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.
There are those who will immediately be drawn to the idea of pattern-seeking, and.
To paraphrase Descartes again: “I think; therefore I have no access to the level where I sum.
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.
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.
It is an inherent property of intelligence that it can jump out of the task which it is performing, and survey what it has done; it is always looking for, and often finding, patterns.
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.
And that is also the way the human mind works – by the compounding of old ideas into new structures that become new ideas that can themselves be used in compounds, and round and round endlessly, growing ever more remote from the basic earthbound imagery that is each language’s soil.
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.
In short, Godel showed that provability is a weaker notion than truth, no matter what axiomatic system is involved.
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.
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.
What goes hand in hand with the willingness to playfully explore a serendipitous connection is the willingness to censor or curtail an exploration that seems to be leading nowhere.
It sometimes feels as if I had shouted a deeply cherished message out into an empty chasm and nobody heard me.
By the time we emerge from childhood, we have acquired a reflex-level intuition for where most of our everyday world’s loci of unpredictability lie, and the more unpredictable end of this spectrum simultaneously beckons to us and frightens us. We’re pulled by but fearful of risk-taking. That is the nature of life.
One must distinguish, it seems to me, between “head pattern” and “heart pattern”, or, in more objective-sounding terms, between syntactic pattern and semantic pattern.
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.
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.
The closer one looks, the more such questions one will find, and the more they are going to seem absurd.
By this point, readers will probably they have endured enough of Nabokov’s trashing of his rivals, and yet I cannot resist including just one last blast. By all means, feel free to skip it, especially if your stomach is turned by extreme boorishness.