Fasten your seat belts, the flight is getting bumpy :-)

This is a series on the book Gödel, Escher, Bach: An eternal golden braid by Douglas Hofstadter.

Earlier diaries are here

Today we'll discuss Chapter 5: Recursive structures and processes.

from the overview:

The idea of recursion is presented in many different contexts: Musical patterns, linguistic patterns, geometric structures, mathematical functions, physical theories, computer programs, and others.

This is a hard chapter!  That said, the chapter is still interesting, and I have some questions and ideas to spur conversation.

I also recommend browsing the comments in the old diaries.  Some very good comments are being made late in the week.

The executive on the phone is pretty clear, but I am not sure how good an exemplar of recursion it is.

The bit on pushing and popping nicely ties in with the previous dialogue; and he then gets into stacks.  But I dislike the way he assumes what a listener can and can't do. Perhaps part of the tension is trying to figure out if we are, in fact, finished?

On recursive transition networks -

1.  Wouldn't it be great if we diagrammed sentences this way, instead of the cockamamie methods we learned in grade school? (Or, anyway, the ways people attempted to teach us?).
1.  How do we avoid infinite loops here? Perhaps there is a sort of 'pressure' gauge on ending the loop, and we know, at some level, that we will lose the reader or listener if we add one more loop?

Diagram G and recursive sequences

1. Someone who can program could probably make a program to draw the shapes on p 135 and 136 as they expand.  That might make it clearer.
1. the Q series is neat.  Probably easy to program - I tried a tiny bit and didn't quite get it.  But one of you can probably do it.

The two graphs - I am just not a visual person.  Discuss amongst yourselves

Feynmann diagrams - aren't these cool?  I mean, at one level, this is how EVERYTHING WORKS

Copies and sameness - I think it was Steven Pinker who came up with the idea (or developed it) that we identify nouns by their closeness to an archetype.  Cats are cats because they are close to some 'cat archetype'.  But this is a big question.

1.  You aren't identical to the you you were 10 minutes ago, much less when you  were a kid, so how are you the 'same'?
1. Is a book the same in different languages?
1. Why are identical twins NOT the same?
1. Is a book the same to different people?

Programming - as may be already evident, I am going to need help, here.  Not so much with this chapter, as with later ones.

Tic tac toe - I am such a geek.  At some point in elementary school, I diagrammed all of tic tac toe to prove how to win.

Chess - one big change since this book came out - back then, the best chess program was so-so.  Now, it may be better than anyone alive.  What does this do to arguments about artifiicial intelligence?

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#### Comment Preferences

• ##### Tip jar(24+ / 0-)

Let's discuss!

This book is getting hard, isn't it?

• ##### You can be the same in one sense and different...(9+ / 0-)

...in others.

I.e., I'm not the same person I was ten minutes ago; my body chemistry is different.  My blood sugar has gone through some fluxuation.  My heart rate could vary.  But, for the most part, my core beliefs, identity, sense of self tends to be the same.  My behavior is similar, even if my mood has changed.

It's forest vs. trees stuff.  A single tree loosing its leaves does not change the nature of the forest.  All the trees losing their leaves changes the short-term nature of the forest, but the overall patterns and structures of it still follow the same cycles.

"Nice to meet you, Rose Tyler. Run for your life!"

• ##### I'm very divided over this diary(8+ / 0-)

Maybe I should split it further

Oh, recursions, foiled again.

;)

I'll be more enthusiastic about encouraging thinking outside the box when there's evidence of any thinking going on inside it.~Terry Pratchett

• ##### I got stuck(5+ / 0-)

on page 140.  Thinking about the skeleton and what I call the butterfly below.  Later on Hofstadter refers to it as the Gplot.  No matter how small it gets its still there in the negative and positive directions.  Beautiful.

I like the idea of the axis representing energy and time.  Each line being an energy band with the empty swaths being forbidden energy.  Infinity in all directions and just magnificent.

• ##### As I noted, I am not at all a visual person(4+ / 0-)

I am, in fact, learning disabled in this area.

So, any explanation you can offer about a diagram like the Gplot figure would be welcome.

