Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter

[nhunter]

Hofstadter is College Professor of Cognitive Science and Computer Science, Adjunct Professor of History and Philosophy of Science, Philosophy, Comparative Literature, and Psychology at Indiana University at Bloomington.

I read this book several years ago. Hofstadter manages to make some very intricate and important ideas available to the non-expert reader, but it's a big book and parts of it will seem like hard work, even if you're interested in the subject and captivated by Hofstadter's presentation, as many people have been.

The list of issues the book addresses includes the philosophy of science, the nature of paradox, and the problem of what is knowable.

I would recommend doing exactly what a previous poster wrote, read the first couple of chapters now and if you don’t feel like proceeding, put it aside for a while.

One warning I will offer is that if you do get into it, be very careful about who you mention it to. I found I got into some extremely boring conversations during and immediately after reading it.

 

[sanyuja]

Thanks for the advice, nhunter! I will be every careful who I mention this book to!

I have read 4-5 chapters and I am still not bored. I will remember your advice -- I will keep the book aside when I get bored.

 

[Libre]

Well folks, it kind of puts me off to try to join a forum, enter in conversations, while everyone talks around me. I realize I'm new here - but I think I have something to contribute. It's not that I need so much recognition, but I can't help but wonder why on nearly every thread I've posted in, the conversations continue along as though I don't exist. For example, sanyuja, you specifically thank nhunter for his input. Well, I put in some input too. And you asked bobbyburns a few times to elaborate, which he didn't, and I did, yet, no response. That's kind of rude around these parts, and this is NY City where pretty much NOTHING is rude.

I'm going back to the classical guitar forum, where you can get a rise out of people there, positive or negative, but at least I don't feel like I'm in a roomful of people having interesting conversations that I can hear perfectly well, but I'm speaking in a frequency outside the audible range of their hearing.

 

[sanyuja]

I am really sorry Libre, I didn't have any intentions of offending you.
Trust me, its not that I wanted to thank nhunter and did not want to thank you.

Just that there was nothing to comment on what you said. I haven't finished the book -- I am just 5 chapters into it. Once I finish it, I can agree/disagree with you on whether the book was boring or an easy read.

Please don't get offended Libre. I am sorry for not replying to your post specifically. I hope you understand.

 

[Peder]

Libre,
Hi, fellow New Yorker!
Gee, I don't know what to say, but I'm gonna try. And without commenting on particulars.
First of all, that must be a very frustrating rotten feeling! I've stopped counting the number of times I have gotten no response, so I don't notice it any more. I figure it comes with the territory, based on the forums that I have been in. Of course I also look for responses after I post, but I figure that in many if not most cases the custom just seems to be to speak one's piece out into the blank unknown and that's it. Everyone has their say, everyone hears, but not a lot of conversation goes on. In other cases regulars just yada away with their friends as if on a private line, and in rare other cases I have seen third parties shushed as if they really were breaking into a private conversation (although not here). All possibilites seem to be possible and I've stopped worrying about it. And in the fortunate case, someone actually does hear what I tried to say and responds. And that makes all the other times go away.

So that's my sharing of experience, but the one thing I am not going to do is offer advice. I don't think you need that just now. But I do hope you give it a little longer and maybe the dry spell will pass.

PS Worse yet is to have every one down on you and to be conducting a one against twenty verbal battle. I've eperienced that (again not here, yet), and this is much better.

Hope to see you around,

Peder
From the streets of the City.

 

[Libre]

Peder-
I appreciate your response. Thank you for your kindness. It IS a rotten feeling to attempt to join in an existing group, and be overlooked. I realize nobody intended any malice.
sanyuja-
Thank you for your response too. It's not like I'm that upset or anything - I just thought I'd say something before just exiting this place for good. I do post on another forum (the GSI classical guitar forum), and I realize it's easy to get involved with one or several other members, and totally overlook somebody that is trying to be heard. That's why I spoke up. Please don't think that you have to acknowledge my every post or I will get upset. But...I was responding to your question about GEB.
Now, GEB. Fascinating and brilliant. Humorous and witty. Groundbreaking. My advice is different from nhunter's. My advice is: keep reading it - don't put it down even if you get bored in certain sections. If your brain is not shut down cold after the first chapter or so, you will reap huge rewards by finishing the book. (I must admit I did skim certain sections).
And don't refrain from mentioning it to others either. Some people, like me, for example, would be thrilled to discuss the book at length.

