The Laws of Nature

This is another posting arising from an intellectually stimulating read: Michael Frayn’s The Human Touch, subtitled, Our Part in The Creation of the Universe. The short essay below is in response to just one chapter, The Laws of Nature. I have to say at the outset that Frayn is far more widely read than I am, and his discussion includes commentary and ruminations by various scientists and philosophers: Popper, Kuhn, Einstein, Planck, Bohr, Born, von Neumann, Feynman, Gell-Mann, Deutsch, Taylor, Prigogine and Cartwright, amongst others. A number of these I have not read at all, but I find it strange that he does not include Penrose (except for one passing reference in his notes) or Davies, who have written extensively on this subject, and have well known philosophical views.

I haven’t finished reading Frayn’s text (though I’ve read his extensive notes on the subject) so I may have more to say later, and the following was originally written in the form of a ‘letter to the author’, which I never sent.

The heart of Frayn’s dissertation on the ‘laws of nature’ seems to be the interaction between the human intellect and the natural world. There are 2 antithetical views, both of which involve mathematics, because, in physics at least, the ‘laws of nature’ can only be expressed in mathematics. We may give descriptions in plain language, creating man-made categories in our attempts, but without mathematics we would not be able to validly call them ‘laws’, whether they be fiction or otherwise.

The first of these antithetical views is that we have invented mathematical methods, which have evolved into, sometimes complex, sometimes simple, mathematical models that we can apply to numerous phenomena we observe, and, in many cases, find a near-perfect fit. The second view is that the laws already exist in nature, and mathematics is the only means by which they can be revealed. I tend to subscribe to the second view. I disagree philosophically with Einstein, who contended, quite reasonably, that 'the series of integers is obviously an invention of the human mind', but agree with him that there is an underlying order in the machinations of the universe. (In regard to Einstein's contention, I discuss this argument in detail in 2 other postings; but, even if we invent the numbers, the relationships between them we do not.)

We humans puzzle over facts like the planets maintaining their orbits for millions of years, or the self-organising properties of galaxies, or of life for that matter, or the predictability of the effects of light shone through slits. We look for patterns, so we are told, and therefore we project patterns onto the things we observe. But science has demonstrated that there are not only patterns in nature, but relationships between events that can be described in mathematics to unreasonable degrees of accuracy. My own view is that the mathematical relationships found in nature are not projected, it’s just that the deeper we look the more unfamiliar the relationships become.

It seems to me the laws, for want of a better word, exist in layers, so that, at different scales different ones dominate. It follows from this that we haven’t discovered them all, and possibly we never will, but it doesn’t mean that the ones we have discovered are therefore false or meaningless. I have had correspondence with philosophers of science who believe that one day we will find the one governing law or set of laws that will make all current laws obsolete, which means the current ones are false and meaningless, but history would suggest that this goal is as mythical as the original Holy Grail.

Everyone posits Einstein’s theories of relativity making Newton’s laws obsolete as the prime example of this process, yet the same set of ‘everyone’ uses Newton’s equations over Einstein’s for most purposes, because they are simpler and just as accurate for their requirements. Einstein made the point (according to Frayn’s reference, Abraham Pais) that Newton’s mechanics were based on ‘fictional principles’, yet gave the same results as his own theories for many phenomena. (Frayn quotes Pais in his belief that Einstein thought all theories were fictions.) I believe the main ‘fictional principle’ inherent in Newton's theory (for gravity at least) arises from the fact that there is no force experienced in gravity if you are in free fall; there is only a force when you are stopped from falling. This is arguably the most significant conceptual difference between Newton's and Einstein's theories, and appears to be one of the key motivations for Einstein seeking a different mathematical interpretation for gravity.

Einstein’s theories are an example of how the laws of nature are not what they appear to be at the scale we experience them, specifically in regard to gravity, space, time and mass. His equations supersede Newton’s, in all respects, because they more accurately describe the universe on cosmological and atomic scales, but they reduce to Newton’s equations when certain parameters become negligible.