Godel, Escher, Bach

is now open

[ Parent ]

Recommended by:
Ahianne, plf515, Texas Revolutionary

If you look at the graph it is exactly the same in all directions, and in every shape and line.  Take the over all look, start in the middle, it looks like two parenthesis.  Now look at each individual line they are all the same no matter in which dimension you view it.

From that you move through Figure 33 and into Figure 34.  You can see the loops.

• ##### I am pretty visual.(2+ / 0-)
Recommended by:
RunawayRose, plf515

Have applied recursion to Celtic knotwork patterns to produce semifractal neoCeltic interlace patterns. I can only carry the recursion so far when using pencil on paper, even less when doing paint on fabric, so I usually can only do about 4 or 5 levels of recursion.

Veni, vidi, farinuxi.

[ Parent ]

• ##### As you zoom in,(1+ / 0-)
Recommended by:
plf515

in any portion of the graph, the zoomed image looks like the whole graph.

Ideally, this would be true no matter what portion of the graph you picked, and no matter how closely you zoomed in.

That's why Hofstadter called it "the face of God".

--Shannon

"It is better to die on your feet than to live on your knees." -- Emiliano Zapata Salazar
"Dissent is patriotic. Blind obedience is treason." --me

[ Parent ]

• ##### Thanks n/t(1+ / 0-)
Recommended by:
plf515
• ##### I think the biggest problem I have with this...(7+ / 0-)

...material is talking about it in a way that captures it.

I'll give an example, which is probably equally ineffective.  When I started studying 3-d plotting on graphs, we talked briefly about 5d & 6d plotting.  A friend of mine, who is extremely smart, but very visual, just couldn't get it.  I tried to explain it to him, but there was just no way to -- if he couldn't understand for himself, I couldn't tell him how it worked.

In my head, it's just cascading possibilities.  I.e., a 4-d graph is an animated 3-d graph.  It's the capturing of 3-d over time.  Well a 5-d graph is the same thing, but accounting for multiple time lines.

I guess this is something that just makes perfect sense to me, but there are no good visuals to explain it, at least none that I've found.

Recursion is similar-- I can pretty much picture how it works in my head, even if I can't work out all the specific details of a given process, but I can't easily convey to anyone else how simple it all is.

"Nice to meet you, Rose Tyler. Run for your life!"

• ##### As a totally nonvisual person(6+ / 0-)

I work differently.

For instance, in statistics, we often deal with matrices that have many many dimensions .... dozens, even hundreds.  But since I don't work visually even with 2D and 3D matrices, I found it very easy to generalize and work with 50D matrices.  The algebra stays the same.

Godel, Escher, Bach

is now open

[ Parent ]

• ##### Exactly(5+ / 0-)

your inability to do the visual work actually proved a benefit for you, not a hinderance.

"Nice to meet you, Rose Tyler. Run for your life!"

[ Parent ]

• ##### Once you have gotten(1+ / 0-)
Recommended by:
plf515

to the level of complete abstraction, additional layers of abstraction don't hurt.

This is why it was always easier for me to visualize an electric circuit than the stresses in a beam. It's in the translation from the abstract to the physical that I get screwed up.

--Shannon

"It is better to die on your feet than to live on your knees." -- Emiliano Zapata Salazar
"Dissent is patriotic. Blind obedience is treason." --me

[ Parent ]

• ##### I showed up this time LOL(4+ / 0-)

Ok, I showed up last week, but I was behind on my reading.  I'm all caught up now, but I have trees calling for me.  I'm heading out the door shortly, to go back to the redwoods.

I really enjoyed the chapter.  The part about Gplot really got me going.  Ok, don't ask.  You're not good with visuals and I'm not good with words.  Not a good mix.  LOL

That wasn't a complaint, by the way.  I figure that you have the words to fill in my blanks. LOL  I only wish I could have gone further in college.  Maybe then, I would have the words to fill in your blanks.  Oh well.

I'm very happy that you're doing this series.  It's giving my brain some exercise and that's never a bad thing.

