Labyrinths of Reason (35 page)

There are probably many Earth-sized planets or moons with the right range of temperatures for ammonia to be liquid. Unlike the other compounds mentioned above, ammonia is common (Jupiter has ammonia clouds) and might well form lakes, oceans, and rivers. Ammonia is a polar compound like water, meaning that it can dissolve a wide range of substances. This quality seems essential for any conceivable biochemistry.

That said, ammonia could not be Putnam’s XYZ—not if Twin Earth is really all that similar to Earth. Look at a few minor points: What would Twin Earthers clean their windows with? They couldn’t use just NH
₃
, because that’s their “water,” and if Twin Earth is so similar to Earth it ought to have a product with the trade name Windex that contains something other than “water.” At the temperatures at which ammonia is liquid, mercury is solid. There could be no mercury thermometers or barometers; no dental fillings compounded with mercury. They couldn’t call some other liquid metal “mercury” because
all
metals are solid at that temperature. Of course, this is the least of it. You don’t have to follow any such train of thought long to see that there would be differences by the thousands. A biochemistry based on ammonia would probably preclude anything similar to the human race evolving (even if we admit the possibility of intelligent life based on ammonia).

Others seize on Putnam’s figure of speech (“meanings ain’t in the head”). The human body is mostly water. Not only do we say and think “water,” but there is water in our head while we do it. If Twin Earth indeed has an XYZ-based chemistry, there would be XYZ “water” in the head of every Twin Earther. The meaning
is
in the head after all!

Although some disagree, I do not think either of the above objections substantially hurts Putnam’s argument. Putnam’s article gave some less dramatic examples that illustrate the issue just as well. He asked, what if the “aluminum” pans on Twin Earth were actually made of molybdenum, and “molybdenum” was really aluminum?

To a chemist, this example is not as compelling as it might be, for molybdenum is much, much heavier than aluminum and different in other important ways too. There are, however, elements with very similar chemical and physical properties. Many of the rare earth (rare twin earth?) elements are indistinguishable except by fairly sophisticated chemical assay. Moreover, they play no role in
human nutrition. You could imagine, if necessary, a human or Twin Earther brain that contains not a speck of either element.

None of the rare earth elements are common enough to be familiar to nonchemists. A better-known case of near-twin elements is nickel and cobalt. Nickel and cobalt are indistinguishable in appearance and have almost exactly the same density and melting point. Both are among the few metals that can be magnetized, and they have similar chemical properties.

Suppose, then, that what they call “nickel” on Twin Earth is cobalt, and vice versa. The Twin Earth countries called “Canada” and “the United States of America” issue coins called “nickels.” They’re called that because they contain the metal “nickel,” which is to say, cobalt. Twin Earth nickels nonetheless look identical to our nickels. Neither nickel nor cobalt plays much of a role in human nutrition, so astronauts on Twin Earth would not develop a deficiency of one or the other. It might well take some time for anyone to notice the difference.

Eventually, an astronaut with training in chemistry might look at a periodic table chart on Twin Earth and note that the symbols “Ni” and “Co” were seemingly swapped (though I imagine that someone who got good grades in college chemistry classes could easily fail to notice the difference too). Another tip-off: In everyday speech on Earth, the word “cobalt” more often means a shade of blue rather than the element. Cobalt blue, an artist’s pigment, is made from cobalt oxide. There would be no cobalt blue on Twin Earth. That particular vivid, slightly greenish blue pigment would have to be called “nickel blue.”

Putnam’s thought experiment demonstrates that all experience is ambiguous. Both Oscars had identical experiences with water. The XYZ water may even taste the same to the Twin Earth Oscar as H
₂
O water does to the Earth Oscar. The very sequence of firings of the neurons in both Oscars’ brains could be identical, yet there is more than one external reality compatible with them.

