Is God a mathematician?

There is a quote from Physics Nobel Laureate, Eugene Wigner, that appears in the first sentence on the front fly leaf cover of Mario Livio’s book, Is God a Mathematician? Actually, it's the title of Wigner's famous essay: The remarkable effectiveness of Mathematics in the Natural Sciences. On the back fly leaf cover we learn that ‘Mario Livio is a senior astrophysicist and head of the Office of Public Outreach at the Hubble Space Telescope Science Institute in Baltimore, Maryland.’ He’s also written a few other books on mathematics, including The Golden Ratio and The Equation That Couldn’t be Solved (neither of which I’ve read).

Wigner’s quote is the one that Livio keeps returning to and attempting to address, rather than any real attempt to address the question on the cover of his book. So I will do the same.

It’s a very good read: erudite, thought-provoking and as balanced as one could expect from someone who has their own philosophical standpoint. I’ve addressed this issue on 2 previous posts: Is mathematics evidence of a transcendental realm? (Jan.08) and Where does mathematics come from? (Sep.07). The Jan.08 post is effectively a review of Gregory Chaitin’s book, Thinking about Godel and Turing, and the Sep.07 post is more of a critique, than a review, of George Lakoff’s and Rafael Nunez’s book, Where Mathematics Comes From. Livio gives a good account of Lakoff’s and Nunez’s views, but he doesn’t mention Chaitin (even in the bibliography).

I don’t wish to reiterate ideas I’ve already explored in those posts, but I do wish to say that Livio demonstrates why scholars like him publish books, and amateurs like me only publish on a blog.

Livio’s book covers topics as varied as statistics and probability theory, Euclidean and non-Euclidian geometry, and logic - all in revelatory detail, yet easy to read. The most interesting topic as far as I was concerned was on knots, and their application to biology and the most recent theoretical investigations in cosmology (string theory).

He also gives brief biographies on, what he considered to be, the giants in mathematics: Archimedes, Galileo, Descartes and Newton.

But it is an extended quote from Wigner that establishes the tone, if not the intent, of Livio’s treatise:

‘The miracle of the appropriateness of the language of mathematics to the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.’

Livio effectively encapsulates his position when he states that there are 2 aspects of mathematics which he calls: ‘active’ and ‘passive’. By ‘active’ he means the deliberate use of mathematics as a tool to investigate and understand natural phenomena. This aspect supports the view that mathematics is ‘invented’ rather than ‘discovered’. We humans, with our preternatural intellectual abilities, create mathematical models that provide accurate facsimiles of nature’s laws, and can even formulate predictions and forecasts by employing the ‘scientific method’.

To appreciate what Livio means by ‘passive’ it is best to quote his own words:

‘But there is a “passive” side to the mysterious effectiveness of mathematics, and it is so surprising that the “active” aspect pales by comparison. Concepts and relations explored by mathematicians only for pure reasons – with absolutely no application in mind – turn out decades (or sometimes centuries) later to be the unexpected solutions to problems grounded in physical reality!’

(I make a similar point, though not as eloquently, in my Mar.08 post, The Laws of Nature.)

Livio gives a number of examples of this ‘passive’ aspect of mathematics, but amongst the most commonly known are: Maxwell’s equations predicting electromagnetic waves traveling at the speed of light (an example of a pure mathematical construction predicting a yet-to-be discovered physical phenomenon); and Einstein using Riemann’s geometry to postulate his General Theory of Relativity (an example of pure mathematics employed for a completely unexpected natural phenomenon). One must remember that, no one, during Riemann’s time, thought the universe was other than Euclidean, which meant Riemann’s geometry was considered to be purely intellectual play with no possible application in reality.

This leads to a view held by Roger Penrose, which is expounded upon in a couple of his books, The Emperor’s New Mind and Shadows of the Mind, and is also referenced by Livio. Penrose makes the observation that there are 3 aspects of the world of mathematics, and they all interrelate. He refers to them as the ‘Platonic world’, the ‘Mental world’ and the ‘Physical world’. He depicts their interrelationship pictorially, a bit like the rock, paper, scissors game. I will try and explain.

Human thought can grasp some of the Platonic world, but not all of it, which we apply to the Physical world, even though some of it seems beyond our abilities of comprehension. Likewise the Physical world seems to incorporate some of the Platonic world but not all of it. So far so consistent. The enigma is turned into the rock, scissor, paper analogy when one realises that the human mind is a product of the physical world, which can then comprehend the Platonic world, of which the Physical world is a ‘shadow’. This is effectively the way Livio explains it as well, but without the analogy.

This leads me to what I consider to be the greatest mystery of the Universe: that it created the means to comprehend itself. As Einstein famously said: ‘The most incomprehensible thing about the universe is that it is comprehensible.’ Now I don’t know if Einstein was making a metaphysical statement, as he certainly wasn’t a Platonist like Penrose or his good friend and Princeton colleague, Kurt Godel. But without mathematics, it is clear that our comprehension of the universe would be severely limited indeed, and whether Einstein was referring specifically to that or not, I would suggest that his statement only makes sense in that context.

This leads to another point that Livio makes, almost in passing, but I consider to be highly relevant and it is to do with the most abused of concepts: ‘truth’.

I recently had an argument with a blogger (Armageddon Thru To You), who referred to

‘absolutes of truth’ which override all so-called scientific truths. I contended that the only truths I can be sure of are mathematical truths, and he responded: ‘There are absolutes of truth that humanists cannot understand because they don't acknowledge the existence of a perfect being (God)’.