On the other hand, quantum mechanics appears to be another set of laws altogether that lie behind the classical laws (including relativity) that only become apparent at atomic and sub-atomic scales. I would suggest, however, that this dissociation between the quantum and classical worlds is a result of a gap in our knowledge, as contended by Roger Penrose, rather than evidence that the ‘laws of nature’ are all fictions. Assuming that this gap can be resolved in the future, new laws expressed in new or different mathematical relationships would be revealed. It’s not axiomatic that these future discoveries will make our current knowledge obsolete or irrelevant, but, hopefully, less mystifying.

I would make the same prediction concerning our knowledge of evolution. In the same way that Darwin proposed a theory of evolution based on natural selection, without any knowledge of genes or DNA, future generations will make discoveries revealing secrets of DNA development which may change our view on evolution. I’m not talking about ‘Intelligent Design’, but discoveries that will prove ID a non sequitur; as ID is currently a symptom of our ignorance, not an aid to future discoveries as claimed by its proponents. (See my Nov.07 post: Is evolution fact? Is creationism myth?)

There are deep, fundamental, inexplicable principles involved when one examines natural phenomena. Not-so-obvious examples are the principle of least time in refraction (referenced in Frayn’s text; intuited by the 17th Century mathematician genius, Pierre de Fermat) and the principle of maximum relativistic time in gravity, expounded brilliantly by Richard Feynman in Six Not-So-Easy Pieces. These principles, I would contend, are not inventions, but discoveries, and they reveal an underlying natural schema that we could never have predicted through speculation alone. In fact, were it not for our powers of intellect and observation, in combination with a predilection for mathematics, we would not even know they exist.

Footnote: James Gleick in his biography of Feynman, GENIUS, gives the impression that these 2 phenomena could be different manifestations of the same underlying 'principle of least action' that Feynman even employed in his examination of quantum mechanics. Anyone who is familiar with both these phenomena will appreciate the connection - it's like the light or the particles choose their own path - as Gleick expounds quite eruditely, but without the equations.


Addendum 1: Since I published this post, I've read Feynman's lecture series that he gave in New Zealand in 1983 published under the title, QED, The Strange Theory of Light and Matter. In his first lecture, he gives a brilliant exposition (in plain English) on how light reflected by a mirror 'follows the least time path' can be explained by quantum mechanics. I need to add the caveat that no one understands quantum mechanics, a point that Feynman is at pains to make himself, right at the start of his lectures.

Addendum 2: I wrote a later post on 'least action' which is more erudite.

Imagination

I first came across the term ‘intentionality’ as a philosophical term when I was reading John Searle’s Mind, and I had difficulties with it until I substituted the term imagination. I had forgotten about this until I read another account in The Oxford Companion to the Mind (edited by Richard L. Gregor, 1987), thinking I was going to read about intentionality as a mental purpose, as it would be used in ordinary language. Once again, forgetting all about my experience with John Searle, I was about half way through the discourse when I found myself substituting the term imagination, and then I realised: I had taken this mental journey before.

This is an example of how I believe we integrate new knowledge into existing knowledge. When we come across a new experience or phenomenon, or new information, we axiomatically look for something we are already familiar with that we can analogise it with. It’s also why metaphor is such a favoured form of description and is so readily adopted and understood without extraneous explanations. So, in the absence of anything better, I substitute imagination for ‘intentionality’ but the more I read the more I conclude that they are the same thing. According to The Oxford Companion to the Mind, intentionality is only evident in mental states and is about 'aboutness’. When I read Searle’s account and the examples he gave of someone being able to conceptualise a real event that had occurred in history or in another place or another time, or an event that had never occurred at all, then that’s imagination. Also I argue that this is not unique to humans. The fact that many species can plan and co-operate, especially when hunting, suggests that they can ‘imagine’ the outcome they are trying to achieve.

