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 (32 page)

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Thus, cracking the Genetic Code is comparable to figuring out the phonetic values of the letters of a foreign alphabet, without figuring out the grammar of the language or the meanings of any of its words. The cracking of the Genetic Code was a vital step on the way to extracting the meaning of
DNA
strands, but it was only the first on a long path which is yet to be trodden.)

Jukeboxes and Triggers

The genetic meaning contained in DNA is one of the best possible examples of implicit meaning. In order to convert genotype into phenotype, a set of mechanisms far more complex than the genotype must operate on the genotype. The various parts of the genotype serve as
triggers
for those mechanisms. A jukebox-the ordinary type, not the Crab type!-provides a useful analogy here: a pair of buttons specifies a very complex action to be taken by the mechanism, so that the pair of buttons could well be described as "triggering" the song which is played. In the process which converts genotype into phenotype, cellular jukeboxes-if you will pardon the notion!-accept "button-pushings"

from short excerpts from a long strand of
DNA
, and the "songs" which they play are often prime ingredients in the creation of further "jukeboxes". It is as if the output of real jukeboxes, instead of being love ballads, were songs whose lyrics told how to build more complex jukeboxes ... Portions of the
DNA
trigger the manufacture of proteins; those proteins trigger hundreds of new reactions; they in turn trigger the replicating-operation which, in several steps, copies the
DNA
-and on and on ... This gives a sense of how recursive the whole process is. The final result of these many-triggered triggerings is the phenotype-the individual. And one says that the phenotype is the revelation-the "pulling-out"-of the information that was present in the
DNA
to start with, latently. (The term

"revelation" in this context is due to

Jacques Monod, one of the deepest and most original of twentieth-century molecular biologists.)

Now no one would say that a song coming out of the loudspeaker of jukebox constitutes a "revelation" of information inherent in the pair buttons which were pressed, for the pair of buttons seem to be mere
triggers
, whose purpose is to activate information-bearing portions of the jukebox mechanism. On the other hand, it seems perfectly reasonable to call t extraction of music from a record a "revelation" of information inherent the record, for several reasons:

(1) the music does not seem to be concealed in the mechanism of the record player; (2) it is possible to match pieces of the input (the record) with pieces of the output (the music) to an arbitrary degree of accuracy;

(3) it is possible to play other records on the same record player and get other sounds out;

(4) the record and the record player are easily separated from one another.

It is another question altogether whether the fragments of a
smashed
record contain intrinsic meaning. The edges of the separate pieces together and in that way allow the information to be reconstituted-t something much more complex is going on here. Then there is the question of the intrinsic meaning of a scrambled telephone call ... There is a vast spectrum of degrees of inherency of meaning. It is interesting to try place epigenesis in this spectrum. As development of an organism takes place, can it be said that the information is being "pulled out" of its
DNA
? Is that where all of the information about the organism's structure reside;

DNA
and the Necessity of Chemical Context

In one sense, the answer seems to be yes, thanks to experiments li Avery's. But in another sense, the answer seems to be no, because so much of the pulling-out process depends on extraordinarily complicated cellular chemical processes, which are not coded for in the
DNA
itself. The
DNA
relies on the fact that they will happen, but does not seem to contain a code which brings them about. Thus we have two conflicting views on the nature of the information in a genotype. One view says that so much of t information is
outside the
DNA
that it is not reasonable to look upon the
DNA
as anything more than a very intricate set of triggers, like a sequence of buttons to be pushed on a jukebox; another view says that
the information is all there
, but in a very implicit form.

Now it might seem that these are just two ways of saying the same thing, but that is not necessarily so. One view says that the
DNA
is quite meaningless out of context; the other says that even if it were taken out context, a molecule of
DNA
from a living being has such a
compelling inner

logic
to its structure that its message could be deduced anyway. To put it as succinctly as possible, one view says that in order for
DNA
to have meaning,
chemical context
is necessary; the other view says that only
intelligence
is necessary to reveal the "intrinsic meaning" of a strand of
DNA
.

An Unlikely UFO

We can get some perspective on this issue by considering a strange hypothetical event. A record of David Oistrakh and Lev Oborin playing Bach's sonata in F Minor for violin and clavier is sent up in a satellite. From the satellite it is then launched on a course which will carry it outside of the solar system, perhaps out of the entire galaxy just a thin plastic platter with a hole in the middle, swirling its way through intergalactic space. It has certainly lost its context. How much meaning does it carry?

If an alien civilization were to encounter it, they would almost certainly be struck by its shape, and would probably be very interested in it. Thus immediately its shape, acting as a trigger, has given them some information: that it is an artifact, perhaps an information-bearing artifact. This idea-communicated, or triggered, by the record itself-now creates a new context in which the record will henceforth be perceived. The next steps in the decoding might take considerably longer-but that is very hard for us to assess.

We can imagine that if such a record had arrived on earth in Bach's time, no one would have known what to make of it, and very likely it would not have gotten deciphered. But that does not diminish our conviction that the information was in principle there; we just know that human knowledge in those times was not very sophisticated with respect to the possibilities of storage, transformation, and revelation of information.