This is relevant to Livio’s book, because he spends 6 pages on the subject of Galileo’s famous confrontation with the Catholic Church in 1633. He ends this section with the following commentary:

‘Still, at a time when there are attempts to introduce biblical creationism as an alternative “scientific” theory (under the thinly veiled title of “intelligent design”), it is good to remember that Galileo already fought this battle almost four hundred years ago – and won!’

 I make a similar reference to Galileo and compare it to the current ID/Creationism debate in my Nov.07 post, Is evolution fact? Is creationism myth?

These days, no one wants to get into an argument about whether the earth goes round the sun or not, so they think it’s irrelevant, but, as Livio points out, in 1600, the Catholic Church saw it as a direct intervention on its intellectual turf. It contradicted the Bible, and as far as they were concerned, the Bible was sacrosanct: the Word of God or ‘absolute truth’, to quote my aforementioned interlocutor. I’ve no doubt that there will come a day when evidence of evolution will be so monumental that only the most die-hard fundamentalists will question it – in other words, it will be no more contentious than Galileo’s position is today.

My point being that one can’t read a text like Livio’s and not be struck by how much we have learnt from the study of science, none of which appears in the Bible or any other religious text. An appeal to ‘absolute truth’ not only rings hollow in the face of thousands of years of accumulated knowledge, it beggars credulity. Mathematics has provided us with more truths, both in abstraction and in physical reality, than any other endeavour. To attempt to trump it with ‘absolute truth’ is to make a mockery of the human intellect.

And this brings me, to what I consider, to be the most revelatory portion of Livio’s book. The relevance of the study of knots to our understanding of DNA. Livio explains how a mathematical ‘discovery’ by John Horton Conway in the 1960s also describes the way enzymes ‘unknot’ DNA to allow for ‘replication or transcription’ (Livio’s description).

DNA is one of the greatest mysteries of the universe – a code for life itself. It raises the metaphysical question of why does the universe exist? Most scientists and philosophers would say it is an accident. Paul Davies attempts to address the question in his book, The Goldilocks Enigma, by expanding on an original idea proffered by his mentor, John Wheeler, that there is a causal loop between conscious intelligence and the universe itself. In a way, it attempts to address the mystery I alluded to in Einstein’s famous quote: that the universe created the means to comprehend itself.

The answers to this question are neither biblical nor scientific – they are philosophical. And perhaps it’s best to quote Bertrand Russell from The Problems of Philosophy, as Livio does in his closing paragraph of his book:

‘Thus, to sum up our discussion of the value of philosophy; Philosophy is to be studied, not for the sake of any definite answers to its question, since no definite answers can, as a rule, be known to be true, but rather for the sake of the questions themselves; because these questions enlarge our conception of what is possible, enrich our intellectual imagination and diminish the dogmatic assurance which closes the mind against speculation; but above all because, through the greatness of the universe, which philosophy contemplates, the mind is also rendered great, and becomes capable of that union with the universe which constitutes its highest good.’ (Emphasis is mine)

P.S. I sent this post as a link to Mario Livio, and I've posted his response in a comment below.

Addendum 1: I came across this very relevant quote in It Must be Beautiful; Great Equations of Modern Science, edited by Graham Farmelo (Granta books, 2002).

'One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them.' (Heinrich Hertz, on Maxwell's equations of electromagnetism.)

Addendum 2:  I've written specifically about Eugene Wigner's famous essay in a later post.

Addendum 3: I've changed the title of the post to reflect the title of Livio's book.

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.

The philosophy of Philippe Petit

I never intended to write movie reviews but this is certainly relevant to philosophy in more ways than one. Last night I saw the film, Man On Wire, which is the story of Philippe Petit, who walked between the New York Trade Centre twin towers in 1974, after he walked between the north pylons of the Sydney Harbour Bridge in 1973 and between the Notre Dame towers in 1971.

After the film, we were then privileged by an interview with Philippe, now 59, who, also, at his own insistence, answered questions from the audience. The film won an award at the 2008 Sundance Film Festival, and deservedly so. It’s an extraordinary film about a truly extraordinary man, and to see and hear him in the flesh is just as revelatory as watching him in the film.

When you meet someone like Philippe you realise that this is evolution in action. He is such an unusual person, who really doesn’t fit in normal society, yet he can do things that the rest of us can’t even contemplate doing. He made the comment in another interview (that I read) that curtailing his activities is like cutting a bird’s wings – it’s what they are meant to do. To quote: ‘Where is imagination? Where is the beauty of living? I am not advocating danger, but at the same time, to force birds to carry a leash is to kill the idea of what a bird is.’

In the interview, I was lucky to be audience to, he continually surprised us with his answers, at once candid and honest, and also deeply profound. He said he does not think about death – he won’t even use the ‘D’ word, it is the ‘L’ word, Life that he looks in the eye, while surrounded by terror. When he is aerial, he truly lives in the moment – I cannot think of anyone more Zen than he is, yet he is typically French: animated, talkative, elfish even, yet, in his own way, deeply philosophical and wise. 'I don't believe in God, but God believes in me,' he said in response to one question.

Go and see the film, and be contaminated by his madness and his energy that is, paradoxically, so, so sane.

Who is the best philosopher?

Once again this is a 'Question of the Month' (though last month) in Philosophy Now. You might have noticed that I haven't created a category or label for this because I haven't got one that really fits. I thought of 'historical' but it seemed a nonsense to create a label just for one post. (I changed my mind.)

As you can tell from my introduction I even question the question: is it really possible to evaluate the 'best philosopher'?

Below is my submission.