I once had a brief correspondence with Peter Watson, author of A Terrible Beauty (an extraordinarily erudite and comprehensive book of the ‘ideas and minds that shaped the 20th Century’), who contended that words like ‘imagine’ and ‘introspection’ have outlived their usefulness, and that they no longer fit in with our comprehension of our mental states, and, possibly, are even misleading. I had serious problems with this dismissal of our inner world, as I saw it. Also he talked about ‘imagination’ as if he really meant ‘creativity', which is an essential but limited aspect of how we imagine (more on that below). When I quizzed him on this, he explained that his real complaint was that he found words like ‘imagination’ vague; according to Watson, 'imagination' was even more vague than ‘mind’. (I must say in passing that I have the utmost respect for Peter Watson, even though we’ve never met, and he responded good-naturedly to all my criticisms.)

But I think the reason that people are uncomfortable with terms like these: imagination, introspection, mind; is that they defy objectivity by their very nature. You cannot talk with any validity about anyone's imagination, introspection or mind, except your own. Our inner world is subjectivity incarnate, yet, because we all have one, we can talk about it in a common language.

In my view, ordinary people know what we mean by ‘imagination’ and ‘introspection’ even if no one can explain how it happens, and they remain essential components of our psychological lives. In my posting, The Meaning of Life, I allude to Watson’s philosophical viewpoint by referring to an extreme position that considers our internal world to be so dependent on the external world, that it makes the inner world we all experience irrelevant (some people do take this view). In fact, Watson did make the point that our inner world is completely dependent on the external world – no one can really claim that anything is created independently of the outer world. And he said that this was his salient point: no one ever came up with a valid theory or idea by introspection alone, without considering external factors. I would agree with him on this, but it doesn’t mean that imagination and introspection have no role to play.

Also he has a point, regarding the dependence of our inner world on the outer world, when one considers that we all think in a language and we all gain our language from the external world (I make this point in my posting on Self). Language is one of the means, arguably the most important, but not the only one, that allows an interaction between the inner and outer world, and it goes both ways – we are not passive participants in the world. And yes, our imagination is fueled by external events, yet, without imagination there would be no art, in any form, and, in particular, no stories; not only for the creator, but also for the recipient.

Being a storyteller myself, this is something I can talk about with some experience. I find it interesting that a writer can compose a story that so engrosses the reader that he or she actually forgets they’re reading. How does one achieve this? It’s simple in principle, but very difficult in execution: one allows the reader to create an imaginary world that he or she inhabits so successfully, they become emotionally involved as if it was real, or as if they were in a dream. It's called suspension of disbelief - essential to the success of any story. And I think dreaming is the link, because writing a story is not unlike having a dream, only you consciously interfere with it, and that’s what ‘creating’ is really all about. I could elaborate on this, but this is not the place.

While it seems I’m getting off the track, I made a point in another posting, The Universe’s Interpreters, that the reason films, video and computer games have not made novels extinct (weakened yes, but not yet endangered) is because we can so readily and effortlessly create pictures in our minds. I contend, though I have no scientific evidence, that if we didn’t think in a language, we would think in images. The basis for this contention is that we dream in images and metaphor, and I believe that is our primal language. (Freudian yes, but without referencing Freud.) So much of imagination involves imagery – a point that Searle somehow misses when he discusses intentionality, yet it is obvious. (It occurred to me that Searle had the same aversion to the term that Watson revealed.) Searle does make the point, however, that intentionality can involve desires and beliefs, which, of themselves, can be manifested in sensory form (he gives the examples of hunger and thirst).

It’s only humans who create art, and it is often proposed that the emergence of art is the first indication of our evolutionary separation from other homo-related species. But imagination, along with the other conscious attributes we have, are not unique to humans, just our ability to exploit them and project them into the external world.

It’s not for nothing that Searle claims the problem of intentionality is as great as the problem of consciousness – I would contend they are manifestations of the same underlying phenomena – as though one is passive and the other active. Searle wrote his book, Mind, in part, to offer explanations for these phenomena (although he added the caveat that he had only scratched the surface), whereas I make no such attempt. That’s not to say that in the future we won’t know more, but I also think that our reductionist approach will find its own limitations – I predict we will uncover more knowledge only to reveal more mysteries, as we have done with quantum mechanics.

