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.

Zen; an interpretation

I recently bought a copy of Godel, Escher, Bach: an Eternal Golden Braid, the Pulitzer Prize winning book by Douglas R.Hofstadter. In fact, I bought the 20th anniversary edition, which includes an overview that effectively explains in synopsis each chapter of the book. The author did this, apparently, because he felt that so many people misinterpreted his intentions. The book is not about Zen at all, as he states himself, yet it’s his simplistic and dismissive representation of Zen that has prompted me to write this post (not quite true - see below).

Naturally, I had heard of the book and its companion, I am a Strange Loop, which I understand expands on some aspects of this one. I have acquired a copy of that as well, though I’m yet to read it. I think I’ve come across this book at just the right time for me. If I had read it 20 years ago (actually, originally published 30 years ago), I would have struggled with it. But, as it is, I think I’m reading it at just the right time of my philosophical development, especially in regard to mathematical philosophy. The book, which is quite lengthy and comprehensive, explores the very areas of philosophy that I’m interested in.

But whilst everything he says about logic is both enlightening and refreshing, as well as scholarly, I disagree with his interpretation of Zen, which he seems to portray as the antithesis of logic. It’s like he uses Zen as a reference for a perspective of non-logic, so his interpretation is that Zen is a 'non-state' (he elaborates on this later in the book). But I don't think Zen is about logic at all - in fact, it's a state of mind. My own interpretation is that Zen represents a particular state of mind when one is intensely involved in some activity. Now the activity could be physical, like tennis or playing cricket, or driving a car; or it could be mental like writing a story or painting a portrait, or playing a musical instrument.

What they all have in common is that it is a mental state where one feels removed, like one is totally involved yet one is ‘not there’, as virtuoso violinist and amateur surfer, Richard Tognetti, once said (no, he's not a Zen Buddhist to my knowledge). So it is a contradictory sense, or, at the very least, paradoxical. My own take on this is that one’s ego is not involved yet one feels totally engaged. It requires one to be completely in the moment, and what I’ve found in this situation is that time disappears. Sportsmen call it being ‘in the zone’ and it’s something that most of us have experienced at some time or another (Refer Addendum 3 below).

So I can understand why Hofstadter may interpret Zen as the representation of ‘contradiction’; even though it implies he’s never experienced a Zen state, or, if he has, he calls it something else. It is contradictory in explanation but not in experience. (To be fair, as I got further into the book, Hofstadter reveals that he knows a lot more about Zen than I first thought.)

Godel, Escher, Bach is an extraordinary and brilliant book, and I don’t wish to take anything away from Hofstadter’s achievement. He’s in another league to me altogether (after all, he has a PhD in solid state physics). For a start, he gives the best exposition of Godel's Incompleteness Theorem I've read, using a number of metaphors and allegorical dialogues, including one with Zen koans.

On the subject of Zen, I’m not a good practitioner, but I don’t try to be. From what I’ve read on Zen, it ideally requires ‘unattachment’, which also includes unattachment to goals and dreams. But without goals and dreams, what do people live for? So it seems contradictory to life, if one takes it literally. But, as a state of mind for when one is involved in an intense, challenging yet rewarding activity, it makes perfect sense. By the way, one only experiences a reward in this sense, when one is challenged. That’s why the most frustrating things in life are also the most rewarding. When one realises that, then one can achieve a sense of perspective as well as purpose. (I make a similar point in one of my earliest posts, The Meaning of Life, Aug.07.)

P.S. For all you pedants, 'unattachment' is not a 'proper' word (should be detachment) but in this context, detachment gives the wrong connotation. Unattachment means exactly that.

Addendum 1: I would challenge anyone to read Hofstadter's book without being forced to view things differently that they previously took for granted. I'm currently about one third through the book, and I am sure I will write another post on it when I'm finished.

Addendum 2: Daisetz Suzuki is the best writer on Zen I've read (in English). In particular, Zen and Japanese Culture (originally published 1959; my copy, 1973).

Addendum 3: I know, I keep adding to this when I should write another post, but my blog is not so much a journal as a collection of essays. On page 387 (Penguin 20th Anniversary Edition) Hofstadter quotes Escher: "While drawing I sometimes feel as if I were a spiritualist medium, controlled by the creatures I am conjuring up." I suspect many artists have felt this way, including myself when writing, and this is what I mean when I say the ego is not engaged. In fact, I have used this exact same description of my own writing on occasion. Australian actress, Kerry Armstrong, once made the point that acting doesn't involve the ego at all, quite the contrary, and I would make the same point about creating characters in fiction. So Hofstadter has described what I consider to be a Zen state of mind, by quoting Escher, but with no reference to Zen at all.

