Types of Greek Numerology

Joel Kalvesmaki

Part of the Theology of Arithmetic website.

This lecture was presented 18 November 2006 at the annual conference of the American Academiy of Religion.

For the last several years I have been researching ancient number symbolism, particularly in early Christianity. I am here today to present a small subset of that research, on Greek numerology—numerology here meaning specifically divination, not number symbolism. My talk has two parts. I will first present the different types of Greek numerology and summarize the contents of major texts that are not well known. Several of these texts have never, to my knowledge, been properly edited, translated, or analyzed, so my communication will be, I hope, a special chance for you to preview and comment on new research in ancient and Byzantine divination. In the second half I will offer some thoughts on what Greek numerology has to tell us about ancient divination in general.

I classify Greek numerology in five types: lot divination, lucky numbers, psephic techniques, geomantic techniques, and miscellaneous. The first two types are well known, so I merely summarize them, without going into details about specific texts.

1. Lot divination, or cleromancy, was one of the most widely practiced forms of prognostication in the ancient world. In those forms of lot divination using numbers, practitioners would have the inquirer throw dice or astragali, or pick a number at random from one to ten. The resultant numbers would be checked against a list of values or responses, either immediately or after further operations. This form of divination is so widespread and widely known that we can easily forget that it is, properly speaking, a form of numerology. The technology is simple and ubiquitous: you need only the ability to count, coupled with a device, such as dice, a fertile imagination, or something else that can generate an unpredictable number. Because such requirements are so simple it is probably, along with the next type, the oldest form of numerology.

2. Lucky or auspicious numbers were used presumably as early as lot divination, or at least as early as humans learned to count and keep time. Certain months, days, or hours were noted for being lucky or unlucky. This practice developed, it seems, in two different but not exclusive ways. First, people began to observe occurrences in various cycles then note which times were auspicious or not. Second, number symbolism and lore about lucky numbers, developed without regard to time, influenced such lists. Many of these lists relate to medical concerns. Will the patient recover? If so, when? When is a good day to bleed a patient? Other lists apply to business transactions. Some texts claim to list “lit and unlit days.” Others go by the name selenodromion, a text sometimes ascribed to David and Solomon. A similar kind of list, ascribed to Esdras, ascribes to the days of the month various Biblical characters, to elucidate the quality of the day. There are variations ascribed to medieval authors, such as the patriarch Nikephoros or the astrologer Melampous. The manuscript tradition is a sprawling morass. I have so far identified around 120 of these lists, and the number grows. The few of these that have been published contradict one another in identifying what day or hour is auspicious or not. We are not likely to have a clear view of this type of numerology for decades, until the manuscript tradition becomes more accessible.

3. Psephic techniques (probably more familiar to you by the term gematria) were developed around the second century CE—about a century after psephy became a popular literary pastime—primarily in the Greek-speaking world, where letters were used for numerals. Because of the widespread use of alphabetic numerals, every word was potentially a number, and sometimes numerals could be words or acronyms. In psephic prognostication, names and terms were converted to numbers by adding the numerical value of their letters, and these sums were then analyzed to predict the future. The earliest attestations to psephic numerology come from three third-century sources: the Christian apologist Hippolytus, who attributes a rather complex system seemingly to a second-century figure; Artemidorus, who uses an idiosyncratic system that did not widely influence the numerological tradition; and the magical Greek papyri from Leyden. Psephic divination was very popular in the Byzantine era. I have identified four major texts and numerous minor ones.

First is called Pythagoras to Telauges, or The Little Pythagorean Plinth. This is what you might call combative psephy. Two names are taken, and a question is posed as to who will win in a fight or whether or not a marriage will be successful. Each name’s letters are added up then divided by nine until reduced to a remainder from one to nine (that is, an operation mod 9). One then consults a simple nine-by-nine table that shows who beats whom. Normally, if one number is odd and the other even, the larger number wins. If both are odd, or both are even, the smaller number wins. In case of a tie based on odd numbers, the challenger wins. For even-numbered ties, the challenger loses. Numerous variations of this technique and its application were developed. (For a description of the technique and its variations see Hippolytus, Refutation of All Heresies 4.14.) I have identified about sixty instances of this text in various manuscripts. Although there are several scholarly studies of this technique, they tend to restrict themselves to derivative traditions (such as Latin versions) or they treat merely one or two manuscripts.