However, from this premise, I would say that imagination, or ‘intentionality’ (if I interpret it correctly) is a manifestation of mental activity, and one that we are unlikely to find in a machine, but that’s another topic for another day.

What is Philosophy?

This is one of those topics that is possibly best introduced by discussing what it is not. Traditionally, Western philosophy is divided into categories: ontology, epistemology, ethics, aesthetics and logic. For the layperson, ontology is often described as the ‘nature of being’, epistemology is to do with ‘knowing’: theories of knowledge may be the best description, and could include aspects of language or linguistics. Ethics relates to moral philosophy, aesthetics relates to philosophies of art and beauty, and logic is related to, but not synonymous with, mathematics. One may also include theology as another category.

From my own essays published in this blog to date, one can see that I cover a variety of topics that infringe on a number of disparate fields. After all, one may see a connection between mathematics and science, science and psychology, psychology and morality, but what about mathematics and morality? And some people may conclude from this, that philosophy is some sort of umbrella discipline that covers all fields of human knowledge and learning. But this would be misleading: ontology is not religion, epistemology is not science, aesthetics is not art, ethics is not justice or politics, and logic is not mathematics. In other words, all these disparate disciplines are not just branches of philosophy.

So what is the relationship? I would argue that the relationship is dialectical: they feed each other. All these fields, of themselves, involve philosophy, even if it’s at a subconscious level. People who practice in these fields, if challenged to explain their motivations and methodologies, will give a philosophical answer. And the significance of this is that it will both agree and differ from others practicing in the same field, even if they have the same level of expertise. To give an example, relating to one of my own postings: Is mathematics evidence of a transcendental realm? I point out how Roger Penrose and Stephen Hawking, who have worked together at the frontiers of cosmology, are philosophically poles apart with regard to their mathematical viewpoints (refer The Large, the Small and the Human Mind by Penrose, Shimony, Cartwright and Hawking).

In that posting, I describe how Kurt Godel ‘proved’ a fundamental premise in mathematical thinking: one cannot derive all mathematics from a set of known axioms. Now some may conclude that this constitutes a ‘philosophical’ proof, but I would contend there are no ‘philosophical proofs’, only proofs that can support a philosophical point of view. You may argue: what is the difference? Well, the difference is that different people, quite commonly, use the same proof to support different philosophical points of view, and Godel’s proof is a case in point. Godel was a Platonist his entire life, while his very good friend, Albert Einstein, was not a Platonist at all. When they lived in Princeton they often took long walks together, which they both apparently enjoyed, able to talk on esoteric subjects at the same level of comprehension (refer A world Without Time by Palle Yourgrau). Obviously, they didn’t always agree, so what was the attraction. Well, based on my own experience, I believe they liked to challenge each other, and be challenged, and that is what practicing philosophy is all about. In a nutshell, philosophy is a point of view supported by rational argument. The corollary to this is that it requires argument to practice philosophy.

To give an entirely different example: many years ago I knew a family of Jehovah Witnesses, and we became good friends, keeping in contact for many years. Every now and then, when they were ‘witnessing’ (as a couple) they would come to my place (I lived alone) and we would have a very good argument. I always enjoyed those encounters because they made me dig very deep into my beliefs and I always felt invigorated afterwards, like one does after some vigorous exercise, like running. I always assumed that they felt the same, otherwise why would they do it? But, most importantly, I believe they came to me, not to be convinced, or even to convince me, but to be challenged, like an exercise.

