Strange Loops
By Uriah Kriegel
The Times Literary Supplement, April 25, 2007
Edited by Andy Ross
I Am a Strange Loop
by Douglas R. Hofstadter
Basic Books, 348 pages
The purpose of Douglas Hofstadter's new book is to make inroads into the
nexus of self, self-awareness and consciousness by examining
self-referential structures in areas as diverse as art and mathematics. His
principal thesis is that we ourselves, qua conscious beings, are emergent
self-referential structures. His book thus revolves around two main ideas:
the idea of an emergent phenomenon and the idea of self-reference, or of a
strange loop.
A strange loop is a phenomenon that involves reference
to itself. Different systems may exhibit different degrees of
self-referential sophistication. For Hofstadter, the more sophisticated a
system's self-referential capabilities, the more soulful it is, the more
robust its existence as an "I".
As an example of an emergent
phenomenon, Hofstadter tells of the time he tried to take out a wodge of old
envelopes from a box in his drawer, and could swear he felt a marble nestled
among them. It turned out that the uncanny appearance of a marble was
produced by the extra layers around the envelopes' V. Ultimately, he
proposes, our self is an emergent appearance of this sort. In fact, it is
the most real emergent object in our inner world.
The issue of
emergence applies already to awareness of things other than oneself. At some
level, we know that all that is really going on in our head is the
propagation of electrical impulses among nerve cells. But we experience our
mental life as involving the continuous representation of the world.
Inside the cranium are billions of neural cells whose behavior is more or
less meaningless. But sometimes large clusters of cells coordinate their
behavior in response to the way the external world impinges on parts such as
the retina or the eardrums. When they do, these clusters come to constitute
symbols that represent external conditions in a sustained manner that
effectively constitutes awareness of the external world.
Our symbolic
representations have a coarse grain, so we are not aware of the millions of
neurons inside our brain, but rather of the various symbols that clusters of
them make up. The cranium is aware of itself as a theater of ideas, desires
and hopes, not as a container of cerebral molecules buzzing about
meaninglessly.
The thesis that conscious selves are emergent
self-referential structures strikes me as sending us in exactly the right
direction.
AR This review soundly
reflects my own take on the book. Strange loops are now respectable
entities, which they were not in my characterization in a book I wrote
exactly thirty years ago.
I blame myself for not having clarified their
logic as far as Hofstadter did.
Going Loopy Over Consciousness
By
David Deutsch
Physics World, July 2, 2007
Edited by Andy Ross
I Am a Strange Loop
by Douglas R. Hofstadter
Basic Books, 348 pages
Douglas Hofstadter expresses disappointment that his 1979 masterpiece Gödel, Escher, Bach was not recognized as explaining the true nature of consciousness, or "I"-ness. It never occurred to me that it was intended to do so.
AR (2007) This is a nice line but it is a trifle disingenuous. It seemed clear to me that Hofstadter did nurse some such ambition, even though the word "consciousness" was not then bandied about so freely as it has been in the last decade.
I Am a Strange Loop is supposed to restate and explain his solution: that a mind is a near-infinitely extendable, self-referential loop of symbols that suffers or benefits from the hallucination of being an "I". Furthermore (Hofstadter says paradoxically), that hallucination is itself an "I".
AR (2007) Here one might reasonably accuse Hofstadter of being excessively cute with the word "hallucination". Can one hallucinate a hallucination? Or does one, rather, have a hallucination, or hallucinate a vision or a face or a self?
Strangely, Hofstadter's half of this theory of consciousness (the loopy half), is quite convincing. The unconvincing half is essentially philosopher Daniel Dennett's theory from his book Consciousness Explained, namely that our opinion that we are conscious is simply mistaken.
AR (2007) This is unfair on Dan, whose critics have lambasted his hubris with excessive gusto. Dennett made it quite clear that what we are mistaken about is the physical or other nature of consciousness, not that the word denotes a quite unexceptional denizen of the curiously nebulous bestiary our folk psychology. For Dan, consciousness is at least as real as ectoplasm or sweet dreams
The central analogy is between minds and other "strange loops": certain self-referential statements discovered by Kurt Gödel within formal mathematical systems. These statements assert their own unprovability within the system but are nevertheless provably true, akin to the paradoxical "this statement is false".
