Gödel, Escher, Bach: An Eternal Golden Braid (127 page)

Other curious tangles which arise in government include the FBI investigating its own wrongdoings, a sheriff going to jail while in office, the self-application of the parliamentary rules of procedure, and so on. One of the most curious legal cases I ever heard of involved a person who claimed to have psychic powers. In fact, he claimed to be able to use his psychic powers to detect personality traits, and thereby to aid lawyers in picking juries. Now what if this "psychic" has to stand trial himself one day? What effect might this have on a jury member who believes staunchly in ESP? How much will he feel affected by the psychic (whether or not the psychic is genuine)? The territory is ripe for exploitation-a great area for selffulfilling prophecies.

Tangles Involving Science and the Occult

Speaking of psychics and ESP, another sphere of life where strange loops abound is fringe science. What fringe science does is to call into question many of the standard procedures or beliefs of orthodox science, and thereby challenge the objectivity of science. New ways of interpreting evidence that rival the established ones are presented.

But how do you evaluate a way of interpreting evidence? Isn't this precisely the problem of objectivity all over again, just on a higher plane? Of course. Lewis Carroll's infinite-regress paradox appears in a new guise. The Tortoise would argue that if you want to show that A is a fact, you need evidence: B. But what makes you sure that B is evidence of A?' To show that, you need meta-evidence: C. And for the validity of that meta-evidence, you need metameta-evidence-and so on, ad nauseam. Despite this argument, people have an intuitive sense of evidence.

This is because-to repeat an old refrain-people have built-in hardware in their brains that includes some rudimentary ways of interpreting evidence. We can build on this, and accumulate new ways of interpreting evidence; we even learn how and when to override our most basic mechanisms of evidence interpretation, as one must, for example, in trying to figure out magic tricks.

Concrete examples of evidence dilemmas crop up in regard to many phenomena of fringe science. For instance, ESP often seems to manifest itself outside of the laboratory, but when brought into the laboratory, it vanishes mysteriously. The standard scientific explanation for this is that ESP is a nonreal phenomenon which cannot stand up to rigorous scrutiny. Some (by no means all) believers in ESP have a peculiar way of fighting back, however. They say, "No, ESP is real; it simply goes away when one tries to observe it scientifically-it is contrary to the nature of a scientific worldview." This is an amazingly brazen technique, which we might call "kicking the problem upstairs".

What that means is, instead of questioning the matter at hand, you call into doubt theories belonging to a higher level of credibility. The believers in ESP insinuate that what is wrong is not their ideas, but the belief system of science. This is a pretty grandiose claim, and unless there is overwhelming evidence for it, one should be skeptical of it. But then here we are again, talking about "overwhelming evidence" as if everyone agreed on what that means!

The Nature of Evidence

The Sagredo-Simplicio-Salviati tangle, mentioned in Chapters XIII and XV, gives another example of the complexities of evaluation of evidence. Sagredo tries to find some objective compromise, if possible, between the opposing views of Simplicio and Salviati.

But compromise may not always be possible. How can one compromise "fairly" between right and wrong? Between fair and unfair? Between compromise and no compromise?

These questions come up over and over again in disguised form in arguments about ordinary things.

Is it possible to define what evidence is? Is it possible to lay down laws as to how to make sense out of situations? Probably not, for any rigid rules would undoubtedly have exceptions, and nonrigid rules are not rules. Having an intelligent AI program would not solve the problem either, for as an evidence processor, it would not be any less fallible than humans are. So, if evidence is such an intangible thing after all, why am I warning against new ways of interpreting evidence? Am I being inconsistent? In this case, I don't think so. My feeling is that there are guidelines which one can give, and out of them an organic synthesis can be made. But inevitably some amount of judgment and intuition must enter the picture-things which are different in different people. They will also be different in

different AI programs. Ultimately, there are complicated criteria for deciding if a method of evaluation of evidence is good. One involves the "usefulness" of ideas which are arrived at by that kind of reasoning. Modes of thought which lead to useful new things in life are deemed "valid" in some sense. But this word "useful" is extremely subjective.

My feeling is that the process by which we decide what is valid or what is true is an art; and that it relies as deeply on a sense of beauty and simplicity as it does on rock-solid principles of logic or reasoning or anything else which can be objectively formalized. I am not saying either (1) truth is a chimera, or (2) human intelligence is in principle not programmable. I am saying (1) truth is too elusive for any human or any collection of humans ever to attain fully; and (2) Artificial Intelligence, when it reaches the level of human intelligence-or even if it surpasses it-will still be plagued by the problems of art, beauty, and simplicity, and will run up against these things constantly in its own search for knowledge and understanding.

"What is evidence?" is not just a philosophical question, for it intrudes into life in all sorts of places. You are faced with an extraordinary number of choices as to how to interpret evidence at every moment. You can hardly go into a bookstore (or these days, even a grocery store!) without seeing books on clairvoyance, ESP, UFO's, the Bermuda triangle, astrology, dowsing, evolution versus creation, black holes, psi fields, biofeedback, transcendental meditation, new theories of psychology ... In science, there are fierce debates about catastrophe theory, elementary particle theory, black holes, truth and existence in mathematics, free will, Artificial Intelligence, reductionism versus holism ... On the more pragmatic side of life, there are debates over the efficacy of vitamin C or of laetrile, over the real size of oil reserves (either underground or stored), over what causes inflation and unemployment-and on and on. There is Buckminster Fullerism, Zen Buddhism, Zeno's paradoxes, psychoanalysis, etc., etc. From issues as trivial as where books ought to be shelved in a store, to issues as vital as what ideas are to be taught to children in schools, ways of interpreting evidence play an inestimable role.