To return to the categories listed in the introduction: in the 20th Century, academically at least, epistemology became the central pillar of modern philosophy, to the extent that, for some philosophers, epistemology and logic are philosophy – everything else is opinion or culture. In this context, many see philosophy as being subordinate to science - a mere footnote to empiricism. This is a philosophical viewpoint in itself, which, many would argue, originated with David Hume. Bertrand Russell, for example, acknowledged that Hume was the most influential philosopher he read. It was Hume who challenged some of our most important assumptions about cause and effect (he argued that we can never know for certain), and who founded the philosophical premise of empiricism which underpins all of science. (John Searle, in Mind, is one of the few I have read who successfully challenges Hume’s philosophy on cause and effect). So one can see the connection between epistemology and science: if science is empiricism and epistemology is knowledge – they go together hand in glove. But there are limits to science, at least in my view, and that’s another topic (see Does the Universe have a Purpose?).

Epistemology logically leads to a discussion on language, because we all think in a language, and all our knowledge acquisition is language based. This leads one to Ludwig Wittgenstein, who was arguably the most influential philosopher of the 20th Century. But before I discuss Wittgenstein, one can’t leave the discussion of epistemology without a reference to mathematics, especially where science is concerned. I’ve already written 2 postings on mathematics: Is mathematics invented or discovered? and Is mathematics evidence of a transcendental realm? So I will be succinct. Arguably, our knowledge of mathematics has provided us with more insight into the machinations of the Universe, at all levels, than any other endeavour. In keeping with the accepted interpretation of epistemology, many would argue that mathematics is just another language, albeit one that is never a first language. This is a philosophical viewpoint that is hard to defend, not least, because numbers (the fundamental elements of all mathematics) never relate to specific entities as descriptors, the way words do. So I would argue that mathematics is totally relevant to epistemology, but in a way that language is not.

Getting back to Wittgenstein, one of his most famous statements was: ‘Philosophy is a battle against the bewitchment of our intelligence by the means of language.' Notice how the statement is deliberately ambiguous, even contradictory: does language bewitch our intelligence or do we combat the bewitchment of our intelligence using language? This statement is more than just a clever wordplay, however, and really does encapsulate Wittgenstein's approach to philosophy. Another philosopher who places language centre stage is Umberto Eco. More famously known as a novelist, he is Professor of semiotics at the University of Bologna. Semiotics, according to my dictionary, is the study of words and signs and their relevance to ideas and the physical world. Eco’s book, Kant and the Platypus, is his attempt to convey to laypeople his philosophy of semiotics, but that is another discussion for another time perhaps.

The key to all this, from my viewpoint, is that language may not be unique to humans, but the manner in which we have exploited it is. We use language not only to describe objects in the real world but to embrace metaphysical ideas and concepts that we structure into arguments for discussion. So the link between language and philosophy goes beyond the mundane and the obvious - it is welded to meaning. Wittgenstein's legacy was that he probably understood this better than anyone else, and he made it his life's work to analyse and explore it in all its ramifications.

A lot could be written on Wittgenstein and the results of his exploration, but, even if I was more familiar with his work, I would not choose this context to do it. For some people however, especially in academia, Wittgenstein represents the culmination of Western philosophical thought from Socrates to the modern day.

This should finish the discussion, but I think there is another misconception that needs to be clarified about what constitutes philosophy and its relationship to other fields. In my introduction I made the point that one can discuss mathematics at a philosophical level as well as morality, as I have done more than once in this blog, but that doesn’t mean that I can support a moral philosophical viewpoint using a mathematical argument or vice versa. This example is obvious, but it’s more relevant when one considers the arguments that arise between science and religion.

There are 3 postings on this blog already that refer specifically to arguments between creationism and evolution, because it’s been a very hot topic in recent decades. It is only because philosophy allows a bridge between these 2 different aspects of human enquiry that this debate exists, yet this very aspect of the debate seems to be lost. I made the point in my posting: Is evolution fact? Is creationism myth? that there is an epistemological divide between science and religion that I’ve never seen considered, let alone discussed. Religion is a personal experience that is unique to the individual who has it, whereas science, being empirically based, requires repetition to make it valid. Science seeks universality and religion is intimately personal, albeit most religious arguments have a historical, cultural context. In the case of creationism versus evolution, the context is both historical and cultural, which is why the debate persists.

