Labyrinths of Reason (36 page)

—E
becomes
V. MESSAGE
becomes
OVXTZLH
.

OVXTZLH
is a much better encoding of
MESSAGE
than
NFTTBHF
is. When any one substitution cipher is used exclusively, clues remain that allow easy deciphering of any quantity of text. The entropy of the text can help identify the original language. From
NFTTBHF
, you know that the original word has a doubled letter in the middle and that the second and last letters are the same. Even on the basis of this single word, you might guess (correctly) that
F
stands for
E
, the commonest letter in English. Nothing in
OVXTZLH
is any help. The doubled
S
has become two different letters. Since a different, randomly selected substitution cipher
was used for each letter, it is clear that
OVXTZLH
could just as easily stand for
any
seven-letter word at all. By being completely ambiguous, the one-time pad system ensures that any attempt at decoding without a key is pointless.

The problem with the one-time pad system is keeping the sender and receiver supplied with keys. Keys cannot be sent with the message. If they were, anyone intercepting the message could decipher it. Hence the pad. Rudolf Abel, a Soviet agent arrested in New York in 1957, had a one-time pad that was a tablet the size of a postage stamp, each page covered with fine print. An actual pad must have hundreds of numbers or letters to the page to accommodate messages of practical length. Such problems restrict the use of the one-time pad to important messages, and ones that are not very long.

With the right key, a one-time pad system will transform any text into
iiiii
… However, you have to tailor the key to a preexisting message. That defeats the usual purpose of a cipher, which is to communicate unknown future messages. Given that the ciphertext is going to be iiiii … no matter what, the system cannot communicate anything new or unexpected. The ciphertext just tells how much of the message to read off.

A ciphertext of iiiii … has the minimum possible entropy, far less than any real language. Usually, a cipher has as much or more entropy than the plaintext. When the entropy is less—as in the Voynich manuscript, unless it was originally in Tahitian!—it means that part of the message information has been shunted into the ciphering system. The ciphertext is ambiguous. Deciphering it depends on information not in the ciphertext: a key or the ability of the original author to reconstruct the message from an equivocal ciphertext.

Suppose that the Voynich plaintext is in a European language using the Roman alphabet, and that each of the manuscript’s squiggles encodes exactly one letter in an unbreakable and unambiguous one-time pad scheme. Identify each of the Voynich symbols with a letter as Bennett did. Assume there are 26 distinct and meaningful symbols in all. With any particular “alphabetic” order for the symbols, there are 26 Caesarian ciphers encoding Roman letters into Voynich symbols.

We do not know the alphabetic order, if any, of the Voynich symbols. Nor do we know that the cipher system uses Caesarian
ciphers only. There are many other ways of matching up letters to symbols. For the sake of simplicity, though, assume that the alphabetic order is known and that only Caesarian ciphers figure in the cipher system.

Then a key would specify which of 26 Caesarian ciphers was used for each symbol in the manuscript. If you had an alleged key to the manuscript’s cipher, you could apply it to a few dozen symbols and see if the result was sensible words of some European language. If it was, you could apply it to the whole manuscript. If it produced a sensible message, the cipher would be solved.

We don’t have a key. It might still seem that we could solve the cipher by brute force. We could check every possible decipherment of the Voynich text.

That is doubly impossible. It would entail checking all 26 keys for the first letter, and all 26 keys for the second, and all 26 keys for the third … (This isn’t even the half of it, for it doesn’t take into account the number of possible alphabetic orders of the Voynich symbols and the possibility of non-Caesarian ciphers.) This is 26
ⁿ
, where
n
is the number of symbols in the sample of ciphertext. If a sample of 100 symbols is taken, the number of possible keys is 26
¹⁰⁰
. This comes to about 10
¹⁴¹
keys—way too many to check, even if you had all the time in the world.

Yes, yes, but one can nevertheless imagine the hyper-herculean task of checking 10
¹⁴¹
keys. It could be done in principle, however hopeless it might be in practice.
Still
the task is futile. Since we are checking every possible key, we are sure to come across a key that, applied in reverse, will transform the Voynich manuscript into
Gulliver’s Travels
. For instance, take the first letter in
Gulliver’s Travels
. One of the 26 Caesarian ciphers will transform that letter into the first symbol in the Voynich manuscript. Another Caesarian cipher will map the second letter into the second Voynich symbol, and so on. (There will be symbols left over at the end of the longer work.)

A different key will transform the Voynich manuscript into the Gettysburg Address. Other keys will decipher the manuscript into every possible text of an equal number of symbols. Even were it physically possible, an exhaustive search would be pointless because it would successively turn up every possible sensible message. All are equally inherent in the ciphertext.

How, then, does anyone ever decipher anything (and more to the point, convince themselves and others that a decipherment is the correct one)? Consider this:

It is a fact verifiable by experience that choosing keys at random
never
produces a sensible decipherment. The chances against it are too great. Testing a random key on the Voynich manuscript invariably produces only a nonsense string of letters.

