Douglas Hofstadter has a new book
amazon.com
amazon.com
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.
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 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.
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.
Can you think about Euler’s identity? Almost certainly. Can you think Euler’s identity? Very unclear.
Then what is it?
What would a thought in print look like? And what print with any meaning at all would not "be a thought" in ordinary parlance?
Exactly my point.
Well, we have a generalized Euler's formula[1] for this identity:
e^(ix) = cos x + i sin x
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.
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.
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.
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.
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.
That's pretty cool right there.
Also, why are the dates all out of order?
The Wikipedia entry on the professor also mentions this fact from the Amazon history (http://en.wikipedia.org/wiki/Douglas_Hofstadter#In_popular_c...).
I can't tell you how happy I am that he's back to research.
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.
"The Mind's I" remains my favourite, by far.
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 oversimplify, of course. But the extent to which Hofstadter is "into" Zen is open to question. (I don't remember much Zen in GEB.)
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...
Explains why great pitches are stories.