 

[Peder]

Hi Libre,
Glad you were good for one more. Hardly anyone ever means malice; you will definitely know it when they do!

But now you definitely have me interested in taking a closer look at the book. From all the things I have heard, all different, I haven't been able to figure out whether is too difficult, too serious, just serious, interesting, dull, boring, over-simplified, simplistic, too technical, for geeks, for wizards, for a general audience, or on and on. And, frankly, I have found the title a little unrevealing and somewhat off-putting.
Guess the only answer is to pick it up and look at it for myself. Duh. I generally do that over coffee at my favorite bookstore(s), like maybe this morning. Good thought Libre!
Thanks for the post,
Peder

 

[Libre]

Hey Peder (now, this is more like it - there are living breathing people here!)
Peder - I can see being put off by the book. The sheer weight of it alone could be enough to make you hesitant to pick it up. Normally, I like a rollicking good tale (see my current book in the header) but I'm also someone that gets AMAZED by certain concepts. If the following causes your eyes to glaze over, and you think this is mental mastur....uh...self abuse, then you do NOT want to invest your time in GEB:
The following sentence is true.
The preceeding sentence is false.
If, on the other hand, such concepts thrill you, fasten your mind on them, and make you think and think, then GEB is a book for you.
It's not all about paradox and unanswerable riddles - but much of it is. But the book covers a great deal of ground - from ant colonies to artificial intelligence to DNA to Zeno. All great stuff. I could spend an evening on the topic - and more.
If aliens came to the Earth and asked for a book that demonstrated our best example of the development of human thinking, I would give them GEB in a heartbeat. That's if anybody asked me which book we should give the aliens, which is highly unlikely.

 

[Peder]

Hey Peder (now, this is more like it - there are living breathing people here!)

The following sentence is true.
The preceeding sentence is false.
If, on the other hand, such concepts thrill you, fasten your mind on them, and make you think and think, then GEB is a book for you.

Good shot, Libre!
About breathing people being here! (Sorry guys but I do that sometimes, the numerous smilies, that is)

And I'm glad you picked that example. The answer is, yes, such things have always intrigued me and I have always been interested in puzzles, paradoxes, etc and how the brain works. And that is probably why I ended up in a technical field.

But to be brutally honest, after so many years on this Earth I have read so many popular treatments that have covered similar ground that I am probably jaded. (I'm a little surprised you didn't pick the barber's paradox, but your example is simpler and even better.) Which is the exact opposite of saying that I yet understand anything much about such things. So the ground is very familiar but still strange. A book that would shed new light (any light!) would be much appreciated. Maybe GEB is it. I'll just have to go look, and have that cup of coffee.

Many thanks,
Peder

 

[Libre]

By the way, I have evidence that sanyuja also lives and breathes, and is a nice person, and I hope I did not cause anybody undue distress. I just thought I'd poke my head up and yell, rather than just go away. And see - it worked.
Peder - I don't know the barber's paradox. I'm interested. The example I wrote, is the 2 part Epimenides paradox. The regular Epimenides paradox is the 1 part form: This sentence is false.

The 2 part form is even more intriguing, to me, because neither part has anything wrong with it, but put the 2 together, and you get a paradox.
Hofstadter illustrates another such, several step paradox:
A is bigger than B; B is bigger than C; C is bigger than A.
Clearly, every part of this train is perfectly ordinary and possible, yet, taken as a whole, it is an impossibility.
I love this stuff.

 

[Peder]

Peder - I don't know the barber's paradox. I'm interested. The example I wrote, is the 2 part Epimenides paradox. The regular Epimenides paradox is the 1 part form: This sentence is false.