Consequently, the chance of an arbitrary
wrong
cipher producing a sensible decipherment is astronomically small. A key that produces a sensible message from a cipher is virtually certain to be the correct one
unless
the decipherer tailored the key to produce a desired message.

A convincing demonstration of the correctness of a decipherment has four steps:

First, you specify the cipher system and its key. Here “key” can mean whatever minimum amount of information must be remembered in order to apply the cipher, whether it takes the form of a printed key or not.

Second, you reverse the cipher system, producing an alleged plaintext from the ciphertext.

Third, the resulting plaintext is a sensible message, not nonsense.

Fourth, the key can be specified concisely. Examples of concise descriptions of keys are: “Use Caesarian cipher ‘J’ throughout”; “The key is the block of letters on a slip of paper found among Roger Bacon’s effects”; “The key is the letters of the first page of the original edition of
Gulliver’s Travels.”

This fourth requirement is necessary to prevent decipherers from working backward from a hoped-for plaintext. The key must be “special.” It must be intrinsically simple, or it must have historic justification. Most of the possible cipher keys have never been explicitly conceived by the mind of man. The ciphers that have been used, or even conceived, are in a very select minority of all possible ciphers. The decipherer must provide reason to believe that the key existed before he started working on the cipher.

The simplest cipher is the one that leaves any plaintext unchanged. Next simplest are those in which the same letter-substitution scheme is used throughout. The cryptograms found in puzzle books, in Edgar Allan Poe’s “The Gold Bug,” or Arthur Conan
Doyle’s “The Adventure of the Dancing Men” are of this type. All such ciphers are in a very small minority, and a demonstration that a ciphertext may be converted to a sensible message via such a cipher is convincing evidence that the cipher was used and the message is genuine.

More difficult ciphers have a varying key that may be represented by a string of arbitrary letters (or numbers). If using the Gettysburg Address
as a key
converts a ciphertext into a sensible message, that is also a convincing demonstration that the message is genuine. (Keys taken from books or other texts are fairly common in real cryptography.) Although many, many keys will convert a given ciphertext to a sensible message, the chance of such a key being itself a sensible message is fantastically small.

This is not to say that the only valid complex keys are those that can be transliterated as literary passages. In a one-time pad, the key is random (else there would be no need for the pad). The random key on a one-time pad is special in a historical sense. Out of all the inconceivable number of possible keys, one was selected and printed on a pad. Finding a page from a one-time pad, and showing that it converts a ciphertext to a sensible message, is a convincing demonstration of the validity of the decipherment.

Where, then, is meaning: in the message, in the “key,” or in the minds of those who understand it? Few would dispute that meaning is ultimately in the mind. It is in the mind the way that color or sound is. The more subtle question is whether the objective counterpart of the meaning resides more in the message or in the language or cipher system.

The answer is that it varies. A cipher consisting solely of the repeated letter i is an example of a system in which all the meaning is in the key. More often the meaning is split between message and key. It is, however, very hard to think of a case where
all
the meaning is in the message and none in the key. Ideally, this would be the case with a perfectly transparent language whose meaning is obvious to all (like airport pictographs, Esperanto, or artificial languages proposed for radio communication with extraterrestrial beings). None of the attempts at this come very close to that goal.

Scientific theories are expected to make sense of the world much as cipher keys do. Some theories put a lot of information in the theory; others only refer to information in the world.

The first extreme, the counterpart of Poe’s iiiii … cipher, is exemplified by brains in vats. The brains-in-vats hypothesis requires an ad hoc assumption for everything. It rained yesterday because of a certain pattern of electrical stimulation. Roses are red because of a jolt of electricity; Gerald Ford became President because of another zap; moods, weather, animals, people, luck, and everything else are explained by stimulation. Brains in vats has no predictive power (compare the iiiii … cipher’s inability to cope with unknown future messages). If we are brains in vats, the next apple you see could just as easily fall up as down. Anything could happen; you never know what those evil geniuses will come up with next.

At the opposite extreme is a theory like Newton’s gravitation that points up an inherent regularity in the world. That apples don’t fall up is built into the world, not into a series of ad hoc assumptions. The theory is simple, and it has predictive power.

Here as always it is impossible to say that one theory is indubitably right and the other wrong. It boils down to convenience. It is easier to use and remember the simpler hypothesis.

O
F ALL THE MYSTERIES of the world, none is more puzzling than mind. Brain is a trifle in comparison. It is one thing to say that a mass of jelly, shaped by natural selection, can perform a wealth of complex functions. But where does consciousness come in?

Biology is well on the road to an understanding of how the brain works. Some say an understanding of consciousness is as remote as ever. The question of mind, long a favorite of philosophers, has lately become almost topical with advances in neurology, cognitive science, and artificial intelligence. The current state of thinking on mind is sharply illuminated by a set of intriguing paradoxes.

The prisoner of the previous chapter’s binary Plato’s cave confronted sensory experience in the most abstract form. The irony is that our brains are such prisoners; the cave is the skull. It seems as if it would be impossible for anyone to duplicate how the brain deals with sensory information. This is the starting point for the thought experiments of this chapter.