The smallest feline is a masterpiece. ~Leonardo Da Vinci~

• ##### You are good with words(3+ / 0-)
Recommended by:
RunawayRose, Ahianne, FrugalGranny

Maybe you just don't know it!

Godel, Escher, Bach

is now open

[ Parent ]

• ##### Not that good. LOL(4+ / 0-)

I feel like I'm gasping for air when looking for the right words.  I figure it's a throwback from my deaf years when words didn't mean much.  Body language and visuals meant everything back then.  Maybe that's why enjoyed this chapter so much.  The Gplot is very visual, though I admit to admiring the math as well.

No matter.  This book makes my brain go through some exercises that I'm enjoying very much.  I took a bit of joy in listening to the vid that you shared in the last diary.  I intend to listen to it more than once.  The joy comes from the fact that I can even hear what was discussed. I don't ever want to take my hearing for granted.

Ok, it's time to pack a few essentials.  We're headed off to get OUT of the city yet again.  I'm so very spoiled now.  We may live in the city (San Francisco), but we can escape to find peace and quiet very quickly.

As usual, I'm saving this diary to read later.  The comments generated are as fascinating as the book.  :)

The smallest feline is a masterpiece. ~Leonardo Da Vinci~

[ Parent ]

• ##### If you're gasping for air,(1+ / 0-)
Recommended by:
plf515

you're closer to getting this book than most.

It's not something that you're ever going to grok at one time.

It's sneaky.

The first couple of times I read GEB, I would wake up in the middle of the night, having a "oh... so that's what it meant!" moment.

This is one of those works that cannot be over-read. No matter how deep you dig, there's more under your shovel.

I don't know anyone who has ever read GEB that has not been profoundly changed by the experience.

--Shannon

"It is better to die on your feet than to live on your knees." -- Emiliano Zapata Salazar
"Dissent is patriotic. Blind obedience is treason." --me

[ Parent ]

• ##### prototypes and categories in linguistics(4+ / 0-)
Recommended by:
RunawayRose, Ahianne, plf515, FrugalGranny

From what I can tell, the exploration of prototypes, categories, radial categories, and "closeness" goes back further and has expanded in different directions than just the one linguist mentioned. Linguistics seems to have some history of rather heated academic debate.  Some participants and observers might pick other persons as prototypes of the protoyping linguist category.

;)

This wiki article on cognitive semantics, for example, offers some other background and links.

Cheers

• ##### recursive abbreviations(4+ / 0-)
Recommended by:
RunawayRose, Ahianne, plf515, FrugalGranny

Recursive self-referential abbreviations occasionally surface in computing. I'm not sure why I find them amusing, but I do.

Curiously, the two that popped off the top of my stack both define themselves by what they're not:

GNU ... GNU's Not Unix

and

XINU ... Xinu Is Not Unix

It seems like I should end with a punchline, but I seem to be stuck in a loop figuring out what it might be.

• ##### To truly understand recursion...(2+ / 0-)
Recommended by:
plf515, etbnc

one must first understand recursion.

--Shannon

"It is better to die on your feet than to live on your knees." -- Emiliano Zapata Salazar
"Dissent is patriotic. Blind obedience is treason." --me

[ Parent ]

• ##### the boat problem, and air pollution(4+ / 0-)
Recommended by:
Ahianne, cfk, plf515, FrugalGranny

Take a boat.  Replace a part.  It's the same boat. Replace another part - still the same.  Continue until all the parts are replaced.  Still the same.

This is why some highly polluting combustion plants remain in operation long after the Clean Air Act intended to clean them up. There's a loophole that allows maintenance of existing combustion equipment. Replacing parts on old, dirty plants (for over 30 years!) has allowed their operators to avoid having them become categorized as "new sources" that would be subject to the EPA's New Source Review process.

I learned about this seven years ago when neo-cons quietly gutted the Clean Air Act by making the maintenance loophole big enough to pilot a coal barge through.

The boat problem has real-life consequences.

• ##### The boat problem was great.(3+ / 0-)
Recommended by:
Ahianne, plf515, FrugalGranny

I actually have a friend who bought a very old wood boat.  Over the years he replaced most of the wood hull with fiberglass.  The shape is still the same, the boat sails the same but it is not the same...but it is the same...it really is the same and yet its not.