For a more edifying discussion of Hofstadter's book, see the next post: Artificial Intelligence & Consciousness.

The God hypothesis (not)

Normally, I leave my arguments on other blogs, on other blogs, but, on this occasion, I feel that this is such a widespread, fundamentally misunderstood philosophical issue, that I should address it here, on my own blog. The argument took place on Dr. William Lane Craig's so-called 'Reasonable Faith' blog, and the original dialogue can be found here. Larry Niven wrote his own commentary on it here, which is arguably more entertaining than the original (he didn't know the 'Paul' he was referring to was me). Dr. Craig is careful about what he publishes, and he has his blog set up as a Q & A, which allows him to not only choose what he publishes, but to portray himself as an authority on whatever he cares to pontificate about. Naturally, he only publishes arguments that he believes make him look good, for which, the following submission didn't qualify. 

Just so you appreciate the context: Dr.Craig laments the fact that the discipline of science only allows for 'naturalistic' explanations, so that, if there are 'non-naturalistic' explanations, we will never know the truth. In his own words, this is a 'methodological constraint' on science, imposed 'philosophically'. If you visit the above link, you will see that I specifically challenged him that he 'won't conjecture' where God may have intervened, and he evades the issue at first, but eventually says it depends on the gaps in the evidence (specifically fossil evidence). Below is my third submission (following his response), which, not surprisingly, he didn't respond to; neither did he respond to the previous two. (I've edited out the intro which refers to the previous 2 submissions.) (Addressed to Dr. Craig.) 

Thinking about this some more, I realised that you haven’t thought this through at all. Basically, you are saying that science restrains itself, philosophically, by only allowing for natural explanations. It could be far more (potentially) successful if it allowed for supernatural explanations – the so-called ‘God hypothesis’ (my terminology, not yours, but I’m sure you’ll agree that it fits your suggested philosophical approach to science). 

My question is why isn’t the God hypothesis already applied? Quantum mechanics is an obvious area. No one understands quantum mechanics, as Richard Feynman famously said, and he should know: he won a Nobel Prize for giving us the best exposition we have so far. So it’s a perfect candidate for the God hypothesis: all quantum phenomena can now be explained as evidence of God’s intervention, including quantum tunneling, quantum effects at a distance and even Schrodinger’s cat; especially Schrodinger’s cat, I would suggest. Extreme weather events are another perfect candidate for the God hypothesis, supported by evidence from the Bible as well, so it has to get a guernsey (an Aussie metaphor). Four hundred years ago, the God hypothesis would have worked for planetary orbits – actually, I think it was the hypothesis at the time - then Newton came along, proposed the universal theory of gravity, and it went out of favour.

And now we have evolutionary theory as another possibility, especially as it involves complexity at many levels, from DNA to entire ecosystems, so it’s the perfect candidate. But what if in the future, someone discovers more about complexity – I mean totally unexpectedly, like the way Einstein discovered relativity - then I guess the God hypothesis would have to be dismissed; but, then, at least, we could still use it in the mean time. The point is, as you explicated yourself, we don’t know where to apply it. And, guess what? We never will. Regards, Paul.

Life, God, the universe and everything

Recently, I was involved in a forum on Stephen Law’s web site (see my blog roll) which critiqued Richard Dawkins’ book, The God Delusion. Stephen, in effect, set up a book club, whereby we went through all of Dawkins’ 10 chapters, one by one, over a period of about 12 weeks. My involvement was miniscule, and the nature of the beast meant that discussions went off on all sorts of tangents. Atheism reigned, as most of Stephen’s contributors, though not all, are staunch Dawkins’ supporters.

I should point out that I have used many of Dawkins’ arguments myself against religious fundamentalists, without knowing they were his. But I don’t share Dawkins’ apparent contempt for religion per se. In Australia, Dawkins tends to be seen as alarmist, but maybe it’s because the politics of religion, and the history of religion in politics, are different here. As Thomas Keneally (Booker prize-winning author of Schindler’s Ark) once said: Australians, generally, have a healthy disrespect for religion (or words to that effect).

I didn’t contribute much to Stephen’s forum at all, but somewhere in the midst of it I threw in a grenade by asking the existential question: ‘What’s the point?’