By what criteria does one judge this? The philosopher with the most influence over historical time? The philosopher who made the greatest contribution to ethics or to epistemology? The philosopher who provided the best answers to ‘all the big questions’? I’m not sure there is a ‘best philosopher’, because philosophy is not a competition like the Olympics. Instead, I will approach this by asking another question: who is my favourite philosopher? Even this is not easy, because there are three who immediately spring to mind, all living in the same century: Buddha, Confucius and Pythagoras. But I will settle with Pythagoras because I believe he really has had the biggest influence historically, and because he was a true polymath, even though all evidence of his teachings, his discoveries and his ‘school’ are second hand at best.

Pythagoras’s most outstanding discovery was not the right triangle proof that bears his name, but the realisation that musical pitch had a mathematical relationship. But the real legacy of Pythagoras’s philosophy was another, not unrelated, revelation. Mathematics had been used by various cultures well before Pythagoras, for the purposes of commerce and accounting, as well as measurements and geometry for construction projects, but it was Pythagoras who appreciated that mathematics was an inherent aspect of the natural world and could provide answers to questions concerning the mysteries of nature, including questions of astronomy. This is a paradigm that is still with us today, and, arguably, has driven science since the time of the Renaissance, 1,000 years after Pythagoras.

The connection is Plato, and consequently, Aristotle. According to Kitty Ferguson (author of The Music of Pythagoras), Plato actively sought out Pythagoras’s most accomplished student, Archytas of Terentum, and back in Athens, Plato set up his famous ‘Academy’ using a ‘Pythagorean curriculum’, that he adopted from Archytas, known as the ‘quadrivium of arithmetic, geometry, astronomy and music’. There is no doubt that Plato’s Pythagorean curriculum, and its influence on Aristotle, paved the way for the paradigm of mathematical scientific enquiry that eventually led us to Newton’s theory of gravity, Maxwell’s equations, thermodynamics, Einstein’s theories of relativity, quantum mechanics and chaos theory, with all the technological spin-offs of flight, space travel, computers and diverse engineering marvels that we embrace in the modern age. So I would argue that, historically, Pythagoras is the most important philosopher in the pantheon and that makes him eligible for the best.

Theism as a humanism

Yes, I know, it’s an oxymoron, but it’s appropriate to my worldview. For over 2 weeks I observed and participated in a discussion on Stephen Law’s blog (see side-bar) with a guy called Sye, who maintains he has a proof for the existence of God. Sye’s idea of an argument is to make an assertion, call it a proof ‘by the impossibility of the contrary’, then insist that you prove him wrong. His favourite ploy is to ask you to prove something that doesn’t exist, doesn’t exist, or something that has never happened, never happened. ‘Prove the Bible is not the Word of God.’ ‘Explain how God did not reveal Himself as an objective reality.’ When I say, ‘I can’t explain something that never happened’, he says, ‘It’s your assertion, you prove it.’ In this way, he deludes himself that he can beat the best ‘atheist’ minds at their own game. But his victory is so hollow that it’s not even hot air, more like a vacuum. Yes, I know, I shouldn’t mix my metaphors. (Sye’s web site, by the way, is www.proofthatgodexists.org)

Stephen was patient in the extreme, and kept coming up with new and original arguments, which was an education in itself, and refused to be drawn into the ‘intellectual black hole’ as someone aptly called it. But even arguing with someone who thinks an argument is an endless round of assertions and refutations, and whose most common response is ‘prove it’, can help you to better understand and appreciate your own beliefs – hence the subject of this post.

Ludwig Feuerbach was a 19^th Century philosopher, whose most famous quote was, ‘God is the outward projection of man’s inner nature’, which I used in the introduction to my essay: Is there a God? (Jun.08). Feuerbach, by the way, claimed he wasn’t an atheist, but perhaps he would have been, if he had lived in an age when being an atheist didn’t make you an instant pariah and social outcast. As I’ve said before, I’m not an atheist, and I live in a different age, so I don’t have the same problem. He saw religion as a ‘consciousness of the infinite’ or as ‘the infinity of the consciousness’, but his attempts to elaborate on this conceptually are not very edifying; at least, not to me. But, more significantly, he saw that God, in whatever guise we perceive Him, Her or It (perhaps One is the best label) does not exist independently of humanity. And this was the particular approach I took in my arguments with Sye on Stephen’s blog. At the risk of offending some people, I have to say that I have ‘issues’ with the Bible, not least, because I believe it was a contributing factor to my neurosis as a child, and that’s all I care to say on the subject.

So how do I justify the statement: theism is a humanism? Well, firstly, I don’t believe God exists independently of humanity, or perhaps, even life, and it is only through human expression that God is given human traits – look no further than the Bible. I read somewhere, possibly in a magazine on Eastern philosophy, when I was studying it, a supposition that the collective karma of humanity creates God. If this is true, then we would not only get the One we believe in, but the One we deserve. So I would suggest, rather provocatively, that we are responsible for God rather than God being responsible for us, simply by living our lives. It's an 'existential' view of God, if you like. And it certainly overcomes the ‘problem of evil’ as philosophers like to call it (read Stephen Law’s satirical post on ‘The God of Eth’). In this worldview, even atheists contribute to the One just by being humanists. Which is why I don’t have a problem with atheists: it is not their beliefs that I judge them on, but their actions and attitudes towards the rest of humanity. And, likewise, I judge all theists as humanists.

Epistemology; a discussion

Recently (1 July) I wrote a post on The Mirror Paradox, which arose from my reading of Umberto Eco’s book, Kant and the Platypus back in 2002. The post was an edited version of part of a letter I wrote to Eco; the rest of the letter was to do with epistemology, and that is the source of this post.

