Douglas Hofstadter Quotes

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

"Now sophisticated operating systems carry out similar traffic-handling and level-switching operations with respect to users and their programs. It is virtually certain that there are somewhat parallel things which take place in the brain: handling of many stimuli at the same time; decisions of what should have priority over what and for how long; instantaneous "interrupts" caused by emergencies or other unexpected occurrences; and so on."

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, sometimes exceedingly beautiful.

Irrationality is the square root of all evil.

"The "space" of all possible programs is so huge that no one can have a sense of what is possible. Each higher-level language is naturally suited for exploring certain regions of "program space"; thus the programmer, by using that language, is channeled into those areas of program space. He is not forced by the language into writing programs of any particular type, but the language makes it easy for him to do certain kinds of things. Proximity to a concept, and a gentle shove, are often all that is needed for a major discovery-and that is the reason for the drive towards languages of ever higher levels."

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.

Any situation permits a host of diverse categorizations.

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

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 one of my firmest conclusions is that we always think by seeking and drawing parallels to things we know from our past, and that we therefore communicate best when we exploit examples, analogies, and metaphors galore, when we avoid abstract generalities, when we use very down-to-earth, concrete, and simple language, and when we talk directly about our own experience.

Such concepts, be they concrete or abstract, are selectively mobilized instant by instant, and nearly always without any awareness on our part, and it is this ceaseless activity that allows us to build up mental representations of situations we are in, to have complex feelings about them, and to have run-of-the-mill as well as more exalted thoughts. No thought can be formed that isn’t informed by the past; or, more precisely, we think only thanks to analogies that link our present to our past.

Thus our categories keep us well informed at all times, allowing us to bypass the need for direct observation. If we didn’t constantly extrapolate our knowledge into new situations — if we refrained from making inferences — then we would be conceptually blind. We would be unable to think or act, doomed to permanent uncertainty and to eternal groping in the dark. In short, in order to perceive the world around us, we depend just as much on categorization through analogy as we do on our eyes or our ears.

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

No, no - I think about thinking

"What is an "I", and why are such things found (at least so far) only in association with, as poet Russell Edson once wonderfully phrased it, "teetering bulbs of dread and dream" — that is, only in association with certain kinds of gooey lumps encased in hard protective shells mounted atop mobile pedestals that roam the world on pairs of slightly fuzzy, jointed stilts?"