But there are other aspects to this debate that need to be aired. I remember reading C.S. Lewis’s account of why he could not accept evolution over a biblical interpretation. He consistently referred to evolution as a ‘story’, and since the biblical interpretation is also a story, it’s just a case of substituting one story for another. One story he believed and the other he didn’t – it was that simple. In philosophical parlance, this would be called a ‘category mistake’, though most category mistakes evoked in philosophical discussions are not so obvious. The point is, that people forget that this is a philosophical debate, and that doesn’t allow one to substitute religion for science or science for religion. Substituting a science theory with a biblical story doesn’t make it science, which is why creationists dress it up in different clothes, which I call deception, even fraud when it comes to passing it off as science education.

I’ve said elsewhere that science and religion can’t answer each other’s questions, and I’m not sure why they believe they should. Science and theism are not mutually incompatible but evolution and creationism are. A scientist who is a theist knows the limitations of their science and their beliefs. They know they can’t use science to prove that God exists, in whatever manifestation, and likewise they can’t use a belief in God to support a scientific theory.

In my posting, Does the Universe have a Purpose? there is a link to the John Templeton Foundation, where a group of philosophers, scientists and theologians give their responses to this question. Interestingly, but not surprisingly, both theists and atheists, use evidence from science to support their particular point of view. It’s not much different to Godel and Einstein disagreeing over the philosophical consequences of Godel’s own theorem.

Creationists exploit the gaps in our current knowledge of evolutionary theory to press their case, with the implication that, because evolution, like most scientific endeavours, is still a theory in progress, the entire theory can be replaced by a pseudo-theory lifted from the Bible, despite the fact that it’s been a hugely successful theory to date. I haven’t heard, or seen, a single creationist suggesting that we should scrap quantum mechanics, even though it defies explanation in plain language, and evolution is arguably no less successful in empirical evidence than quantum theory is.

So this is an area in philosophy where disciplines collide, but they collide in philosophy, not in science or religion. If people recognised this, and thankfully many theologians do, the debate would be more sane and less politically malleable.

Footnote: Some of the best philosophical arguments I've read against creationism have been written by theologians. For an example see link: www.cosmosmagazine.com/features/print/15/bad-faith

Left or Right

This is a letter I wrote to New Scientist in response to an article by Jim Giles. In a nutshell, 'twin studies' have revealed that personality traits like openness, conscientiousness and extroversion/introversion are inherited, and he argues that these traits indirectly affect one's acceptance of new ideas or tendency to resist change.

Reference: New Scientist, 2 February 2008, pp29-31.

The following text is my response, but the last two paragraphs on fundamentalism were added later.

The dichotomy described by the article ‘Are your genes left wing or right wing?’ goes beyond politics, albeit that is where it has its biggest impact. The human population seems divided between those who seek change and those who want to maintain the status quo, and I would argue we need both. While this division seems to be close to 50/50, it is probably more of a spectrum than a polarisation. There are arch-conservatives who want to turn back the clock, and arch-radicals who want change overnight, but most people have more tempered views.

In the 1960s, Carl Rogers commented on the correlation found by people who were certain about how far a point of light jiggles against a dark background with no point of reference, and their level of racial intolerance as determined by a questionnaire. (The point of light experiment is a well known illusion, even though it doesn’t move at all.) In effect, people who seek and believe in absolute certainties are more likely to be conservative in other respects as well, like resisting change to perceived stereotypes.

I’ve always found it curious, that, by and large, artists are more liberal than other sectors of society. But it’s not so surprising, if one considers that artists are most open to new ideas, are more empathetic to the eccentric and the outsider, and also lack discipline (I’m speaking from personal experience on the last attribute). Even amongst scientists, there are those who are more sceptical, more loyal to traditional ideas, and those who are more likely to entertain fringe concepts, even at the risk of criticism and sometimes ridicule. As I said, I believe we need both.