Some people think that because we can’t explain something, either it is wrong or it doesn’t exist. Two examples from the opposite sides of philosophy (materialism and fundamentalist religion) illustrate this point very clearly. In a previous post, The Ghost in the Machine (Apr.08), I reviewed an article in SEED magazine (Henry Markram’s Blue Brain project). In the same magazine, there is an essay by Nicholas Humphrey on the subject of consciousness. Effectively, he writes a page-length treatise arguing that consciousness must be an illusion because we have no explanation for it. This is despite the fact that he, and everyone he meets in life, experiences consciousness every day. Humphrey’s argument, in synopsis, is that it is easier to explain it as an illusion than as reality, therefore it must be an illusion. Personally, I would like to know how he distinguishes dreaming from living, or even if he can (please refer Addendum below, 4 April 2010). Another example from the polar opposite side of rational thinking is evolution. Fundamentalist Christians tend to think, because we can’t explain every single aspect of evolution, it can be challenged outright as false. This is driven, of course, by a belief that it is false by Divine proclamation, so any aspect of the theory that is proven true, of which there is evidence at all levels of biology, is pure serendipity. (Refer my Nov.07 post, Is evolution fact? Is creationism myth?)

I’m making a fundamental epistemological point that we don’t understand everything – another, excellent example is quantum mechanics (see The Laws of Nature, Mar.08), where I quote Richard Feynman, probably the world’s best known expert on quantum mechanics (he had a Nobel Prize to prove it), and arguably its best expositor, who said quite categorically in his book, QED, ‘…I don’t understand it. Nobody does.’ There is nothing that makes less sense than quantum mechanics, yet it is arguably the most successful scientific theory of all time. Historically, we’ve always believed that we almost know everything, and Feynman was no less optimistic, believing that we would one day know all physics. But, if history is any indication of the future, I choose to differ. In every avenue of scientific endeavour: biology, cosmology, quantum theory, neuroscience; there are enormous gaps in our knowledge with mysteries begging inquiry, and, no doubt, behind those mysteries, lay a whole gallery of future mysteries yet to be discovered.

None of this was in the letter I wrote to Umberto Eco, but it seems like a good starting point: we don’t know everything, we never have and we probably never will. The only thing we can say with confidence is that we will know more tomorrow than we know today, and that is true for all the areas I mentioned above. As I’ve already said in previous posts: only future generations can tell us how ignorant the current generation is.

Actually, this is not so far removed from Eco’s introduction in Kant and the Platypus, where he hypothesises on the limits of our ability to comprehend the universe, which may include metaphysical elements like God. He postulates 4 hypotheses based on matching items of knowledge (symbols) with items of physical entities (elements), which he calls, for convenience sake, 'atoms', and various combinations of these. As a corollary to this approach, he wonders if the graininess of the universe is a result of our language rather than an inherent feature of it, as all the hypotheses require segmentation rather than a continuum.

I won’t discuss Eco’s hypotheses, only mention them in passing, as I take a different approach. For a start, I would use ‘concept’ instead of ‘symbol’ or ‘atom,’ and ‘phenomena’ instead of ‘elements’. It’s not that I’m taking explicit issue with Eco’s thesis, but I choose a different path. I define science as the study of natural phenomena in all their manifestations, which is really what one is discussing when one questions the limits of our ability to comprehend the physical universe. Secondly, it is becoming more and more apparent that it is mathematics rather than language that is determining our ability to comprehend the universe – a philosophical point I’ve already discussed in 2 posts: Is mathematics evidence of a transcendental realm? (Jan.08) and The Laws of Nature (Mar. 08).

Some people argue that mathematics is really just another language, but I would contend that this is a serious misconception of the very nature of mathematics. As Feynman points out in his book, The Character of Physical Law, translating mathematical ideas into plain English (or any other verbal language) is not impossible (he was a master at it) but it’s quite different to translating English into, say, French. To describe mathematics in plain language requires the realisation of concepts and the use of analogies and examples. Mathematics is inherently paradoxical, because it is conceptually abstract, yet it can be applied to the real world in diverse and infinitely numerous ways. Whereas plain language starts with descriptors of objects (nouns) which are then combined with other words (including verbs) that allow one to communicate actions, consequences, histories and intentions; you could argue that mathematics starts with numbers. But numbers are not descriptors – a number is a concept – they are like seeds that have infinite potential to describe the world in a way that is distinctly different to ordinary language.

Nevertheless, Eco has a point, concerning the limits of language, and one may rephrase his question in light of my preceding dissertation: is it our use of number that projects graininess onto the universe? This question has a distinctly Kantian flavour. One of the problems I had with Kant (when I studied him) was his own ‘Copernican revolution’ (his terminology) that we project our models of reality onto the world rather than the converse. As a standalone statement, this is a reasonable assertion, and I will return to it later, but where I disagreed, was his insistence that time and space are projections of the human mind rather than a reality that we perceive.

I truly struggled to see how this fitted in with the rest of his philosophy which I find quite cogent. In particular, his idea of the ‘thing-in-itself’, which essentially says that we may never know the real essence of something but only what we perceive it to be. (I think this is Kant's great contribution to philosophy.) He gave the example of colour, which, contrary to many people’s belief, is a purely psychological phenomenon. It is something that only happens inside our minds. Some animals can’t see in colour at all and some animals see colours that we don’t, for example, in the ultra-violet range. Some animals, that use echo-location, like bats, dolphins and whales, probably see in ultra-sound. It would be hypothetically possible for some creatures to see in radar, if they ever evolved the ability to transmit radar signals. But, more significantly, our discoveries in quantum mechanics and relativity theory, are proof that what we perceive as light and as time respectively are not necessarily what they really are, depending on what level of nature we examine. This leads to another aspect of epistemology that I will return to later – I don’t want to get too far off the track.

