BTRIPP (btripp) wrote,

Glad THAT'S over with ...

I bought this book used a very long time ago, perhaps a decade, perhaps longer, and it's sat there on various to-be-read shelves, in to-be-read boxes, and amid to-be-read stacks of books, somehow untouchable. Why? It's freak'n 750 pages long, like 3 normal books. Plus, it's math, and as much as I like physics, I'm always hesitant to delve into too much math because my mental processing does not lend itself to the necessary discipline (or even bondage … waka, waka, waka). However, this was a “big deal” among circles I was at least in contact with (although it didn't come out until I was past college). Much as I held Lombard for years as an example of a suburban wasteland (eventually finding myself having to spend 2.5 hours each way on public transit commutes to a writing job out there for a period of time), this was something of a bête noire in terms of a “mountain too high to climb” reading project – a commitment that would no doubt totally screw up my reading patterns.

And it was.

I started reading Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid at the beginning of January, and by mid-April, I wasn't quite half-way done. However, earlier this week I went on a journey that, over a 35-hour period, had me on a bus for 18 hours and hanging out waiting for a bus for another 8 hours, time that I largely devoted to trying to knock this beast down. I did not succeed in finishing it on my trip, but got close enough that I was able triage out enough “in between” times this week to get it read.

I wish I could say it was worth it, but I found this quite frustrating, on a number of levels. First of all, and this is (obviously) “on me”, I have never “gotten” music aside from as a listener, no matter how many attempts I've made, the whole “music theory” stuff just flies by me … and, as one would guess from the title, music (aka the “Bach” parts here) is about a third of the basis of the book. I am also (and, no doubt, relatedly) not particularly good with “pure logic”, something that the mathematician Hofstadter seems to think is a delightful game that all of his readers would love to play with … and invites said readers to “work out” various extremely vague (to me) structures and puzzles in bizarre (again, to me) codings (see pic at right for an example). What's worse is that the author tends to define his system of symbols once and then apparently assumes that “you've got it” and will go back to using it hundreds of pages later without any “catching us up” on it, even as little as “name checking” abbreviations like TNT when they crop up a book length past when they're initially defined (that's Typographic Number Theory, if you were wondering).

The book rotates between three different types of presentation. The most identifying one of these, and no doubt what got the book its fame, is what is referenced in a sub-sub-title added by its publisher: A Metaphorical Fugue on Minds and Machines in the Spirit of Lewis Carroll … discussions between various characters, beginning with Achilles and a Tortoise, with added others such as a Crab, a Sloth, and ultimately up to Hofstadter himself. As anybody who reads my reviews regularly will realize, I “have issues” with “teaching stories”, and these aren't even necessary (although being about a third of the book) features, having more the character of trying to present the material in a “cute” way that allowed the author to mess about with framing the logical questions being discussed in the other sections in a “Lewis Carroll” inspired format. Across the course of the book I tended to find these parts irritating rather than illuminating, but I am willing to cede the point that “your mileage may vary” on this, and that it could well be a “it's me” rather than “it's the book” here.

The other two “types” are where the author is going through the various symbolic systems (he has several, most of which are “cutesy” in that they're structured to reflect, as initials, to other elements in the material), which generally made no sense to me at all (and, again, this is likely due to my disconnect with that sort of symbolic thinking). And, finally, the parts where he's actually EXPLAINING what the book's about … like a regular book on a subject. Frankly, were the book just this latter material, I would have probably quite liked the book … which might have been only 350 pages or so of lucid prose. But, noooooo.

That “core conceptual arc” would have been fascinating, as it addresses a lot of intriguing issues on logic, consciousness, and artificial intelligence, but it's so munged up with the other stuff that it's rather difficult to follow. I'll try to pull out some of the more cogent bits here to give a sense of where this goes.

