between traditional and modern societies. Think of the Roman Empire in all its colorful variety of local customs and religions. Now, is the Roman Empire a tradition or modern society? It is neither. It is off Crump’s scale, altogether. The most obvious case in point is the Roman habit of dating years according to the indiction. Crump’s system doesn’t seem prepared to account for a system of time whose numbers are based on the taxman.

Thus, my enthusiasm for Crump’s work is not based on his consistency with the early Christian theology of arithmetic, but on the unusual way he sees the phenomenon as currently performed. Crump's paradigm may not hold, but at least he ventures to suggest interpretations of social numeracy extending to the horizons of our interpretive capabilities. I have been stirred to rethink how numbers work, in all their applications, in both Late Antiquity and the present, and for that I am grateful to him.

The Search for a Method

In one study of medieval number symbolism, the editor suggests that the subject awaits its Christopher Columbus. I hope, from the basis of this short survey of the secondary literature, you will agree that the subject actually needs a few more Leif Ericssons. There have been very few attempts to study or to understand a very widespread, multi-formed practice that was and is prevalent and meaningful. The several methods of research I have presented occasionally make valuable insights into this world, but ultimately fail in terms of consistency or completeness. When I suggest that I am in a "search for a method," I do not mean that I intend to discover a method or scheme whereby all use of numbers in late antiquity can be universally understood. I would be suspicious of such a powerful explanation. Rather, my search is for a method—any method—that can hold its form and maintain its consistency across any arithmological passages relevant to the thesis. Thus, mine is a search for a method, not the method, that can successfully circumvent the flaws of modern scholarship and yet happily circumscribe the insights.

The very attempt to create a set of categories into which various ancient uses of numbers fall is fraught with difficulty. The primary sources cannot be cleanly divided between instances of utilitarian and symbolic use; between Christian, Jewish, and pagan (here I admit my own culpability!); between physical or psychological; between scientific, allegorical, and magical. I do not deny that these are occasionally distinct tendencies, but when taken absolutely they quickly lead to myopic mistakes. Had I room for another lecture, I would present you with a wider, more extensive survey of the primary sources of number symbolism so you could see for yourself how difficult is this job of classification.

To get a handle on the early Christian theology of arithmetic I do not think it is enough to simply take the latest interpretive theory and zealously apply it. Although I’ve done this occasionally in my mind, the primary sources seem to insist on release, as if from a straightjacket, and my intuitions tell me that in twenty years or so—when that latest literary theory has yielded to the next—I shall be grateful for not having tried in vain. It is also clearly insufficient to attempt to divest oneself of any theory. Some of the poorest articles I’ve read have been marked by something resembling this kind of positivism. I hope that the methods I use will avoid both these mistakes.

It seems that one requisite element for any approach is a sensitivity to, and interaction with the living successor traditions of number symbolism. Crump’s involvement in seimeiguku is, I think, a case in point. There is much to be gained by looking at the way numbers are handled and symbolically used today. I confess, there is a bit of distaste I feel when I think of modern numerology, such as biorhythms or enneagrams. But as I have considered the matter, I think we cede too easily the mantle of "successor tradition" to modern practices that may not be as worthy of the honor as other number symbolism much closer to thoughtful, modern habits. There was, for instance, a scramble for meaning in the aftermath of the terrorist attacks on Tuesday, September 11, 2001 in numbers, and the need of a society was satiated by linking the event to the emergency telephone number 9-1-1. The association was reinforced all the more when, on the one year anniversary of the attacks, one of the winning numbers for the New York State Lottery was 9, 1, 1. There are more respectable forms of modern arithmology. We use chaos theory to explore in nature the simple, repetitive patterns of numbers; for some of us, the recognition of Fibonacci’s sequence—2, 3, 5, 8, 13, etc.—throughout nature has instilled in us a wide-eyed childlike wonder. The use of number symbolism remains an important part of our mythology and intellectual life. We should observe it more closely.

Finally, there is one other approach that may have some promise. Some of the most profitable treatments of arithmology I have presented were written to attend to some other object. Thus, Collins’s work on the pseudepigrapha gets much of its force from her attempt to grasp the meaning of eschaton; Quacquarelli’s work, from the desire to prove the incommensurate character of the Christian tradition; Crump’s work, from issues of languages, money, time, and games. The number of interests and specialties with which concerns of arithmetic intersect is quite large, and it may be that the proper method is the one already in force. That is, the way to approach the early Christian theology of arithmetic might be to work on ecclesiology or art or politics, or whatever it may be, but with an attentive eye on the numerological component. Thus, an image of the ancient Christian use of numbers might emerge from a shared effort. In this scenario, the stroke of the numerically-informed art historian would complement that of the numerate numismatist and the arithmetical rhetorician. I have doubts whether such collaboration would yield insights with the size of canvas I would like, but it would be better than no effort at all.