The Information (26 page)

“According to which,” wrote Wilkins, “these words,
I am betrayed
, may be thus described:
Bd aacb abaedddbaaecaead
.” So even a small symbol set could be arranged to express any message at all. However, with a small symbol set, a given message requires a longer string of characters—“more Labour and Time,” he wrote. Wilkins did not explain that 25 = 5
²
, nor that three symbols taken in threes (aaa, aab, aac,…) produce twenty-seven possibilities because 3
³
= 27. But he clearly understood the underlying mathematics. His last example was a binary code, awkward though this was to express in words:

Two symbols. In groups of five. “Yield thirty two Differences.”

That word,
differences
, must have struck Wilkins’s readers (few though they were) as an odd choice. But it was deliberate and pregnant with meaning. Wilkins was reaching for a conception of information in its purest, most general form. Writing was only a special case: “For in the general we must note, That
whatever is capable of a competent Difference, perceptible to any Sense, may be a sufficient Means whereby to express the Cogitations
.”
^♦
A difference could be “two Bells of different Notes”; or “any Object of Sight, whether Flame, Smoak, &c.”; or trumpets, cannons, or drums. Any difference meant a binary choice. Any binary choice began the expressing of cogitations. Here, in this arcane and anonymous treatise of 1641, the essential idea of information theory poked to the surface of human thought, saw its shadow, and disappeared again for four hundred years.

The contribution of the dilettantes is what the historian of cryptography David Kahn calls the excited era triggered by the advent of the telegraph.
^♦
A new public interest in ciphers arose just as the subject bloomed in certain intellectual circles. Ancient methods of secret writing appealed to an odd assortment of people, puzzle makers and game players, mathematically
or poetically inclined. They analyzed ancient methods of secret writing and invented new ones. Theorists debated who should prevail, the best code maker or the best code breaker. The great American popularizer of cryptography was Edgar Allan Poe. In his fantastic tales and magazine essays he publicized the ancient art and boasted of his own skill as a practitioner. “We can scarcely imagine a time when there did not exist a necessity, or at least a desire,”
^♦
he wrote in
Graham’s Magazine
in 1841, “of transmitting information from one individual to another, in such manner as to elude general comprehension.” For Poe, code making was more than just a historical or technical enthusiasm; it was an obsession. It reflected his sense of how we communicate our selves to the world. Code makers and writers are trafficking in the same goods. “The soul is a cypher, in the sense of a cryptograph; and the shorter a cryptograph is, the more difficulty there is in comprehension,”
^♦
he wrote. Secrecy was in Poe’s nature; he preferred mystery to transparency.

“Secret intercommunication must have existed almost contemporaneously with the invention of letters,” he declared. This was for Poe a bridge between science and the occult, between the rational mind and the savant.
^♦
To analyze cryptography—“a serious thing, as the means of imparting information”—required a special form of mental power, a penetrating mind, and might well be taught in academies. He said again and again that “a peculiar mental action is called into play.” He published as challenges to his readers a series of substitution ciphers.

Along with Poe, Jules Verne and Honoré de Balzac also introduced ciphers into their fiction. In 1868, Lewis Carroll had a card printed on two sides with what he called “The Telegraph-Cipher,” which employed a “key-alphabet” and a “message-alphabet,”
^♦
to be transposed according to a secret word agreed on by the correspondents and carried in their memories. But the most advanced cryptanalyst in Victorian England was Charles Babbage. The process of substituting symbols, crossing levels of meaning, lay near the heart of so many issues. And he enjoyed the challenge. “One of the most singular characteristics of the art of
deciphering,” he asserted, “is the strong conviction possessed by every person, even moderately acquainted with it, that he is able to construct a cipher which nobody else can decipher. I have also observed that the cleverer the person, the more intimate is his conviction.”
^♦
He believed that himself, at first, but later switched to the side of the code breakers. He planned an authoritative work to be known as
The Philosophy of Decyphering
but never managed to complete it. He did solve, among others, a polyalphabetic cipher known as the Vigenère,
le chiffre indéchiffrable
, thought to be the most secure in Europe.
^♦
As in his other work, he applied algebraic methods, expressing cryptanalysis in the form of equations. Even so, he remained a dilettante and knew it.