First of all, there's this Gödel guy … Kurt Gödel was a German mathematician whose “discovery involves the translation of an ancient paradox in philosophy into mathematical terms. That paradox is the so-called Epimenides paradox which is at its base the statement “This statement is false.”. This is, perhaps, the least convoluted part of it. Hofstadter goes on to say:
The Epimenides paradox is a one-step Strange Loop … but how {sic} does it have to do with mathematics? That is what Gödel discovered. His idea was to use mathematical reasoning in exploring mathematical reasoning itself. The notion of making mathematics “introspective” proved to be enormously powerful, and perhaps its richest implication was the one Gödel found: Gödel's Incompleteness Theorem. What the Theorem states and how it is proved are two different things. We shall discuss both in quite some detail in this book. …

Gödel's Theorem appears as Proposition VI in his 1931 paper “On Formally Undecidable Propositions in Principia Mathematica and Related Systems I.” …
here is a paraphrase …
All consistent axiomatic formulations of number theory include undecidable propositions.
The author refers to that last line as “the pearl” and goes on for several hundred pages exploring it, in the various approaches detailed above.

Of course, none of this is particularly straight-forward … the concepts, based on Gödel's mathematics, get dragged through the complex recursive musical structures of Bach's multi-voiced fugues, etc. (sometimes in excruciating detail), as well as being cast in reflections of Escher's convoluted graphics (which the characters in the dialog parts spend a good deal of time popping in and out of – acting out aspects of the mathematics in doing so), and getting the “Lewis Carroll” treatment at every hand, which seemed to more muddy the waters than anything. There are some truly fascinating bits here, like the discussion on translation, looking at approaches taken to convert Dostoevsky to English, or Jabberwocky into French and German … or how viruses use DNA to attack cells … but these tend to stand out because they're self-contained and not bounced around between conceptual frames!

One of the topics examined across the book is consciousness in humans and the possibilities of Artificial Intelligence. Obviously a book that came out in 1979 has a whole different perspective on computers than a reader approaching the information in 2016. At the time of its writing, the first models of the Apple, Atari, Commodore, TRS-80, etc. were out, but most of what is discussed here is far more primitive. On one hand, this is probably a good thing, as it keeps the discussion largely in the theoretical/mathematical side, but it's somewhat painful to read, when you realize that the capabilities of machines back then were so minimal that it's hard to even frame a comparison to current tech.

Needless to say, there's so much stuff going on in here, that it's a challenge to even try to summarize in a couple of thousand words. I was somewhat surprised that this eventually rolled around to something of an existential essay by the end of the book. There was a particularly cogent section called “Strange Loops as the Crux of Consciousness” that I think is worth taking a look at here:
      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 … The self comes into being at the moment it has the power to reflect itself.

      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 examination of mind, for we will have to admit causes that propagate both upwards and downwards in the Tangled Hierarchy of mentality, just as in the Central Dogmap.
Oh, that last thing there … it's typical of a lot of stuff happening in the book, Hofstadter takes Crick's “Central Dogma of Molecular Biology”, spins out his own “version”of it as a “Central Dogma of Mathematical Logic”, and “maps” them against each other as the “Central Dogmap” … and, trust me, that's not the “worst” of the groaners that are in here – he weaves puns through the core structures of a lot of the key concepts here that, honestly, don't add anything to the coherence of the presentation (perhaps, as a college professor, the author had gotten into the habit of putting this sort of stuff into class materials to keep his students involved).

Again, I would have both enjoyed and gotten more out Gödel, Escher, Bach had it been cut down to the expository parts, with maybe some sub-sections dealing with the math/logic behind the assorted theoretical concepts involved. However, it's a “classic” in its own way (Amazon has it listed as the #1 best-seller in the “Artificial Intelligence and Semantics” category, for whatever that's worth), and I'm glad to have gotten it moved from the to-be-read limbo into the proverbial rear-view mirror. If you feel like you want to take up the challenge that this book represents, it can be had in various formats … used copies of the 1979 and 1989 editions are available, and the 1999 edition is still in print. Oddly, the used copies of the older editions (this may be a “text book” thing happening) aren't particularly cheap, and you'd only be saving a bit (with shipping) vs. the nearly half-off pricing of the new book.

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