The 2 part form is even more intriguing, to me, because neither part has anything wrong with it, but put the 2 together, and you get a paradox.
Hofstadter illustrates another such, several step paradox:
A is bigger tha n B; B is bigger than C; C is bigger than A.
Clearly, every part of this train is perfectly ordinary and possible, yet, taken as a whole, it is an impossibility.
I love this stuff.

Libre,
Well, I have had that coffe and it was great!
And I have looked at the book and it was much more and totally different than anything I ever expected. In a sense I am sorry I did (a happy sorry, that is ), because now I have to figure out how to describe something that is totally undescribable. Hofstadter, Jr, would appreciate that! There are two parts to the description, I suppose. One would be a description of the book (the hard part) and the second would be my reaction to it (the easier part).

I guess the best way to start to describe the book is to compare it to a large encyclopedia. GEB covers an enormous scope and certainly touches on almost every logical, or computational, or mentally gymnastic topic that I have ever heard about in my life, plus 100 times as much more! (Except, oddly it doen't seem to mention the barber's paradox.) Different from an encyclopedia, however, I feel that the author (who is no doubt brilliant) only skims over the surface of his topics, where an encyclopedia would present each explanation in a manner that was satsifyingly complete in some sense.

As a result, GEB has the feel to me of a magician who might say "See now, the way you produce a rabbit is to rub your fingers together and, lo, there is the rabbit! And now that you understand that ......" At which point I say "Whoa! I don't understand that! And moreover when I do rub my fingers together I don't make a rabbit."

Or to put it another way, it is like trying to drink from a firehose.

Or yet a third way. Sometimes I think the purpose of the author is to dazzle, whereas the purpose of an encyclopedia is to inform.

On a personal level, I am suspicious of the book, is the only word I can use. In disussing rules of the Propositional Calculus, the author points out Contraposition, using its usual name, but then also has a rule he calls Switcheroo, after having renamed it from its usual name. An author who is that flippant with respect to serious material raises my supicions about how much more flippancy there is which is hiding serious content. He might have called modus ponens exactly that and not lost his audience, I don't think. Especially since it is the most basic deductive principle there is.

His Phantasy View is likewise not necessary, IMO, and only clouds the matter, again IMO. I don't think that it helps to have to say "Now, you have to remember that not all the formula fragments are true, only the last one." as he more or less does when discussing Left and Right brackets. Having to remember what is true defeats the purpose IMO, which is precisely to sort out what is true and what is not. Proceeding only from true formula to true formula in the conventional completely deductive manner may not be as quick but it seems clearer to me. Or maybe I miss the point.

Re "A greater than B, and B greater than C, implies that A is greater than C," is ordinary transitivity and a true statement. However, I suspect that the complete statement really also includes the preliminary statement somewhere that "For three distinct integers (or reals) A, B and C..." As a result, A greater than A is never allowed as a true statement, and the substitution of A for C in the conclusion 'A is greater than C' is also not allowed. (Unless one is using the weak inequality A is greater than or equal to A. Either way no paradox arises.)

But by now you can tell the book irritates me.

However, just to prove that he didn't conquer me, here by derivation, and not from memory, is his sequence:

1, 3, 7, 12, 18, 26, 35, 45, 56, 69

Short form: it is just too much of a book for me to tackle and in the wrong style for my taste,
Sorry,
Peder

 

[Peder]

Barber paradox

In a certain town, all the people cut their own hair.
Or, if they wish, the barber will cut their hair.
So the barber cuts the hair of people who do not cut their own hair.
Who cuts the barber's hair?

An old, old, old paradox,
Peder

 

[Libre]

Well, I thought it was great.
I wouldn't compare it to an encyclopedia though.

Oh as far as the paradox about A>B>C>A, of course there are ways to invalidate it, as I suppose any paradox can be invalidated. For example, the barber, who, if everyone in the town can cut their own hair, and is a person in the town, then unparadoxically, can cut his own hair as well.

