In , he moved to the University of Michigan in Ann Arbor, where he was hired as a professor of psychology and was also appointed to the Walgreen Chair for the Study of Human Understanding. In he returned to Bloomington as "College of Arts and Sciences Professor" in both cognitive science and computer science. He was also appointed adjunct professor of history and philosophy of science, philosophy, comparative literature, and psychology, but has said that his involvement with most of those departments is nominal. Other more recent models include Phaeaco implemented by Harry Foundalis and SeqSee Abhijit Mahabal , which model high-level perception and analogy-making in the microdomains of Bongard problems and number sequences, respectively, as well as George Francisco Lara-Dammer , which models the processes of perception and discovery in triangle geometry. He seeks beautiful mathematical patterns, beautiful explanations, beautiful typefaces, beautiful sonic patterns in poetry, etc. Hofstadter invented the term "ambigram" in ; many ambigrammists all over the world have since taken up the concept.

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In the basic canon, the first voice enters, and after a period, the second voice enters at the same beginning as the first, layering on top of each other. There are also more complicated canons, where the second voice may enter at a different pitch as well. The transition is seamless, and allows it to continue rising forever. Such as in the famous Escher paintings like the infinite staircase.

For example, the set of all walruses is not itself a walrus. Or, they are self-swallowing, such as the set of all things that are no Joan of Arc. So sets are either run of the mill, or self-swallowing, but we can define a set as The Set of All Run of the Mill Sets which must be neither self-swallowing or run of the mill. The culprit in these paradoxes is self reference, or strange loopiness. But a complete system requires self reference, thus, strange loops.

In formal systems, theorems are merely produced according to certain rules of the system. A car will never pick up the idea that it is supposed to avoid other cars. This is the M-Mode mechanical mode and the I-Mode intelligent mode. It applies when two complex structures can be mapped onto each other, in such a way that to each part of one structure there is a corresponding part in the other corresponding structure, where the two parts play similar roles in their respective structures.

The first letters of the different lines in the dialogue spell out a sentence that is itself self-referential. People attribute inherent meaning to words, when their context is just as important. The noise requires a certain medium. Little Harmonic Labyrinth In this dialogue, Tortoise and Achilles end up being abducted into a hot air balloon off of the ferris wheel.

They then go in a step further to the alligator painting. Then they go down one more story into the labyrinth. But in circular definitions it continues forever. Canon by Intervallic Augmentation In this dialogue, they discuss modifying a tune to get different tunes but with the same ratio of note changes, e.

Alternatively, a molecule of DNA is a set of information genotype which is converted into a physical organism phenotype. Can a text have enough inner logic that its meaning is fully restored whenever intelligence comes into contact with it? Or must there always be some element of the information revealer bestowing meaning to it? We can say that meaning is part of an object to the extent that it acts upon intelligence in a predictable way.

To understand the inner message is to understand the message intended by the sender To understand the frame is to recognize that there is some need for a decoding mechanism To understand the outer message is to build, or know how to build, the proper decoding mechanism for the message Consider a bottle on a beach: the frame is found when you pick up the bottle and see it contains a message.

Chromatic Fantasy, and Feud This is the dialogue where the Tortoise insists on challenging things Achilles repeats that the Tortoise has just said, e. A Mu Offering This is the discussion of Koans and zen strings. IX: Mumon and Godel The monk Mumon collected 48 koans with poems and short commentaries that accompanied them.

A concise explanation of enlightenment: transcending dualism. As soon as you perceive an object, you draw a line between it and the rest of the world. You divide the world, artificially, into parts and thereby miss the Way. It is the fate of us as higher beings to have to strive for ism without ever being able to attain it fully.

There is no such thing as an uncoded message, only a message written in a more familiar code. X: Levels of Description and Computer Systems Intelligence depends on the ability to create high-level descriptions of complex arrays, such as chess boards, printed pages, or paintings.

There are certain epiphenomena, consequences of the system that are not contained in the system. Perhaps the mind can be understood without understanding the lower levels on which it both depends and does not depend. Is consciousness an epiphenomenon? Or do you have to go down to the level of the nerve cell to understand the mind?

Just as every individual neuron need not be intelligent to create an intelligent being. You might think of your brain as an ant colony. There are emergent pieces of a system. The intensionality of thought gives it its flexibility, it lets us imagine new worlds and combine and chop up descriptions. A single neuron can only respond by firing or not firing. There are two challenges: one is to explain how the low-level traffic of neuron firings gives rise to the high-level traffic of symbol activation.

The other is to explain the high-level traffic of symbol activation in its own terms, to make a theory which does not talk about the low-level neural events. If the latter is possible, then intelligence can be realized on non-brain hardware. Rather, it happens naturally from your stored symbols of cars and mountains, without being explicitly declared. Knowledge is not stored explicitly, but implicitly, in a spread out manner, rather than as a local packet of information.

Simple facts such as relative sizes of objects have to be assembled rather than merely retrieved. Could we map part of one mind onto another one? Clearly not entirely, since if it did, there would be two humans with identical thoughts.

