Read Labyrinths of Reason Online
Authors: William Poundstone
Labyrinths of Reason (33 page)
There was more. If any letter pair contained one of the letters in the word
conmuta
, it was subjected to a further coding process that Newbold called “commutation” but never fully explained. Next the whole message was scrambled so that it was an anagram (!) of the prior stage.
Then
came the topper: The visible symbols of the manuscript were just a cover, Newbold said. They didn’t mean anything. Newbold believed that if you examined the symbols with a magnifying glass, you would find them to be made out of about ten tiny separate strokes each. He supposed that Bacon had used his newly invented microscope to create these tiny symbols. These tiny strokes were symbols of ancient Greek shorthand. The real message was in this microdot Greek shorthand. To decode the manuscript, then, you had to transliterate these microscopic symbols into letters, and
then
reverse the Byzantine process of anagramming, commutation, and assigning letter pairs.
Newbold’s microscopic symbols were as fleeting as the canals of Mars—more so, for Newbold was the only one who saw them. To the extent that they had any reality outside Newbold’s head, they were the irregularities of a coarse ink on rough paper.
Had the manuscript’s author used Newbold’s method, it would have been maddening indeed to encode anything. And once encoded, there would be no reliable way of decoding it. What you got could always be an
anagram
of letters that
sound like
the real message, etc., etc., etc.
Newbold’s comments on his microscopic symbols are a poignant monument to self-deception. He wrote:
But the difficulty of reading the cipher characters is very great indeed. When first the letters were written they were, I think, distinctly visible under the proper degree of magnification, but after the lapse of more than six hundred years the writing on many pages has been so injured by fading, scaling, and abrasion, that the characters can scarcely be seen at all. In the second place, much depends upon the degree of magnification which was used by Bacon at the time of writing. The line which to the naked eye seems quite simple, when magnified three or four or five diameters is frequently seen to be composed of individual elements, and if it be magnified still further some of the elements will be resolved into still other elements, many of which may be taken as characters…. Another very great difficulty is that offered by the elusiveness of the characters themselves. The differences between them are very slight; when they are written under a microscope, even Bacon’s own hand often gives to the differences but faint and ambiguous expression. Furthermore the characters are so interwoven one with another that it is often all but impossible to disentangle them…. I frequently, for example, find it impossible to read the same text twice in exactly the same way.
Stranger yet is American physician Leo Levitov’s recent alleged solution of the Voynich manuscript. In 1987 Levitov claimed that the manuscript is in an unknown European language used by a cult of Isis worshipers around the twelfth century. Levitov believed that all other traces of the cult had been destroyed by the Spanish Inquisition. Levitov offers the most gruesome exegesis of the illustrations yet. The cult believed in euthanasia by opening a vein in a warm bathtub, and the pictures of enigmatic bathers show devices for draining off blood!
Levitov’s peculiar language consists of twenty-four verbs and four pronouns of mutable spelling. His chaotic and uniformly morbid translations (“ones treat the dying each the man lying deathly ill the one person who aches Isis each that dies treats the person,” begins folio 1) do not inspire confidence.
There is a certain pathos in these “decipherments.” We all interpret language and even experience in a way that is both complex and difficult to describe. It is not that Newbold and Levitov are undeniably wrong. It is at least
conceivable
that the supposed authors wrote just what they thought and encoded it just as they said.
Most rational people do not ponder Newbold’s and Levitov’s cases long before rejecting them. To say exactly
why
we reject them is something else. Susan Sontag defined intelligence as a “taste in ideas.” It is difficult to codify that taste.
The relationship between cryptographic problems and the experimental method has often been remarked upon. Cryptographer John Chadwick wrote:
Cryptography is a science of deduction and controlled experiment; hypotheses are formed, tested and often discarded. But the residue which passes the test grows until finally there comes a point when the experimenter feels solid ground beneath his feet: his hypotheses cohere, and fragments of sense emerge from their camouflage. The code “breaks.” Perhaps this is best defined as the point when the likely leads appear faster than they can be followed up. It is like the initiation of a chain-reaction in atomic physics; once the critical threshold is passed, the reaction propagates itself.
For the sake of argument, suppose that the Voynich manuscript was written by a clever con man and is completely without meaning. There
does
seem to be a simple way of telling whether it’s gibberish, even without deciphering it.
The work of cryptographers depends on the statistics of language. Not all letters are equally common. With many types of ciphers, this means that the visible symbols have different frequencies.
The commonest letter in English is
e
. It is not everywhere the commonest letter (it’s
o
in Russian), but every natural language favors some letters over others.
You might think a forger picking meaningless symbols at random would fail to favor some over others. Not necessarily. Try writing a “random” string of letters or numbers. It is very difficult not to favor certain letters or numbers unconsciously. True randomness is all but impossible for the human mind to create. A forger might happen to favor some symbols in a way that would approximate the letter frequencies of his native language or some other language.
That does not mean that the statistical approach is useless. There are more subtle considerations. In a real letter-substitution cipher, certain pairs of letters ought to be more common than others. For instance,
th
and
is
are quite common in English, and
q
is almost certainly followed by a
u
.
It works the other way too. Some pairs of letters are relatively uncommon. The letters
c
and
d
are common, but you rarely see
cd
in English text. The same principles apply to triplets of letters or larger groups. All the vowels are common, and many pairs of vowels
are common, but most instances of three consecutive vowels are rare or nonexistent.
