Paul P. Mealing

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Saturday 14 February 2009

Godel, Escher, Bach - Douglas Hofstadter's seminal tome

The original title of this post was Artificial Intelligence and Consciousness.

This is perhaps the hardest of subjects to tackle. I’ve just finished reading Douglas R. Hofstadter’s book, Godel, Escher, Bach: an Eternal Golden Braid, which attempts to address this very issue, even if in a rather unusual way.

Earlier in the same year (last year) I read Roger Penrose’s book, Shadows of the Mind, which addresses exactly the same issue. What is interesting is that, in both cases, the authors use Godel’s Incompleteness Theorem to support completely different, one could say, opposing, philosophical viewpoints. Both Penrose and Hofstadter are intellectual giants compared to me, but what I find interesting is that both apparently start with their philosophical viewpoints and then find arguments to support them, rather than the other way round. Hofstadter quotes, more than once, the Oxford philosopher, J.R. Lucas, whom he obviously respects, but philosophically disagrees with. Likewise, I found myself often in agreement with Hofstadter on many of his finer points, but still in disagreement with his overall thesis. I think it’s obvious from other posts on this blog, that I am much closer to Penrose’s philosophy in many respects, not just on AI.

Having said all that, this is a very complex and difficult subject, and I’m not at all sure I can do it justice. What goes hand in hand with the subject of AI, and Hofstadter doesn’t shy away from this, is the notion of consciousness. Can AI ever be conscious in the way we are? Hofstadter says yes, and Penrose, I believe, would say no. (Penrose effectively argues that algorithm-using machines – computers - will never think like humans.) Another person who has much to say on this subject is John Searle, and he would almost certainly say no, based on his famous ‘Chinese Room’ thought experiment. (I expound on this in my Apr.08 post: The Ghost in the Machine).

Larry Niven in one of his comments on his own blog, in response to one of my comments, made the observation that science hasn’t resolved the brain/mind conundrum, and gave it as an example of ‘…the impotence of scientific evidence to affect philosophical debates…’ (I’m sure if I’ve misinterpreted him, or quoted him out of context, he’ll let me know.)

To throw a googly into the mix, since Hofstadter first published the book 30 years ago, a lot of work has been done in this area, and one of the truly interesting ideas is the Bayesian model of the brain based on Bayesian probability, proposed by Karl Friston (New Scientist 31 May 08). In a nutshell, Friston proposes that the brain functions on the same principle at all levels, which is to make an initial assessment then modify it based on additional information. He claims this works even at the neuron level, as well as the cognitive level. (I report on this in my July 08 post titled, Epistemology; a discussion.) I even extrapolate this up the cognitive tree to include the scientific method, whereby we hypothesise, follow up with experimentation or observation, then modify the hypothesis accordingly.

Hofstadter makes a similar point about ‘default options’ that we use in everyday observations, like the way we use stereotypes. It’s only by evaluating a specific case in more detail that we can break away from a stereotypic interpretation of an event. This is also an employment of the Bayesian principle, but Hofstadter doesn’t say this because it hadn’t been proposed at the time he wrote it.

What Searle points out in his excellent book, Mind, is that consciousness is an experience, which is so subjective that we really don’t know if anyone else experiences it the way we do – we only assume they do. Stephen Law writes about this in his book, The Philosophy Gym, and I challenged him (by snail mail at the time) that this was a conceit on his part, because he obviously expected that people who read his book, could think like him, which means they must be conscious. It was a good natured jibe, even though I’m not sure he saw it that way at the time, but he was generous in his reply.

Descartes famous statement, ‘I think therefore I am’, has been pilloried over the centuries since he wrote it, but I would contend that ‘I think’ is a tautology, because ‘I’ is your thoughts and nothing else. This gets to the heart of Hofstadter’s thesis, that we, individually, are all ‘strange loops’. Hofstadter employs Godel’s Theorem in an unusual, analogous way to make this contention: we are ‘strange loops’. By strange loop, Hofstadter means that we can effectively look at all the levels of our thinking except the ground level, which is our neurons. In between we have symbols, which is language, which we can discuss and analyse in a dispassionate way, just like I’m doing now. I can talk about my own thoughts and ideas as if they weren’t mine at all. Consciousness, in Hofstadter’s model (for want of a better word) is the top level, and neurons are the hardware level. In between we have the software (symbols) which is effectively language.

I think language as software is a good metaphor but not necessarily a literal interpretation. Software means algorithms, which are effectively instructions. Whilst language obviously contains rules, I don’t see it as particularly algorithmic, though others, including Hofstadter, may disagree. On the other hand, I do see DNA as algorithmic in the way it creates organisms, and Hofstadter makes the same leap of interpretation.

