Douglas Hofstadter Quotes

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.

There exist formal systems whose negative space (set of non-theorems) is not the positive space (set of theorems) of any formal system.

Consider the fact that you are now experiencing death, in a curious way. Not being in Paris right now, you know what it is like to be dead in Paris. No lights, no sounds — nothing. The same goes for Timbuctu. In fact, you are dead everywhere — except for one small spot. Just think how close you are to being dead everywhere!

A term meant to convey a person's inability to make sense of the numbers that run their lives.

(1) Blurting may be considered as the reciprocal substitution of semiotic material (dubbing) for a semiotic dialogical product in a dynamic reflexion.

The human-written sentences are numbers (1) to 3; they were drawn from the contemporary journal Art-Language and are — as far as I can tell — completely serious efforts among literate and sane people to communicate something to each other.

Computers are ridiculous. So is science in general. CHURCH_TURING Thesis, Theodore Rosak Version
This view is prevalent among certain people who see in anything smacking of numbers or exactitude a threat to human values. It is too bad that they do not appreciate the depth and complexity and beauty involved in exploring abstract structures sch as the human mind, where, indeed, one comes in intimate contact with the ultimate questions of what to be human is.

The perception of an isomorphism between two known structures is a significant advance in knowledge-and I claim that it is such perceptions of isomorphism which create meanings in the minds of people.

"We believe in marbles that disintegrate when we search for them but that are as real as any genuine marble when we're not looking for them. Our very nature is such as to prevent us from fully understanding its very nature. Poised midway between the unvisualizable cosmic vastness of curved spacetime and the dubious, shadowy flickerings of charged quanta, we human beings, more like rainbows and mirages than like raindrops or boulders, are unpredictable self-writing poems — vague, metaphorical, ambiguous, and sometimes exceedingly beautiful. [...] What one gives up on is a childlike sense that things are exactly as they appear, and that our solid-seeming, marble-like "I" is the realest thing in the world; what one acquires is an appreciation of how tenuous we are at our cores, and how wildly different we are from what we seem to be."

We should have great respect for what seem like the most mundane of analogies, for when they are examined, they often can be seen to have sprung from, and to reveal, the deepest roots of human cognition.

"An amusing way to see the incorrectness of Lucas' argument is to translate it into a battle between men and women ... In his wanderings, Loocus the Thinker one day comes across an unknown object — a woman. Such a thing he has never seen before, and at first he is wondrous thrilled at her likeness to himself; but then, slightly scared of her as well, he cries to all the men about him, "Behold! I can look upon her face, which is something she cannot do — therefore women can never be like me!" And thus he proves man's superiority over women, much to his relief, and that of his male companions. Incidentally, the same argument proves that Loocus is superior to all other males, as well — but he doesn't point that out to them. The woman argues back: "Yes, you can see my face, which is something I can't do — but I can see your face, which is something you can't do! We're even." However, Loocus comes up with an unexpected counter: "I'm sorry, you're deluded if you think you can seemy face. What you women do is not the same as what we men do — it is, as I have already pointed out, of an inferior caliber, and does not deserve to be called by the same name. You may call it 'womanseeing'. Now the fact that you can 'womansee' my face is of no import, because the situation is not symmetric. You see?" "I woman-see," womanreplies the woman, and womanwalks away..."

We have a very hard time “seeing” our cognitive activity because it is the medium in which we swim. The attempt to put our finger on what counts in any given situation leads us at times to making connections between situations that are enormously different on their surface and at other times to distinguishing between situations that on first glance seem nearly identical. Our constant jockeying back and forth among our categories runs the gamut from the most routine behaviors to the most creative ones.

Seeing anything as waves suggests immediate knobs: wavelength, frequency, amplitude, speed, medium, and a host of other basic notions that define the essence of undularity. Seeing anything as particles suggests totally different knobs: mass, shape, radius, rotation, constituents, and a host of other basic notions that define the essence of corpuscularity.

There are those who will immediately be drawn to the idea of pattern-seeking, and

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,.....

"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."