Let’s suppose that another minor difference between Earth and Twin Earth is that Twin Earth has an extra continent called Atlantis. Atlantis has its own language, which has no linguistic affinities with the other Twin Earth languages (which, aside from a few problem words like “water” and “molybdenum,” are identical with Earth languages).

An astronaut from Earth visits a library in Atlantis with an interpreter who speaks both English and Atlantean. The astronaut is surprised to find on the shelves a copy of
Gulliver’s Travels
by Jonathan Swift. At least, that’s what it seems to be. The cover bears those words, in English, in the Roman alphabet. Flipping through the book, the astronaut sees that it tells the familiar Swift satire in English. Another case of parallel evolution!

The astronaut comments to the interpreter that we have the same book by the same author on Earth. “Really?” says the interpreter. “It’s based on a true story, you know.”

“Now don’t tell me there’s really a place called Lilliput on Twin Earth!”

“What? Oh! No—the book you’re holding is an Atlantean copy of a play,
Henry VI
, by an author called William Shakespeare. This confuses people all the time. When
Henry VI
is translated into the Atlantean language, it looks,
superficially
, like
Gulliver’s Travels
in English.”

It further turns out that the real
Gulliver’s Travels
in Atlantean looks just like
The Grapes of Wrath
in English, and
The Grapes of Wrath
in Atlantean looks like the 1982 Tallahassee phone book. According to the interpreter, an English speaker and an Atlantean speaker can read the same book, and for one it will be
1001
Jokes for Toastmasters
and for the other a commentary on the Koran. Hence the Twin Earth saying: “Meanings just ain’t in the book.”

Is the interpreter pulling the astronaut’s leg?

It is, of course, extremely unlikely that two languages would happen to bear the relationship described. The question is whether it is at all possible. All the books mentioned, except possibly the phone book, repeat many common words like “the,” “of,” and “a.” It could be, for example, that “the” in English translates into “of” in Atlantean. Maybe every word in Atlantean is spelled the same as a (different) English word. Then a translation from English into Atlantean would indeed produce a jumble of “English” words. But they certainly wouldn’t form meaningful sentences, and in any case, the pattern of repeated words in
Gulliver’s Travels
is not the same as in
Henry VI
. A translation of
Henry VI
from English to any language could not produce
Gulliver’s Travels
.

Not if the translation is word for word, anyway. But it is far from clear that the apparent words in Atlantean text
are
words. It could be that the space between “words” is really a letter in the Atlantean alphabet. And it could be that some “letter” is actually a null character inserted to separate words.

More to the point, most translation is not word for word. In some cases (as in English to German) that is impossible because of a different word order in sentences. There may be languages so alien to English that is necessary to translate a paragraph or more of the text at a time. It is then conceivable (if fantastically unlikely) that
any
book could be any other book in some alien language.

Cryptographic systems have yet more freedom than languages. To take an extreme example, it is possible that the Voynich manuscript encodes the text of the Gettysburg Address. How? One way is the following cryptographic system: “If you want to encode the text of the Gettysburg Address, make this sequence of squiggles: (insert Voynich manuscript here). If you want to encode anything else, just write it in Pig Latin.” You can’t
prove
this wasn’t the enciphering system used to create the Voynich manuscript.

Edgar Allan Poe, an amateur cryptographer, once ran a magazine competition in which readers were invited to send in ciphers to be deciphered. In a follow-up article on cryptography, he mentioned the possibility of finding this string of letters in a cipher:
iiiiiiiiil
How would you decipher that, knowing that no word of English has that many repeated letters?

A string of ten i’s is possible; it just couldn’t arise in a simple cipher where one letter stands for a different letter throughout. You could even have a cipher in which the entire message was an unbroken string of the same letter.

For one thing, it could be a totally ambiguous cipher in which the letter i stands for all 26 letters and the encipherer relies on his ability to reconstruct the plaintext later. Or it could be a cipher in which a different letter-substitution rule is used for each letter of the plaintext.

