“You know that in ancient times religion, astronomy, medicine, and magic were all mixed up so that it was difficult to tell the beginning of one and the ending of the other and to-day the Gypsies, hoboes, free masons, astronomers, scientists, almanacs, and physicians still use some of the old magical emblems. So there is no reason why the boys of to-day should be debarred from using such of the signs as may suit their games or occupations and we will crib for them the table of numerals from old John Angleus, the astrologer. He learned them from the learned Jew, Even Ezra, and Even Ezra learned them from the ancient Egyptian sorcerers, so the story goes; but the reader may learn them from this book.” (Beard 1918: 91)

So begins the chapter, “Numerals of the Magic: Ancient System of Secret Numbers”, by Daniel Carter Beard in his 1918 volume The American boys’ book of signs, signals, and symbols, which you can download from Google Books for free. Beard was one of the founders of the Sons of Daniel Boone in the early 20th century, which merged with the Boy Scouts of America (of which Beard was a key founder) in 1910 when that famous group was formed. Beard wrote a number of popular books intended for boys in the Scouting movement, including this one. Scouting books today do not, as a rule, make reference to esoteric Egyptian sorcery or Freemasonry or ‘John Angleus’ (who is Johannes Engel (1453-1512)) or ‘the learned Jew, Even Ezra’ (Abraham ibn Ezra (1089-1164)), or, for that matter, have a chapter on number magic at all. At least, I never heard about it, and I was in Scouts for over a decade. But we are fortunate that this one did, because it has a couple of real treasures inside, not previously recognized as such.

Let’s take the second one first. It appears on p. 92 immediately following the passage I just quoted:

For those of you familiar with my book Numerical Notation, these are the numerals used primarily by Cistercian monks from the 13th – 15th centuries, and thereafter described in early modern numerology and astrology for several centuries, though largely at that point as an intellectual curiosity rather than a practical notation. David King’s wonderfully detailed Ciphers of the Monks (King 2001), which is one of the few books at that price point (somewhere around $150, if I recall) that may be worth it, lists every example the author could find of these numerals, from medieval astrolabes to Belgian wine barrels to 20th-entury German nationalist texts. It’s extremely comprehensive. However, it does not mention Beard’s book – and why should it? What a bizarre place to find such a numerical system! It’s what I describe as a ciphered-additive system, which is to say that there is no zero because none is needed: there is a distinct sign for each of 1-9, 10-90, 100-900, and 1000-9000. The Cistercian numerals are a little anomalous typologically; another interpretation of them would be that they are positional, but use rotational rather than linear position – the signs for 9, 90, 900, and 9000 (e.g.) are rotations or flips of one another, so we could consider them the same sign (9) in four different orientations. Zero is superfluous (thus not present) because unlike linear texts, there is no ‘gap’ to be accounted for by an empty place-value.

I became curious and tried to figure out why Beard attributed these to ‘Angleus’ and to ‘Even Ezra’. Engel’s Astrological Optics was translated into English (1655) but contains no Cistercian numerals, and King doesn’t note him as using or depicting the system. Similarly, ibn Ezra was not a known user of the system. And I haven’t even been able to find any other source that attributes the system to those individuals; rather, it’s almost always Agrippa of Nettelsheim or Regiomontanus who are invoked in the scholarship. We know that Beard was a Freemason, so he may have had access to some Masonic texts that said as much, but I can’t find any such reference, and King doesn’t mention any likely sources either, although he does note that many Masons (especially in France) were familiar with the Cistercian system. So it’s not entirely clear where Beard learned about the system (although see below), and he’s got a lot of things mixed up in the account.

The other numerical treasure in Beard’s book is even more fascinating, although it appears in the previous chapter on codes and ciphers and is less prominent, on p. 85, the ‘tit-tat-toe’ numerals:

So what we see here, again, is a ciphered-additive decimal system in which there is a ‘family resemblance’ between 9, 90, 900, and 9000 (and the other numbers so patterned), but no zero. The signs are designed after their place in a hash / tic-tac-toe / octothorpe with the power indicated through ornamentation. As a ciphered-additive system, it’s like the Cistercian numerals (although the signs are completely different) but instead of placing signs around a vertical staff, the signs are constructed into a box. Note that the signs in each numeral-phrase are not strictly ordered, but are packed compactly in whatever way suits the resulting box aesthetically. This is one of the advantages of ciphered-additive systems that, if desired, for cryptographic purposes or for any other reason, the signs can be re-ordered without loss of numerical meaning. But I know of no system quite like this, where numerals are arranged in a box-like shape, or where there is such a novel means of forming individual signs.

Beard is explicit that this system is newly designed: “The tit-tat-toe system of numerals here shown for the first time is entirely new and possesses the advantage of being susceptible of combinations up to four figures which suggests nothing to the uninitiated but a sort of Japanese form of decoration” (Beard 1918: 84). He claims that the alternate name ‘Cabala’ is just another name for the tit-tat-toe, which is a highly dubious claim, but he is clearly trying to invoke a connection between his newly-developed system and Jewish mysticism – in the hope that Boy Scouts will use it as a numerical code. Ciphered-additive numerals are rare enough in the modern era – most of the systems are obsolescent at best. So it’s fascinating to see a twentieth-century system right at the moment of its development. It’s also fascinating to see how mystical, spiritual, and numerological knowledge from early-modern authors is incorporated into a manual for Boy Scouts and recommended for use in cryptography.

We’re not quite done, though. Based on some of the (otherwise uncited) quotations in Beard’s book, I concluded that he was taking some of his ‘insight’ about the ‘Cabala’ from L.W. De Laurence’s Great Book of Magical Art (1915), which was a popular American book of spiritualism and Oriental mysticism at the time. And, looking into de Laurence’s book, lo and behold, what did I find?

De Laurence, whose work is also not noted by King, gives a more standard attribution than does Beard for what we now know to be the Cistercian numerals: he attributes them to the ‘Chaldeans’, which is a very common descriptor for the system and is even found in the scholarly literature. He doesn’t mention Angelus or Even Ezra or any other of the medieval and early modern authors who use the system, so it’s still a mystery how Beard made that attribution. But, given that there really are not a lot of texts that discuss this system at all, I suggest that Beard encountered them through De Laurence and possibly confounded their origin with some other understandings he had picked up along the way, possibly through Masonic writings.

It’s not every day that I discover a new numerical notation system, and it’s great to do that, even when it’s one that seems to have been developed once but never adopted more widely. So it was neat to find the ‘tit-tat-toe’ system, even if it never appeared anywhere else. But I also found it fascinating to track the transmission of the much more widespread (but still under-appreciated) Cistercian numerals through their roundabout path to a Scouting manual for boys. As King’s book amply demonstrates, the system has a tendency to show up in the oddest places, so perhaps we should (ahem) ‘be prepared’ to find them anywhere.

Beard, Daniel Carter. 1918. The American boys’ book of signs, signals and symbols. Philadelphia: Lippincott.

De Laurence, L. W. 1915. The great book of magical art, Hindu magic and East Indian occultism. Chicago, Ill., U. S. A.: De Laurence Co.

King, David A. 2001. The ciphers of the monks: a forgotten number-notation of the Middle Ages. Stuttgart: F. Steiner.