Even within yourself your brain changes, imagine looking at something you wrote even a few months ago. The symbols among people with the same native language will likely be similar, but how does that change in new languages? Aria with Diverse Variations Here they introduce the diagonals, first talk about DH himself, and make allusions to ending the discussion earlier than the written discussion ends.

But if your system is not sufficiently powerful, then your system is by virtue incomplete. Birthday Cantatatata…. No matter how much it twists and turns, it is still following the rules inherent in itself. Including us. But you cannot quite break out of yourself and be outside of yourself.

In zen we can see this idea of self transcendence. Edifying Thoughts of a Tobacco Smoker This is the dialogue with the surreal paintings that the Crab keeps interacting with while talking to Achilles. Self-Ref: Self referential object or entity. Incompleteness Theorem and DNA: It is always possible to design a strand of DNA which, if injected into a cell, would, upon being transcribed, cause such proteins to be manufactured as would destroy the cell or the DNA , and thus result in the non-reproduction of that DNA.

XVIII: Artificial Intelligence: Retrospects The Turing Test imagines a computer and a person in another room, with you asking them questions trying to figure out which one is the human and which the computer. If you cannot tell, then the computer must be conscious. One objection might be that it puts too much challenge on the machine. Is the car truly speaking? Is it the writer? Is it the phrase itself? The dust? He has to reconsider the problem space. Representation of knowledge is at the crux of AI.

Contrafactus This dialogue has the football game and the television that lets them view counterfactual situations. XIX: Artificial Intelligence: Prospects In everyday thought, we are imagining slightly different versions of situations that happened. Symbols interact via fission and fusion. Fission is where they gradually separate into multiple new symbols. Fusion is where they come together to create larger meta symbols. They just pop out at us. DH gives some speculations at the end of this chapter, including that a computer program will write beautiful music, emotions will not be explicitly coded into a machine, chess programs will not be exclusively chess players and thus could refuse to play chess , and that AI programs may not become super intelligent.

Sloth Canon In this dialogue, the music and the piano are backwards, creating an odd feel to the sound. Do words and thoughts follow formal rules?

Yes, if you go down to the lowest level, the hardware, to find the rules. Certain rule sets are inviolate, they cannot be changed. Author Z could have author E in a story, who has author T in a story, who has author Z in a story… but only if there is a fourth author, author H, who has them all in his own story! They are the strange loop, or tangled hierarchy, but H is outside of it.

We feel self-programmed, but we have no access to our lower levels. Once you begin to question your own sanity, you can get caught in an ever tightening vortex of self-fulfilling prophecies. Death, personal non-existence, is incomprehensible. When you try to imagine your nonexistence you have to try to jump out of yourself. Yet we still feel drawn to the hierarchy of realness. Constant level crossing is what creates our sense of self, it will be necessary to be able to slip between multiple levels comfortably to understand the full richness of the mind-brain system.

Self-reference and loopiness is likely at the core of understanding minds and developing AI. We, on the outside, can know that the print gallery image is incomplete in a way that the man in it can never know. We can step outside and see the hole in the system, which he can never observe.

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Gödel, Escher, Bach: un Eterno y Grácil Bucle

Not even its publishers or readers who just absolutely love it. A quick glance at the back cover will give you the same impression - even the glowing, two-sentence blurbs are hilariously vague, all of them variations on the theme of "Well, that certainly was Yes, quite a wonderful something indeed. Or put less delicately, how are you supposed to know whether reading all dense, sprawling pages is worth your while? The short answer is: "Read this book if you like to think about thinking, as well as to think about thinking about thinking. At its heart, this book is about whether you can start with simple parts and from them, build a system which is so complicated that it becomes more than the sum of its parts in a significant sort of way. For example, scientists have a very clear understanding of how a single neuron functions.

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Gödel, Escher, Bach: An Eternal Golden Braid

In the basic canon, the first voice enters, and after a period, the second voice enters at the same beginning as the first, layering on top of each other. There are also more complicated canons, where the second voice may enter at a different pitch as well. The transition is seamless, and allows it to continue rising forever. Such as in the famous Escher paintings like the infinite staircase. For example, the set of all walruses is not itself a walrus. Or, they are self-swallowing, such as the set of all things that are no Joan of Arc.


Gödel, Escher, Bach: un'eterna ghirlanda brillante

Ad analisi logico-matematiche dal taglio originale e creativo, ma molto rigoroso, si alternano capitoli di dialogo tra due personaggi immaginari, Achille e la tartaruga che con i loro approcci analitici molto immediati introducono al tema di volta in volta in esame, nella ricerca di un filo logico che unisca le idee, le opere e il sentire dei protagonisti del saggio. Discute anche cosa significhi comunicare, di come la conoscenza possa essere rappresentata e conservata, dei metodi e dei limiti della rappresentazione simbolica e anche la nozione fondamentale dello stesso "significato". Struttura[ modifica modifica wikitesto ] GEB ha la forma di un intreccio di varie narrazioni. Hofstadter basa gli altri dialoghi su questo, introducendo a volte nuovi personaggi come il Granchio, il Genio e altri.

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