an Eternal Golden Braid
by Douglas Hofstadter
GEB
The following are my notes as I read the book. Some day in the future I’ll ironically complete this review.
1. I read this book because I needed to understand what motivated my eldest son to pursue the study of cognitive science. If you need a different reason to inspire your to read this book, go to the book store and open GEB to pages 532- 533 and comprehend Hofstadter's "Dogmap" you would begin to appreciate the essence of the book. In this essence there is a blend of multi level constructs of thought that provides a scientific or academic understanding of cognitive science mixed in with unique blend of Hofstadter humor to clearly place this book in any philosophy college as well. . It may be just enough to lure you not just in to this book but the world of cognitive science.
2. In a self referential way, this book is about "level thinking", where knowledge at a high level may or may not have been constructed or made evident at a lower level. The notion that understanding things at a high level with the understanding of its lower level constructs is the mark of intelligence, of biological or any other means. This book examines the meaning of life if life were to begin at the thought level. In the course of discussion meaning, the scientific and then esoteric of theorems and truth come out. What is a self evident truth an undeniable proof, and what an accepted truth a bottomed out recursive analysis of any subject where bottoming out is most apropos in an every day practical world. For this reader coming to that understanding of the material put forth was a mental workout 740 pages long.
3. This Book is about
a. Meaning truth
i. evidence
b. Math – Music - Art
c. microbiology
i. how the brain works
ii. how protein works
iii. DNA, symbols
iv. RNA, the messenger
v. Thought is in the RNA message not the DNA symbols.
d. AI
i. Math
ii. symbols
iii. Logic
iv. Programming said logic
e. The Eternal Golden Braid
i. Godel’s incompleteness theorem
ii. Bach’s, Fugues and the famous Musical Offering
iii. Escher’s Tangled Hierarchy of multilevel thinking
iv. The most remarkable concept that is only implied by the author in his title at least, and can only be constructed in the context of the mind of this reader/writer, is the author’s word choice of “Eternal”, a symbol of thought that eludes to time. Eternal suggests an endless lifespan. While Hodstadter’s analytical delivery goes to the depth of constructive scientific thought, it takes on a feel of Zen Buddhism and also implies the same message of Jesus Christ that we are not of this world and that through transcendence, may you find your self at peace, one with all that is.
4. Knowing that every aspect of our physical make up is incomplete, and every aspect of every other physical manifestation of the universe is also incomplete is exactly what makes us whole in our oneness of the universe.
This is Christ's message of transcendence; your being is not of this world.
5. The book spawned TJ's DNA model of a helix reflecting symbols. Now I am envisioning a model of symbols and signals where a massive amount of laser light patterns of a mesh as in Indra's Net each of a color all rotating at different rates of speed around an axis. When the intersections of one nets mesh passes through the intersection of another net's mesh; the mixing of the individual color creates a new color. When each net is connected to a terminal bus for input that bus controls the rate of rotation. The AI comes in where when and individual net becomes so influenced by the interaction of other nets that the base color of that net changes as in changing your mind on some basic premise. The changing of color in that one mesh will now cause a change in color patterns representing a higher level of a changing of the mind. Then on a higher level each of the rotating Indra Armatures are networked. I haven't worked that out at even the idea level yet.
6. This book is like a gymnasium for the brain. Reading it is a mental workout. Your brain comes out of each workout with yet a fresher look on your world. Each degree of freshness adds a new level of thinking. Just when you think you have bottomed out Hoffstadter takes you up a level or ten and associates a presentation of a complex description of the way things work to an outward phenomena of every day occurrences that an average person can not just understand but appreciate to the extent that the mental workout will change the very way you interact with your world around. Being always conscious of your red blood cell count is not required to have a conscience understanding that a healthy diet will contribute to your red blood cell count.
7. Self referential games; without self is there meaning?
8. My thought: in a novel, why do symbols of ideas or otherwise understood as words to tell a story produce a more meaningful interaction with the reader than images, voice if a movie?
9. Page vii Hofstadter suggests a paradox that reasoning of motion as an example makes reasoning impossible.
My thoughts: if your original perspective is incongruent with reality then Hofstadter’s paradox is not a paradox at all it just faulty reasoning.