That this does provide a means of distinguishing a real cipher from nonsense is demonstrated by the false cipher in Balzac’s
The Physiology of Marriage
. Published in 1829,
The Physiology of Marriage
is a satirical handbook on marriage and adultery. Inserted after the words “L’auteur pense que la Bruyère s’est trompé. En effet, …” is a two-page cipher that has never been deciphered. Many readers tried to decipher it, goaded by the suspicion that the passage must have been so scandalous that the publisher dared not print it as written. Balzac dropped hints about it for years after the book was published.
The cipher contains uppercase and lowercase letters, many with accents and some upside down. There are numerals and punctuation marks, but only a few blank spaces. It was significant, some thought, that the cipher ends with “end” and contains the exclamation “sin!” (both in English).
The statistics of the Balzac cipher are wildly at variance with French or any other European language. In this case there is little doubt that the symbols were picked at random, probably by the typesetter. Some later editions of the book even have different “ciphers.”
The Voynich manuscript has been subjected to similar scrutiny. Unlike the Balzac pseudo-cipher, the Voynich symbols have statistical patterns much like real languages. There are pairs of symbols that often go together
(AM, AN, QA
, and
QC
, according to Bennett’s labels). There are common symbols that are rarely combined. In fact, these patterns are even more pronounced than in English. The Voynich text is less “random” than any known European language.
A statistic called “entropy” measures the degree to which letters or other symbols form recurring patterns in the text. By a weird coincidence, the entropy per symbol of the Voynich manuscript is about that of Polynesian languages. None of the many suppositions about the manuscript had it enciphered from Hawaiian or Tahitian.
The Polynesian languages are known for their economy of letters. The Hawaiian alphabet has just twelve, plus a heavily used apostrophe. The Voynich manuscript uses twenty-one common symbols plus a few rare ones. The manuscript’s entropy suggests that its source text was much more ordered than most natural languages.
That is strong evidence that the Voynich manuscript is a real
cipher, not gibberish. It is hard to believe that a forger was sophisticated enough to simulate the statistics of language.
It also confirms that the text is not a simple encipherment of any Éuropean tongue. The manuscript seems to be in a “language” with fewer common letters than European languages. Perhaps the author lumped similar-sounding letters together, somewhat as Newbold conjectured. Or the plaintext could be an Esperanto-like language of the author’s invention. The bulk of contemporary scholarly opinion thinks the manuscript was written after Columbus’s return (not by Bacon, obviously).
Many of the questions raised in cryptography are far from mundane. The way we interpret experience is much like the unraveling of a cipher. Is our mental picture of the world inherent in the stream of sensory experience, or is it largely in a key, in a way our brains translate this experience?
A classic forebear of the thought experiments in this book is the Parable of the Cave in Plato’s
Republic
. Book VII begins with this dialogue between Socrates (the first speaker) and Glaucon:
And now, I said, let me show in a figure how far our nature is enlightened or unenlightened: — Behold! human beings living in an underground den, which has a mouth open towards the light and reaching all along the den; here they have been from their childhood, and have their legs and necks chained so that they cannot move, and can only see before them, being prevented by the chains from turning round their heads. Above and behind them a fire is blazing at a distance, and between the fire and the prisoners there is a raised way; and you will see, if you look, a low wall built along the way, like the screen which marionette players have in front of them, over which they show the puppets.
I see.
And do you see, I said, men passing along the wall carrying all sorts of vessels, and statues and figures of animals made of wood and stone and various materials, which appear over the wall? Some of them are talking, others silent.
You have shown me a strange image, and they are strange prisoners.
Like ourselves, I replied; and they see only their own shadows, or the shadows of one another, which the fire throws on the opposite wall of the cave?
True, he said; how could they see anything but the shadows if they were never allowed to move their heads?
And of the objects which are being carried in like manner they would only see the shadows?
Yes, he said.
And if they were able to converse with one another, would they not suppose they were naming what was actually before them?
Very true.
And suppose further that the prison had an echo which came from the other side, would they not be sure to fancy when one of the passers-by spoke that the voice which they heard came from the passing shadow?
No question, he replied.
To them, I said, the truth would be literally nothing but the shadows of the images.
The relationship between our mental images of the world and the external reality continues to fascinate and vex. Several modern paradoxes twist this correspondence to the breaking point.
Many technological versions of Plato’s scenario are possible. Imagine a cave-bound prisoner who watches the outside world on a closed-circuit TV screen. As in Plato’s allegory, this prisoner has been chained to the cave wall from birth. A video camera outside the cave constantly transmits pictures to the prisoner’s TV. Furthermore, the prisoner’s head is in a swiveling harness. As he moves his head to the right, the TV swings to the right on silent, perfectly balanced bearings so that the screen always fills the visual field. Outside, the camera rotates a like angle so that the field of view on the screen changes in what must seem a perfectly natural fashion to the prisoner.
With this setup, the cave dweller’s captors could play even stranger tricks on his perception. What if, unknown to the prisoner, the TV camera forever shoots into a mirror at a 45-degree angle? Everything the prisoner saw would be reversed right to left. The cave dweller would be unaware that he was seeing a mirror image of reality. If he learned to read books placed in front of the camera, he would learn to read backwards.
The TV image could be permanently upside down. Again, the cave dweller would think the way he saw the world was the right way. The fact that his TV image was upside down would be no more relevant than the fact that the images on our retinas are physically upside down. As long as the prisoner spent his whole life
looking at an upside down image (a right-side-up retinal image) he could no more be aware of the reversal than a fish is aware of water.
1
The cave dweller’s severest limitation (both in these variants and in Plato’s original story) would be the lack of feedback. The cave dweller could not push something and watch it move in response. He could not observe any of the thousands of other ways that one’s will may modify the environment.