Douglas Hofstadter Quotes

It now becomes clear that consistency is not a property of a formal system per se, but depends on the interpretation which is proposed for it. By the same token, inconsistency is not an intrinsic property of any formal system.

The theorem can be likened to a pearl, and the method of proof to an oyster. The pearl is prized for its luster and simplicity; the oyster is a complex living beast whose innards give rise to this mysteriously simple gem.

I would like to understand things better, but I don’t want to understand them perfectly.

And yet, something of Jim is surviving strongly — surviving in other brains, thanks to human love. His easy-going sense of humor, his boundless joy at driving the wide open spaces of the prairies, his ideals, his generosity, his simplicity, his hopes and dreams — and (for what it’s worth) his understanding of credit cards. All of these things survive at different levels in many people who, thanks to having interacted with him intimately over many years or decades, constitute his “soular corona” — his wife, his three children, and his many, many friends. Even before Jim’s body physically dies, his soul will have become so foggy and dim that it might as well not exist at all — the soular eclipse will be in full force — and yet despite the eclipse, his soul will still exist, in partial, low-resolution copies, scattered about the globe. Jim’s first-person perspective will flicker in and out of existence in other brains, from time to time. He will exist, albeit in an extremely diluted fashion, now here, now there. Where will Jim be? Not very much anywhere, admittedly, but to some extent he will be in many places at once, and to different degrees. Though terribly reduced, he will be wherever his soular corona is. It is very sad, but it is also beautiful. In any case, it is our only consolation.

We claim that cognition takes place thanks to a constant flow of categorizations, and that at the base of it all is found, in contrast to classification (which aims to put all things into fixed and rigid mental boxes), the phenomenon of categorization through analogy-making, which endows human thinking with its remarkable fluidity.

"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."

"It was a hundred years later that Einstein gave a theory (general relativity) which said that the geometry of the universe is determined by its content of matter, so that no one geometry is intrinsic to space itself. Thus to the question, "Which geometry is true?" nature gives an ambiguous answer not only in mathematics, but also in physics"

if one keeps climbing upward in the chain of command within the brain, one finds at the very top those over-all organizational forces and dynamic properties of the large patterns of cerebral excitation that are correlated with mental states or psychic activity…. Near the apex of this command system in the brain…. we find ideas. Man over the chimpanzee has ideas and ideals. In the brain model proposed here, the causal potency of an idea, or an ideal, becomes just as real as that of a molecule, a cell, or a nerve impulse. Ideas cause ideas and help evolve new ideas. They interact with each other and with other mental forces in the same brain, in neighboring brains, and, thanks to global communication, in far distant, foreign brains. And they also interact with the external surroundings to produce in toto a burst-wise advance in evolution that is far beyond anything to hit the evolutionary scene yet, including the emergence of the living cell.

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..."

At the outset, there is a concrete situation with concrete components, and thus it is perceived as something unique and cleanly separable from the rest of the world. After a while, though — perhaps a day later, perhaps a year — one runs into another situation that one finds to be similar, and a link is made.

Where There’s Pattern, There’s Reason The key thought in the preceding few lines is the article of faith that this pattern cannot merely be a coincidence. A mathematician who finds a pattern of this sort will instinctively ask, “Why? What is the reason behind this order?” Not only will all mathematicians wonder what the reason is, but even more importantly, they will all implicitly believe that whether or not anyone ever finds the reason, there must be a reason for it. Nothing happens “by accident” in the world of mathematics.

Meaning lies as much
in the mind of the reader
as in the Haiku.

Any situation permits a host of diverse categorizations.

in fact we all know many more categories than we know words.