10. Page 49: isomorphism applies when two complex structures can heaped to each other I. Such a way that to each part of one structure there is a corresponding part on the other structure where corresponding means that the two parts play similar roles in there respective structures.....Information perceiving information
11. Contracrostipunctus: truth is found in the feedback loop of I. When I is a perfect mirror, forward and backwards, converse and inverse, of what is projected, no matter how multifaceted the individual, you reach the same transcendence as Jonathon Livingston Seagull’s grey to white, Gandalf's grey to white, J. S, Bach's final Contrapunctius, Christ's resurrection.
12. Meaning requires context. A DNA genome can only have a mechanical ability to grow in to it's phoneme. In the DNA of man, exists exotic propensity for the initiation of thought, a higher degree of conscience separate from consciousness. That thought only has meaning within the context of all thought, whether consciously available to the subject thinker or not. The agent of thought is the trigger responsible for the word symbol God where with standing all it's variations, derivative meanings is the context of life for mankind. Where the mystery comes in to play is the context of an environment that nourishes man without his thought. We call this nature, the nature of our context within our context. The closer we come to understanding this the more we appreciate the mechanics of nature in the study of the mystery of the universe, God..
13. Is the pursuit of AI along the lines of programming possible when programming uses logic and within logic, a derivative of the mathematical sciences, looms Godel's incompleteness theorem that states the answer lay out side the equation? In other words logic can be mapped and intelligence cannot. Intelligence is when a being can think both logically and illogically to discover or really to possibly create a new axiom. Edison thought through 15,000 experiments logically before the light came on. I am curious if the eventual success had a pre ordained logic that was proved or was there accidental discoveries along the way. Logically and illogically as said is a paradox. Is there a string of logic that contains all truths within itself? Says Godel no. So must one defy logic to find truth. Is truth separate from meaning? Can there be meaning in things that are false?
14. If in all things that are not axiomatic having a possibility of contradicting each other when is it prudent to accept a "thing" on faith and when do you take the test to the "bottom" where the shouting match occurs?
15. In TNT Hofstadter states in the context of determining truth from that which is false that it is important to follow the rules and not one's knowledge of the passive meanings of the symbols, he further states the latter type of knowledge is invaluable in guiding the route of derivation.
I interpret this invaluable route to be that of intelligence of which is the essence of breaking through mans yet to be completed understanding of the universe. To do this would be to prove Godel’s incompleteness theorem to be false. Is breaking this paradox like transcending "apparent" realities such a time?
16. In the context of bottoming out in a recursive pattern does a man’s mind have a bottom? And if so and machines are made capable to run loops adnauseum is that intelligent life? Or is that analysis paralysis? Is not a continuous loop and a bottomless recursion the same thing of which both by there definition would be very limited in determining axioms?
17. Intelligence depends crucially on the (ability to create high-level descriptions of complex arrays, such as chess boards, television screens, printed pages or paintings."
18. On recursive-ness: because we find breaking all events and object down to it's core code not only too difficult but also in many cases void of meaning anyway we break it down to appropriate levels creating symbols and each level sends signals to other symbols creating new symbols which are all abstracts of reality. Your meaning of life is at best an abstract of mine.
19. Because man freely chooses which data to hold and which to discard and which to discard abstracts are the precise results of free will. Or is it instinctive will until you are awakened to this phenomena of man over all other species. Is this not what we mean by creation...we each create our own abstract of the world around us
20. As we ramble through the arithmoqueinification logic to rationalize supernatural numbers and find Lincoln's answer to how long a man’s legs should be; you come to a demonstrable bottoming out of recursive-ness. Is there a point where deriving an axiom without proving it becomes profitable? Or in the vernacular of Hofstadter, is there a ~profit in pursuit of supernatural numbers, the pursuit of numbers that have no unique definition?
21. When a computer can see three dimensions on a flat piece of paper like humans do the discussion on artificial intelligence may begin
22. Page 521. What RNA is to life itself, agents of the DNA message to ribosome, protein, and amino acids; are people's thoughts, the message between the synapse dendrites are to each other. The balance of life rests on a scale in the context of the universe. All things must be interpreted in the context of the whole.
23. If you were to go to the book store and open GEB to pages 533- 533 and comprehend Hofstadter's "Dogmap" you would begin to appreciate the essence of the book. It may be just enough to lure you not just in to this book but the world of cognitive science.
24. Page 582. It is certain that Hofstadter is circling around the mechanics and the definition of meaning. Then by page 582 he suggests that because if the endless connections to all possibilities in a decision, time is the one variable that renders the whole definition futile. However the mechanics remain sound.
