Metamagical Themas

Questing for the Essence of Mind and Pattern

Douglas R. Hofstadter

An anthology of Hofstadter’s articles in Scientific American


One of my personal mottos is: “Apathy on the individual level translates into insanity at the mass level (Thursday, December 31, 2015, 08:20 PM, page 10)

Life is not worth living if one can never afford to be delighted or have fun. (Thursday, December 31, 2015, 08:25 PM, page 11)

many people-even remarkably smart people-turn off when faced with issues that are too big. We need to make such issues graspable. To make xxvii Introduction them graspable and fascinating as well, we need to entice people with the beauties of clarity, simplicity, precision, elegance, balance, symmetry, and so on. (Friday, January 01, 2016, 02:24 PM, page 11)

Ray Hyman, a psychologist who studies deception. (Friday, January 01, 2016, 02:27 PM, page 15)

The Tao Is Silent (Friday, January 01, 2016, 02:55 PM, page 16)

How should one translate the French sentence Cette phrase en francais est difficile a traduire en anglais ? Even if you do not know French, you will see the problem by reading a literal translation: “This sentence in French is difficult to translate into English.” The problem is: To what does the subject (“This sentence in French”) refer? If it refers to the sentence it is part of (which is not in French), then the subject is selfcontradictory, making the sentence false (whereas the French original was true and harmless); but if it refers to the French sentence, then the meaning of “this” is strained. (Friday, January 01, 2016, 03:42 PM, page 18)

am simultaneously writing and being written. (Friday, January 01, 2016, 03:52 PM, page 21)

am the thought you are now thinking. (Friday, January 01, 2016, 03:53 PM, page 21)

As long as you are not reading me, the fourth word of this sentence has no referent. The reader of this sentence exists only while reading me. (Friday, January 01, 2016, 03:56 PM, page 22)

urn to a most interesting (Friday, January 01, 2016, 03:59 PM, page 23)

David Moser, a composer and writer, (Friday, January 01, 2016, 04:05 PM, page 25)

This gubblick contains many nonsklarkish English flutzpahs, but the overall pluggandisp can be glorked from context. (Friday, January 01, 2016, 04:06 PM, page 25)

Does this sentence remind you of Agatha Christie? (Friday, January 01, 2016, 04:45 PM, page 27)

Machines, in trying to make sense of sentences, have access to nothing more than the form of such sentences. The content, if it is to be accessible to a machine, has to be derived, extracted, constructed, or created somehow from the sentence’s physical structure, together with other knowledge and programs already available to the machine. (Friday, January 01, 2016, 04:57 PM, page 31)

Content is just fancy form.” (Friday, January 01, 2016, 05:06 PM, page 32)

a history exam I encountered in boarding school that contained the following: ‘IV. Write a question suitable for a final exam in this course, and then answer it.’ (Friday, January 01, 2016, 11:50 PM, page 36)

Readers are asked to complete the following sentence: In this sentence, the number of occurrences of 0 is __, of 1 is __, of 2 is __, of 3 is __, of 4 is __, of 5 is _, of 6 is __, of 7 is __, of 8 is __, and of 9 is _. Each blank is to be filled with a numeral of one or more digits, written in decimal notation. Robinson states that there are exactly two solutions. (Friday, January 01, 2016, 11:58 PM, page 37)

This thesis is dedicated to all those who did not dedicate their theses to themselves. (Saturday, January 02, 2016, 12:11 AM, page 41)

n Japanese due to the relative lack of pronouns in ordinary speech. (Tuesday, January 05, 2016, 05:37 PM, page 52)

Would not be anomalous if were in Italian. When one this sentence into the German to translate wanted, would one the fact exploit, that the word order and the punctuation already with the German conventions agree. (Monday, February 01, 2016, 09:57 AM, page 53)

My own law, “Hofstadter’s Law”, states: “It always takes longer than you think it will take, even if you take into account Hofstadter’s Law.” (Tuesday, February 02, 2016, 09:46 AM, page 57)

deas like W can sometimes take on a life of their own and drive their own propagation. (Friday, February 05, 2016, 05:08 PM, page 65)

The scheme of things is a system of order. Beginning as our view of the world, it finally becomes our world. We live within the space defined by its coordinates. It is self-evidently true, is accepted so naturally and automatically that one is not aware of an act of acceptance having taken place. (Friday, February 05, 2016, 05:13 PM, page 67)

eflexivity dilemmas of the Protagoras-vs.-Euathlus (Friday, February 12, 2016, 09:49 AM, page 81)

in any modality, perception consists of many layers of processing, from the most primitive or “syntactic” levels, to the most abstract or “semantic” levels. The zeroing-in on the semantic category to which a given raw stimulus belongs is carried out not by a purely bottom-up (stimulus-driven) or purely topdown (category-driven) scheme, but rather by a mixture of them, in which hypotheses at various levels trigger the creation of new hypotheses or undermine the existence of already-existing hypotheses at other levels. (Wednesday, February 17, 2016, 10:31 AM, page 96)

Therefore any recognition program must have at its core a tiered structure precisely like that of government (or that of the rules of Nomic), in which there are levels that are “easily mutable”, “moderately mutable”, “almost mutable”, and so on. The structure of a recognition program-a “choice” program-is seen inevitably to be riddled with reflexivity. (Wednesday, February 17, 2016, 10:35 AM, page 96)

His “golden rule” is: “To be popular with your fellow man, tell him what he wants to hear. He wants to hear about himself. So tell him about himself. But not what you know to be true about him. Oh, no! Never tell him the truth. Rather, tell him what he would like to be true about himself! (Saturday, February 20, 2016, 06:05 PM, page 106)

We have to bring our knowledge and expectations to bear in order to comprehend anything in our world. In most ordinary situations, this use of context and memory enables us to correctly interpret statements and supply the necessary inferences to do this. But this powerful mechanism can go astray in situations where there is no actual message being conveyed. Instead of picking up random noise, we still manage to find meaning in the situation. (Saturday, February 20, 2016, 06:08 PM, page 107)

Chunking is the perception as a whole of an assembly of many parts. An excellent example is the difference between 100 pennies and the concept of one dollar. We would find it exceedingly hard to deal with the prices of cars and houses and computers if we always had to express them in pennies. A dollar has psychological reality, in that we usually do not break it down into its pieces. The concept is valuable for that very reason. (Saturday, February 27, 2016, 10:14 AM, page 140)

Metamagical Themas, Hofstadter

Theories of musical quality are still descriptive and not generative

Metamagical Themas, Hofstadter

Zez Confrey

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the knobs on any one concept depend on the set of concepts that happen to be awake simultaneously in the mind of the person.

Metamagical Themas, Hofstadter

An example of such a slip is furnished to us whenever we make a typo or a grammatical mistake, utter a malapropism (“She’s just back from a one-year stench at Berkeley”) or a malaphor (a novel phrase concocted unconsciously from bits and pieces of other phrases, such as “He’s such an easy-go-lucky fellow” or “Uh-oh, now I’ve given the cat away”), or confuse two concepts at a deeply semantic level (e.g. , saying “Tuesday” but meaning “February”, or saying “midnight” in lieu of “zero degrees”). These types of slip are totally accidental and come straight out of our unconscious mind.

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George P51ya’s How to Solve It

Metamagical Themas, Hofstadter

Newton said that if he had seen further than others, it was only by standing on the shoulders of giants

Metamagical Themas, Hofstadter

Scott Kim’s brilliant article “Noneuclidean Harmony

Metamagical Themas, Hofstadter

The Mathematical Gardner, an anthology dedicated to Martin Gardner, edited by David Klarner

Metamagical Themas, Hofstadter

Philosophers and artificial-intelligence researchers by and large have not paid much attention to the “catchiness” of a given counterfactual. Logicians have devoted a lot of time and effort to trying to figure out what it would mean for a given counterfactual to be true, but to my mind, that’s not nearly as interesting-or even as meaningful-a question as these more psychological questions: Which counterfactuals are likely to be triggered in a human mind by various types of events in the world? Why are some events perceived to be “near misses”, while others are not? Why are some deaths of innocent people viewed as more tragic than other deaths of innocent people?Variations on a Theme as the Crux of Creativity 258

Metamagical Themas, Hofstadter

shall first describe the key misconception. It is to try to capture the essence of each separate concept in a separate “knobbed machine”-that is, to isolate the various Platonic spirits. The key insight is that those spirits overlap and mingle in a subtle way

Metamagical Themas, Hofstadter

Even a program that could act like a mentally retarded person would be a huge advance. The commonest mental abilities-not the rarest ones-are still the central mystery. John McCarthy, one of the founders of the field of artificial intelligence, is fond of talking of the day when we’ll have “kitchen robots” to do chores for us, such as fixing a lovely Shrimp Creole. Such a robot would, in his view, be exploitable like a slave because it would not be conscious in the slightest. To me, this is incomprehensible. Anything that could get along in the unpredictable kitchen world would be as worthy of being considered conscious as would a robot that could survive for a week in the Rockies. To me, both worlds are incredibly subtle and potentially surprise-filled. Yet I suspect that McCarthy thinks of a kitchen as Sampson thinks of book faces: as some sort of simple and “closed” world, in contrast to “open-ended” worlds, such as the Rockies. This is just another example, in my opinion, of vastly underestimating the complexity of a world we take for granted, and thus underestimating the complexity of the beings that could get along in such a world.Ultimately, the only way to be convinced of these kinds of things is to try to write a computer program to get along in a kitchen, or to generate book faces. That’s when you finally come face to face with the extremely limiting notion of what a knob really is. People’s notion of knobs has too much intuitive fluidity to it. It’s hard to identify with a computer and to see things utterly and foolishly rigidly-but that’s where you have to begin if you want to understand why knobbifying the alphabet is a task of vast magnitude, and is a microcosm of the task of knobbifying all of human thought.*** It is very tempting to think that a few degrees of freedom, when combined, can cover any possible situation. After all, the number of possible states of a multi-knob machine is the product of the numbers of settings of each of Metafont, Metamathematics and Metaphysics 292

Metamagical Themas, Hofstadter

Even a program that could act like a mentally retarded person would be a huge advance

Metamagical Themas, Hofstadter

Mathematical structures are among the most beautiful discoveries made by the human mind

Metamagical Themas, Hofstadter

Randomness and Mathematical Proof” by Gregory Chaitin

Metamagical Themas, Hofstadter

y =4 kx (1-x)

Metamagical Themas, Hofstadter

Gödel’s work is, to me, the most beautiful possible demonstration of how meaning emerges from and only from isomorphism, and of how any notion of “direct” meaning (i.e. , codeless meaning) is incoherent. In brief, it shows that semantics is an emergent quality of complex syntax, which harks back to my earlier remark in the Post Scriptum to Chapter 1, namely: “Content is fancy form

Metamagical Themas, Hofstadter

Gödel’s remarkable series of 46 function definitions is, in my book, the world’s first serious computer program-and it is in Lisp.(The Norwegian mathematician Thoralf Skolem was the inventor of the study of recursive functions theoretically, but Gödel was the first person

Metamagical Themas, Hofstadter

Novelflo, a new pseudo-natural language invented by Rhoda Spark of Golden, Colorado. Novelflo

Metamagical Themas, Hofstadter

is impossible for all the papers in a field to be both right and significant. Either many will be wrong or many will be trivial

Metamagical Themas, Hofstadter

you can’t have both total correctness and total novelty

Metamagical Themas, Hofstadter

Patterns of Discovery by Norwood Russell Hanson

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Will your answer to this particular question be `no

Metamagical Themas, Hofstadter

Victoria Fromkin’s book Errors of Linguistic Performance: Slips of the Tongue, Ear, Pen, and Hands

Metamagical Themas, Hofstadter

The Question of Animal Awareness

Metamagical Themas, Hofstadter

what establishes the “concepthood” of something is the way it is integrated into memory

Metamagical Themas, Hofstadter

Dean Wooldridge’s book Mechanical Man: The Physical Basis of Intelligent Life, and

Metamagical Themas, Hofstadter

Well, language is far slipperier than dictionary definitions would have you believe

Metamagical Themas, Hofstadter

The definition not only should be general, but also should incorporate some indication of what the spirit of the idea is.*** Computers have a hard time getting the spirit of things; they prefer to know things to the letter. And so people spend an enormous amount of timeAnalogies and Roles in Human and Machine Thinking 548

Metamagical Themas, Hofstadter

Rigidity comes in many forms, and a rigid drive toward abstraction is no less stupid than a rigid refusal to abstract

Metamagical Themas, Hofstadter

translation is the quintessential form of analogy

Metamagical Themas, Hofstadter

I feel safe in suggesting that translating a novel’s title may sometimes be the most challenging aspect of translating the whole novel

Metamagical Themas, Hofstadter

Awful Days Are Here Again” (traditionally sung by mournful Democrats right after they lose an election) and Frederic Pichon’s celebrated Baptismal March (from his piano sonata in B-flat major)

Metamagical Themas, Hofstadter

In fact, a sense of essence, in essence, is, in a sense, the essence of sense, in effect.*** Any analogy can be viewed as an attempt to reproduce in one metaphorical grid a form that exists in another metaphorical grid. The more coarse-grained the two “grids” are, the more ingenious the analogy-maker has to be to perform the mapping. Roles and substructures must be extracted and weighed and mapped against each other. Shifts of all sorts,Analogies and Roles in Human and Machine Thinking 601

Metamagical Themas, Hofstadter

fact, a sense of essence, in essence, is, in a sense, the essence of sense, in effect.*** Any analogy can be viewed as an attempt to reproduce in one metaphorical grid a form that exists in another metaphorical grid. The more coarse-grained the two “grids” are, the more ingenious the analogy-maker has to be to perform the mapping. Roles and substructures must be extracted and weighed and mapped against each other. Shifts of all sorts,Analogies and Roles in Human and Machine Thinking 601

Metamagical Themas, Hofstadter

In fact, a sense of essence, in essence, is, in a sense, the essence of sense, in effect.*** Any analogy can be viewed as an attempt to reproduce in one metaphorical grid a form that exists in another metaphorical grid. The more coarse-grained the two “grids” are, the more ingenious the analogy-maker has to be to perform the mapping. Roles and substructures must be extracted and weighed and mapped against each other. Shifts of all sorts,Analogies and Roles in Human and Machine Thinking 601

Metamagical Themas, Hofstadter

me, the major question of AI is this: “What in the world is going on to enable you to convert from 100,000,000 retinal dots into one single word `mother’ in one tenth of a second?” Perception is where it’s at

Metamagical Themas, Hofstadter

The central problem of AI is the question: What is the letter a'? Donald Knuth, on hearing me make this claim once, appended, "And what is the letter T?"-an amendment that I gladly accept. In fact, perhaps the best version would be this: The central problem of AI is: What are a’ and `i’

Metamagical Themas, Hofstadter

Once, about ten years back, the MIT “blocks world” was a very fashionable domain. Roberts and Guzman and Waltz wrote programs that pulled visions of three-dimensional blocks out of twodimensional television-screen dot matrices; Winston, building on their work, wrote a program that could recognize instantiations of certain concepts compounded from elementary blocks in that domain (“arch”, “table”, “house”, and so on); Winograd wrote a program that could “converse” with a person about activities, plans, past events, and some structures in that circumscribed domain; Sussman wrote a program that could write and debug simple programs to carry out tasks in that domain, thus effecting a simple kind of learning.Why, then, did interest in this domain suddenly wane?

Metamagical Themas, Hofstadter

In my opinion, the proper choice of domain is the critical decision that an Al researcher makes, when beginning a project

Metamagical Themas, Hofstadter

Terman and Binet and their IQ; test problems

Metamagical Themas, Hofstadter

The premise of Al is that thoughts themselves are computational entities at their own level. At least this is the premise of the information-processing school of AI, and I have very serious doubts about

Metamagical Themas, Hofstadter

strong AI”-is still possible, but thought will simply not turn out to be the formal dream of people inspired by predicate calculus or other formalisms. Thought is not a formal activity whose rules exist at that level

Metamagical Themas, Hofstadter

Symbol Triggering Patterns Are the Roots of Meaning

Metamagical Themas, Hofstadter

The prognosis is good, for “neural” rearranges into “u learn

Metamagical Themas, Hofstadter

Under normal conditions, a ribosome in a bacterial cell can translate about twenty codons per second. In a rabbit cell, things are slower: a little better than one codon per second. I have no idea why rabbits are so much slower than -bacteria

Metamagical Themas, Hofstadter

that rewriting the structural genes will lead, by chance, to the appearance of new, spurious typographical signals. It appears that neither of these conditions is satisfied. Regarding the first, typographical sequences, presumably active ones, have been found within structural genes. As for the second, one cannot exclude the creation of spurious typographical sequences by a new genetic code, except through direct checking of all the structural genes.Lastly, let me make two remarks.First, the existence of two codes means that even with the existing machinery, some messenger RNA sequences must be forbidden, namely those that would have typographical significance.Second, the locking-in of the code means that the logic of the machinery is deeply interwoven with its hardware. One may still distinguish various logical `levels’, but the connections between them will not let themselves be forgotten.Touche! This is precisely my own favorite point used back on me, and I am so delighted by it. It is none other than the statement that in deep translation, you cannot translate content alone-you must pay attention to the interaction between form and content. It harks back to the idea of translating self-referential sentences from one language to another-and what is more self-referential than the beautifully tangled DNA-RNA proteins loop? Consider “This sentence is in English. " Graduates of the A-ooga-Duhhh Memorial School of Translation, if asked to translate it into Chinese, would produce a Chinese sentence asserting of itself that it is in English. But that’s nonsense! Either it should refer to the original English sentence and say that that sentence is in English, or it should refer to itself and say that it is in Chinese. This wishy-washy halfway stuff won’t do! And such remarks hold with a vengeance for the self-documenting sentences that Lee Sallows struggled with so (see Chapters 2 and 3). If you substitute the word “pun” or “allusion via form” for “typographical signal” in Gueron’s commentary, and think of switching one natural language for another, then you have another way of seeing what he is getting at. It is quite strange but absolutely undeniable that DNA is full of puns and allusions via form. One remarkable example is the overlapping-genes pun found in the DNA of the virus 4X 174.There, two completely different proteins were discovered to be coming from the same section of DNA. Two genetic codes? No, nothing of the sort. Two different reading frames. That is, by shifting the DNA over one notch, you get a new set of codons. For example, what reads as “…-TGC-CAA-GGT-C … " one way reads as “…T-GCC-AAG-GTC- T-GCwhen you shift the frame to the right. And both ways code for proteins indispensable to the virus’s tiny quasi-life! Such incredible literary creativity is something nobody could ever have anticipated. DNA is a marvel of selfreferential game-playing that I daresay has no rival in human literature. But then, human literature hasn’t had three billion years to develop

Metamagical Themas, Hofstadter

Such incredible literary creativity is something nobody could ever have anticipated. DNA is a marvel of selfreferential game-playing that I daresay has no rival in human literature. But then, human literature hasn’t had three billion years to develop! I couldn’t agree more with Gueron’s concluding point

Metamagical Themas, Hofstadter

The Evolution of Cooperation, published in 1984

Metamagical Themas, Hofstadter

apathy at the individual level translates into insanity at the mass level

Metamagical Themas, Hofstadter

Garrett Hardin, an evolutionary biologist, Wrote a famous article about this type of phenomenon, called “The Tragedy of the Commons

Metamagical Themas, Hofstadter

Science: Good, Bad, and Bogus, Martin Gardner

September 10, 2016 |