But the other thing, that history has demonstrated, is that, despite the enormous inertia to change that seems almost natural, change occurs anyway, which would suggest that there is a healthy interaction between these 2 ‘types’ over the long term. In politics, in particular, what was considered radical in the past becomes the norm in the present day, otherwise we would still have slavery and women would not be able to vote. So over the long term, change seems to occur for the better, but in such a way that the conservatives who want to maintain the status quo can accept it as well. It should not be surprising then, that the most radical changes are generational, whereby the new conservatives have new conservative values that were previously considered liberal.

What I have found, from my own experience, is that, despite the prejudices that seem to arise from this divide, qualities like honesty, loyalty and integrity appear to be neither monopolised nor decidedly lacking from either side.

Sometimes, of course, the change can go the other way, and I’m thinking specifically of fundamentalism, which provides an attractive refuge for anyone who feels they’re a lost soul, especially an alienated lost soul. It provides certainty in a world full of unknowns. Fundamentalism is the ultimate form of certainty: it provides an answer to all situations and all questions. Everything is black and white: there is no grey, no doubt and no need to wonder.

In a sense, fundamentalism is a radical form of conservatism, the end result being a complete intolerance of any other point of view. There is no greater conflict than that experienced between 2 or more fundamentalist groups, as we are currently witnessing on a global scale. Fundamentalism is always considered an ultra-conservative position, and the logical consequence is that, in the case of conflict, only moderates can broker a peace, which is rather ironic for the parties involved. As far as the fundamentalists are concerned, peace can only come with the annihilation of the other, which translates to conflict without end.

Footnote: In reference to the third last paragraph, there is an example, albeit a fictional one, in my novel, ELVENE. For anyone who has read the book, it's obvious that the character, Elvene, is liberal, and her immediate superior, Roger, is conservative. Yet both display qualities of loyalty and integrity, and both will buck the system if they feel morally compromised. I have witnessed this in real life.

Is mathematics evidence of a transcendental realm?

This is a title sure to raise the hackles of a number of philosophers, assuming they would read it.

I am currently reading a book called Thinking about Godel and Turing by Gregory J. Chaitin. This book, I must admit, is slightly over my head, so I walk on tippy toes holding my head back in order to keep my nose above water. I read a lot of books by people who are much cleverer than me, but then I guess I am the audience they are writing for. Richard Feynman was once called the smartest person in the world, or some such honorific, by OMNI magazine (the first issue if I recall correctly), which suitably embarrassed him, but he was one of the great physicists of his generation, if not the greatest, and yet also one of the greatest teachers. I have read no one who writes so well for people with lesser abilities than himself. I can think of other writers: Roger Penrose comes to mind, who can write for people less clever than himself; Paul Davies is another, and one would also have to include Stephen Hawking. These are to be contrasted with other academic writers I have read, who do their best to show how much cleverer they are than their readers, but risk misleading them by talking authoratively on topics outside their field. I am not an academic and I have no expertise, so, if I be so charged, I stand guilty. I am the first to admit that I am not as clever as I may appear. I am intellectually curious and I can write well, that is all. And yes, I am provocative – no apologies there.

Gregory Chaitin’s book is really a collection of essays, often transcripts of lectures or public addresses he’s given over the past 30 years. As such, he is also writing for people less clever than himself, and I think he does a commendable job. He also generously acknowledges his heroes (especially Leibniz). I only hope I don’t misinterpret him in my attempt to glean something philosophically meaningful from his text. I have to say that I found his ideas, and his exposition of them, exciting to read.

The 20th Century will be remembered for a number of things: Peter Watson performs an excellent job documenting many of its achievements in art and science in a narrative form with his magnum opus, A Terrible Beauty. (Another writer who knows how to illuminate without his ego intruding in the process.) I’ve had disagreements with Watson, philosophically, and we’ve had brief correspondence, but I think this book is an achievement of almost heroic proportions, not least because he can write with equal erudition on art and science.

