Douglas R. 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.

[...] provability is a weaker notion than truth

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

I can't help but recall, at this point, a horribly elitist but very droll remark by one of my favorite writers, the American "critic of the seven arts", James Huneker, in his scintillating biography of Frédéric Chopin, on the subject of Chopin's étude Op. 25, No. 11 in A minor, which for me, and for Huneker, is one of the most stirring and most sublime pieces of music ever written: "Small-souled men, no matter how agile their fingers, should avoid it."

"Small-souled men"?! Whew! Does that phrase ever run against the grain of American democracy! And yet, leaving aside its offensive, archaic sexism (a crime I, too, commit in GEB, to my great regret), I would suggest that it is only because we all tacitly do believe in something like Hueneker's' shocking distinction that most of us are willing to eat animals of one sort or another, to smash flies, swat mosquitos, fight bacteria with antibiotics, and so forth. We generally concur that "men" such as a cow, a turkey, a frog, and a fish all possess some spark of consciousness, some kind of primitive "soul" but by God, it's a good deal smaller than ours is - and that, no more and no less, is why we "men" feel that we have the perfect right to extinguish the dim lights in the heads of these fractionally-souled beasts and to gobble down their once warm and wiggling, now chilled and stilled protoplasm with limitless gusto, and not feel a trace of guilt while doing so.

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

(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.

What does it matter if two brains are isomorphic, or quasi-isomorphic, or not isomorphic at all? The answer is that we have an intuitive sense that, although other people differ from us in important ways, they are still 'the same' as we are in some deep and important ways. It would be instructive to be able to pinpoint what this invariant core of human intelligence is, and then to be able to describe the kinds of 'embellishments' which can be added to it, making each one of us a unique embodiment of this abstract and mysterious quality called 'intelligence.

The paraphrase of Gödel's Theorem says that for any record player, there are records which it cannot play because they will cause its indirect self-destruction.

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.

But finally I realized that to me, Godel and Escher and Bach were only shadows cast in different directions by some central solid essence. I tried to construct the central object, and came up with this book.

This computer-generated pangram contains six a's, one b, three c's, three d's, thirty-seven e's, six f's, three g's, nine h's, twelve i's, one j, one k, two l's, three m's, twenty-two n's, thirteen o's, three p's, one q, fourteen r's, twenty-nine s's, twenty-four t's, five u's, six v's, seven w's, four x's, five y's, and one z.

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

We human beings are macroscopic structures in a universe whose laws reside at a microscopic level. As survival-seeking beings, we are driven to seek efficient explanations that make reference only to entities at our own level. We therefore draw conceptual boundaries around entities that we easily perceive, and in so doing we carve out what seems to us to be reality.

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!

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.

For now, what is important is not finding the answer, but looking for it.

Some of us, perhaps all of us, believe that it is legitimate to kill enemy soldiers in a war, as if war were a special circumstance that shrinks the sizes of enemy souls.

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.

GEB is in essence a long proposal of strange loops as a metaphor for how selfhood originates, a metaphor by which to begin to grab a hold of just what it is that makes an "I" seem, at one and the same time, so terribly real and tangible to its own possessor, and yet also so vague, so impenetrable, so deeply elusive.

Godel showed how a statement about any mathematical formal system (such as the assertion that Principia Mathematica is contradiction-free) can be translated into a mathematical statement inside number theory (the study of whole numbers). In other words, any metamathematical statement can be imported into mathematics, and in its new guise the statement simply asserts (as do all statements of number theory) that certain whole numbers have certain properties or relationships to each other. But on another level, it also has a vastly different meaning that, on its surface, seems as far removed from a statement of number theory as would be a sentence in a Dostoevsky novel.

It turns out that an eerie type of chaos can lurk just behind a facade of order - and yet, deep inside the chaos lurks an even eerier type of order.

Please, Oh please, publish me in your collection of self-referential sentences!

To paraphrase Descartes again: "I think; therefore I have no access to the level where I sum.

What gives us word-users the right to make life-and-death decisions concerning other living creatures that have no words? Why do we find ourselves in positions of such anguish (at least for some of us)? In the final analysis, it is simply because might makes right, and we humans, thanks to the intelligence afforded us by the complexity of our brains and our embeddedness in rich languages and cultures, are indeed high and mighty, relative to the "lower" animals (and vegetables). By virtue of our might, we are forced to establish some sort of ranking of creatures, whether we do so as a result of long and careful personal reflections or simply go along with the compelling flow of the masses. Are cows just as comfortably killable as mosquitoes? Would you feel any less troubled by swatting a fly preening on a wall than by beheading a chicken quivering on a block?

Concepts in the brains of humans acquired the property that they could get rolled together with other concepts into larger packets, and any such larger packet could then become a new concept in its own right. In other words, concepts could nest inside each other hierarchically, and such nesting could go on to arbitrary degrees.

Why is some music so much deeper and more beautiful than other music? It is because form, in music, is expressive–expressive to some strange subconscious regions of our minds. The sounds of music do not refer to serfs or city-states, but they do trigger clouds of emotion in our innermost selves; in that sense musical meaning IS dependent on intangible links from symbols to things in the world–those 'things', in this case, being secret software structures in our minds.

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

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.

Consistent or inconsistent, no one is exempt from the mystery of the self. Probably we are all inconsistent. The world is just too complicated for a person to be able to afford the luxury of reconciling all of his beliefs with each other. Tension and confusion are important in a world where many decisions must be made quickly. Miguel de Unamuno once said, 'If a person never contradicts himself, it must be that he says nothing.' I would say that we all are in the same boast as the Zen master who, after contradicting himself several times in a row, said to the confused Doko, 'I cannot understand myself.'.

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.

I personally cannot imagine that consciousness will be fully understood without reference to Godelian loops or level-crossing feedback loops.

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,.....

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.

This idea that there is generality in the specific is of far-reaching importance.

If words were nuts and bolts, people could make any bolt fit into any nut: they'd just squish the one into the other, as in some surrealistic painting where everything goes soft. Language, in human hands, becomes almost like a fluid, despite the coarse grain of its components.

A mirror mirroring a mirror

The key question is, no matter how much you absorb of another person, can you have absorbed so much of them that when that primary brain perishes, you can feel that that person did not totally perish from the earth ... because they live on in a 'second neural home'? ... In the wake of a human being's death, what survives is a set of afterglows, some brighter and some dimmer, in the collective brains of those who were dearest to them ... Though the primary brain has been eclipsed, there is, in those who remain ... a collective corona that still glows.

Sometimes it seems as though each new step towards AI, rather than producing something which everyone agrees is real intelligence, merely reveals what real intelligence is not.