In fact, relativity theory tells us that time and space are inherent features of the universe, and, again, it is only through mathematics that we can decipher the enigma that is relativity, as well as quantum phenomena. But we don't need relativity theory to challenge Kant's thesis on the nature of space and time. We sense time and space through our eyes (our eyes are literally like a clock that determines how fast the world passes us by) and, again, this is different for different species. Many birds, and insects, see the world in slow motion compared to us because their eyes perceive the world in more ‘frames per second’ than we do (for us I think it’s around 24). The point is, contrary to Kant’s assertion, if our senses didn’t perceive the reality of space and time, then we would not be able to interact with the world at all. We would not even be able to walk outside our doors.

I once had an argument with a professor in linguistics, who claimed that 3 dimensional Cartesian axes are a human projection, and therefore all our mathematical interpretations, including relativity, based on Reimann geometry (which is curved), are also projections. The fact is that we live in a 3 dimensional spatial world and if we lived in a higher dimensional spatial world, our mathematical interpretation of it would reflect that. In fact, mathematically, we can have as many-dimensional worlds as we like, as string theory demonstrates. Einstein’s genius was to appreciate that gravity made the universe Reimann rather than Cartesian, but, at the scale we observe it, it’s not noticeable, in the same way that we can survey our little blocks of land as if they are flat rather than curved, even though we know the earth’s surface is really a sphere.

After all that, I haven’t answered the question: is the perceived graininess of the universe a result of our projection or not? One of the consequences of Kant’s epiphany, concerning the thing-in-itself, is that it seems to change according to the level of nature we observe it at. The example I like to give is the human body, which is comprised of individual cells. If one examines an individual cell there is no way we could appreciate the human body of which it is a part. At an even smaller scale we can examine its DNA, which is what determines how the human body will eventually turn out. The DNA is actually like a code, only it’s more than an analogy, it really is a code; it contains all the instructions on how to construct the creature it represents. So what is the thing-in-itself? Is it the genome? Is it the fully grown adult body? Humans are the only species that we know of who have the ability to conceptualise this, and, therefore, are able to comprehend at least some of the machinations of the natural world. And this, I believe, lies at the heart of Eco’s introductory hypotheses. It’s not to do with matching symbols with elements, or combinations thereof, but matching concepts with phenomena, and, more significantly, concepts within concepts, and phenomena that emerge from other phenomena.

Many people talk about the recursive ability of the human brain, which is to hold multiple relationships within one’s mind, like my friend’s mother’s lover has a cat with an injured foot. I understand that 5 is the norm, after which we tend to lose the thread. In which case, I ask: how can we follow a story, or even an argument, like the one I’m writing now? In another post (Imagination, Mar.08) I suggest that maybe it was storytelling that originally developed this aspect of our intellectual ability. We tend to think of words as being the ‘atoms’ of a story, but, as a writer of fiction, I know better, as I will explain shortly. Individual words do have a meaning of their own, but, as Wittgenstein pointed out, it is only in the context of a sentence that the true meaning is apparent. In fact, it is the sentence, or phrase, that has meaning rather than the individual words, as I’m demonstrating right now. But it really requires a string of sentences, and a lengthy one at that, to create an argument or a story. The shortest component of a story is actually a scene, and a scene is usually delineated by a break in time or location at its beginning and its end. But, of course, we don’t keep all the scenes in our memory for the course of the story, which may unfold over a period of days, so how do we do it?

Well, there is a thread (often times more than one) which usually involves a character, and we live the thread in the moment just like we do with our lives. It’s like when we are in contact with that thread we have the entire thread in our mind yet we are only interested in its current location in time and space. The thread allows us to pull out memories of it, make associations, into the past and future. This is the really extraordinary attribute of the human brain. I’ve no doubt that other animals have threads as well, but I doubt they have the same ability as we do. It is our ability to make associations that determines almost everything intellectually about us, including our ability to memorise and learn. It is only when we integrate new knowledge into existing knowledge that we actually learn it and understand it. To give an example, again, from Wittgenstein, if you come across a new word, you can only comprehend it when it is explained in terms of words you already know. In a story, we are continually integrating new information into existing information, yet we don’t see it as learning; we see it as entertainment. How clever is that?

I argue that recursiveness in the human brain is virtually limitless because, like the cells and the human body, we can conceptualise concepts within concepts ad infinitum, as we do in mathematics. For example, calculus requires the manipulation of infinite elements yet we put them all into one function, so we don’t have to even think of an infinite number of elements, which, of course, would be impossible.

I’ve made the point in other posts, that the reason we comprehend the universe to the extent that we do is because we have this ability to perceive concepts within concepts and the universe is made up of elements within elements, where the individual element often has nothing in common with the larger element of which it is a part, so graininess is not the issue. I don’t believe this is a projection; I believe that this is an inherent attribute of the entire universe, and the only reason we can comprehend it, in the esoteric way we do, is because we are lucky enough to have the innate ability to perform the same trick mentally (see The Universe's Interpreters, Sep.07).

I’ve almost exhausted this subject, but I want to say something about schemas. I mentioned, earlier in this essay, Kant’s assertion that we project our ideas, or models, onto the universe in order to comprehend it. I discuss this as well in The Laws of Nature, but in a different context. Eco also talked about schemas, and while he said it was different to the psychological term, I will attempt to use it in the same sense as it is used in psychology. A schema is a template, is the best description I can give, whereby we apply it to new experiences and new knowledge. We even have a schema for the self, which we employ, subconsciously, when we assess someone we meet.