Levels of Understanding of a Message

Nowadays, the idea of decoding is extremely widespread; it is a significant part of the activity of astronomers, linguists, archaeologists, military specialists, and so on. It is often suggested that we may be floating in a sea of radio messages from other civilizations, messages which we do not yet know how to decipher. And much serious thought has been given to the techniques of deciphering such a message. One of the main problems perhaps the deepest problem-is the question, "How will we recognize the fact that there is a message at all? How to identify a frame?" The sending of a record seems to be a simple solution-its gross physical structure is very attention-drawing, and it is at least plausible to us that it would trigger, in any sufficiently great intelligence, the idea of looking for information hidden in it. However, for technological reasons, sending of solid objects to other star systems seems to be out of the question. Still, that does not prevent our thinking about the idea.

Now suppose that an alien civilization hit upon the idea that the appropriate mechanism for translation of the record is a machine which

converts the groove-patterns into sounds. This would still be a far cry from a true deciphering. What, indeed, would constitute a
successful
deciphering of such a record?

Evidently, the civilization would have to be able to ma sense out of the sounds. Mere production of sounds is in itself hart worthwhile, unless they have the desired triggering effect in the brains that is the word) of the alien creatures. And what is that desired effect? would be to activate structures in their brains which create emotional effects in them which are analogous to the emotional effects which experience in hearing the piece.

In fact, the production of sounds cot even be bypassed, provided that they used the record in some other way get at the appropriate structures in their brains. (If we humans had a w of triggering the appropriate structures in our brains in sequential order, as music does, we might be quite content to bypass the sounds-but it see] extraordinarily unlikely that there is any way to do that, other than via o ears. Deaf composers-Beethoven, Dvofák, Faure-or musicians who can "hear" music by looking at a score, do not give the lie to this assertion, for such abilities are founded upon preceding decades of direct auditory experiences.)

Here is where things become very unclear. Will beings of an alien civilization have emotions? Will their emotions-supposing they have some-be mappable, in any sense, onto ours? If they do have emotions somewhat like ours, do the emotions cluster together in somewhat the same way as ours do? Will they understand such amalgams as tragic beauty courageous suffering? If it turns out that beings throughout the universe do share cognitive structures with us to the extent that even emotions overlap, then in some sense, the record can never be out of its natural context; that context is part of the scheme of things, in nature. And if such is the case, then it is likely that a meandering record, if not destroyed en route, would eventually get picked up by a being or group of beings, at get deciphered in a way which we would consider successful.

"Imaginary Spacescape"

In asking about the meaning of a molecule of
DNA
above, I used t phrase

"compelling inner logic"; and I think this is a key notion. To illustrate this, let us slightly modify our hypothetical record-into-spa event by substituting John Cage's "Imaginary Landscape no. 4" for the Bach. This piece is a classic of
aleatoric
, or
chance
, music-music who structure is chosen by various random processes, rather than by an attempt to convey a personal emotion. In this case, twenty-four performers attar themselves to the twenty-four knobs on twelve radios. For the duration the piece they twiddle their knobs in aleatoric ways so that each radio randomly gets louder and softer, switching stations all the while. The tot sound produced is the piece of music. Cage's attitude is expressed in 14

own words: "to let sounds be themselves, rather than vehicles for man made theories or expressions of human sentiments."

Now imagine that this is the piece on the record sent out into space. It would be extraordinarily unlikely-if not downright impossible-for an alien civilization to understand the nature of the artifact. They would probably be very puzzled by the contradiction between the frame message ("I am a message; decode me"), and the chaos of the inner structure. There are few "chunks" to seize onto in this Cage piece, few patterns which could guide a decipherer. On the other hand, there seems to be, in a Bach piece, much to seize onto-patterns, patterns of patterns, and so on. We have no way of knowing whether such patterns are universally appealing. We do not know enough about the nature of intelligence, emotions, or music to say whether the inner logic of a piece by Bach is so universally compelling that its meaning could span galaxies.

However, whether Bach in particular has enough inner logic is not the issue here; the issue is whether any message has, per se, enough compelling inner logic that its context will be restored automatically whenever intelligence of a high enough level comes in contact with it. If some message did have that context-restoring property, then it would seem reasonable to consider the meaning of the message as an inherent property of the message.

The Heroic Decipherers

Another illuminating example of these ideas is the decipherment of ancient texts written in unknown languages and unknown alphabets. The intuition feels that there is information inherent in such texts, whether or not we succeed in revealing it. It is as strong a feeling as the belief that there is meaning inherent in a newspaper written in Chinese, even if we are completely ignorant of Chinese. Once the script or language of a text has been broken, then no one questions where the meaning resides: clearly it resides in the text, not in the method of decipherment just as music resides in a record, not inside a record player! One of the ways that we identify decoding mechanisms is by the fact that they do not add any meaning to the signs or objects which they take as input; they merely reveal the intrinsic meaning of those signs or objects. A jukebox is not a decoding mechanism, for it does not reveal any meaning belonging to its input symbols; on the contrary, it supplies meaning concealed inside itself.

Now the decipherment of an ancient text may have involved decades of labor by several rival teams of scholars, drawing on knowledge stored in libraries all over the world ... Doesn't this process add information, too? Just how intrinsic is the meaning of a text, when such mammoth efforts are required in order to find the decoding rules? Has one put meaning into the text, or was that meaning already there? My intuition says that the meaning was always there, and that despite the arduousness of the pulling-out process, no meaning was pulled out that wasn't in the text to start with. This intuition comes mainly from one fact: I feel that the result was inevitable; that, had the text not been deciphered by this group at this time, it would have been deciphered by that group at that time-and it would have come

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