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Surfaces and Essences: Analogy as the Fuel and Fire of Thinking

Douglas R Hofstadter, Emmanuel Sander · 132 HN points · 5 HN comments
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Amazon Summary
Analogy is the core of all thinking. This is the simple but unorthodox premise that Pulitzer Prize -- winning author Douglas Hofstadter and French psychologist Emmanuel Sander defend in their new work. Hofstadter has been grappling with the mysteries of human thought for over thirty years. Now, with his trademark wit and special talent for making complex ideas vivid, he has partnered with Sander to put forth a highly novel perspective on cognition. We are constantly faced with a swirling and intermingling multitude of ill-defined situations. Our brain's job is to try to make sense of this unpredictable, swarming chaos of stimuli. How does it do so? The ceaseless hail of input triggers analogies galore, helping us to pinpoint the essence of what is going on. Often this means the spontaneous evocation of words, sometimes idioms, sometimes the triggering of nameless, long-buried memories. Why did two-year-old Camille proudly exclaim, "I undressed the banana!"? Why do people who hear a story often blurt out, "Exactly the same thing happened to me!" when it was a completely different event? How do we recognize an aggressive driver from a split-second glance in our rearview mirror? What in a friend's remark triggers the offhand reply, "That's just sour grapes"? What did Albert Einstein see that made him suspect that light consists of particles when a century of research had driven the final nail in the coffin of that long-dead idea? The answer to all these questions, of course, is analogy-making -- the meat and potatoes, the heart and soul, the fuel and fire, the gist and the crux, the lifeblood and the wellsprings of thought. Analogy-making, far from happening at rare intervals, occurs at all moments, defining thinking from top to toe, from the tiniest and most fleeting thoughts to the most creative scientific insights. Like Gö, Escher, Bach before it, Surfaces and Essences will profoundly enrich our understanding of our own minds. By plunging the reader into an extraordinary variety of colorful situations involving language, thought, and memory, by revealing bit by bit the constantly churning cognitive mechanisms normally completely hidden from view, and by discovering in them one central, invariant core -- the incessant, unconscious quest for strong analogical links to past experiences -- this book puts forth a radical and deeply surprising new vision of the act of thinking.
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it has a tendency to be just 15 years away - the deadline keeps on moving though.

I think that the main obstacle is language - language is terribly ambiguous, and its very difficult to deal with these ambiguities in a program.

Hofstadter [1] says that the core of thinking are analogies and that many of the allusions in language can be thought of as analogies, however this does not seem to be the main focus of inquiry right now.

[1] (my review & summary is here )

Is it? Based on this post (and associated papers etc.) it looks like Google has very good grasp on this:

I don't think that means they are close to General AI though.

> language is terribly ambiguous

I never get this argument. Sure, maybe it is from the point of the computer, but we humans use it just fine.

Much of our comedy stems from how ambiguous our language is. How many petabytes on the Internet are wasted with comments correcting someone's use of language? How many hours are spent as kids in classrooms learning all of the context around our languages, and we still get it wrong often enough to be corrected on the Internet and made fun of in comedy TV shows. We're certainly not using it just fine, we're using it in spite of all its shortcomings.

Do you know how often I'm driving while my wife is navigating and I ask "turn left here?" and she says "right"? Now, is she saying "correct, you should turn left" or is she saying "don't turn left, turn right"?

Outside of a dog, a book is man’s best friend. Inside of a dog, it’s too dark to read. –Groucho Marx

I haven’t slept for ten days, because that would be too long. –Mitch Hedberg

> Much of our comedy stems from how ambiguous our language is.

Yes, but we laugh because we understand there is an ambiguity, not because we don't see it.

> How many petabytes on the Internet are wasted with comments correcting someone's use of language?

People are pedantic on the net, plus on the world wide web not everyone is going to be an English first speaker. Spoken conversations don't have people correcting your grammar every 5 seconds.

> wife is navigating and I ask "turn left here?" and she says "right"

Well in this case she is being deliberately ambiguous. So you either tell by her tone inflection, or rely on previous memory. And of course you have the ability to ask her.

> Outside of a dog, a book is man’s best friend. Inside of a dog, it’s too dark to read. –Groucho Marx

> I haven’t slept for ten days, because that would be too long. –Mitch Hedberg

Again, I see and understand the ambiguity. I'm not sitting here dumbfounded; I 'get' that they turned the words back on themselves to mean something else.

I'm quoting someone, and I don't remember who, so I can't give credit where due. But they said that we'll know we have real AI when we ask the computer "Do you think?" and it replies "That reminds me of a story..."
Crows also seem to be doing analogies

Douglas Hofstadter says that thinking is all about making analogies, so that is all pretty remarkable.