I argue that the brain is a contextual instrument in that it axiomatically looks for a context when it encounters something new, or will even create one where one doesn’t readily exist. By this I mean we always try and understand something on the basis of what we already know. To give an example, taken from Eco’s book, when Europeans first saw a platypus they attempted to categorise it as a mammal or a reptile (it lays eggs). But, if I was a European, or from the northern hemisphere, I would probably think it was a type of otter or beaver, assuming I was familiar with otters and beavers, because it is air-breathing yet it spends most of its time in river water or underground. Another example: assume you had never seen a man on a horse, but mythically you had seen pictures of centaurs, so the first time you saw a mounted man you might assume it was all one animal.

My point is that we apply schemas to everything we meet and perceive, often subconsciously, and when we become more familiar with the new experience, phenomenon or knowledge, we adjust our schema or create a new one, which we then apply to the next new experience, phenomenon or whatever.

There is a logical connection here, to what I suggested earlier, that we only understand new knowledge when we integrate it into existing knowledge. A schema is a consequence of existing experiences and knowledge, so cognitively it's the same process. The corollary to this is that when we encounter something completely alien, we need a new schema altogether (not unlike Kuhn's paradigm-shift).

I read recently in New Scientist (31May 2008) that someone (Karl Friston) had come up with a Bayesian interpretation of the brain (using Bayesian probability), at all levels, including neurons (they strengthen connections based on reinforced signals). The brain makes predictions, then adjusts its predictions based on what it senses in a reiterative process. He gives the everyday example of seeing something out of the corner of your eye, then turning your head to improve your prediction.

Schemas, their interaction with the world and our modification of them accordingly, is such a reiterative process, only on a different scale. Previously, I've talked about the dialectic in science between theory and observation, or theory and experimentation, which is another example of the same process, all be it's at another level altogether and is performed in a more disciplinary manner.

This is where I should write a conclusion, but I think I already have.

Having completed this essay, it has little resemblance to my letter to Umberto Eco in 2002, in either content or style, but some ideas and some arguments are the same.

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

Layers of Being

You’ve probably noticed that a recurring theme of some of my essays is the virtue of self-honesty. I guess that’s why I am attracted to existentialism – in fact, I think it’s fair to say I was attracted to it long before I knew what it was.

I am going to discuss 3 layers of being, based on my own experience and observations, and I am sure some will argue that there are more, while others may argue that they don’t exist at all, but, basically, this is possibly the most personal of my essays thus far on this blog, so it’s not very scientific.

What do I mean by layers of being? I’ve already said that it’s important in philosophy to define one’s premises and concepts. I think a good starting point is another one of my recurring themes: the inner and outer world. Some people, especially some philosophers, would prefer not to make any distinction, but I find it unavoidable. I’m a writer of fiction, and it was whilst writing fiction that I first appreciated the significance of the inner and outer world. Fiction, in a Paul Mealing defined nutshell, entails a character’s journey. Once you take that approach, it generates its own corollary: the character is changed and altered by the events in the plot that he or she encounters. To extend the metaphor, the plot becomes a vehicle for the character’s own inner journey. I was aware of this from my very first attempts to write fiction. Of course, it’s exactly the same in life, only we don’t use the terms, plot and character, in real life.

So I already have 2 layers: the inner and outer world. Before I introduce the third, I need to elaborate on these 2, as they are the most obvious and also, they are experienced by everyone, even if you would prefer to conflate them. The most obvious interface or interaction between these 2 layers is found in relationships. It is through relationships that we practice integrity or deception, generosity or rejection, engagement or apathy. There are other terms: love, jealousy, anger, hate, envy, revenge, charity, empathy, compassion. All these terms only acquire meaning within the context of relationships, but, of course, it’s unavoidable that they also reflect something deeper within the individual.

But there is one simple rule or criterion, which, I believe, puts all relationships into perspective, and that’s expectation. In any relationship: family, work, love, sport, even legal; there are expectations. It is when an individual’s expectation is in agreement with the group’s that there is harmony. When this expectation is either above or below the group’s, or the other’s, there will be conflict. By above or below, I mean we either expect more or less of our own role compared to what others might think. And one can see that honesty plays a key role here – if we deceive someone into an expectation that can’t be met, either by them or by us, then we have already started on a bad footing.

Paradoxically, this leads to the third layer of being, and the one I started off with: deception to oneself. Our relationships with others have a direct internal reflection and vice versa. To take an example, if we hate someone it corrodes our own soul, leaves us bitter in a way we can’t fathom. Likewise, jealousy alienates the person we love. These are contradictory causes and effects, yet we have all experienced them. Surely, you say, this is not dependent on a third layer, this is merely a further extrapolation of the inner and outer world.

What then is self-deception? I’m talking about neurosis where one has a distorted view of oneself. The dissociation that can occur between individuals and others can also occur within oneself. I know this because I have experienced it. When I read of people who have gone off the rails, I can sometimes see myself, as I know how easy it is to have a distorted view of oneself and feel like one has lost their core, or what we sometimes call our identity. Of course, this self distortion directly affects our relationships with others – it has an impact on the outer world – the two are not independent.

And this is why I place so much emphasis on self-honesty, because, without it, one can’t be honest in one’s relationships with others. But, I believe, it is also this third, deeper layer of being that provides the spiritual dimension that some people claim. In other words, it comes from a self-examination and a level of self-honesty that most of us fail to achieve. It doesn’t require a belief in God, but, ideally, it should lead to a sense of egolessness. What Buddhists most likely call the no-self, though I’m no expert in Buddhism.

One must also define what one means by ego. Again, I think Buddhism provides a key - to do with attachment, though I’m not opposed to attachments per se. There are healthy and unhealthy attachments, all to do with choices, but I’m getting off the track. Buddhism deals with attachment to life in general (samsara) and I would say that ego is an essential aspect, arguably, the very consequence of this. Again, ego can be healthy or unhealthy, so the egolessness I refer to is an ideal, whereby one becomes ‘unattached’ even to oneself, albeit sounds like a complete contradiction.

