Douglas Hofstadter has a new book(amazon.com)
amazon.com
Douglas Hofstadter has a new book
http://www.amazon.com/gp/product/0465018475/
11 comments
A great read by Hofstadter on Analogy as the Core of Cognition is here: http://prelectur.stanford.edu/lecturers/hofstadter/analogy.h...
I'm a big fan of Hofstadter and his emphasis on analogy. George Lakoff has and others from cognative semantics provide strongly supporting views from linguistics.
And in Machine Learning, Deep Learning is now providing new support for these views on analogy. This isn't immediately obvious until realizing that analogy is not necessarily an active process more likely a passive result of how thoughts and memories are encoded and stored. I'm curious as to whether Hofstadter will address this in this book - I would imagine so as he was long ago excited by earlier similar ML approaches (Sparse Distributed Memory).
I'm a big fan of Hofstadter and his emphasis on analogy. George Lakoff has and others from cognative semantics provide strongly supporting views from linguistics.
And in Machine Learning, Deep Learning is now providing new support for these views on analogy. This isn't immediately obvious until realizing that analogy is not necessarily an active process more likely a passive result of how thoughts and memories are encoded and stored. I'm curious as to whether Hofstadter will address this in this book - I would imagine so as he was long ago excited by earlier similar ML approaches (Sparse Distributed Memory).
Hm, so back in 2000 I met a girl at Stanford whose senior thesis was based on the idea that metaphor is the core of all thought.
I remember giving the counterexample of a mathematical formula. In what way is e^i*pi = -1 a metaphor for anything? What role does analogy play in this idea?
Looking back, I am open to the fact that mathematicians use analogy to come up with their ideas (but perhaps not metaphor, which seems essentially literary) Mathematics is funny because it is presented in "reverse", i.e. not the way it was derived.
Anyway I will have to read it, although I am slightly skeptical of ideas that try to explain "everything". In retrospect Taleb's Antifragile had some of that flavor, although I thought it was very good.
EDIT: I think it's probably accurate to say that the brain is fundamentally an association machine. Analogies are a form of association, but not all associations are analogies. This very post is a great example of an association (not an analogy), because when I read "analogy is the core of all thought" it made me think of the disputed "metaphor is the core of all thought" idea I heard a long time ago.
I remember giving the counterexample of a mathematical formula. In what way is e^i*pi = -1 a metaphor for anything? What role does analogy play in this idea?
Looking back, I am open to the fact that mathematicians use analogy to come up with their ideas (but perhaps not metaphor, which seems essentially literary) Mathematics is funny because it is presented in "reverse", i.e. not the way it was derived.
Anyway I will have to read it, although I am slightly skeptical of ideas that try to explain "everything". In retrospect Taleb's Antifragile had some of that flavor, although I thought it was very good.
EDIT: I think it's probably accurate to say that the brain is fundamentally an association machine. Analogies are a form of association, but not all associations are analogies. This very post is a great example of an association (not an analogy), because when I read "analogy is the core of all thought" it made me think of the disputed "metaphor is the core of all thought" idea I heard a long time ago.
> In what way is e^i*pi = -1 a metaphor for anything?
> Mathematics is funny because it is presented in
> "reverse", i.e. not the way it was derived.
I appreciate what you're saying, but see my response below about semantics.
If you are calling it a metaphor, then aren't you calling ALL equations metaphors? That is doing violence to the meaning of the word "metaphor".
There is for sure a "relation" (or association) between the symbols e^i*pi = -1 and the picture of a unit vector on a complex plane. But that relation is not a metaphor.
If you are calling it a metaphor, then aren't you calling ALL equations metaphors? That is doing violence to the meaning of the word "metaphor".
There is for sure a "relation" (or association) between the symbols e^i*pi = -1 and the picture of a unit vector on a complex plane. But that relation is not a metaphor.
You can prove that equality using pure analysis, or pure geometry, using appropriate definitions. The metaphor is the intuition that the two proofs are equivalent in an abstract sense.
You’ll need to convince me that “e^ipi = -1” is actually a “thought" before I’ll buy it as a counter example. This will be an uphill battle.
