Counting Glyphs

Three Outstanding Numbers &
a Century of the Voynich Enigma

For budding mathematicians, the Number Pi is sacred territory. For mystics, there’s the cryptic Belphegor’s Prime. Some social pundits give currency to the Dunbar Number. But after one hundred years, no one has come even close to decipher the Voynich Manuscript.
While Pi is called an ‘irrational number,’ Belphegor is a palindrome with a religious cipher at its core, and a glyph lifted from the Voynich. Now, about the Dunbar, guess what? is not even a number.
We’ll go over each one in more detail, of course. But we do love this sort of thing, even without quite fully understanding their implications. So what? Does anyone need to be an astronomer to admire the stars at night? OK, that was a cheap shot.
But there are definitely ways of immersing oneself in the beauty of these mysterious landmarks of the human thought, without necessarily being current with quantum semantics and the intricacies of code-breaking and algorithmic calculations.
One of them is, naturally, shut the hell up and just enjoy them. But we, dilettantes and amateurs of all stripes, fancy ourselves to be able to gather the powdery substrata that may lay a notch below the surface of such far-advanced scientific research.
Not too far down, or we wouldn’t find our way back up. Not too thin a layer, so not to be filed away along tabloids and wholesale techies. Just enough to get a good, pleasurable taste of privy knowledge, and, without any doubt, impress the hell out of our friends.

For many a bright mind, the moment they found out about the Number Pi is seared on their memory, along with the first exchange of spit and other personal hallmarks of the private experience. Not us, feeble mentalities, incapable of even grasp the depths of square roots and unwavering hypotenuses, as straight as no hypotheses will ever be.
That’s probably why words such as ‘transcendental’ and ‘randomness’ are routinely tossed in with abandon, whenever the number that was probably familiar to the builders of the ancient pyramids of Egypt is invoked. It’s also beyond our limited scope what did come first, the Greek letter or the pie, but please, don’t quote us on that.
Pi is very likely to be the only number to have its own day, March 14, probably because Piday would stand out in any calendar. You may do yourself a great disservice, though, trying to find out whether that date has anything to do with Welsh William Jones or Swiss Leonard Euler, both 1700s mathematicians credited with popularizing the number.

Perhaps out of pure mischief, the following day was consecrated to yet another math concept (cue the Medieval trumpets here, please), the Belphegor’s Prime. In itself, it’s a beautiful sequence of two series of 13 zeroes on each side of the number 666, bracketed at both ends by the number 1. Thus 1000000000000066600000000000001.
It’s a palindrome way before digital sequences of zeroes and ones became commonplace, but it still has a delicate balance in its configuration as no other prime, which as you probably know, is a number greater than one and divisible only by one and itself. That should be enough to awe any rational mind, well acquainted with these kind of hidden treasuries of the universe.
This being the 18th century, though, it’d also have been advisable not to tell any of that to the not quite enlightened members of the clergy. But someone did, and the resulting reaction was enough to fund a few temples and send countless souls to eternal damnation. Someone had to pay for those three sixes smacked in the middle of so many zeroes, and it had to be some demon worshiper.
So they called the much demoted and vilified number Belphegor, one of the seven Princes of Hell. Thanks to Cliff Pickover’s The Math Book, we also know that John Milton’s Paradise Lost and Victor Hugo’s The Toilers of the Sea have Belphegor as the seductive prince of vanity and sloth, who’d suggest great inventions to make the chosen ones rich.
Never mind that inventor and rich are not usually words found in the same sentence. Two more curiosities about Belphegor’s Prime, then, before we move on: according to 16th century demonologists, Belphegor’s power is strongest in April, so the fact that the day associated with him is in March may be part of some twisted humorous mind. Or devil worshiper.
And its symbol, which looks like an upside down Pi, was first spotted on the Voynich Manuscript, as a bird glyph of some kind. As with everything else about that book, if you want to know what it’s all about, we may not be the people to ask.
Not that we’ve advanced much farther than the age of sending people to eternal damnation, mind you. Only time will tell whether the contemporary version of The Plague is the spread of social networks, and we promise that the image will be our sole hyperbole for the evening, thank you very much.
We’re talking about the ominousness of online connections in contemporary life, of course, and their unfulfilled potential of boosting exchange and closeness among people. What we wound up having, instead, is another excuse not to connect at all, as the medium itself has replaced even the need for personal contact.

