Reading "Gödel, Escher, Bach" in 20 days

I didn't actually achieve reading it in twenty days.

Introduction 

So, now that I have a bit of free time, I've decided to devote some of that free time to reading something that's been on my list for a few months: Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hoestadter. I first came across this book when Stuart Reges recommended it to the CSE 143 Honors section (after all, the class was abbreviated Meta Memes Math and More). Reges said it's one of those books that people keep, but do not completely read; he said it would be quite a feat if a student were to complete this book, so I took this as a challenge. After taking that section, and PHIL 120: Introduction to Logic, I became very keen in developing my understanding of systems in general. So far, I have read the 20th Anniversary Edition Preface (around 20-30 pages) which goes over the development of the book and a short overview. It is currently 2AM on July 20th and I have not yet started reading the actual book; however, so far what I have read has captivated me - it feels as if this book was meant for me - so I am determined to set a solid reading schedule to keep me on track. This is the schedule as follows. 


Reading Schedule 

Preface to GEB's Twentieth-anniversary Edition  P-1

Overview  p. viii

List of Illustrations  p. xiv

Words of Thanks  p. xix

[]BEGIN - 7/20/17

Part I: GEB   

Introduction: A Musico-Logical Offering  p. 3

  Three-Part Invention  p. 29

Chapter I: The MU-puzzle  p. 33

  Two-Part Invention  p. 43

[✔]Finish Through p.45 by 11:59PM 7/20

Chapter II: Meaning and Form in Mathematics  p. 46

  Sonata for Unaccompanied Achilles  p. 61

[✔]Finish Through p.63 by 11:59PM 7/21

Chapter III: Figure and Ground  p. 64

  Contracrostipunctus  p. 75

[✔]Finish Through p.81 by 11:59PM 7/22

Chapter IV: Consistency, Completeness, and Geometry  p. 82

  Little Harmonic Labyrinth  p. 103

[✔]Finish Through p.126 by 11:59PM 7/23

Chapter V: Recursive Structures and Processes  p. 127

  Canon by Intervallic Augmentation  p. 153

[.✔]Finish Through p.157 by 11:59PM 7/24

Chapter VI: The Location of Meaning  p. 158

  Chromatic Fantasy, And Feud  p. 177

[.✔]Finish Through p.180 by 11:59PM 7/25

Chapter VII: The Propositional Calculus  p. 181

  Crab Canon  p. 199

[✔]Finish Through p.203 by 11:59PM 7/26

Chapter VIII: Typographical Number Theory  p. 204

  A Mu Offering  p. 231

[✘]Finish Through p.245 by 11:59PM 7/27

Chapter IX: Mumon and Godel  p. 246

[✘]Finish Through p.274 by 11:59PM 7/28

Part II EGB  p. 275

  Prelude ...  p. 285

Chapter X: Levels of Description, and Computer Systems  p. 285

  ... Ant Fugue  p. 311

[✘]Finish Through p.336 by 11:59PM 7/29

Chapter XI: Brains and Thoughts  p. 337

  English French German Suite  p. 366

[✘]Finish Through p.368 by 11:59PM 7/30

Chapter XII: Minds and Thoughts  p. 369

  Aria with Diverse Variations  p. 391

[✘]Finish Through p.405 by 11:59PM 7/31

Chapter XIII: BlooP and FlooP and GlooP  p. 406

  Air on G's String  p. 431

[✘]Finish Through p.437 by 11:59PM 8/1

Chapter XIV: On Formally Undecidable Propositions of TNT and Related Systems p. 438