Have I personally reached this state? No. Maybe when I die. After all, one doesn’t have to be a Buddhist to believe that death is the final letting go of ego (I think a Jewish philosopher once said that, but I can’t remember who it was). Of course, I’m yet to prove it.

The Mirror Paradox

The mirror paradox is best stated as a question: why is a mirror image seen as left to right reversed but not top to bottom? I’m not sure why this is always seen as a philosophical conundrum, when it involves science, and, to a lesser extent, psychology. Having said that, I’ve rarely seen it explained correctly, so maybe it is a philosophical conundrum after all. Certainly, Stephen Law, in his excellent book, Philosophy, believes it’s ‘a puzzle science cannot solve’. But I beg to differ: it’s a real optical phenomenon entailed by the 3 dimensional spatial world in which we live.

In the Oxford Companion to the Mind (1987), Richard L. Gregory (Professor of Neuropsychology at University of Bristol, UK) in my view, talked all around the solution, without actually delivering it. He certainly understood that there is no rotation in the mirror (see below). However, he seemed to think (like Stephen Law and Umberto Eco) that there is no reversal at all, though he once obliquely referred to an 'inversion', so maybe he knew without knowing that he knew.

In 2002, whilst working in America, I read Umberto Eco’s Kant and the Platypus, which was as stimulating a book as I’ve ever read on epistemology, though I think it would be a difficult read for anyone who wasn’t familiar with Kant, at least at a rudimentary level. When I had completed it, I wrote a long letter to Umberto, who acknowledged receipt of my letter but never followed up with a response. I learned later that he had a fight with throat cancer, so I take it as no slight that he didn’t respond further.

In one of his chapters, he gives a lengthy discourse on the mirror paradox, and that was one of my points of contention. He argued that a mirror ‘reverses nothing’, but a second reflection did reverse left to right, which restores the image to what we normally see. I pointed out to him that this was illogical, nevertheless there is a specific case where he is correct. I will return to this specific example at the end of my discourse. I need to say that I have great respect for both Stephen Law and Umberto Eco, as both of these men are far more knowledgeable than me in their respective fields.

Most people explain the mirror reflection in terms of rotation, as it appears that the mirror rotates the image around, and this is particularly compelling for mirror-reflected writing, as I explicate below. But this merely raises another question, effectively transcribing the paradox, not solving it. Why does it rotate the image about the vertical axis, not the horizontal axis? Stephen Law gives an analogy: if you walk through a door that opens on the right side, why does it open on the left side when you come back the other way? The answer is because you turn yourself around. Law argues that if we lived in zero gravity, whereby you could turn yourself upside down to open the door, it would still open the same way, so the implication is that it’s gravity that creates the emphasis on the vertical axis. In fact, Stephen Law speculates that if we lived in a weightless environment then perhaps the ‘mirror puzzle would not even be a puzzle’. But I believe he'd be wrong: it's the left-right symmetry of the human body that creates the emphasis on horizontal over vertical reflection.

All these explanations and descriptions seem to overlook the fact that there is no rotation in the mirror at all – in fact, it’s the lack of rotation that gives us mirror reflection. I believe that most of these explanations actually appreciate this fact; they just fail to explain it. But I have been keeping you in suspense – the answer to this puzzle is deceptively simple: the mirror doesn’t reverse left to right, or top to bottom, it reverses back to front. We live in 3 dimensions, not 2, and a mirror reverses everything in the dimension perpendicular to its plane. So the rotation is a genuine illusion (it doesn’t happen), but the reversal is a true optical phenomenon.

Below is an edited version of my exposition that I sent to Umberto Eco.

Normally, if we want to see something back to front we have to turn it around. Generally we do this by turning the object through its vertical axis but we can also turn it through its horizontal axis. If we turn it through its vertical axis, as happens when someone turns to face us, their left side appears on our right and their right side appears on our left. This is unavoidable. But they could also turn to face us by standing on their hands, in which case they would appear upside down but their left side would still be on our left and their right side on our right. Then if they stood by doing a half cart wheel they would resume their normal stance but left to right would be reversed. The mirror quite literally reverses the image back to front without rotating it through any axis at all. So we don’t see the image upside down but likewise we don’t see the left side on the right or the right side on the left. This is the illusion pure and simple. The illusion, when we face a mirror, is that it appears to rotate us around a vertical axis, when in fact it doesn’t, it turns us back to front. If we look at something between us and the mirror, we see the front of it facing us, and the back of it facing us in the mirror. This is the key to the illusion. When we look at ourselves in a mirror we expect to see ourselves as others see us, but we can only do this when we have 2 mirrors, which appears to really rotate everything about the vertical axis (as Eco contended), but, in actuality, restores front to back to front again. But I’m fast-forwarding - I will elaborate on double reflections later.

In other respects we are not fooled by the mirror’s conservation of left and right. If we see in the mirror someone standing behind us and to our left, we automatically look over our left shoulder, not our right. Where we are fooled is when we reach for something on a table between us and a mirror, as in the case of an object on a dressing table or a bathroom bench top, while watching the object in the mirror. If we reach for an object at the back of the table, we appear in the mirror to be reaching forward towards us, rather than away. Likewise, if we drag an object on the table towards us, we appear in the mirror to be pushing it backwards not forwards. If you doubt this, try shaving or combing your hair with your left hand instead of your right (or your right hand if you're left-handed). We’ve trained our preferred hand through years of practice.

