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.
American physicist, computer scientist and professor of cognitive science
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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.
I am not shooting at immortality through my books, no. Nor do I think Chopin was shooting at immortality through his music. That strikes me as a very selfish goal, and I don't think Chopin was particularly selfish. I would also say that I think that music comes much closer to capturing the essence of a composer's soul than do a writer's ideas capture the writer's soul. Perhaps some very emotional ideas that I express in my books can get across a bit of the essence of my soul to some readers, but I think that Chopin's music probably does a lot better job (and the same holds, of course, for many composers). I personally don't have any thoughts about "shooting for immortality" when I write. I try to write simply in order to get ideas out there that I believe in and find fascinating, because I'd like to let other people be able share those ideas. But intellectual ideas alone, no matter how fascinating they are, are not enough to transmit a soul across brains. Perhaps, as I say, my autobiographical passages — at least some of them — get tiny shards of my soul across to some people. But such autobiographical story-telling is not nearly as effective a means of soul-transmission as is living with someone you love for many years of your lives, and sharing profound life goals with them — that's for sure!
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.
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.
Solomon: Your entry in Wikipedia says that your work has inspired many students to begin careers in computing and artificial intelligence.
Hofstadter: I have no interest in computers. The entry is filled with inaccuracies, and it kind of depresses me.
Solomon: So fix it.
Hofstadter: The next day someone will fix it back.
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.
What gives this zeugma its flavor of oddness is that one of the meanings of the verb “restore” that it depends on is “to return something that has been lost”, while the other meaning used is “to make something regain its former, more ideal state”, and although these two senses of the same word are clearly related, they are just as clearly not synonymous.