The analogy with Godel’s Theorem is that, in any formal mathematical system, there will always exist a mathematical statement that expresses something about the system but can’t be found in the system, if I’ve got it right. In other words, there will always exist the possibility of a ‘correct’ mathematical statement that is not part of the original formal system, which is why it is called the Incompleteness Theorem – no mathematical formal system can ever be complete in that it will include all mathematical statements. In this analogy, the self or ‘I’ is like a Godelian entity that is a product of the system but not contained in it. Again, my interpretation may not be what Hofstadter intended, but it’s the best I can make of it. It exists at another level, I think is what Hofstadter would say.

In another part of the book, Hofstadter makes a direct ‘mapping’ which he calls a ‘dogmap’ (play on words for dogma) where he compares DOGMA I ‘Molecular Biology’ with DOGMA II ‘Mathematical Logic’, using Godel’s Theorem ‘self-referencing’ as directly comparable to DNA/RNA’s ‘self reproduction’. He admits this is an analogy but later acknowledges that the same mapping may be possible from Godel's Theorem to consciousness.

Even without this allusion by Hofstadter, and no Godelian analogy required, I see a direct comparison between the way DNA/RNA creates complex organisms and the way neurons create thoughts. In both cases there is a gulf of layers in between that makes one wonder how they could have evolved. Of course, this is grist for ID advocates and I’ve even come across a blogger (Sophie) who quotes Hofstadter to make this very point.

In one of my earliest posts on this blog (The Universe’s Interpreters, Sep. 07) I make the point that the universe consists of worlds within worlds, and the reason we can comprehend it to the extent that we do, is because we can conjure concepts within concepts ad infinitum. Hofstadter makes a similar point, though not in the same words, but at least 2 decades before I thought of it.

DNA/RNA exists at a level far removed from the end result, which is a living complex organism, yet there is a direct causal relationship. Neurons are cells that exist at a level far removed from the end result, which is consciousness, yet there is a direct causal relationship.

These 2 cases, DNA to complex organisms and neurons to consciousness, I think remain the 2 greatest mysteries of the natural world. To say that they can only be explained by invoking a ‘Designer’ (God) is to say we’ve uncovered everything we know about the universe at all of its levels of complexity and only God can explain everything else. I would call this the defeatist position if it was to be taken seriously. But, in effect, the ID advocates are saying that whilst any mysteries remain in our comprehension of the universe, there will always be a role for God. Once we find an explanation for these mysteries, there will be other mysteries, perhaps at other levels, that we can still employ God to explain. So the argument will never stop. Before Newton it was the orbits of the planets, and before Mendel it was the passing down of genetic traits. Now it is the origin of DNA. The mysteries may get deeper but past experience says that we will find an answer and the answer won’t be God (see my Dec .08 post: The God hypothesis; not).

As a caveat to the above argument, I've said elsewhere (Emergent phenomena, Oct. 08) that we may never understand consciousness as a direct mathematical relationship to neuron activity (although Penrose pins his hopes on quantum phenomena). And I'm unsure that we will ever be able to explain how it becomes an experience, and that's one of the reasons I'm sceptical that AI will ever have that experience. But this lack of understanding is not evidence of God; it's just evidence of our lack of understanding.

To quote Confucius: 'To realise that you know something when you do, and to realise that you do not know when you do not, this is knowing.' Or to quote his near contemporary, Socrates, who put it more succinctly: 'The height of wisdom is to know how thoroughly ignorant we are.'

My personal hypothesis, completely speculative with no scientific evidence at all, is that maybe there is a feedback mechanism that goes from the top level to the bottom level that we’ve yet to discover. They are both mysteries that most people don’t contemplate and it took Hofstadter’s book, written over 3 decades ago, to bring them fully home to me, and to appreciate how analogous they are: base level causally affects top level, yet complexity of one level seems independent to complexity of the other - there is no obvious 1 to 1 correlation. (Examples: it can take a combination of genes to express a single trait; there is not a specific 'home' in the brain for specific memories.)

I guess it’s this specific revelation that I personally take from Hofstadter’s book, but I really can’t do it justice. It is one of the best books I’ve read, even though I don’t agree with his overall thesis: machines will eventually think like humans, therefore they will have consciousness.