The whole point of analogy problems is to test reasoning skills. Specifically, logical skills, inferences, categorization, and so forth. The vocabulary test nested within the analogy test is incidental. It creates a bivariate challenge (vocabulary + categorization), which is not necessarily an invalid test. It's just not a pure test of analogies, and it's also duplicative of the vocabulary portion of the test.

In re the value of analogies, there are some computer scientists and philosophers who believe analogy-drawing is the irreducible core of higher cognition. I'm not sure I'd go that far, but Douglas Hofstadter has come close:

Jan 24, 2014 · jrs99 on Debunking Princeton
writing can help you organize your thoughts and that can lead to new epiphanies. Writing helps you explore, helps you think, and helps you find ideas. Some people really hate that though. They don't like non-linear thinkers who use analogies and metaphors. They like to start with the proof. Other people enjoy surprising, sometimes ludicrous connections and analogies.

Some people also don't want facebook to fail. If you go deep into their comment history, many of them have argued that facebook cannot be the next myspace.

"The large ball crashed right through the table because it was made of Styrofoam. What was made of Styrofoam? (The alternative formulation replaces Stryrofoam with steel.) a) The large ball b) The table"

And a very large styrofoam ball can crash a comparatively small table made of wood, all depends on relative definition of 'large' right?

I think the problem is that everybody can pick his favorite feature and define it as the key of 'general intelligence'. Some say Anaphora, some say machine learning; I like Hofstaedter he says that it is all about analogy.

Also: The problem is that these statements can't be proven; it is all about opinions and dogmas; I think the argument is s question of power: the one who wins the argument has the power over huge DARPA funds, or whoever else gives out grants for this type of research. The run after defining problems (expert systems, big data) in AI might have something to do with the funding problem.

The 'Society of Mind' argument says that there are many agents that together somehow miraculously create intelligence. This argument sounds good, but it makes it hard to search for general patterns/universal explanations of intelligence.

On the one hand they have to focus on some real solvable problem, on the other hand that makes it very hard to ask and find answers to general questions; I don't know if there will be some solution to this dilemma.

Maybe western civilization is not very good at answering this type of general big questions, maybe Indian civilization has a better chance, after all they invented structural linguistics some 2500 years ago (so that was not Chomsky at all ;-)

Maybe the problem needs and idle class of Brahmi who can ask questions and ponder about them without end, without having to worry about questions of funding ?

Apr 03, 2013 · 132 points, 53 comments · submitted by yarapavan
A great read by Hofstadter on Analogy as the Core of Cognition is here:

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.

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.

> You’ll need to convince me that “e^ipi = -1” is actually a “thought"

Then what is it?

a pattern if repeated enough times.
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?

> And what print with any meaning at all would not "be a thought" in ordinary parlance?

Exactly my point.

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:

    e^(ix) = cos x + i sin x
Metaphorically, you can visualize the function e^(ix) tracing the unit circle out in the complex plane.


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.

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.

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.

> 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.

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

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 thought quality was at the core of all thought? ;-)
Haha, yes I also enjoyed ZAMM, which again has the tendency to explain "everything" using one concept. It is just a tempting thing, I guess. But the exercise does lead to interesting thoughts, even if the grand thesis isn't true.

  > In what way is e^i*pi = -1 a metaphor for anything?
Its a metaphor for taking the unit length vector [1,0] represented by the complex number 1+0i and rotating it 180 degrees to -1+0i...

  > Mathematics is funny because it is presented in
  > "reverse", i.e. not the way it was derived.
Its usually presented in both ways in most curricula, sometimes depending on where you read about it or who teaches/tells you about it. Most mathematical books include historical contexts and non-formal accounts of the way results were derived, specially for classic and old results such as Euler's Formula. In most modern topics sometimes the historical context for a theorem is not easy to understand (i.e. discrete signal processing or optimal control) and is only briefly mentioned.
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.

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.
July 1994: sells first book, "Fluid Concepts & Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought" -- at

That's pretty cool right there.

July 1995... the years are above the months.
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?

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 (

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:
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.
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.
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.

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 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.

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 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.
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.
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.

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.

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.)

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.
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...

Analogy is inspiration, not proof.
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.
>Analogy is the core of all thinking.

Explains why great pitches are stories.

Great news! Even when it's overwrought and opinionated, Hofstadter's writing is never boring, Le Ton Beau de Marot is, I think, one of the best books on translation. There isn't too much (English) information on Emmanuel Sander (other than his homepage:, Google seriously needs a semantic clustering algorithm for results, btw, had to laboriously sift through results for Emmanuel Sanders).

Looking at the excerpt at Amazon, I learned that (i) Hofstadter married again (see them dancing here: 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 (, mentioned on pg. 5.

"I am a Strange Loop" had quite a bit of fixation on his wife's death as well, I'm glad to hear he has re-married.
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