When Babbage attacked cryptography with a calculus, he was employing the same tools he had explored more conventionally in their home, mathematics, and less conventionally in the realm of machinery, where he created a symbolism for the moving parts of gears and levers and switches. Dionysius Lardner had said of the mechanical notation, “The various parts of the machinery being once expressed on paper by proper symbols, the enquirer dismisses altogether from his thoughts the mechanism itself and attends only to the symbols … an almost metaphysical system of abstract signs, by which the motion of the hand performs the office of the mind.”
^♦
Two younger Englishmen, Augustus De Morgan and George Boole, turned the same methodology to work on an even more abstract material: the propositions of logic. De Morgan was Babbage’s friend and Ada Byron’s tutor and a professor at University College, London. Boole was the son of a Lincolnshire cobbler and a lady’s maid and became, by the 1840s, a professor at Queen’s College, Cork. In 1847 they published separately and simultaneously books that amounted to the greatest milestone in the development of logic since Aristotle: Boole’s
Mathematical Analysis of Logic, Being an Essay Towards a Calculus of Deductive Reasoning
, and De Morgan’s
Formal Logic: or, the Calculus of Inference, Necessary and Probable
. The subject, esoteric as it was, had stagnated for centuries.

De Morgan knew more about the scholastic traditions of the subject, but Boole was the more original and free-thinking mathematician. By post, for years, they exchanged ideas about converting language, or truth, into algebraic symbols.
X
could mean “cow” and
Y
“horse.” That might be one cow, or a member of the set of all cows. (The same?) In the algebraic fashion the symbols were to be manipulated.
XY
could be “name of everything which is
both X
and
Y
” while
X,Y
stood in for “name of everything which is either
X
or
Y
.”
^♦
Simple enough—but language is not simple and complications reared up. “Now some
Z
s are not
X
s, the
ZY
s,”
^♦
wrote De Morgan at one point. “But they are
nonexistent
. You may say that
nonexistents
are not
X
s. A nonexistent horse is not even a horse; and (
a fortiori
?) not a cow.”

He added wistfully, “I do not despair of seeing you give meaning to this new kind of negative quantity.” He did not post this and he did not throw it away.

Boole thought of his system as a mathematics without numbers. “It is simply a fact,”
^♦
he wrote, “that the ultimate laws of logic—those alone on which it is possible to construct a science of logic—are mathematical in their form and expression, although not belonging to the mathematics of quantity.” The only numbers allowed, he proposed, were zero and one. It was all or nothing: “The respective interpretation of the symbols 0 and 1 in the system of logic are
Nothing
and
Universe
.”
^♦
Until now logic had belonged to philosophy. Boole was claiming possession on behalf of mathematics. In doing so, he devised a new form of encoding. Its code book paired two types of symbolism, each abstracted far from the world of things. On one side was a set of characters drawn from the formalism of mathematics:
p
’s and
q
’s, +’s and –’s, braces and brackets. On the other were operations, propositions, relations ordinarily expressed in the fuzzy and mutable speech of everyday life: words about truth and falsity, membership in classes, premises and conclusions. There were “particles”:
if
,
either
,
or
. These were the elements of Boole’s credo:

The encoding, the conversion from one modality to the other, served a purpose. In the case of Morse code, the purpose was to turn everyday language into a form suitable for near-instantaneous transmission across miles of copper wire. In the case of symbolic logic, the new form was suitable for manipulation by a calculus. The symbols were like little capsules, protecting their delicate cargo from the wind and fog of everyday communication. How much safer to write:

1 −
x
=
y
(1 −
z
) +
z
(1 −
y
) + (1 −
y
)(1 −
z
)

than the real-language proposition for which, in a typical Boolean example, it stood:

The safety came in no small part from draining the words of meaning. Signs and symbols were not just placeholders; they were operators, like the gears and levers in a machine. Language, after all, is an instrument.

It was seen distinctly now as an instrument with two separate functions: expression and thought. Thinking came first, or so people assumed. To Boole, logic
was
thought—polished and purified. He chose
The Laws
of Thought
as the title for his 1854 masterwork. Not coincidentally, the telegraphists also felt they were generating insight into messaging within the brain. “A word is a tool for thinking, before the thinker uses it as a signal for communicating his thought,”
^♦
asserted an essayist in
Harper’s New Monthly Magazine
in 1873.

Boole’s influence was subtle and slow. He corresponded only briefly with Babbage; they never met. One of his champions was Lewis Carroll, who, at the very end of his life, a quarter century after
Alice in Wonderland
, wrote two volumes of instruction, puzzles, diagrams, and exercises in symbolic logic. Although his symbolism was impeccable, his syllogisms ran toward whimsy: