Read Gödel, Escher, Bach: An Eternal Golden Braid Online

Authors: Douglas R. Hofstadter

Tags: #Computers, #Art, #Classical, #Symmetry, #Bach; Johann Sebastian, #Individual Artists, #Science, #Science & Technology, #Philosophy, #General, #Metamathematics, #Intelligence (AI) & Semantics, #G'odel; Kurt, #Music, #Logic, #Biography & Autobiography, #Mathematics, #Genres & Styles, #Artificial Intelligence, #Escher; M. C

Gödel, Escher, Bach: An Eternal Golden Braid (33 page)

BOOK: Gödel, Escher, Bach: An Eternal Golden Braid
5.28Mb size Format: txt, pdf, ePub
ads

FIGURE 39. The Rosetta Stone [courtesy of the British Museum.

out the same way. That is why the meaning is part of the text itself; it acts upon intelligence in a predictable way. Generally, we can say: meaning is part of an object to the extent that it acts upon intelligence in a predictable way.

In Figure 39 is shown the Rosetta stone, one of the most precious of all historic discoveries. It was the key to the decipherment of Egyptian hieroglyphics, for it contains parallel text in three ancient scripts: hieroglyphic demotic characters, and Greek. The inscription on this basalt stele was firs deciphered in 1821 by Jean Francois Champollion, the "father of Egyptology"; it is a decree of priests assembled at Memphis in favor of Ptolemy Epiphanes.

Three Layers of Any Message

In these examples of decipherment of out-of-context messages, we can separate out fairly clearly three levels of information: (1) the
frame
message; (2) the outer message; (3) the
inner
message. The one we are most familiar with is (3), the inner message; it is the message which is supposed to be transmitted: the emotional experiences in music, the phenotype in genetics, the royalty and rites of ancient civilizations in tablets, etc.

To understand the inner message is to have extracted the meaning intended by the sender..

The frame message is the message "I am a message; decode me if you can!"; and it is implicitly conveyed by the gross structural aspects of any information-bearer.

To understand the frame message is to recognize the need for a decoding-mechanism.

If the frame message is recognized as such, then attention is switched to level (2), the outer message. This is information, implicitly carried by symbol-patterns and structures in the message, which tells how to decode the inner message.

To understand the outer message is to build, or know how to build, the correct decoding mechanism for the inner message.

This outer level is perforce an implicit message, in the sense that the sender cannot ensure that it will be understood. It would be a vain effort to send instructions which tell how to decode the outer message, for they would have to be part of the inner message, which can only be understood once the decoding mechanism has been found. For this reason, the outer message is necessarily a set of triggers, rather than a message which can be revealed by a known decoder.

The formulation of these three "layers" is only a rather crude beginning at analyzing how meaning is contained in messages. There may be layers and layers of outer and inner messages, rather than just one of each. Think, for instance, of how intricately tangled are the inner and outer messages of the Rosetta stone. To decode a message fully, one would have to reconstruct the entire semantic structure which underlay its creation and thus to understand the sender in every deep way. Hence one could throw away the inner message, because if one truly understood all the finesses of the outer message, the inner message would be reconstructible.

The book
After Babel
, by George Steiner, is a long discussion of the interaction between inner and outer messages (though he never uses that terminology). The tone of his book is given by this quote:

We normally use a shorthand beneath which there lies a wealth of subconscious, deliberately concealed or declared associations so extensive and intricate that they probably equal the sum and uniqueness of our status as an individual person.'

Thoughts along the same lines are expressed by Leonard B. Meyer, in h book
Music, the
Arts, and Ideas:

The way of listening to a composition by Elliott Carter is radically different from the way of listening appropriate to a work by John Cage. Similarly, a novel by Beckett must in a significant sense be read differently from one by Bellow. A painting by Willem de Kooning and one by Andy Warhol require different perceptional-cognitive attitudes.'

Perhaps works of art are trying to convey their style more than an thing else. In that case, if you could ever plumb a style to its very bottom you could dispense with the creations in that style. "Style", "outer message "decoding technique"-all ways of expressing the same basic idea.

Schrodinger's Aperiodic Crystals

What makes us see a frame message in certain objects, but none in other; Why should an alien civilization suspect, if they intercept an errant record that a message lurks within? What would make a record any different from a meteorite? Clearly its geometric shape is the first clue that "something funny is going on". The next clue is that, on a more microscopic scale, consists of a very long aperiodic sequence of patterns, arranged in a spiral If we were to unwrap the spiral, we would have one huge linear sequence (around 2000 feet long) of minuscule symbols. This is not so different from a
DNA
molecule, whose symbols, drawn from a meager "alphabet" of four different chemical bases, are arrayed in a one-dimensional sequence, an then coiled up into a helix. Before Avery had established the connection between genes and
DNA
, the physicist Erwin Schrödinger predicted, o purely theoretical grounds, that genetic information would have to be stored in "aperiodic crystals", in his influential book
What Is Life
? In fact books themselves are aperiodic crystals contained inside neat geometric forms. These examples suggest that, where an aperiodic crystal is found "packaged" inside a very regular geometric structure, there may lurk a inner message. (I don't claim this is a complete characterization of frame messages; however, it is a fact that many common messages have frame messages of this description. See Figure 40 for some good examples.)