  Birthday Cantatatata ...  p. 461

[✘]Finish Through p.464 by 11:59PM 8/2

Chapter XV: Jumping out of the System  p. 465

  Edifying Thoughts of a Tobacco Smoker  p. 480

[✘]Finish Through p.494 by 11:59PM 8/3

Chapter XVI: Self-Ref and Self-Rep  p. 495

  The Magnificrab, Indeed  p. 549

[✘]Finish Through p.558 by 11:59PM 8/4

Chapter XVII: Church, Turing, Tarski, and Others  p. 559

  Shrdlu, Toy of Man's Designing  p. 586

[✘]Finish Through p.593 by 11:59PM 8/5

Chapter XVIII: Artificial Intelligence: Retrospects  p. 594

  Contrafactus  p. 633

[✘]Finish Through p.640 by 11:59PM 8/6

Chapter XIX: Artificial Intelligence: Prospects  p. 641

  Sloth Canon  p. 681

[✘]Finish Through p.683 by 11:59PM 8/7

Chapter XX: Strange Loops, Or Tangled Hierarchies  p. 684

  Six-Part Ricercar  p. 720

[✘]Finish Through p.494 by 11:59PM 8/8

[]END - 8/8/17


FAILED

Schedule, Version 2

Goal: Complete the book in a month, that is, by august 20th, 2017

Schedule v2 Created at 9:48PM on August 10th, 2017


Reading Schedule V2

Chapter VIII: Typographical Number Theory  p. 204

  A Mu Offering  p. 231

[.✔]Finish Through p.245 by 11:59PM 8/10

Chapter IX: Mumon and Godel  p. 246

[.✔]ALSO Finish Through p.274 by 11:59PM 8/10

Part II EGB  p. 275

  Prelude ...  p. 285

Chapter X: Levels of Description, and Computer Systems  p. 285

  ... Ant Fugue  p. 311

[✘]Finish Through p.336 by 11:59PM 8/11

Chapter XI: Brains and Thoughts  p. 337

  English French German Suite  p. 366

[✘]ALSO Finish Through p.368 by 11:59PM 8/11

Chapter XII: Minds and Thoughts  p. 369

  Aria with Diverse Variations  p. 391

[✘]Finish Through p.405 by 11:59PM 8/12

Chapter XIII: BlooP and FlooP and GlooP  p. 406

  Air on G's String  p. 431

[]Finish Through p.437 by 11:59PM 8/13

Chapter XIV: On Formally Undecidable Propositions of TNT and Related Systems p. 438

  Birthday Cantatatata ...  p. 461

[]Finish Through p.464 by 11:59PM 8/14

Chapter XV: Jumping out of the System  p. 465

  Edifying Thoughts of a Tobacco Smoker  p. 480

[]Finish Through p.494 by 11:59PM 8/15

Chapter XVI: Self-Ref and Self-Rep  p. 495

  The Magnificrab, Indeed  p. 549

[]Finish Through p.558 by 11:59PM 8/16

Chapter XVII: Church, Turing, Tarski, and Others  p. 559

  Shrdlu, Toy of Man's Designing  p. 586

[]Finish Through p.593 by 11:59PM 8/17

Chapter XVIII: Artificial Intelligence: Retrospects  p. 594

  Contrafactus  p. 633

[]Finish Through p.640 by 11:59PM 8/18

Chapter XIX: Artificial Intelligence: Prospects  p. 641

  Sloth Canon  p. 681

[]Finish Through p.683 by 11:59PM 8/19

Chapter XX: Strange Loops, Or Tangled Hierarchies  p. 684

  Six-Part Ricercar  p. 720

[]Finish Through p.742 by 11:59PM 8/20

[]END - 8/20/17


Chapter Responses 

These are to be filled as I progress through the above reading schedule, with respect to each (often occurring by chapters) milestone. They are meant to act like the reading responses from English 111

Chapter 1 (finished at 11:54 PM 7/20) 

I barely made this checkpoint, but I have done so thoroughly and with satisfaction. I attempted the MU puzzle for ten minutes, but as the reader advised, came back to the reading to understand more about my process (and THE process). I hope to pick this up tomorrow, and perhaps analyze more tomorrow and add to this vague "response." As far as I can tell from these first 45 pages, I LOVE this book *knocks on wood*. Understanding how Bach and Escher used "strange loops" (which for a person who hasn't read the book can consider self-reference or paradoxes which involve infinite looping); how Godel and others found faults withing mathematics; the discussions and meta-discussions (in which the reader and portrayed author and actual author are all highly involved) with Achilles and the turtle and Zeno; establishing a formal system, solving a puzzle through it, and observing the process of doing so; all of it feels very intuitive to me, as if this was some understanding I had lost and was learning again (not to be egotistical). The dialogues keep me very entertained, since I'm a very "meta" reader (which also makes me a pretty slow one - reaching this checkpoint took almost exactly two hours). I'm itching to read the next section. 

Chapter 2 (finished at 11:12 PM 7/21)

Again, I made it to this checkpoint a bit late; it is to be noted that today's reading and tomorrow's is significantly shorter than the forty page quota I had yesterday. In any case, it is probably a good idea for me to get ahead on these readings tomorrow morning for I have a busy weekend with concerts and hikes. A PQ formal system is introduced, and through figuring out a decision procedure for identifying (or certifying) theorems in this system, I initially produced a "bottom-down" procedure which takes a specific given "theorem" to be validated, and subtracts dashes from certain places until it becomes an axiom (whilst validating each well-formed step along the way). This is how I would implement it, from an iterative or recursive programming standpoint (this problem may make more sense with recursion). The "bottom-up" decision procedure would involve creating every possible theorem with the same length as the given well-formed formula and find if it matches, which is also possible with today's computing abilities, but certainly less efficient. The most significant part of this chapter was reintroducing the term isomorphism - succinctly defined as an "information-preserving transformation." You can take this PQ system, and it turns out that you can map it with addition - and now you've created a bridge (isomorphism) between two different systems which are abstractly related. There are meaningful and meaningless transformations, and each meaningful transformation can be active or passive. It's a bit wordy to define, but it is important to note that words in languages are active whilst anything introduced in a formal system is passive. There is a relation between formal systems and reality - the chapter then delved into how we know mathematics is in a sense "real" by citing a simplified Euclid's Proof. We put our faith in the reasoning to put our faith into the derived result. The next dialogue is interesting, and I'll talk more about it once I get to know more about the next chapter. I re-read the dialogue from the last reading (intended for this chapter) and I'm trying to reason out how the turtle kept stating that the next logical step was a hypothetical, when it was simply the next step. Perhaps he could not understand how the end result could have been reached without every possible step in between, but it turns out sometimes that trying to define a statement that "since all the previous things are true, this other thing must be true" adds another thing into the mix, and you fall into an infinitely deep hole. So we put our faith in each step of reasoning, and we reach the result, and that seems to be the only way in these scenarios. 