Can you think about Euler’s identity? Almost certainly. Can you think Euler’s identity? Very unclear.
Can you think about Euler’s identity? Almost certainly. Can you think Euler’s identity? Very unclear.
> You’ll need to convince me that “e^ipi = -1” is actually a “thought"
Then what is it?
Then what is it?
A statement of grammar? A picture? A string of characters?
What would a thought in print look like? And what print with any meaning at all would not "be a thought" in ordinary parlance?
What would a thought in print look like? And what print with any meaning at all would not "be a thought" in ordinary parlance?
> And what print with any meaning at all would not "be a thought" in ordinary parlance?
Exactly my point.
Exactly my point.
a pattern if repeated enough times.
Haha, sounds like you've met a Lacanian (Lacan was famous for saying, among other things, that "the unconscious is structured like a language"). Such reductionist intellectualizations (aka "man, everything is a pineapple!") are neat to meditate on, but they alone won't give you tangible results or something you can use to forecast events and test hypotheses.
> In what way is e^i*pi = -1 a metaphor for anything?
Well, we have a generalized Euler's formula[1] for this identity:
[1]: http://en.wikipedia.org/wiki/Eulers_formula
Well, we have a generalized Euler's formula[1] for this identity:
e^(ix) = cos x + i sin x
[1]: http://en.wikipedia.org/wiki/Eulers_formula
Writing the formula down on a piece of paper doesn't by itself count as thought though. I haven't read the book so can't really comment what the author would say, but to load the formula into your brain and think about it in a useful way is very different than plugging it into a calculator or reading the formula.
> e^i*pi = -1
Gee, I think that extending the power series for e^x to the complex domain is a pretty fair interpretation of `metaphor' in the context.
Gee, I think that extending the power series for e^x to the complex domain is a pretty fair interpretation of `metaphor' in the context.
Like a lot of philosophical debates, this comes down to semantics. I don't think there's any useful way in which Euler's identity is a 'metaphor' for anything.
Metaphor has a fairly specific definition; it is a type of analogy. An analogy is a type of association.
As mentioned, I think it's fair to say that all thought is based on associations. But it isn't true that all thought is analogies or metaphors.
There are simply other types of associations. I would call this case a "generalization", an extremely common thought process in mathematics, and an example of a kind of analogy (not a metaphor) where the original domain is a proper subset the new one.
In other words, applying an idea from one domain to another is an analogy, not necessarily a metaphor. To claim otherwise is just being loose with words in a way that has no meaning.
Metaphor has a fairly specific definition; it is a type of analogy. An analogy is a type of association.
As mentioned, I think it's fair to say that all thought is based on associations. But it isn't true that all thought is analogies or metaphors.
There are simply other types of associations. I would call this case a "generalization", an extremely common thought process in mathematics, and an example of a kind of analogy (not a metaphor) where the original domain is a proper subset the new one.
In other words, applying an idea from one domain to another is an analogy, not necessarily a metaphor. To claim otherwise is just being loose with words in a way that has no meaning.
> I don't think there's any useful way in which Euler's identity is a 'metaphor' for anything.
Euler's Identity isn't itself the metaphor, it's the equation we use to teach and understand it that is metaphorical. The letters themselves only mean "Euler's Identity" when imbued with the extra meanings that come from the symbolic framework of mathematics.
Euler's Identity isn't itself the metaphor, it's the equation we use to teach and understand it that is metaphorical. The letters themselves only mean "Euler's Identity" when imbued with the extra meanings that come from the symbolic framework of mathematics.
The problem is that as we understand them today, mathematical formulas like yours are void of meaningful semantics unless you have any objective abstract notion of "infinite set", which seems not to be the case because "everything is a set", and "everything" is not an abstraction.
So we have to deal with them as pure sequences of signs which are part of the set of deducible formulas.
Your "understanding" (or mine or Euler's) of the formula is most likely a metaphor (well I'd say an analogy in this case) and is what led to its proof.
So we have to deal with them as pure sequences of signs which are part of the set of deducible formulas.