In my one and only published novel, ELVENE, there is an AI entity, Alfa, who plays an important role in the story. I was very careful in my construction of Alfa to demonstrate that he didn’t think like humans (yes, I gave him a gender and that’s explained) but that he was nevertheless extremely intelligent and able to converse with humans with cognitive ease. But I don’t believe Alfa was conscious albeit he may have given that impression (this is fiction, remember). I agree with Searle, in that simulated intelligence at a very high level will be achievable, but it will remain a simulation. AI uses algorithms and brains don’t – on this, I agree with Penrose. On the other hand, Hofstadter argues that we use rule-based software in the form of ‘symbols’, which we call language. I’m sure whoever reads this will have their own opinions.


Addendum 1: I've just read (today, 21 Feb.09) an article in Scientific American (January 2009) that tackles the subject: From Atoms to Traits. It points out that there is good correlation between genes and traits, and expounds on the latest knowledge in this area. In particular, it gives a good account (by examples) of how random changes 'feed' the natural selection 'engine' of evolution. I admit that there is still much to be learned, but, if you follow this topic at all, you will know that discoveries and insights are being made all the time. The mystery of how genes evolved, as opposed to the organisms that they create, is still unsolved in my view. Martin A. Nowak, a Harvard University mathematician and biologist, profiled in Scientific American (October 2008) believes the answer may lie in mathematics: Can mathematics solve the origin of life? An idea hypothesised by Gregory J. Chaitin in his book, Thinking about Godel and Turing, which I review in my Jan.08 post: Is mathematics evidence of a transcendental realm?

Addendum 2: I changed the title to more accurately reflect the content of the post.

10 comments:

Eli said...

Well, I've got good news and I guess not-good news (although I wouldn't call it bad news). The good news is that's a perfectly acceptable usage of my quote. The bad news is I feel like the brain does use algorithms, just ones that could well be complex enough to exceed our ability to formalize them.

For me, the problem comes in the disconnect between physical and nonphysical processes. There are things that really do seem like magic that we can nonetheless explain, like iPhones, and then there are things that really do seem like magic that we cannot yet explain, like minds and other emergent properties. The key insight for me is that I get the same kind of dizzy feeling trying to figure out how a bunch of metal and plastic makes an iPhone as I do trying to figure out how a bunch of gray matter makes a mind. Not that I don't still feel dizzy about (especially human) minds, but that dizziness is not a reliable indicator of anything except - as you say - my own lack of knowledge.

There is, however, a question about whether machines will ever think like humans. It'd be nice if we tried to get machines to think like, say, slugs first to at least get a proof of concept (and maybe we are), but I'd be willing to hypothesize that human consciousness is a complex enough sort of consciousness that we would be exceedingly lucky to reproduce it artificially. (Think, for example, of how it gets exponentially more unlikely to correctly guess every digit in an increasingly long string.) I'm not sure we won't ever be able to build something of equal complexity or power, but reproducing something exactly like human consciousness sounds very much like an implausible task. Then you throw in the question of how complex a biological system has to be to trigger the Godel condition ("strong enough to axiomatize the natural numbers" isn't really all that strong in the math world, but what the heck does that mean in terms of cells??), and I really start to lose track.

It is, I guess I'm trying to say, complicated.

Paul P. Mealing said...

Thanks Larry,

I appreciate your input. As I said: 'I'm sure whoever reads this will have their own opinions.' So you don't disappoint.

I think that artificial intelligence will complement human intelligence rather than replace it, as it is already doing - its strengths are our weaknesses, and vice versa.

On another subject altogether, 'Fleet of Worlds' (Tor) gets a mention amongst the top 5 in science fiction in Australia's COSMOS magazine (Feb/Mar 2009). I assume you are the same Larry Niven.

By the way, have you read either of Hofstadter's books, the other one being 'I am a Strange Loop'?

Regards, Paul.

Eli said...

Unfortunately, the world is not so awesome that I am actually the famous sci-fi author Larry Niven - though you're not the first to ask. At some point I should probably change my screenname, but I really like this one...

I absolutely agree that AI has a much brighter future as an addition to rather than a replacement for human intelligence. If for no other reason than we already have human intelligence, I really doubt there will be that much need for very human-like machine intelligences. Some day I'll pick up Hofstadter's other work to see if he says anything about this, but I haven't yet. I assume, though, that it's also very good.

Paul P. Mealing said...

I've been wanting to ask for some time - I just needed an excuse. So you are Larry Niven, philosopher and political commentator, not SF writer. Well, I don't know the other Larry Niven (I have read Ringworld, many years ago) but the one I'm talking to is a good conversationalist and a provocative thinker, and that's what matters.

One of the reasons I sign off as Paul P. Mealing (my nom-de-plume)is because there is another Paul Mealing in Melbourne, who inhabits the Web, but neither of us are famous (and we've never met).