• ##### Reminds me of the story ...(0+ / 0-)

... of the farmer who owned the same ax his whole life. He changed the head only three times and the handle four.

• ##### btw, added a GEB tag to this diary .... n/t(3+ / 0-)
Recommended by:
Ahianne, plf515, FrugalGranny

~we study the old to understand the new~from one thing know ten thousand~to see things truly one must see what is in the light and what lies hidden in shadow~

• ##### okay, i am really gonna need to read this book,(3+ / 0-)
Recommended by:
Ahianne, plf515, FrugalGranny

to actually read it, or the very least, as a start, to acquire a copy ... my brother in NY has one, but unfortunately, I am not in NY ... I am very visual, so I do wish I could review those diagrams and comment, especially, as a programmer ... btw, I am a programmer, yes, but my particular focus/forte is Database Design/Architecture, and, in fact, I use, quite extensively, recursive structures, constructs, and libraries, etc .... hmmm ..... I have so very much to say on these subjects, but alas, I am feeling more and more handicapped, with each chapter, not having read this wonderful book, hmmm, maybe I just might have to hit some used book store and see if I can procure a cheap used copy .... where is THE STRAND (a very large, rather famous, used book Store in NYC, the village), when you need it ...

(btw, I will try to comment later, when I have more time)

~we study the old to understand the new~from one thing know ten thousand~to see things truly one must see what is in the light and what lies hidden in shadow~

• ##### This book suits you(3+ / 0-)
Recommended by:
Ahianne, FrugalGranny, ArthurPoet

You can get it used, at bn.com, for pretty cheap, depending on condition.  "Very good" for less than \$10.

Also available used at amazon.com

Later on in the book, he gets into varieties of loops, and all sorts of computer science stuff.

Godel, Escher, Bach

is now open

[ Parent ]

• ##### KYMATICA (vid) - This just seems related ..(3+ / 0-)
Recommended by:
Ahianne, plf515, FrugalGranny

(I haven't actually had a chance to view this entire video yet, but from the opening message, about the DNA's true purpose, this seems relevant to this discussion)

KYMATICA (vid)

~we study the old to understand the new~from one thing know ten thousand~to see things truly one must see what is in the light and what lies hidden in shadow~

• ##### Regarding RTNs and highly recursive sentences...(1+ / 0-)
Recommended by:
plf515

I was reminded of a comment in Suzette Haden Elgin's "The Judas Rose" [Epigraph to Ch. 13]

The human brain has a hard time handling sentences when they're embedded inside one another.  We can manage 'The man the woman spoke to left the room' without much trouble; that's just one embedding.  But make that 'The man the woman the child kissed spoke to left the room' and our minds begin to gasp for clarification.  And with each additional sentence embedded inside a sentence it gets more impossible to understand.  Now that's a handy thing to know, because it has applications well beyond the construction of sentences.

The epigraph then goes on to compare the idea of embedding a task within a task within a task...in order to hide the really crucial one from being discovered/interrupted.

The theory [and the applications in computer science] doesn't seem to limit the depth of the embedding; but actually having to communicate with other people seems to.

Of course, the other classical literature citation of recursive stories is the "1001 Nights"...but maybe DH already mentioned that one.

...among these are Life, Liberty and the Pursuit of Happiness* *Void where prohibited

• ##### He did, (1+ / 0-)
Recommended by:
plf515

In passing.

As to the potential depths of recursion, the limitation, in both computer science and human interactions, is the ability of the relevant humans to keep track of where they are in the stack.

DRH gives a great, albeit degenerate, example of this when referring to an absent-minded German professor, who, at the end of his lecture, fires off all of the verbs from every sentence he has uttered.

Acceptable, within the formal rules of the language, but totally incomprehensible to his audience.

Same idea.

--Shannon

"It is better to die on your feet than to live on your knees." -- Emiliano Zapata Salazar
"Dissent is patriotic. Blind obedience is treason." --me

[ Parent ]