Your "understanding" (or mine or Euler's) of the formula is most likely a metaphor (well I'd say an analogy in this case) and is what led to its proof.
For interest's sake, the book "Metaphors We Live By" concerns that idea. It's a pretty good book though I personally think they take it a bit far
http://www.amazon.com/gp/aw/d/0226468011/
http://www.amazon.com/gp/aw/d/0226468011/
This goes way back before 2000. See George Lakoff and Mark Johnson’s 1980 book, Metaphors We Live By.
> See George Lakoff and Mark Johnson’s 1980 book, Metaphors We Live By
I highly recommend this book! You'll find yourself nodding in agreement at one line and then realizing that you're agreeing with a deeper truth than you knew. At the very least, you'll start reading newspapers at multiple levels.
I highly recommend this book! You'll find yourself nodding in agreement at one line and then realizing that you're agreeing with a deeper truth than you knew. At the very least, you'll start reading newspapers at multiple levels.
[deleted]
Art:Science::Analogy:Isomorphism
July 1994: Amazon.com sells first book, "Fluid Concepts & Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought" -- at http://phx.corporate-ir.net/phoenix.zhtml?c=176060&p=iro...
That's pretty cool right there.
That's pretty cool right there.
I don't mean this in a rude way; I'm just confused: How is your comment at all relevant to this submission?
Also, why are the dates all out of order?
Also, why are the dates all out of order?
The first book sold was written by the same author the submission is about.
The Wikipedia entry on the professor also mentions this fact from the Amazon history (http://en.wikipedia.org/wiki/Douglas_Hofstadter#In_popular_c...).
The Wikipedia entry on the professor also mentions this fact from the Amazon history (http://en.wikipedia.org/wiki/Douglas_Hofstadter#In_popular_c...).
July 1995... the years are above the months.
The idea that analogy underpins all thought is also argued by Ian McGilchrist in his book Master and His Emissary, which I'd highly recommend to people interested in the sort of epic philosophical undertaking GEB was: http://www.iainmcgilchrist.com/The_Master_and_his_Emissary_b...
I agree with the premise that analogy is the core of all thinking, but the idea isn't new, at the very least I can trace it back to Julian Jaynes' 1976 book "The Origin of Consciousness in the Breakdown of the Bicameral Mind" and it's highly probable other's have thought this through even before then.
Sounds like he's getting back to his research; which is good, since maybe it won't be as maudlin and self-indulgent as _I Am A Strange Loop_ was.
His wife fell to the floor one day with a previously unsuspected brain tumor while they were on sabbatical in Italy and died days later; Doug was left to raise their two children alone. I was always amazed he functioned at all, honestly.
I can't tell you how happy I am that he's back to research.
I can't tell you how happy I am that he's back to research.
I wasn't a fan of 'Strange Loop' either. I'll be buying this one though.
Glad to hear I wasn't the only one disappointed by it.
How interesting - I've been leaving GEB on the coffee table in hopes that I might pick it up and start it again (made it halfway about 10 years ago) but now I wonder whether I ought to pick this up. Thanks for letting us know.
GEB is the most popular book nobody has read.
I think it just doesn't work for everyone. While many people seem to love it, I failed to read it, twice. I think I got his point about self-reference and conciousness in the introduction, but from then on I found it so mind-numbingly boring I just couldn't continue reading past a couple of chapters. To me it seemed like he was going round and round re-explaining the same points over and over. In fact I thought reading GEB must be a hazing exercise for geeks. But then, since lots of people do seem to enjoy it, I guess it might just be one of those love-it-or-hate-it things.
Agreed. It seems disjoint and mostly hot air recycled over and over. Its not just you: there are a lot of us. My copy has done the rounds in the office and the conclusion is the same universally.
If the content was concise or written in the style of say Persig, Neal Stevenson or Ray Bradbury, I could stomach it.
Then again even worse is Ray Kurzweil who manages to do a GEB with far less content and that content is dubious and contrived rubbish.
If the content was concise or written in the style of say Persig, Neal Stevenson or Ray Bradbury, I could stomach it.