The second text is what I call Petosiris to Nechepso, based on the pseudepigraphal letter that frequently prefaces the technique. It is also known as the Circle or Sphere of Petosiris or Democritus, from the circular diagram that often accompanies the text. Unlike the previous text, Petosiris to Nechepso uses only one name, usually that of a sick person. The day of the month on which the patient fell ill is determined. The letters in the spelled-out number of the day are added up, then combined with the psephic value of the patient’s name. That sum is reduced mod twenty-nine or thirty. The result is found on the Sphere of Petosiris, where all the numbers from one to twenty-nine or thirty are dispersed within a circle, divided into upper and lower halves, each half sometimes subdivided. The location of the number on the sphere provides the prognosis for the patient’s recovery. Note, this technique builds upon the previous type of numerology—lucky or auspicious numbers—to determine whether the outcome will be good or not. I have identified around ninety instances of this technique in various manuscripts. The most complete study of this technique is a 1988 article by Neugebauer and Saliba, who solved many important problems but left many more outstanding. Further, they handled only a dozen or so manuscripts, and they conflated this technique with the previous one, Pythagoras to Telauges.

The third text is what I call the Technique of Hermes, because many manuscripts attribute the technique to Hermes Trismegistos. This technique is very similar to Petosiris to Nechepso, but it employs conventions of the Egyptian calendar, and the resultant chart is based on predictable arithmetical patterns, not on the apparently random assignments of the numbers in the Sphere of Petosiris. This text might be a variation on Petosiris to Nechepso, but there is no prefatory letter and the manuscript tradition is extensive enough to warrant separate treatment: to date I have identified around twenty instances of this technique in various manuscripts.

The fourth major text is Approved Psephos Concerning the Sick, another psephic technique used mainly for medical prognosis. The text allows one to learn the chances of the recovery of a patient. You calculate the psephic value of the patient’s name and reduce mod three. This number, coupled with the day of the week when the illness began, is identified on a table that indicates whether or not the patient will die. If the patient gets the bad news that he or she is about to die, the same technique will tell them what day of the week he or she can expect that to happen. I have identified about a dozen instances of this text in various manuscripts.

Those are the four major psephic texts. To them should be added a host of variations and individual techniques. For instance, Artemidoros’s Dream Book reports unusual numerological techniques that depend on psephy, but the rules he uses are not found in the larger tradition. There are numerous other variations, attested usually in merely one or two manuscripts.

4. Geomancy, our fourth type, became popular first in the Muslim world, although its specific ethnolinguistic provenance and date of invention is impossible to determine. Whether or not the technique originated with the Arabs, Arabic forms became the exemplar for Greek and Latin forms. In geomancy the person asking about the outcome of an affair writes eight lines of dots, casts pebbles, or does something to generate eight groups of various sizes. The eight groups of dots or pebbles are grouped into four pairs. Each pair is reduced to one dot or two, depending on whether it comprises an odd or even number of dots or pebbles. Thus, everything is reduced to a figure consisting of four lines, each line containing one or two dots. This figure is then manipulated to produce a total of sixteen similar figures, and the whole tableau is analyzed to determine the answer to whatever question is being posed.

As I mentioned, the Byzantines embraced geomancy, but they also developed their own special version, which combines it with psephic techniques and cleromancy. The text in question is called either the Method of Chaleth (said in one manuscript to be one of the 70 translators of the LXX) or the Method of Leo the Wise, referring to the ninth century emperor and litterateur. In this method the inquirer is to pray to the Trinity and the Theotokos, then take the Gospels or the Psalter and pick a line at random. The first four letters of the line are taken, and determined to be odd or even (based on their numerical value mod 9). The result then becomes the first figure for the geomantic calculation. I have identified more than twenty instances of this technique in various manuscripts.