When we look in the rear view mirror at a car parked behind us while standing at a traffic light, we see that the driver is sitting on the same side of the car as we are and we are not confused. Because we know the car is behind us, the same as in the previous example, when we knew that the person standing behind us in the mirror was on our left or right side just as the mirror dictated. If the car was traveling towards us, we would expect to see the driver on the opposite side to us because the car has been turned around it’s vertical axis. If we turned around to look at the driver behind us at the traffic light, we would still see that he or she is on the same side of the car as we are, because both cars are facing the same direction, even though we have turned around to look backwards. Therefore, when we look at the driver in the rear view mirror we can see that left and right have been conserved. So why is it that when we look at the number plate we have to read it backwards, as if it's been rotated?

Writing not only provides the best illustration of the illusion, it also provides the best means to understand it. If you hold up a page of a book with writing on both sides while facing a mirror, the side facing you is readable, but the side facing the mirror is mirror-reversed. However, if the page was transparent, then the writing on the other side would also appear mirror reversed exactly as it does in the mirror. Take a sheet of plastic or cellophane, or anything clear that can be written on. If you hold up this transparent sheet so that the writing is mirror-reversed to you then it will also appear mirror-reversed in the mirror. Likewise if you hold it up so that the writing is readable to you then it will appear readable in the mirror. So where did the illusion of rotation go?

The illusion has gone but the reversal hasn't. Because when you hold up the sheet so you can read it, you are looking at the front of the sheet whereas the image you see in the mirror is the back of the sheet. Left to right is not reversed but front to back is. The front you see in the mirror is actually the back to you. If you were to place yourself between the sheet and the mirror, without changing its orientation, you would see the writing mirror-reversed. The mirror mirror-reverses the back of the sheet. And, of course, you would have to turn yourself around to read it, which only emphasises the illusion that the mirror rotates the image, but actually it doesn’t. The reason writing always appears reversed left to right, is because we always turn it left to right to face the mirror. We do the rotation, not the mirror.

This brings me to the third image created by a second mirror. If you set a book upright on a dressing table (or a table with a mirror behind it) with the front cover facing you, then the back cover will be mirror-reversed in the mirror. If you then took a small mirror (say a shaving mirror) and place it between yourself and the book, but facing back into the main mirror (or background mirror) you can create a third image of the cover in the main mirror. This is very easy to do by small adjustment of the angle of the foreground mirror. Naturally enough (but only because we know in advance) we can read the front cover in the third image exactly as it appears to us on the table. If we didn’t already know this, I believe it would be a complete surprise. The important point is that the image is not rotated at all, it is simply reversed back to front twice, using an intermediary mirror that is facing away from us.

In fact the foreground mirror behaves in exactly the same way as the transparent sheet I referred to in the previous example. If you could see through the foreground mirror so it’s image could be read from the back (in other words if it was a transparent screen with the book cover projected onto it) we would be able to read it exactly as we can in its reflection in the background mirror. The point is though, that the foreground mirror reverses the image, not from left to right but back to front. The foreground mirror only has the writing in the right order because it is facing away from us. If you were to place yourself between it and the background mirror (and turn yourself around) you would see the writing is mirror-reversed as you would with the transparent sheet. So the background mirror mirror-reverses the foreground mirror.

But, as I alluded to earlier, there is a specific situation, and a common one, where a second mirror does translate the image directly from left to right, which upholds the illusion of rotation. We often find ourselves in a bar, or a bathroom, with 2 vertical mirrors joined at right angles like 2 walled mirrors. In this case the image you would see is a double reflection no matter which mirror you looked in. In fact, if there were 2 extended wall mirrors, then there would be 4 images of you, including the prime image. If you were to press your finger into the corner, you would see 4 symmetrical images of it, one of which would be you. Another unique feature of this third image is that it would always remain in the corner of the room as you moved about, whereas the other 2 images would follow you around. This also means, of course, that everyone in the room would see themselves in the corner (assuming they had a clear line of sight).

The (apparent) non-reversed image results from a secondary reflection coming off a primary reflection that you cannot see, because the two reflections simultaneously 'swap' over on the adjacent mirrors. This, in fact, does resemble a rotation about the vertical axis, simply because the mirrors are joined on a vertical axis. And this is what led Umberto Eco to argue that the first mirror image is not reversed left to right but the second image is. He is correct, in this specific case, but only because we create a virtual vertical axis of rotation by the very careful alignment of the 2 mirrors.

So now I have turned a simple answer into more than 2,000 words, and either have confused you completely or explained a common phenomenon thoroughly. I hope the latter.

Footnote: I had a brief discussion with Stephen Law on this topic. We agree to disagree over my belief that science does solve this puzzle. You can visit his post on this subject (and our dialogue) at the following: http://stephenlaw.blogspot.com/2007/04/mirror-puzzle-solution.html And explore the rest of his excellent site.

Addendum 1: If you think this exhausts the subject of mirrors, you should read Richard Feynman's quantum mechanical explanation of reflection in his truly fantastical book, QED, The Strange Theory of Light and Matter.

Addendum 2: There is something I need to tidy up. There is one situation where a mirror does reverse an image left to right, and it’s literally the exception that proves the rule, because it doesn’t reflect the image back to itself.

If you set up a mirror at 45 degrees along its vertical axis, it allows you to see around corners and there are lots of examples in car parks and other places. Note that you can’t see what’s behind you as you would normally expect from a mirror. Most of these (seen in real life) are convex so that you can see more using a smaller mirror.

The best way to demonstrate this is with a graphic that shows how the light rays reflected at 45 degrees axiomatically reverse their relative orientation from left to right. Note that if you were to tilt a mirror at 45 degrees along the horizontal axis, it would turn an image on the ground (facing you) upside down.