Seeing Oneself

One of the most severe of all problems of evidence interpretation is that of trying to interpret all the confusing signals from the outside as to who one is. In this case, the potential for intralevel and interlevel conflict is tremendous. The psychic mechanisms have to deal simultaneously with the individual's internal need for self-esteem and the constant flow of evidence from the outside affecting the self-image. The result is that information flows in a complex swirl between different levels of the personality; as it goes round and round, parts of it get magnified, reduced, negated, or otherwise distorted, and then those parts in turn get further subjected to the same sort of swirl, over and over again-all of this in an attempt to reconcile what is, with what we wish were (see Fig. 81).

The upshot is that the total picture of "who I am" is integrated in some enormously complex way inside the entire mental structure, and contains in each one of us a large number of unresolved, possibly unresolvable, inconsistencies. These undoubtedly provide much of the dynamic tension which is so much a part of being human. Out of this tension between the inside and outside notions of who we are come the drives towards various goals that make each of us unique. Thus, ironically, something which we all have in common-the fact of being self-reflecting conscious beings-leads to the rich diversity in the ways we have of internalizing evidence about all sorts of things, and in the end winds up being one of the major forces in creating distinct individuals.

Gödel’s Theorem and Other Disciplines

It is natural to try to draw parallels between people and sufficiently complicated formal systems which, like people, have "self-images" of a sort. Gödel’s Theorem shows that there are fundamental limitations to consistent formal systems with self-images. But is it more general? Is there a "Gödel’s Theorem of psychology", for instance?

If one uses Gödel’s Theorem as a metaphor, as a source of inspiration, rather than trying to translate it literally into the language of psychology or of any other discipline, then perhaps it can suggest new truths in psychology or other areas. But it is quite unjustifiable to translate it directly into a statement of another discipline and take that as equally valid. It would be a large mistake to think that what has been worked out with the utmost delicacy in mathematical logic should hold without modification in a completely different area.

Introspection and Insanity: A Gödelian Problem

I think it can have suggestive value to translate Gödel’s Theorem into other domains, provided one specifies in advance that the translations are metaphorical and are not intended to be taken literally. That having been said, I see two major ways of using analogies to connect Gödel’s Theorem and human thoughts. One involves the problem of wondering about one's sanity. How can you figure out if you are sane? This is a Strange Loop indeed. Once you begin to question your own sanity, you can get trapped in an ever-tighter vortex of self-fulfilling prophecies, though the process is by no means inevitable. Everyone knows that the insane interpret the world via their own peculiarly consistent logic; how can you tell if your own logic is "peculiar" or not, given that you have only your own logic to judge itself? I don't see any answer. I am just reminded of Gödel’s second Theorem, which implies that the only versions of formal number theory which assert their own consistency are inconsistent ...

Can We Understand Our Own" Minds or Brains?

The other metaphorical analogue to Gödel’s Theorem which I find provocative suggests that ultimately, we cannot understand our own minds/ brains. This is such a loaded, many-leveled idea that one must be extremely cautious in proposing it. What does

"understanding our own minds/brains" mean? It could mean having a general sense of how they work, as mechanics have a sense of how cars work. It could mean having a complete explanation for why people do any and all things they do. It could mean having a complete understanding of the physical structure of one's own brain on all levels. It could mean having a complete wiring diagram of a brain in a book (or library or computer). It could mean knowing, at every instant, precisely what is happening in one's own brain on the neural level-each firing, each synaptic alteration, and so on. It could mean having written a program which passes the Turing test. It could mean knowing oneself so perfectly that such notions as the subconscious and the intuition make no sense, because everything is out in the open. It could mean any number of other things.

Which of these types of self-mirroring, if any, does the self-mirroring in Gödel’s Theorem most resemble? I would hesitate to say. Some of them are quite silly. For instance, the idea of being able to monitor your own brain state in all its detail is a pipe dream, an absurd and uninteresting proposition to start with; and if Gödel’s Theorem suggests that it is impossible, that is hardly a revelation. On the other hand, the age-old goal of knowing yourself in some profound way-let us call it "understanding your own psychic structure"-has a ring of plausibility to it. But might there not be some vaguely Godelian loop which limits the depth to which any individual can penetrate into his own psyche? Just as we cannot see our faces with our own eyes, is it not reasonable to expect that we cannot mirror our complete mental structures in the symbols which carry them out?

All the limitative Theorems of metamathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally.

Gödel’s Incompleteness Theorem, Church's Undecidability Theorem, Turing's Halting Theorem, Tarski's Truth Theorem-all have the flavor of some ancient fairy tale which warns you that "To seek self-knowledge is to embark on a journey which ... will always be incomplete, cannot be charted on any map, will never halt, cannot be described."

But do the limitative Theorems have any bearing on people? Here is one way of arguing the case. Either I am consistent or I am inconsistent. (The latter is much more likely, but for completeness' sake, I consider both possibilities.) If I am consistent, then there are two cases. (1) The "low-fidelity" case: my self-understanding is below a certain critical point. In this case, I am incomplete by hypothesis. (2) The "high-fidelity" case: My self-understanding has reached the critical point where a metaphorical analogue of the limitative Theorems does apply, so my self-understanding