25. Page 665-8. As Hofstadter discusses his epigenesis of the crab canon and describes the fission of thought (his) he draws a parallel to bio chemistry and implies through a parallel mapping that the construct of thought and life are replicas of each other in a self refererential way
26. The reason we need a mate is we are incapable of judging whether our rough system is peculiar or not through self reference.
Bibliography
1. Page 65 things become quite confusing as soon as your perceive :meaning” in the symbols which your are manipulating.
2. Page 87 Thus, at first sight, it seems that Godel has unearthed a hitherto unknown, but deeply significant, difference between human reasoning and mechanical reasoning. The mysterious discrepancy in the power of living and non living systems is mirrored in the discrepancy between the notion of truth, and that of theorem-hood…or at least that is the romantic way to view the situation.
3. Page 133 This is the crucial fact that distinguishes recursive definitions from circular ones. There is always some part of the definition which avoids selfe reference. So that the action of constructing an object which satisfies the definition will eventually bottom out.
4. Page 142 An agnostic friend of mine once was struck by G-plot’s infinitely many infinities that he called it “ a picture of God”, which don’t think is blasphemous at all.
5. Page 162 To put it as succinctly as possible, one view says that in order for DNA to have meaning, chemical contest is necessary; the other view says that only intelligence is necessary to reveal the “intrinsic meaning” of a strand of DNA.
6. Page 192 Once again, we are up against the issue which Lewis Carrol set forth in his Dialogue: you can’t go on defending your patterns of reasoning forever. There comes a point where faith takes over.
7. Page 193 in Propositional Calculus…rules are derived. It is a part of knowledge which we have about the system. That this rule always keeps you within the space of theorem needs proofs, of course – but such a proof is not like a derivation inside the system. It is a proof in the ordinary intuitive sense – a chain of reasoning carried out in the I-mode.
8. Page 197 More radical attempts abandon completely the quest for completeness or consistency, and try to mimic human reasoning with all its inconsistencies. Such research no longer has as its goal to provide a solid underpinning for mathematics, but purely to study human thought processes.
9. Page 210 Now the translations of “6 is even” are quite different strings and it is by no means obvious that theoremhood of any one of them is tied to theoremhood of any of the others….The evidence lies in our minds, since as humans, we almost automatically think about interpretations, not structural properties of formulas.
10. Page 228 Thus, it is important to embed TNT within a wider context, a context which enables new rules of inference to be derived, so that derivations can be speeded up. This would require formalization of the language in which rules of inference are expressed-that is, the metalanguage. And one could go considerably further. However, none of those speeding up tricks would make TNT any more powerful; they would simply make it more usable.
11. Page 285 or to take a sequence of images on a television screen which shows Shirley McLean laughing. When we watch that sequence, we know that we are actually looking not at a woman, but it is the furthest thing from out min. We have these two wildly opposing representations of what is on the screen, but that does not confuse us. We can just shut one out, and pay attention to the other-which is what all of us do, Which is “more real”? It depends on whether you’re a human, a dog, a computer, or a television set.
12. Page 287 intelligence depends crucially on the ability to create high-level descriptions of complex arrays such as chessboards, television screens, printed pages.
13. Page 302 This is kind of primordial self-knowledge which is so obvious that it is hard to see it all: it is like being conscious that the air is there. We never really bother to think about what might cause these defects of our minds: namely, the organization of our brains. To suggest ways of reconciling the software of the mind with the hardware of the brain is a main goal of this book.
14. Page 309 In coming Chapters, where we discuss the brain, we shall examine whether the brain’s top level-the mind-can be understood without understanding the lower levels on which it both depends and does not depend. Are there laws of thinking which are “sealed off” from the lower laws that govern the microscopic activity in the cells of the brain? Can mind be “skimmed” off of the brain and transplanted into other systems? Or is it possible to unravel thinking processes into neat and modular subsystems? Is the brain more like an atom, a renormalized electron, a nucleus, a neutron, or a quirk? Is consciousness an epiphenomenon? To understand the mind, must one go all the way down to the level of the nerve cells?
15. Page 322 I find it much easier to change points of view. When I do so, vocabulary of technology comes back: the MEANING of the caste distribution and PURPOSFULNESS of signals. This not only happens when I think of aunt colonies, but also when I think about my own brain and other brains. However, with some effort I can always remember the other point of view if necessary, and drain all these systems of meaning too.