Then again even worse is Ray Kurzweil who manages to do a GEB with far less content and that content is dubious and contrived rubbish.
A similar thing happened to me. I picked it up, read 200-300 pages and thought I could see where the book was going but found that it took such an agonizingly long time to reach its conclusion that I put it down.
Those simplistic-seeming explanations are subtly different, which turns out to be quite helpful when dealing with the conceptual difficulties of TNT. Of course, some more accessible language than TNT would make the book more approachable, but Hofstadter's objective is to demonstrate why you will not be able to circumvent the incompleteness theorem by adding syntactic sugar.
The longer ago you've read it, the more you like. Like so many nostalgic things.
I only appreciated GEB after I took an advanced logic course featuring Cantor/Godel/Turing in university. Before that I didn't really get it. Well, I still don't, but now I can live with the ideas.
"The Mind's I" remains my favourite, by far.
"The Mind's I" remains my favourite, by far.
I'm amused by that joke even though I managed to read GEB twice in the 1980s. I've seen more people try & bounce off of it than make it through. It takes patience and tenacity.
It's the Infinite Jest of the Cognitive Science / Mathematics world
I wrote to DH around 2000 after a discussion I had with a friend about Wittgenstein and GEB. It was a pretty callow email, but he was kind enough to send a thoughtful reply.
He said he didn't know much about Wittg., but didn't like his vagueness, which I found interesting from someone who was into Zen.
He said he didn't know much about Wittg., but didn't like his vagueness, which I found interesting from someone who was into Zen.
I'd suggest that the difference is that Zen (at least in some schools) is after a meta-cognitive experience (by definition inexpressible in concrete terms) which transcends (even short circuits) cognition - whereas the aim of Western philosophy (at least in some schools) is a description of experience in concrete terms accessible to the intellect.
I oversimplify, of course. But the extent to which Hofstadter is "into" Zen is open to question. (I don't remember much Zen in GEB.)
I oversimplify, of course. But the extent to which Hofstadter is "into" Zen is open to question. (I don't remember much Zen in GEB.)
Precisely. Wittgenstein was (in approach at least) a reaction against Western philosophy, and his "vagueness" was a consequence of that.
An interesting subject. Elon Musk has been saying that it's important to reason from first principles and not by analogy. A lot of reasoning in startup world seems to be by analogy - the epitome being "AirBnB for Cars" type of elevator pitches.
I was just watching a talk by him where he clearly says that it's impossible to do this all the time, that you would go insane without using analogical thinking all day. But that it's a useful exercise when you are trying to sit down and find an innovative solution to a problem.
Somewhere in this comment, and in the first principles vs. analogy dichotomy, is the dichotomy showcased in the book/film "Moneyball".
Something has always bothered me about it. Something like ... is it better for a human to make a wrong decision than it is for a machine to make a right one ? Perhaps "it depends" ? If so, what is the threshold ? How wrong does a human decision have to be to be inferior to a machine decision ?
The same thing is showing up in Talebs _Antifragile_ ... he argues quite clearly for analogy, and skewers decision making from first principles.
It troubles me somehow...
Something has always bothered me about it. Something like ... is it better for a human to make a wrong decision than it is for a machine to make a right one ? Perhaps "it depends" ? If so, what is the threshold ? How wrong does a human decision have to be to be inferior to a machine decision ?
The same thing is showing up in Talebs _Antifragile_ ... he argues quite clearly for analogy, and skewers decision making from first principles.
It troubles me somehow...
Analogy is inspiration, not proof.
>Analogy is the core of all thinking.
Explains why great pitches are stories.
Explains why great pitches are stories.
Looking at the excerpt at Amazon, I learned that (i) Hofstadter married again (see them dancing here: http://www.youtube.com/watch?v=oeB-wu7aV0w) recently, which is totally irrelevant to the book, but was interesting to me since I was much moved from his heartfelt sorrow after his wife's death so eloquently expressed in Le Ton beau and (ii) there's a figure of speech called zeugma that I've never heard before (http://en.wikipedia.org/wiki/Zeugma), mentioned on pg. 5.