In addition to The God Delusion, I also read Paul Davies’ God and the New Physics, published in 1983, which covers much of the same material, some of it in greater depth if not greater overall length; but unlike Dawkins, Davies doesn’t have an axe to grind. It was after reading Davies’ book that I submitted the following comment.

‘The more I read about this and the more I contemplate it, the more I tend to conclude that the universe is not an accident. In other words, it’s purpose-built for life. This does not axiomatically lead to the existence of God, as both Paul Davies and Christian de Duve point out. The ‘God’ question is almost irrelevant; it’s the wrong question. The question should be: What’s the point?

Imagine the universe with no consciousness at all, and then ask yourself: what’s the point? There are only 2 answers to this question: there is no point; or the point is consciousness, because that’s the end result.’

Now, by asking the question in the paradoxical context of imagining there is no consciousness, it highlights the very enigma one is attempting to grasp. As someone pointed out, without consciousness, who asks the question?

The first response to this (on Stephen’s site) came from an ‘anonymous’ contributor, who seemed personally insulted, and, following a short diatribe, asked, ‘What’s wrong with no point?’ To which I responded, ‘Nothing wrong with no point. We agree to disagree.’ After all, I’d already said it is one of only two answers in my view. My antagonist allowed this through to the keeper (to use a hackneyed cricketing metaphor) and pursued it no further.

Recently, in another post, I speculated that we may never truly understand consciousness, because it is an emergent property, and we are now faced with the epistemological possibility that emergent properties may never be explained in terms of their underlying parts, at least, mathematically (see my Oct.08 post, Emergent phenomena).

But there is more to this: according to Dawkins, we are all just ‘gene-replicating organisms’; so consciousness is totally irrelevant – a byproduct of nature that allows us to ask totally irrelevant existential questions. I’ve said before that if we actually didn’t experience consciousness, science would tell us that it doesn’t exist, just like science tells us that free will doesn’t exist (see my Sep.07 post on Free Will). This suspicion was reinforced earlier this year, when I read an article by Nicholas Humphrey in SEED magazine, who concluded that consciousness is an illusion, and its sole (evolutionary) purpose is to ‘make life more worth living’, which could be translated into one word: ‘happiness’. So, syllogistically, one could conclude that happiness is an illusion too. As a pertinent aside, I wonder how Humphrey can distinguish his dreams from reality. (Refer Addendum below)

Paul Davies attempts to tackle this conundrum head-on in his book, The Goldilocks Enigma, and concludes, if I interpret him correctly, that the universe exists because we are in it - in a sort of causal loop. He’s elaborated on an idea originally formulated by his mentor, John Wheeler, more famously known for coining the term, ‘Black Hole’.

So in a way, Dawkins and Davies represent 2 polar views on this, and I tend to side closer to Davies. Davies, who is an astro-biologist, as well as a physicist and philosopher, says that he’s ‘agnostic’ about life existing elsewhere in the universe, but, while he may be scientifically agnostic, he’s said elsewhere that, philosophically, he favours it. Davies is far from a crank, I might add – even Dawkins treats him with respect.

In another post, earlier this year (Theism as a humanism, Aug.08), I postulated the completely ad-hoc idea that God is the end result of the universe rather than its progenitor. Now, I’ve said on many occasions, that the only evidence we have of God is inside our minds, not ‘out there’, yet the experience of God, because that’s what God is (an experience) always feels like it’s external. There is actually neurological brain-imaging evidence to support this (New Scientist, 1 Sep.2007, pp 32-6) by Andrew Newberg at the University of Pennsylvania, showing that ‘Religious feelings do seem to be quite literally self-less…’ In the same context, I’ve also quoted Ludwig Feuerbach: ‘God is the outward projection of man’s inner nature.’ My conclusion is that there are as many different versions of God as people who claim to experience him, her or it. So God is, at least partly, a projection.

Where is all this leading? Fuerbach’s assertion, and all our cultural attributions, would suggest that God is the projection of our ideals. But, if one takes Feuerbach’s postulate to its logical and literal conclusion, then God could be the emergent property of all of our collective consciousness. In that case, the universe really would have a purpose.

Addendum (4 April 2010): I may have misrepresented Nicholas Humphrey - please read the addendum to my post Consciousness explained (3 April 2010)

Is psychology a science?

This is another letter I wrote to New Scientist in response to an article by Dorothy Rowe, an Australian psychologist apparently, and author of What Should I Believe? No, I haven't read her book, but the article is erudite and intellectually provocative enough to suggest that she's worth reading.