16. Page 349 on Modules Which Mediate Thought Processes: Philosophically, the most important question of all this: What would the existence of modules-for instance, a grandmother module-tell us? Would this give us any insight into the phenomenon of our own consciousness? Or would it still leave us as much in the dark about what consciousness is, an does knowledge that a brain is built out of neurons and glia? The crucial step that needs to be taken is from a low-level – neuron to neuron – description of the same state of brain. ….we want to shift the description of the brain state from signal level to symbol level.
a. My thought; I am not sold on this as I get from the same material that intelligence is a construct of colliding ideas at the messenger level-the RNA level, not the DNA symbol level.
17. Page 349 It is an interesting question whether in each symbol there are certain core neurons, which invariably fire when the symbol is activated. If such a core set of neurons exists, we might refer to it as the “invariant core” of the symbol.
18. Page 355 Sometimes conditions can arise where two previously unlinked symbols get activated simultaneously and in a coordinated fashion. The may fit together so well that it seems like an inevitable union. And a single new symbol is formed by the tight interaction of the two old symbols. If this happens, it would be fair to say that the new symbol “always had been there but never had been activated” – or should one say it has been “created”?
19. Page 360 Our facility for making instances out of classes and classes out of instances lies at the basis of our intelligence, and it is one of the great differences between human thought and the thought processes of other animals.
20. Page 378 reliable pathways of (thought or reason) are what constitute knowledge. Pieces of knowledge merge gradually with beliefs, which are also represented by reliable pathways, but perhaps ones which are more unsusceptible to replacement if, so to speak, a bridge goes out, or there is a heavy fog. This leaves us with fancies, lies, falsities…
21. Page 381 You will again chunk these programs in your mind, looking for conceptual hardware, you are not comparing software-you are comparing “etherware” the pure concepts which lie back of the software. There is some sort of abstract “conceptual skeleton” which must be lifted out of the low levels before you can carry out a meaningful comparison of two programs in different computer languages, of two animals, or of sentences in different natural languages.
22. Page 383 The physical status of a brain, if read correctly, gives information telling not which pathways could be followed, but rather how much resistance could be offered along the way.
23. Page 385 To be precise, by “subsystem”, I mean a constellation of symbols, each of which can be separately activated under the control of the subsystem itself. The image I wish to convey of a subsystem is that it functions almost as an independent “subbrain”, equipped with its own repertoire of symbols which can trigger each other internally.
24. Page 389 Although conscious beings have the power of going on, we do not wish to exhibit this simply as a succession of tasks they are able to perform, nor do we see the mind as an infinite sequence of selves and super-selves. Rather, we insist that a conscious being is a unity, and though we talk about parts of the mind, we do so only as a metaphor, and will not allow it to be taken literally.
25. Page 407 the pq system does not include enough of the core truths of N to count as “a number theory.” What, then, are these core truths of N? They are the primitive recursive truths: that means the involve only predictably terminating calculations.
26. Page 429 If we accept CT-Thesis, we have to conclude that Gloop is a myth – there are no restrictions to remove in Floop, no ways to increase its power by unshackling it as we did ion Bloop.
This puts us in the uncomfortable position of asserting people can calculate Reddiag [N] for any value of N, but there is no way to program a computer to do so. For if it could be done at all, it could be done in Floop – and by construction, it can’t be done in Floop. This conclusion is so peculiar that it should cause us to investigate very carefully the pillars on which it rests. And one of them if you will recall, was our shaky assumption that there is a decision procedure which can tell terminating form non terminating Floop programs. The idea of such a decision procedure already seemed suspect, when we saw the existence would allow all programs of number theory to be solved in a uniform way. Now we have double the reason for believing that any termination test is a myth – that there is no way to put Floop programs in a centrifuge and separate out terminators from non terminators.
27. Page 438 The first key idea of Godel’s proof is the deep discovery that there are strings of TNT which can be interpreted as speaking about other strings of TNT; in short, that TNT as a language, is capable of “introspection”, or self scrutiny. This is what comes from Godel-numbering. The second key idea is that the property of self scrutiny can be entirely concentrated into a single string; thus that string’s sole focus of attention is itself. This “focusing trick” is traceable, in essence, to Cantors diagonal method.