 

[Peder]

Libre,
I have probably said many more words about the book than I needed to. I happen to like encyclopedias, so that was not meant as a put down at all. They were among my earliest introduction to reading. Perhaps comprehensive rather than encyclopedic would be a better descriptor. In any event, I am very impressed that you were able to read through such a monumental work, in whatever length of time it took you. Clearly my own impatience would quickly doom such a project for me -- probably to my own loss.
Hope you find someone to swap ideas with,
Cordially,
Peder

 

[Libre]

Hey Peder-
I didn't take it as a put-down. It's just that it didn't read like a reference book to me - although with the extensive index, and breadth of topics covered, I can see what you mean.
I did feel some sense of accomplishment about reading it through - and at the end of it, was very glad to put it down, and felt no compunction to read Hofstedter's other work.
Another thing that appealed to me about the book, that I haven't mentioned, is that I am a life-long admirer of Bach, and I'm familiar with all of the works referenced in GEB, which only added to my enjoyment of it.
Thanks for your input, Peder.

 

[Peder]

Libre,
Maybe someday, when my life has settled down into a truly reflective mood.....

/shifting topic/
I have only recently come across the Goldberg Variations and consider it a greeat loss that I never heard them earlier. If I played an instrument, Bach would be the one! There you are way ahead of me also.

Peder

 

[Libre]

Peder-
Warning - if I get started on Bach, there is no stopping me - I'll be impossible to live with. When I said I was an admirer of Bach, I put it very lightly. I've been adoring Bach since I was 20, and that was .... a really long time ago.
If you have the inclination, click on my link at the bottom of my posts, and you'll see that music is a huge influence in my life, and the unusual way that I approach it.
The Goldberg Variations. My favorite recording is the immortal 1956 Glenn Gould version. Have you heard it? That recording made Glenn Gould an overnight celebrity (or as much of a celebrity as a concert pianist can be).
There is so much TO the Goldberg Variations. I can't get started on them - this is after all a book forum - but suffice it to say that I'm intimately familiar with them and, consider them one of the most splendid jewels in the keyboard literature.

 

[Peder]

Peder-
...one of the most splendid jewels in the keyboard literature

Libre,
That was my instant and immediate reaction, amateur though I am with respect to music appreciation!

No, I haven't heard the Gould rendition. My acquaintance is with the earlier (earliest?) harpsichordist, whose name eludes me but which you know, and I don't think it is Wanda Landowska but the harpsichordist before her. The jacket said she was credited with bringing the Goldberg Variations to light, as I recall. Try a name.

Peder

 

[Libre]

I can't come up with it. Wanda Landowska is the first "modern" harpsichordist I know of. I might recognize the name you are thinking of, but I don't know it off hand.
Peder - I hate to be overbearing, but it is of the utmost importance that you hear (if not aquire) Glenn Gould's 1954 recording. I'm being specific about the year, because he had a 1980something recording of the Goldbergs too, and the 1954 one is the far greater one (IMO). Not that Gould is without his detractors, by the way. "Purists" sometimes hate him. I love love love his playing of Bach. And if you like the Goldbergs, the Well Tempered Clavier books I and II ARE NOT TO BE MISSED!!! - also recorded definitively by Glenn Gould of course. Then there are the English Suites, the French Suites, the Keyboard Partitas, all Glenn Gould. But there I go - see, you got me started.
Then there are the Unaccompanied Violin Sonatas and Partitas, the Cello Suites............

 

[Peder]

Libre,
I don't regard your enthiusisam for the topic as overbearing at all; I view your suggestions and advice as solid gold. I am supposing the Air in G is one of the Unacompanied Violin Sonatas?
In any event, with a little help from google, it is a CD by Rosalyn Tureck that i have stashed away (still) somewhere in a moving carton from last year. I walked around for days and weeks down at the office humming, trying to get that beautiful long melodic line into my head. I have never heard anything like it before or since.
But you can now bet I'll try to catch up with the 1954 Glenn Gould as well!
Many thanks,
Peder