I once commented about 'writing' as an art on your blog, and you didn't say anything, so I should have known from that.

I've just started reading I am a Strange Loop, and it seems to continue from where the earlier book left off (albeit written decades later). It might be the catalyst for another post in the future - we'll see.

Regards, Paul.

Paul P. Mealing said...

I've also added an addendum to my post, complete with hyper-links.

Regards, Paul.

Eli said...

Well, as much as I would like to be a writer, I don't really have the patience for it - at least, not yet. I'm trying to get there, though it's slow going.

Anyway, I checked out those links - good stuff! It warms my heart, as someone with a math degree, to see math being used to help science. Something else I don't have the patience for, but it's good to see that others do.

Anonymous said...

A "logic" is a means by which finitistically to express an infinite number of statements each of which can be demonstrated to be true, given a set of axioms and a set of rules of inference, the truth of the former and the validity of the latter consensually agreed upon a priori by everyone party to the exercise. (Even as formal language theory, by a similar use of rules, allows us finitistically to "capture" the (aleph-one) infinite set of sentnces theoretically syntactically well-formed in any given human language. Absent the need for finite characterization of an infinite set, we could make do (albeit unimaginably awkwardly) with the simple expedient of enumeration.) *Anyway* -- all Goedel said was that no logic rich enough even fully to axiomatize the natural numbers system (which you mention) could enable us mechanically to generate *all* of the statements that would be true in such a system.

I'm at least as much in awe of Hofstadter as are you, and have taught courses using his book, but the Goedelian limitation on the generative fecundity of logics doesn't automatically imply that consciousness couldn't somehow arise as an epiphenomenon of algorithmic activity -- only that such a consciousness would be precluded from embracing the one convoluted, self-referential statement encoded by the number n, whose decrypted meaning is that the statement encoded by the number n is false (which isn't a limitation, or at least not obviously to *this* particular pretender to intermittent consciousness, that would preclude sentience at almost any level). As an erstwhile AI practioner of the classical school, one deeply immured in rationalism (even as was Chomsky, whose fame originally derived from his loathing of Skinner) prior to the advent of neural networks as an ostensibly more plausible model of consciousness (Winograd having been, as I recall, the first prominent tergiversator from what I considered *our* camp), and a native speaker of LISP since 1975, I still *like* logics and algorithms as a means by which to replicate the observable product of human cogitations -- not saying that that has to be how the brain does it, or in any way isomorphic thereto -- but also quite unwillling to embrace the idea that only wetware-instantiated activity, perhaps enhanced by some as-yet-fully-to-be-explicated numinous quantum component, could ever produce a sentient, thinking being (in *our* sense, if we're not solipsists, and can manage more or less to agree on one collectively) of what such a beastie has to be like.

Paul P. Mealing said...

Hi PK,

Thanks for your comment. You obviously know more about this subject than me, so I don't feel I'm in a position to challenge your thesis, and I appreciate your learned contribution.

As I said in my post: 'I'm sure whoever reads this will have their own opinions.' So I'm not surprised to find an alternative viewpoint to mine. In fact, I know that my view is in the minority.

Noel Sharkey is one other who has 'heretical' views on AI that I'm aware of (though that's based on one interview I heard a couple of years ago).

Have you read Roger Penrose's Shadows of the Mind? Because I believe he puts the most erudite case against an 'algorithmic' driven brain.

Thanks again for your comment.

Regards, Paul.

Anonymous said...

Paul,
Thanks for your gracious reply. You do yourself too little honor. I find your "personal hypothesis" not at all implausible, but in any case, so much enjoyed your essay on the subject that I allowed a wave of nostalgia to overcome my usual disinclination to commit mathematical and/or epistemological logorrhea on other people's websites. :) In this case, though, I really couldn't resist.

As for Penrose, "back in the day," I used cheerfully to loathe him, but now, in my time of superannuation and incipient senility, I've mellowed and can actually read his name without experiencing apoplectic seizures. I've read The Emperor's New Mind, and a few of his papers, but nothing since my retirement, so I'm not able to comment on Shadows. I don't in the least disagree about Roger's erudition, though, and it may be that he's had some thoughts in recent years that I mightn't find altogether rebarbative. :) But I've officially withdrawn from the fray, so I'll leave those judgments to the *active* artificial intelligentsia, in their presumably still-opposing camps (and hippocampi).

Howsoever, I'm delighted to have discovered your blog, and will add it to my shortlist of must-reads.

Best wishes,

Peter

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