For evolutionary anthropologist Robin Dunbar, for example, the illusion of having an ever-expanding circle of friends is not just unattainable but utterly foreign to our evolution as primates. The Oxford University’s Institute of Cognitive and Evolutionary Anthropology director has a solid reason for that: brain size, which is related to the size of our social groups.
Thus, throughout the ages, research showed that humans and great apes form meaningful relationships along and in relation to determined social group structures. And even that our brain grew in size and we became more interconnected within a larger physical space than our ancestors, our current stage of evolution prevents us from being able to manage more than 150 relationships at a time.
Which is an approximation too, since the Dunbar Number is not a fixed number at all, but a concept. So no matter how much we obsess about the number of followers we may have on Tweeter, or FaceBook friends, we could only keep up with so many of them if we had handlers to do what we humanly can’t: keep in touch.
Which is exactly how celebrities and important people do, even though you may have flattered yourself when you realized that some TV personality started following you. They most likely did not; a flak found your name and, well, let’s not burst your bubble too much just yet. Besides, we’re sure you’ve already had your suspicions.
Dunbar’s also the author of How Many Friends Does One Person Need?, which is an apt title for the kind of work (and great service) he does for all of us. Because, seriously, how many of your dear ones you’d like to hold your forehead while you throw up in some filthy toilet in the middle of the night? Really. Actually, shouldn’t you be at home instead, checking your messages, and ‘unfriending’ people away?
The first time we’ve heard about the Voynich Manuscript was through Lawrence and Nancy Goldstone’s brilliant The Friar and the Cipher, purportedly about Roger Bacon and the manuscript. In reality, their work is an extensive, scholarly journey from the the Middle Ages through Elizabethan times and the Enlightenment Era to the 20th Century and WWII, touching the work of pretty much every celebrated code-breaker in the world along the way.
Centered on the genius of Bacon, giant even among giants such as Leonardo and Michelangelo, and tracing a parallel of his life with St. Thomas de Aquinas, one of the Catholic Church’s heroes, the book makes a pretty good case of Bacon as the author of the Voynich. As it goes, though, it wasn’t to be, for recent research proved that it may have been written after his time.
You may have read here about the manuscript’s exquisite and intricate patterns of drawings and writings, and about some of the greatest minds who either attempted and failed to decipher its meaning, or in some way had their names attached to its trajectory through the centuries.
But even if it’s eluded us for so long, the Voynich can still be studied as a document of the evolution, development and turbulent confluence of rational, scientific knowledge with the magical, fearful ardor of faith and religiosity.
Theories about its authorship and influence abound. Leonardo himself has been enlisted as a potential but unlikely candidate. Some see in the drawings, resembling treatises on medicinal herbs with astrological tinges, the proof that the author or authors were also interested in empirical experimentation. And for that, they were not above showing graphic depictions of human anatomy and sex.

That’s one of the reasons that many scholars believe that it may have been written in anagrams, to make it difficult its translation. And as such, it’s also not devoid of a certain mischief and playfulness. Perhaps. There’s no way of knowing, so far.
If the latest Carbon-14 dating proved to be correct, which points to the 15th Century as its origins, then some of these theories have at least a foot in credible reality. It was, after all, a time of great turmoil, what, with the Discovery Era, the new worlds, and, naturally, the urge for Catholicism to reaffirm and expand its realm of influence.
The mere existence of such a manuscript implies that mortal danger tracked its trajectory all along, as the Inquisition was about to get deep into the business of killing people, and heretic was a word with equivalent weight and meaning to what ‘terrorist’ has now.
As the expression ‘witch hunt’ acquired its most bloody-thirsty meaning, the period marked the decline of the Asian culture’s influence over Europe, and the switch to the more pragmatic slash and conquer hegemonic tactics of conquistadors.
The sword and the cross, regardless if held up by the British, the Spanish, the Portuguese, the French, the Dutch, or by the multinational divisions of Catholicism, proved an unbeatable alliance that swept the known world.
Last Friday, May 11, marked the one hundred year anniversary of the re-discovery and purchase of the Voynich Manuscript, by Wilfrid M. Voynich, and the event was celebrated at the same Villa Mondagone, near Frascatti, Italy, where it all happened.
That’s also when our feeble minds falter and we get too close of being burned at the stake for a much more consequential reason than any witch or wizard: speak about what we know little about. So before you light up the bonfires, let’s leave it at that.

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