Languages for the Three Levels

The three levels are very clear in the case of a message found in a bottle washed up on a beach. The first level, the frame message, is found when one picks up the bottle and sees that it is sealed, and contains a dry piece c paper. Even without seeing writing, one recognizes this type of artifact an information-bearer, and at this point it would take an extraordinary almost inhuman-lack of curiosity, to drop the bottle and not look further.

'

Next, one opens the bottle and examines the marks on the paper. Perhaps, they are in Japanese; this can be discovered without any of the inner message being understood-it merely comes from a recognition of 1 characters. The outer message can be stated as an English sentence: "I in Japanese." Once this has been discovered, then one can proceed the inner message, which may be a call for help, a haiku poem, a lover’s lament ...

It would be of no use to include in the inner message a translation the sentence

"This message is in Japanese", since it would take someone who knew Japanese to read it. And before reading it, he would have recognize the fact that, as it is in Japanese, he can read it. You might try wriggle out of this by including translations of the statement

"This mess2 is in Japanese" into many different languages. That would help it practical sense, but in a theoretical sense the same difficulty is there. . English-speaking person still has to recognize the "Englishness" of the message; otherwise it does no good. Thus one cannot avoid the problem that one has to find out how to decipher the inner message from the outside the inner message itself may provide clues and confirmations, but those ; at best triggers acting upon the bottle finder (or upon the people whom enlists to help).

Similar kinds of problem confront the shortwave radio listener. First he has to decide whether the sounds he hears actually constitute a message or are just static. The sounds in themselves do not give the answer, not e% in the unlikely case that the inner message is in the listener's own native language, and is saying, "These sounds actually constitute a message a are not just static!" If the listener recognizes a frame message in the soup then he tries to identify the language the broadcast is in-and clearly, he is still on the outside; he accepts triggers from the radio, but they cam explicitly tell him the answer.

It is in the nature of outer messages that they are not conveyed in any
FIGURE 40. A collage of scripts. Uppermost on the left is an inscription in the un ciphered
boustrophedonic writing system from Easter Island, in which every second lin upside down. The
characters are chiseled on a wooden tablet, 4 inches by 35 inches. Mov clockwise, we encounter
vertically written Mongolian: above, present-day Mongolian, below, a document dating from
1314. Then we come to a poem in Bengali by Rabindran Tagore in the bottom righthand corner.

Next to it is a newspaper headline in Malayalam (II Kerala, southern India), above which is the
elegant curvilinear language Tamil (F Kerala). The smallest entry is part of a folk tale in
Buginese (Celebes Island, Indonesia). In center of the collage is a paragraph in the Thai
language, and above it a manuscript in Rn dating from the fourteenth century, containing a
sample of the provincial law of Scania (so Sweden). Finally, wedged in on the left is a section of
the laws of Hammurabi, written Assyrian cuneiform. As an outsider, I feel a deep sense of
mystery as I wonder how meanin cloaked in the strange curves and angles of each of these
beautiful aperiodic crystals. Info there is content. [From Ham Jensen, Sign, Symbol, and Script
(New York: G. Putnam's S. 1969), pp. 89 (cuneiform), 356 (Easter Island), 386, 417 (Mongolian),
552 (Runic); from Keno Katzner, The Languages of the World (New York: Funk & Wagnalls,
1975), pp. 190 (Bengali),

(Buginese); from I. A. Richards and Christine Gibson, English Through Pictures (New Y

Washington Square Press, 1960), pp. 73 (Tamil), 82 (Thai
).

explicit language. To find an explicit language in which to convey outer messages would not be a breakthrough-it would be a contradiction in terms! It is always the listener's burden to understand the outer message. Success lets him break through into the inside, at which point the ratio of triggers to explicit meanings shifts drastically towards the latter.

By comparison with the previous stages, understanding the inner message seems effortless. It is as if it just gets pumped in.

The "Jukebox" Theory of Meaning.

These examples may appear to be evidence for the viewpoint that no message has intrinsic meaning, for in order to understand any inner message, no matter how simple it is, one must first understand its frame message and its outer message, both of which are carried only by triggers (such as being written in the Japanese alphabet, or having spiraling grooves, etc.). It begins to seem, then, that one cannot get away from a

"jukebox" theory of meaning-the doctrine that no message contains inherent meaning, because, before any message can be understood, it has to be used as the input to some

"jukebox", which means that information contained in the "jukebox" must be added to the message before it acquires meaning.

This argument is very similar to the trap which the Tortoise caught Achilles in, in Lewis Carroll's Dialogue. There, the trap was the idea that before you can use any rule, you have to have a rule which tells you how to use that rule; in other words, there is an infinite hierarchy of levels of rules, which prevents any rule from ever getting used. Here, the trap is the idea that before you can understand any message, you have to have a message which tells you how to understand that message; in other words, there is an infinite hierarchy of levels of messages, which prevents any message from ever getting understood. However, we all know that these paradoxes are invalid, for rules do get used, and messages do get understood. How come?

BOOK: Gödel, Escher, Bach: An Eternal Golden Braid
5.28Mb size Format: txt, pdf, ePub
ads

Other books

Scarlet Dawn by Megan J. Parker
The Soulstoy Inheritance by Jane Washington
Descent by Charlotte McConaghy
Shadow Country by Peter Matthiessen
Vintage Attraction by Charles Blackstone


readsbookonline.com Copyright 2016 - 2024