Douglas R. Hofstadter - Gödel, Escher, Bach: An Eternal Golden Braid (Basic Books, 1979) *****

This fascinating and genial book was published in 1979, when I was at university. It was a kind of a hype among my fellow-students, and even if I did not understand (or read) half of it, it opened a world, or rather a universe of thinking, while at the same time presenting it in an incredibly creative way. Earlier this year, I decided to read it in full and buy a copy. Fourty-five years later, it is still as enthralling as it was then. Hofstadter explores the boundaries of our thinking, where reason and logic meet their limits in paradoxes, contradictions, self-references and loops. The subject is about cognitive science, logic and computer sciences (and Artificial Intelligence), and he learns us how meaning and meaninglessness exist and how they come to life (or not) in abstract systems, including the human mind and the perception or delusion of the self or the "I". 

I do not think the book would have so much resonated with larger audiences or with us at that time, if it were not for the extensive illustrations of Dutch artist M.C. Escher and his impossible drawings, or the long dialogues between Achilles and the Tortoise, occasionally joined by the Crab, and further illustrated by analysing the compositions of Johann Sebastian Bach, and their inherent structural elements of self-reference and loops, as in the sentence sequence: 

"The following sentence is false

The preceding sentence is true"

The starting point of course are the theorems of German mathematician Kurt Gödel: "The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure(i.e. an algorithm) is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system" (Wikipedia)

On top of this, Hofstadter develops dozens of new ways of looking at familiar or less familiar problems of logic and computation. He creates his own different logical systems in the book to illustrate his points, to take the reader without knowledge of mathematics or the formal language of computer scientists by the hand, and explain whatever elements he wants to demonstrate. 

He describes it as follows: 

"Here one runs up against a seeming paradox. Computers by their very nature are the most inflexible, desireless, rule-following of beasts. Fast though they may be, they are nonetheless the epitome of unconsciousness. How, then, can intelligent behavior be programmed? Isn't this the most blatant of contradictions in terms? One of the major theses of this book is that it is not a contradiction at all. One of the major purposes of this book is to urge each reader to confront the apparent contradiction head on, to savor it, to turn it over, to take it apart, to wallow in it, so that in the end the reader might emerge with new insights into the seemingly unbreachable gulf between the formal and the informal, the animate and the inanimate, the flexible and the inflexible.  This is what Artificial Intelligence (AI) research is all about." (p.26)

or:  

"No one knows where the borderline between non-intelligent behavior and intelligent behavior lies; in fact, to suggest that a sharp borderline exists is probably silly. But essential abilities for intelligence are certainly:

• to respond to situations very flexibly; 
• to take advantage of fortuitous circumstances; 
• to make sense out of ambiguous or contradictory messages; 
• to recognize the relative importance of different elements of a situation; 
• to find similarities between situations despite differences which may separate them; 
• to draw distinctions between situations despite similarities which may link them; 
• to synthesize new concepts by taking old concepts and putting them together in new ways; 
• to come up with ideas which are novel. "

"This little debate shows the difficulty of trying to use logic and reasoning to defend themselves. At some point, you reach rock bottom, and there is no defense except loudly shouting, "I know I'm right!" Once again, we are up against the issue which Lewis Carroll so sharply set forth in his Dialogue: you can't go on defending your patterns of reasoning forever. There comes a point where faith takes over." (p. 192)

On the origin of life:  

"A natural and fundamental question to ask, on learning of these incredibly intricately interlocking pieces of software and hardware is: "How did ever get started in the first place?" It is truly a baffling thing. One has to imagine some sort of a bootstrap process occurring, somewhat like that which is used in the development of new computer languages - but bootstrap from simple molecules to entire cells is almost beyond our power to imagine. There are various theories on the origin of life. The run aground on this most central of all central questions: "How did Genetic Code, along with the mechanisms for its translation (ribosome_ tRNA molecules), originate?" For the moment, we will have to content ourselves with a sense of wonder and awe, rather than with an answer and perhaps experiencing that sense of wonder and awe is more satisfying than having an answer-at least for a while". (p. 548)

 Or using nice examples to make the reading easier to digest: 

"Here is a well-known children's joke which illustrates the open-endedness of real-life situations: 

• A man took a ride in an airplane. 
• Unfortunately, he fell out. 
• Fortunately, he had a parachute on. 
• Unfortunately, it didn't work. 
• Fortunately, there was a haystack below him. 
• Unfortunately, there was a pitchfork sticking out of it. Fortunately, he missed the pitchfork. 
• Unfortunately, he missed the haystack. 

It can be extended indefinitely. To represent this silly story in a frame­based system would be extremely complex, involving jointly activating frames for the concepts of man, airplane, exit, parachute, falling, etc., etc." (p. 675)

His ultimate endeavour is to link the world of abstract logic with the physical reality we live in, and of course especially our brain and its capacity to for abstract thought, to cross the levels set by scientific disciplines and to come to an more holistic understanding of the interactions. 

"My belief is that the explanations of "emergent" phenomena in our brains-for instance, ideas, hopes, images, analogies, and finally consciousness and free will-are based on a kind of Strange Loop, an interaction between levels in which the top level reaches back down towards the bottom level and influences it, while at the same time being itself determined by the bottom level. In other words, a self-reinforcing "resonance" between dif­ferent levels-quite like the Henkin sentence which, by merely asserting its own provability, actually becomes provable. The self comes into being at the moment it has the power to reflect itself. 

 This should not be taken as an antireductionist position. It just implies that a reductionistic explanation of a mind, in order to be comprehensible, must ring in "soft" concepts such as levels, mappings, and meanings. In princi­ple, I have no doubt that a totally reductionistic but incomprehensible explanation of the brain exists; the problem is how to translate it into a language we ourselves can fathom. Surely we don't want a description in terms of positions and momenta of particles; we want a description which relates neural activity to "signals" (intermediate-level phenomena)-and which relates signals, in turn, to "symbols" and "subsystems", including the presumed-to-exist "self-symbol". This act of translation from low-level physical hardware to high-level psychological software is analogous to the translation of number-theoretical statements into metamathematical state­ments. Recall that the level-crossing which takes place at this exact transla­jon point is what creates Gödel's incompleteness and the self-proving character of Henkin's sentence. I postulate that a similar level-crossing is what creates our nearly unanalyzable feelings of self. In order to deal with the full richness of the brain/mind system, we will have to be able to slip between levels comfortably. Moreover, we will have to admit various types of "causality": ways in which an event at one level of description can "cause" events at other levels to happen. Sometimes event A will be said to "cause" event B simply for the reason that the one is a translation, on another level of description, of the other. Sometimes 'cause" will have its usual meaning: physical causality. Both types of causality-and perhaps some more-will have to be admitted in any expla­nation of mind, for we will have to admit causes that propagate both upwards and downwards" (p. 709)

And of course also the existence of free will. Are we the consequence of algorithms (historical/cultural/social/genetic/contextual/...) or not. 

"One way to gain some perspective on the free-will question is to replace it by what I believe is an equivalent question, but one which involves less loaded terms. Instead of asking, "Does system X have free will?" we ask "Does system X make choices?" By carefully groping for what we really mean when we choose to describe a system - mechanical or biological - as being capable of making "choices", I think we can shed much light on free will." (p. 711)

We will come back to this topic when reading Robert Sapolsky's "Determined". 

Even if in some respects the book is a little dated, especially when describing Artificial Intelligence or genetics, it remains one of the milestone books on cognitive science and logic, absolutely unique in terms of content and form, incredibly complex yet fun to read, even if it is impossible to understand everything, as most readers such as myself will have to confess.