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.

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"We have seen recursion in the grammars of languages, we have seen recursive geometrical trees, which grow upwards forever, and we have seen one way in which recursion enters the theory of solid state physics. Now we are going to see yet another way in which the whole world is built out of recursion. This has to do with the structure of elementary particles: electrons, protons, neutrons, and the tiny quanta of electromagnetic radiation called "photons". We are going to see that particles are - in a certain sense which can only be defined rigorously in relativistic quantum mechanics- nested inside each other in a way which can be described recursively, perhaps even by some sort of "grammar"."

"the Godelian strange loop that arises in formal systems in mathematics (i.e., collections of rules for churning out an endless series of mathematical truths solely by mechanical symbol-shunting without any regard to meanings or ideas hidden in the shapes being manipulated) is a loop that allows such a system to "perceive itself", to talk about itself, to become "self-aware", and in a sense it would not be going too far to say that by virtue of having such a loop, a formal system acquires a self."

I am a lifelong lover of form–content interplay, and this book is no exception. As with several of my previous books, I have had the chance to typeset it down to the finest level of detail, and my quest for visual elegance on each page has had countless repercussions on how I phrase my ideas. To some this may sound like the tail wagging the dog, but I think that attention to form improves anyone’s writing. I hope that reading this book not only is stimulating intellectually but also is a pleasant visual experience.

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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.

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.

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.

(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.