Chapter 3 (finished at 3:30 PM 7/22) 

I'll comment more on this later, because I'm a day late on this report because I came back from the Capitol Hill Block Party, got two hours of sleep, then went for an all-day hike and now I'm back so time to get onto the next reading. Done with the next reading, now I'm back to summarize what I learned about "Figure and Ground." The interesting thing is, I had a very similar, if not identical, perspective on the nature of how people view figure and ground with my facet experiments in photography and in the cover pages for MIND, BODY, and SOUL in the homepage of this website - in which the "foreground" which consists of some detailed object and the "background" which consists of some white or plain structure are switched. The analogy between this figure and ground is similar to that between truths and falsehoods - and all the logical structures that come with both sides. If you think of all non-primes as the figure which can be determined and the prime as the ground, it turns out that since there's a decision procedure for the non-primes, there's also a decision procedure outlined for "determining" primes - in the same way that you're determining the other side of the figure. 

Chapter 4 (finished at 11:33 PM 7/23)

Well, a lot happened. 

  • There are certain kinds of record players and records - and some record players which are claimed to play anything are not able to play a record which destroys the player.
  • In the Conatracrostipunctus story, there are many isomorphisms, or analogies, which make Godel's Theorem much easier to understand (several, but not all, are outlined on page 85).
  • A history of Euclidean and Non-Euclidean geometry is presented, delving into the properties of consistency and completeness in formal systems. 

Now, this story is meant for Chapter 5 (Little Harmonic Labyrinth) and it is EXTREMELY meta, I mean meta by several layers and there's so much intricacy to the story; it is extremely fun to read and I'll have to read it again after reading the next chapter on recursion, which I hope will solidify my understanding of that matter. Additionally, I should have a notebook by my side whilst reading through this material to help me keep track of key points and questions; for there is so much matter that I have read through, that by the time I log onto the webpage to write a response and I re-traverse through the material, what ends up happening is a summary of what stuck out to me and I'd rather delve deeper.

Chapter 5 (Finished at 12:14 AM 7/25)

Okay, I was a few minutes late, but I finished it. I got distracted by some household responsibilities which I could've hastened with mindfulness. So, this chapter was really nice to read, and I wish I had read it much, much earlier. I find myself wishing I had read the entire book earlier. Many of the core concepts of recursion I was aware of due to the CSE 143 course at UW. However, this chapter gave a far deeper, far more intuitive, far better (in every aspect) sense of recursion than what I had learned in a few days of the lecturers giving brief examples and repeating simple concepts (which actually muddles my understanding and creates confusion because they leave out the seemingly "extraneous" concepts which I believe is essential in understanding what recursion is, unless you ONLY want to ephemerally apply the concept but I believe this form of teaching-through-application is flawed because they failed to capture recursion as beautifully as this chapter did, like they didn't even teach us about stacks in recursion it was just implicit, as were several other important concepts (like Recursive Transitive Networks and Augmented Transitive Networks and whatever Gloop Floop and Gloop are in the upcoming chapters) and patterns, but I guess that's what you have to do if you're [RANT] Okay so back to what I was talking about, the recursion seen in art and music and graphs and particle physics was enlightening, and I'm glad I read the material now; there's nothing in particular that really stood out - again I didn't have a paper with me while reading because I was partly rushing, so I'll do that next time - it might be easier to have a bookmark with a paper sleeve on it to write down points - because I take this book with me and I shouldn't have to carry around a piece of paper with it everywhere. Also I just realized I've written several dashes in the last sentence - I should stop doing that. 