5. Many miscellaneous techniques cannot be placed easily into the above four categories. Some are ancillaries to other methods of divination. For instance, there is an anonymous, untitled text that I call Zodiacal Isopsephy, attested in the manuscript tradition at least six times. This technique, a preliminary step to starting an astrological calculation, is intended to find out the zodiacal house or birth planet for the person inquiring. Presumably this would be very helpful for people whose birthday was unknown. One takes the value of the name of the person, adds the value of the name of his or her mother or spouse, then reduces mod 7 or mod 12 to find the appropriate house or planet. After surveying the manuscript tradition, I believe there are probably dozens of these kinds of minor techniques, and we will not know the full extent of the tradition until all Greek manuscripts have been properly catalogued, an event we shall not see in our lifetime.

Given all the above, a basic historical outline of numerology would be the following: cleromancy and lucky or unlucky numbers developed very early, well before any literary attestation. In the second century CE there developed a new type of numerology: psephic divination. With Islam came geomancy, which the Byzantines adopted and developed into unique forms. Each new technique was added to the others. Thus, by the middle Byzantine period Greeks had a wide variety of numerological techniques.

In some texts there is a strong emphasis on the random or unpredictable, a factor especially evident in lot divination. Some scholars have emphasized the randomizing factor in divination. But numerology need not have been randomized, by any means. Psephic techniques, which depend for their outcome on a given name, are rooted in the predicable, not the random. In areas where psephic numerology were well known and learned possibly from childhood, people would be well aware of the numeric value of their name. If Ἰωάννης (1119) wants to fight Πέτρος (755), there is no random element in the calculation that tells you that John is in for a licking, because 8 beats 3 (even when you include the variations described by Hippolytus). There is a determinism at work here, a determinism evident also in astrology, whose principle randomizing factor is the navigation of the labyrinth of rules.

The comparison with astrology highlights another special function of psephic numerology, that of accessibility. No doubt anyone who wrote about divinatory techniques wanted to make them available and accessible to a certain group of people. So it could be argued that any written divinatory text is democratic; that is, it attempts to teach and propagate a given technique. But a technique like astrology remained opaque, no matter how many treatises were written about it. Astrological texts were meant to be understood in conversation or apprenticeship with an adept, to help explain the rules. Psephic numerology, however, is far more accessible, a do-it-yourself affair. Many of the texts I’ve described not only use simple rules and explain their techniques in full, but they sometimes provide tables showing the psephic values of common personal names or of the names of the zodiac and planets. That is, some of these numerological texts try to help the reader who cannot add well. No doubt, with some of these techniques you still needed an expert to help interpret your results, but with others the results are crystal clear. If your number winds up at the bottom of Petosiris’s sphere, you’d better shop for a coffin.

It is commonly believed that all prognostic texts were systematically eliminated by ecclesiastical authorities. I do not wish to minimize Christian opposition to many of these texts, but it remains to be explained how they could appear in so many manuscripts, including codices that contain theological treatises. From a sample of 123 Byzantine manuscripts that have at least one of these numerological techniques, twenty-five of them comprise, chiefly or completely, religious texts: writings of the Fathers, liturgical material, hagiography, even a Gospel book. So what kinds of people used these texts, and for what purpose? Evidence gleaned from Latin and Old English translations suggest that in the West these numerological texts were used commonly in monastic contexts. Can this be claimed of the Greek East, too? At this early stage, such a conclusion is hasty. Many Greek manuscripts indicate clearly that these numerological texts were used in other contexts. In Paris gr. 2009, Pythagoras to Telauges and Petosiris to Nechepso come just before the political text De administrando imperio. Many manuscripts contain chiefly astrological texts, which would scarcely appear in monastic settings. But nearly as many manuscripts contain medical texts, which cannot be assigned a priori to any one setting, religious or not. What do the contents of the various codices tell us about how these texts were handled and received? Were some but not other techniques acceptable? Was a given technique used seriously by some readers, but by others treated as an amusing pastime? There are many unexplored areas that need to be studied to understand better the relationships among numerological texts, the Church, and Byzantine society in general. This initial survey of new territory to explore will hopefully stimulate that study.


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