In such a cipher all meaning has been purged from the ciphertext itself. You can demonstrate this by imagining that someone finds a cipher manuscript filled with i’s and nothing else. The finder claims that it can be deciphered into the text of the Gettysburg Address. This claim would be ridiculous. You could just as well claim that it meant anything else. The “meaning,” if any, evidently resides in the cipher system or in the head of whoever wrote the plaintext. Since there is no meaning in the ciphertext, it is an unbreakable cipher.

Most familiar “codes” are really ciphers. The Morse “code” is a cipher; so are most “codes” of military importance. In a true code,
symbols stand for ideas. The no-smoking glyph of a cigarette in a red circle with a slash through it is an example; so are the dozens of other international symbols seen in airports and other public places. A code attaches meaning to individual symbols.

It is difficult to express oneself in code. A code has symbols only for the common words and messages that have been anticipated by the designer of the code. Codes are awkward, often useless, in communicating the unexpected. For that reason the important military, espionage, and diplomatic “codes” are ciphers.

In a cipher, symbols stand for letters. A cipher lets you compose your message in plain English (or plain anything) and then convert it into symbols. The symbols are decoded by the recipient to recover the precise original message.

A cipher replaces one letter or other typographic symbol with another. Some rules are simple; some are more complex. Any letter-for-letter substitution can be represented by writing the alphabet (which here will mean all permissible symbols, including punctuation and numerals, if used in the cipher) in conventional order, and below it, the letters that are substituted. One simple substitution scheme is:

A
becomes
B, B
becomes
C, C
becomes
D
, and so on. All the letters are encoded by their successors in a circular alphabet. The word
MESSAGE
becomes
NFTTBHF
. The process is easily reversed by the message’s recipient.

Ciphers using this type of substitution throughout are called Caesarian, after their use by the Roman emperors. Augustus Caesar used the cipher above; Julius Caesar used the similar one in which plaintext
A
is replaced by
D; B
by
E
, etc.

There are 26 Caesarian ciphers. The bottom row of letters could have been shifted two letters, three letters, etc. (The 26th “cipher” merely replaces each letter with itself.) Each Caesarian cipher can be easily designated by a number or letter. You might designate the cipher by the ciphertext equivalent of the plaintext letter
A
. Then Augustus Caesar’s cipher is cipher “B,” and Julius Caesar’s is cipher “D.”

Caesarian ciphers are readily solved.
E
, for instance, might always be encoded as
U
. Then, since
E
is the commonest letter in many languages,
U
is likely to be the commonest letter in the
ciphertext. That’s a dead giveaway. A decipherer can identify the few most common letters, use them to recognize common short words, and quickly recover the message.

Cryptography has come a long way since the days of the Caesars. No nation today would use such a transparent cipher. However, simple Caesarian ciphers can be used to construct an unbreakable cipher, one that is used by modern superpowers.

The trick is to vary the Caesarian cipher from letter to letter. You use one of the 26 Caesarian ciphers for the first letter, another for the second, still another for the third, etc.

On the one hand, this complicates things enormously. You need a “key” telling which Caesarian cipher to use with which letter. The key must be at least as long as the message. The advantage is that the cipher is quite secure. Any letter of the ciphertext can encode anything at all. With a certain key, the Gettysburg Address would be encoded as a long string of i’s. With another key, it would be encoded as part of
Gulliver’s Travels
. With another key (most possible keys, in fact), it would be the expected “random” mix of letters.

This type of cipher is the “one-time pad.” The key is printed on a paper tablet. Each leaf of the pad is a key to be used once and then destroyed. The keys tell (for instance) which Caesarian ciphers to use with successive letters of the message. When the Caesarian ciphers are designated with letters as above, the keys look like random blocks of letters.

Use Caesarian ciphers “C,” “R,” “F,” “B,” “Z,” “F,” and “D” to encode the letters of the word
MESSAGE
. In cipher “C,”
M
becomes
O
. In cipher “R,” which looks like this—