One thing that reminds me of recursion is when I was doing photography and paper folding, and Mr. Wierusz (my Design & Technology Teacher) suggested that I read White by Kenya Hara because I took Japanese also and he was thinking about implementing Japanese design in the curriculum. I read halfway through it, and there was this one poem inside, and I don't recall what it was exactly but it went something along the lines of 

A white square
within it
a white square
within it
a white square
within it
a white square
...

and so on and so forth until some end. And it was hard to visualize this because when you try to see the distinction between one square and the other, you'll have to perceive one as a different shade of the other or visualize some sort of border which isn't really allowed. You'll have different shades of white, maybe, but if they were all the same shade, perhaps you would only see the one square. It's recursion, but more specifically it's self-reference which can cause a bit of blurring, a bit of confusion. This analogy hasn't come up in this book yet, perhaps because this poem came out after the book, but I believe the author would have included it somewhere - for it is a strange loop in a visual form in a literary form. 

Chapter 6 (Finished at 1:44 AM 7/26)

I'm sleepy and I finished this late. Inner, outer, and frame message and something about the location of meaning. Cool. 

Chapter 7 (Finished at 11:59 PM 7/27)

Finished right on the dot (or maybe a bit after who knows). I've confidently mastered the propositional calculus so there wasn't much for me in this chapter - but the story afterwards was so cool - the entire short story was a palindrome (talking about palindromes) (not letter-by-letter, but dialogue-by-dialogue). 

Explanation and Examination of Failure

It's been a while since I stopped reading. I stopped reading on-schedule on chapter 8 which should have been read by the 28th, I believe, and I'm confused because there seems to be some discrepancy between the schedule and my response times (they seem to be a day behind?). In any case, I dramatically failed to read the book within the 20-day timespan I set for myself. There are 20 chapters in the book and I stopped reading by chapter 8. If I view this goal as a binary one, something that's either a success or a failure, I've already determined this a failure. If I view this goal as something that's a bit fuzzy - perhaps divide up the goal into subgoals (such as achieving each chapter), then I failed 12/20ths of the goal. This means I wasn't even able to reach half my goal - this is a low bar from my perspective, because I would have forgiven myself more if I had at least gone halfway through something. 

However, there's still hope. 

I can pull an Apollo 13 on this and reach a "successful failure," because

"Failure is not an option." - Slogan of Apollo 13 (origins doubtuful) 

If I can finish this book at all, I will have achieved a successful failure. If I can read it within a month, which was my original preconception, then I will have achieved an even more successful failure. I'm curious to see how I perform given this second chance. I got bogged down in the insipidness of Chapter 8 on Typographical Number Theory. Hopefully this upcoming dialogue will re-spark my curiosity in the book and propel me towards the finish line. 

Chapter 8 (Finished at 1:05 AM 8/11) 

So, I have to admit this was probably the most intriguing and revelatory chapters thus far. The preceding story 'A Mu Offering' really prepared the reader for the chapter ahead; by giving a meta-example of topics discussed which include the strange loops of genetic coding, Zen philosophy (history, structure, basics, and examples), typographical formal systems, isomorphisms between systems, transcription and translation, self-reference, and (seemingly) undecidability in Zen. Moreover, all of Escher's paintings mentioned in the chapter ("Another World," "Day and Night," "Verbum," and "Three Spheres II") were all extremely well done and beautiful. In Three Spheres II, I wondered what would happen if he were to move his hand, partially or completely, across the drawing; how would it be represented; is the current drawing technically inaccurate since he cannot draw the infinite complexity; if the hand was moved completely over the drawing, is this the only way he can achieve full accuracy; can an abstract analogy be made from the previous thoughts - can we only find truthfulness by ignoring the strange loops of self reference - and by abstracting that - can ignorance preserve truth? In addition, all the Zen philosophies and koans and poems and explanations reminded me of topics brought up in English 111 - the language problem and The Beat Movement. Which lead to beatitude: could God, religion, and self-reference all be intertwined? I'm not sure what I was thinking when I wrote this; perhaps it had to do with my essay in English 111 where I portrayed Ginsberg's philosophy as a revitalized form of transcendentalism where morality is a spectrum on a piece of paper and he taped the two ends of it, but twisted it while doing so. There is something so intriguing about nonsense, such that you'll find in Zen koans or Ginsberg's works, which is oddly enlightening. In any case, the last part of the chapter discussed isomorphisms by translating the MU-puzzle from a while back into a numerical system, and the previous chapter's Typographical Number System was applied, via number theory, to represent those numbers. It will be further discussed in upcoming chapters, but each of these formal systems has a method of self-reference which embodies incompleteness. Whilst translating the MU-puzzle into numbers, I realize I had already done this by writing out several powers of two, trying to reach a number which was divisible by three, then realizing that none of them can and that the MU-puzzle was impossible. I had come to this same conclusion, and I'm glad I had done so on my own before reading this. This chapter certainly re-sparked my interest in this book after going through reading the boring Typographical Number Theory, and I've got a good feeling it'll keep my interest aflame for at least a little while longer.