Douglas R. Hofstadter

Think of a dentist who has a list of
patients, and for each patient, a list of teeth. It makes perfect sense (and
plenty of money) to hold the patient fixed and vary his teeth-but it makes
no sense at all to hold one tooth fixed and vary the patient. (Although
sometimes it makes good sense to vary the dentist ... )

And that is also the way the human mind works — by the compounding of old ideas into new structures that become new ideas that can themselves be used in compounds, and round and round endlessly, growing ever more remote from the basic earthbound imagery that is each language’s soil.

Deep understanding of causality sometimes requires the understanding of very large patterns and their abstract relationships and interactions, not just the understanding of microscopic objects interacting in microscopic time intervals.

Kurt Gödel was the first person to realize and exploit the fact that the positive integers, though they might superficially seem to be very austere and isolated, in fact constitute a profoundly rich representational medium. They can mimic or mirror any kind of pattern.

"the Godelian strange loop that arises in formal systems in mathematics (i.e., collections of rules for churning out an endless series of mathematical truths solely by mechanical symbol-shunting without any regard to meanings or ideas hidden in the shapes being manipulated) is a loop that allows such a system to "perceive itself", to talk about itself, to become "self-aware", and in a sense it would not be going too far to say that by virtue of having such a loop, a formal system acquires a self."

Saying that studying the brain is limited to the study of physical entities would be like saying that literary criticism must focus on paper and bookbinding, ink and its chemistry, page sizes and margin widths, typefaces and paragraph lengths, and so forth.

We don't want to focus on the trees (or their leaves) at the expense of the forest.

Therefore Godel's theorem had an electrifying effect upon logicians, mathematicians, and philosophers interested in the foundations of mathematics, for it showed that no fixed system, no matter how complicated could represent the complexity of the whole numbers: 0,1,2,3,.....

It sometimes feels as if I had shouted a deeply cherished message out into an empty chasm and nobody heard me.

"We have seen recursion in the grammars of languages, we have seen recursive geometrical trees, which grow upwards forever, and we have seen one way in which recursion enters the theory of solid state physics. Now we are going to see yet another way in which the whole world is built out of recursion. This has to do with the structure of elementary particles: electrons, protons, neutrons, and the tiny quanta of electromagnetic radiation called "photons". We are going to see that particles are - in a certain sense which can only be defined rigorously in relativistic quantum mechanics- nested inside each other in a way which can be described recursively, perhaps even by some sort of "grammar"."

Just as science is permeated with 'conceptual revolution' on all levels at all times, so the thinking of individuals is shot through and through with creative and new acts. Computer programs today do not yet seem to produce many small creations. Most of what they do is quite 'mechanical' still. That just testifies to the fact that they are not close to simulating the way we think–but they are getting closer.

Perhaps what differentiates highly creative ideas from ordinary ones is some combined sense of beauty, simplicity, and harmony.

In the end, we self-perceiving, self-inventing, locked-in mirages are little miracles of self-reference.

No one knows where the borderline between non-intelligent behavior and intelligent
behavior lies; in fact, to suggest that a sharp borderline exists is probably silly. But
essential abilities for intelligence are certainly:
to respond to situations very flexibly;
to take advantage of fortuitous circumstances;
to make sense out of ambiguous or contradictory messages;
to recognize the relative importance of different elements of a
situation;
to find similarities between situations despite differences which may separate them;
to draw distinctions between situations despite similarities may link them;
to synthesize new concepts by taking old them together in new ways; to come up
with ideas which are novel.

It is numbers like 545 billion that we are dealing with when we talk about a Defense Department overrun of $750 billion for the next four years. A really fancy single-user computer (the kind I wouldn’t mind having) costs approximately $75,000. With $750 billion to throw around, we could give one to every person in New York City, which is to say, we could buy about ten million of them. Or, we could give $1 million to every person in San Francisco, and still have enough left over to buy a bicycle for everyone in China! There’s no telling what good uses we could put $750 billion to. But instead, it will go into bullets and tanks and fighters and war games and missile systems and jet fuel and marching bands and so on. An interesting way to spend $750 billion, but I can think of better ways.

A computer program can modify itself but it cannot violate its own instructions — it can at best change some parts of itself by *obeying* its own instructions.