AR (2007) I first read GEB some five years after writing a well regarded thesis on Gödel's results, so I was optimally primed to absorb and evaluate its message. I was persuaded. The logic is as sound as, given its loopiness, it can be. I agree with Hofstadter that Gödel not only torpedoed the mighty flagship of Russell and Whitehead's ramified theory of types but also gave us a defining metaphor for a new view of logic.
Hofstadter imagines a computer made of toppling dominoes that is designed to factorize integers. It is presented with the input "641" and set in motion to perform its computation. Why is one particular domino left standing? The most fundamental explanation does not refer to the sequence in which the other dominoes fell; rather it is "because 641 is prime".
AR (2007) This is a great example, but unfortunately it invites extrapolation to wild excess. The claim that 641 is prime is a typical truth about Platonic heaven. Roger Penrose and many others have waxed lyrical enough about this heaven to make its attractions quite undeniable, at least to those of a certain psychological disposition. But another truth about the realm of concepts, analogous to truths about Hamlet or unicorns, is the claim that God is perfect. Deutsch would appear to agree that the "most fundamental explanation" of the manifest glory of creation is that God is perfect! Reductio ad absurdum, I trust.
Hofstadter's claim that our nature prevents us from understanding our nature cannot be taken at face value. Like a Gödelian claim to be unprovable, it applies only inside the system from which it is derived, namely Hofstadter's own philosophical framework. But, again like Gödel's construction, this simultaneously reveals that there is a truth to be discovered outside of that framework.
AR (2007) Sorry, David, but yes it can. You are right that it applies only inside the system and so on, but think for a second. There is no framework that I can appeal to outside of my "I" since the very act of invoking it brings it inside my I-horizon. Of course, you can be outside my horizon and vice versa, but we are both stuck inside our own horizons. Dennett tried to sneak around this circularity with his talk of autophenomenology and heterophenomenology, which breaks out of any particular loop, but "my" loop always remains, even as "I" drift toward solipsism.
Something new is needed to discover that truth, and Hofstadter's loops are probably involved. "Strange loopiness" is a distinctive form of emergence, rooted not in complexity but in universality, the real substrate of "I"-ness.
AR (2007) Yes, I agree that
the loop story is a decisive step forward on all this. We have a logical
paradigm that gives us a technical hold on something that is otherwise too
slippery to work with. We can program robots to loop their self-images
indefinitely, and if they are smart enough and so on, that should do the
trick.
Douglas Hofstadter
Edited by Andy Ross
Douglas R. Hofstadter says the idea that changed his life came to him on the
road. Discouraged by the way his doctoral thesis was going, in the summer of
1972 he packed his things into a car and drove eastward across the
continent. Each night he pitched his tent somewhere new. Free to think about
whatever he wanted, he chose to think about thinking itself.
Seven
years later, his notes had become a 777-page book called Gödel, Escher,
Bach: An Eternal Golden Braid, which won him the 1980 Pulitzer Prize for
general nonfiction. Martin Gardner: "Every few decades, an unknown author
brings out a book of such depth, clarity, range, wit, beauty and originality
that it is recognized at once as a major literary event."
Hofstadter
was 35 when he won the Pulitzer Prize and was awarded tenure. Now he is 68.
For more than 30 years, he has worked at Indiana University at Bloomington.
He has no official obligations and spends most of his time in his study. "I
have always felt that the only hope of humans ever coming to fully
understand the complexity of their minds is by modeling mental processes on
computers and learning from the models' inevitable failures."
Modern
artificial intelligence began some 25 years ago with machine translation.
The goal was to make a device that takes an English sentence as input and
spits out a French sentence. You feed the machine English sentences whose
French translations you already know. You enter a pair, then take the
English half and feed it into your machine to see what comes out in French.
If that sentence is different from what you were expecting, you twist the
knobs and try again. After enough trial and error, you get the correct
French equivalent of your English sentence.
By repeating this process
with millions of pairs of sentences, you will gradually calibrate your
machine, to the point where you can enter a sentence whose translation you
don't know and get a reasonable result. And the beauty is that you never
needed to program the machine explicitly or explain why you twisted the
knobs this way or that.
Google director of research Peter Norvig says
Google is the world's biggest AI system. Modern AI is about data, and Google
has lots of data. Google Translate engineer Josh Estelle: "You can take one
of those simple machine-learning algorithms ... when you go from 10 000
training examples to 10 billion training examples, it all starts to work.
Data trumps everything."
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