28. Page 479 In Zen too, we can see this preoccupation with the concept of transcending the system.
29. Page 501 But recall that in Chapter VI, we made the concept of “intrinsic meaning” dependent on a hypothesized universal notion of intelligence. The idea was that, in determining the intrinsic meaning of an object, we could disregard some types of outer message – those which would be universally understood. That is, if the decoding mechanism seems fundamental enough, in some ill-defined sense, then the inner message which it lets be revealed is the only meaning that counts.
30. Page 503 Clearly an individual is never identical to either of its parents: why, then, is the act of making young called “self reproduction”? The answer is that there is a course grained isomorphism between parent and child; it is an isomorphism which preservers information about species, Thus what is reproduced is the class, rather than the instance.
31. Page 517 As was mentioned above, in many cells, DNA, the ruler of the cell, dwells in its private “Throne Room” the nucleus of the cell. But most of the “living” in the cell goes on outside of the nucleus, namely the cytoplasm – the “ground” to the nucleus “figure” In particular, enzymes which make practically every life process go, are manufactured by ribosome in the cytoplasm, and they do most of their work in the cytoplasm.
32. Page 519 Now when a strand of mRNA, after it escapes into the cytoplasm, encounters a ribosome, a very intricate and beautiful process called translation takes place. It could be said that this process of translation is at the very heart pf all life, and there are many mysteries connected with it.. But essence it is easy to describe. First let us give a picturesque image, and then render it more precise. Imagine the mRNA to be like a long piece of magnetic recording tape, and the ribosome to be like the tape recorder. As the tape pass through the playing head of the recorder, it is “read” and converted into music, or other sounds. Thus magnetic markings are “translated” into notes. Similarly,, when a “tape” of mRNA passes through the “playing head” of a ribosome, the “notes” which are produced are amino acids, and the “pieces of music” which they make up are proteins. This is what translation is all about.
33. Page 541 Henkin Sentences and Viruses: Now both of these contrasting types of self-reference in molecular biology have their counter parts in mathematical logic. We have already discussed the analogue of self-defeating phages – namely, strings of the Godal type, which assert their its own unproducibility within specific formal systems. But one can also make a counterpart sentence to a real phage: the phage asserts its own producibility in a specific formal system. Sentences of this type are called Henkin Sentences, after the mathematical logician Leon Henkin. They can be constructed exactly along lines of Godal sentences, the only difference being the omission of a negation. One begins with an “uncle” pf course: 3a3a’:
34. Page 547 Illustrative of this is the amazing fact that in biological systems,all the various features necessary for self replication (viz language, program, data, interpreter and processor) cooperate to such a degree that all of them are replicated simultaneously – which show how much deeper is biological self-rep’ing than anything else yet devised along those lines by humans.
35. Page 559 We have come to the point where we can develop one of the main theses of this book: that every aspect of thinking can be viewed as a high-level description of a system which, on a low level, is governed by simple, even formal rules. The system is of course is the brain – unless one is speaking of thought processes flowing in another medium, such as computer circuits.
36. Page 577 There is no reason to believe that a computer’s faultlessly functioning hardware could not support high-level symbolic behavior which would represent such complex states as confusion, forgetting, or appreciation of beauty. It would require that there be massive subsystems interacting with each other according to a complex logic. The overt behavior could appear either rational or irrational, but underneath it would be the performance of reliable, logical hardware.
37. Page 582 by contrast, the semantic aspects of form are those which cannot be tested in predictable lengths of time: the require open ended test. Such an aspect is theoremhood of TNT-strings, as we have seen. You cannot just apply some standard test to a string and find out it is a theorem. The act of pulling out a string’s meaning involves, in essence, establishing all the implications of its connections to all other strings, and this leads, to be sure, down open-ended trail. So semantic properties are connected to open ended searches because an object’s meaning is not localized within the object itself. This is not to say that no understanding of any object’s meaning is possible until the end of time, for as time passes, more and more of the meaning unfolds. However there are always aspects of its meaning which will remain hidden arbitrarily long.
38. Page 618 Representing Knowledge In a Logical Formalism: The basic operations in such representations are, not surprisingly, formalizations of deductive reasoning. Logical deductions can be made using rules of inference analogous to some of those in TNT. Querying the system about some particular idea sets up a goal in the form of a string to be derived.
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