I have to point out that I don't have a degree in psychology or science, or philosophy, for that matter, but I've studied all three at tertiary level, and I've read widely in all fields. The reason I was prompted to write this is that I've always held an opinion on it ever since I did study psychology at Uni and was struck by the obsession of the faculty to be taken seriously as a science. Having also studied science, and physics in particular, I was always aware that there were differences. This is not to denigrate psychology, at all, but to point out that whilst the study of psychology becomes more technical I believe there are fundamental aspects of psychology that make it uniquely different to the study of other 'natural phenomena', which is how I define science.

Below is the letter I wrote. By the way, I haven't really addressed Dorothy Rowe's article, which was titled, Ask better questions, just responded to her opening question.

'Is psychology a science?' is the opening question in Dorothy Rowe's article in New Scientist (1 November 2008, p.18). Somehow, psychology still seems to sit somewhere between science and philosophy, involving both, but not belonging to either. Human behaviour will never be distilled into a set of laws, even remotely like physics, or even biology. In other words, the ability to predict behaviour outcomes, will be statistical at best. In psychology, an aberrational datum will be seen as an outlier, whereas, in physics, it's either an error or the genesis of a new theory. Also, different theories attempting to provide insight into the same behaviour, generally don't provide any synergy. Example: attachment theory and Lee's 6 types of love both deal with relationships, but have no common ground. This is not an atypical example.

I was taught that psychology was a dialectical process - opposing theories are combined into a new thesis; like the nature and nurture debate (genes versus environment) having to be both taken into account. Science is also a dialectic process, though, between theory and experiment, rather than between opposing theories.

I found that psychology is a very good tool for tackling philosophical problems, like the social dynamics that lead to acts of evil (see my Oct.07 post on Evil). So, at the end of the day, they deal with different issues, different problems. Science may tell us where we came from, but it can't tell us why we kill each other. So I still see them as separate, but having some methodologies in common.

Emergent phenomena

A couple of weeks ago in New Scientist (4 October 2008), there was one of those lesser featured articles that you could skip over if you were not alert enough, which to my surprise, both captured and elaborated on an aspect of the natural world that has long fascinated me. It was titled, ‘Why nature is not the sum of its parts’.

It referenced an idea or property of nature, first proposed apparently by physicist, Philip Anderson, in 1972, called ‘emergence’. To quote: ‘the notion that important kinds of organisation might emerge in systems of many interacting parts, but not follow in any way from the properties of those parts.’ As the author of the article, Mark Buchanan, points out: this has implications for science, which is reductionist by methodology, in that it may be impossible to reduce all phenomena to a set of known laws, as many scientists, and even laypeople, seem to believe.

The article specifically discusses the work of Mile Gu at the University of Queensland in Brisbane, Australia, who believes he may have proved Anderson correct by demonstrating that mathematical modeling of the magnetic forces in iron could not predict the pattern of atoms in a 3D lattice as one might expect. In other words, there should be a causal link between individual atoms and the overall effect, but it could not be determined mathematically. To quote Gu: “We were able to find a number of properties that were simply decoupled from the fundamental interactions.” To quote Buchanan quoting Gu: ‘This result, says Gu, shows that some of the models scientists use to simulate physical systems have properties that cannot be linked to the behaviour of their parts.’

Now, obviously, I’ve simplified the exposition from an already simplified exposition, and of course, others, like John Barrow from Cambridge University, challenge it as a definitive ‘proof’. But no one would challenge its implication if it was true: that the physics at one level of nature may be mathematically independent of the physics at another level, which is what we already find, and which I’ve commented on in previous posts (see The Universe’s Interpreters, Sep.07).

This is not dissimilar to arguments produced in some detail by Roger Penrose in Shadows of the Mind, concerning the limitations of formal mathematical reasoning. According to Penrose, there are mathematical ‘truths’ that may be ‘uncomputable’, which is a direct consequence of Godel’s ‘Incompleteness Theorem’ (refer my post, Is mathematics evidence of a transcendental realm? Jan.08). But Penrose’s book deals specifically with the enigma of consciousness, and this is where I believe Anderson and Gu’s ideas have particular relevance.

I would argue, as do many others (Paul Davies for one) that consciousness is an ‘emergent’ phenomenon. If science is purely reductionist in its methodology, as well as its philosophy, then arguably, consciousness will remain a mystery that can never be solved. Most scientists dispute this, including Penrose, but if Anderson and Gu are correct, then the ‘emergent’ aspect of consciousness, as opposed to its neurological underpinnings, may never be properly understood, or be reducible to fundamental laws of physics as most hope it to be.