For my mind, the 2 outstanding events of the 20th Century, which will be remembered throughout human history, are powered flight leading to exploration beyond our planet and the invention of the computer with all its consequences. But Chaitin rightly points out that there were 2 revolutions that occurred early last century, at about the same time that humankind took flight in a literal sense, that will also be remembered as historical milestones. I’m talking about Einstein’s theories of relativity and the development of quantum mechanics. In addition to these revolutions, Chaitin adds a third: Kurt Godel’s proof of his ‘Incompleteness Theorem’ in mathematics (1931) and Alan Turing’s related theorem concerning the so-called ‘halting problem’ for computers (1936). This particular revolution requires some elaboration.

Firstly, when Turing developed his thesis, computers didn’t exist, and, in fact, Turing’s paper is better remembered for containing the purely conceptual idea of the ‘Universal Turing Machine’, which is what all modern computers are, including the one I’m now writing on. So this revolution is directly related to the more concrete revolution I referred to in the opening of my last paragraph. But Chaitin’s point, that this revolution, first enumerated by Godel, being of equal significance as relativity theory and quantum mechanics, should not be lost.

But before I continue on this theme, I would like to say something about Turing, one of my heroes. Turing is probably best known for his pivotal role in breaking the ‘enigma’ code during WWII, but I would also hope he be remembered for his tragic death, so that ignorance and prejudice would not claim such a brilliant mind in the future. Turing was one of the greatest minds of the 20th Century, arguably, second only to Einstein. Turing may not have physically invented the computer (a moot point), and it certainly would have evolved without him, in the same way that Einstein didn’t invent the Lorentz transformations that lie at the heart of relativity, and certainly relativity’s consequences would have also been discovered without him. But both men thought outside the square in a way that goes beyond cliche, and both men were ahead of their time by at least a generation, and both men were undisputed geniuses.

Turing’s death, however, is comparable to the deaths of two other great minds of science and philosophy: Socrates and Lavoisier. Socrates (arguably the father of Western philosophy) was forced to suicide for political reasons, and Lavoisier (the ‘father of chemistry’) was guillotined in the aftermath of the French Revolution. All these deaths were the result of political and social forces present at the time, and all were regretted almost immediately afterwards. One might say that they were all victims of ignorance, and that includes Turing. Turing suicided by eating an apple injected with cyanide after he was legally prosecuted for being homosexual (he was blackmailed first) and forced to take hormonal treatment that had him growing breasts. This should be kept in mind when we have conservatives in both religion and politics who think the legal attitude towards homosexuality has been ‘socially disastrous’ (Cardinal George Pell quoted by a reviewer of his latest book, God and Caesar). Unfortunately and tragically, Turing was born ahead of his time in more ways than one.

A philosophical detour onto another path, we’re now back to the topic at hand. Not quite 10 years ago, when I was studying philosophy in an undergraduate course, I had to write an essay on Immanuel Kant with the subject: What is transcendental idealism? In preparation I read large parts of his seminal work, The Critique of Pure Reason, about as dense a text as one could find. Apparently Kant’s lectures were very popular and much more accessible than his writings. Unfortunately, he lived before the age of electronics, otherwise we might have transcripts of his lectures rather than his essays. The Critique of Pure Reason is the only book I’ve read that contains at least one sentence over a page long. You may be wondering what this has to do with Godel and Turing: well, Kant wrote a great deal about epistemology which is effectively the subject of Chaitin’s book. Of more relevance to this discussion, is my conclusion in that essay: if there is a ‘transcendental idealism’, it must be the world of mathematics.

I won’t reiterate my arguments here (perhaps a future posting), but it suggests a starting point for the question that heads this essay. Kant understood that our knowledge, our perception and our interpretation of the world had 2 components: an empirical component based on experience and an ‘a priori’ component based on reasoning and imagination. It is this latter component that leads to the concept of ‘transcendental idealism’ and has more than a passing resemblance to Plato’s ‘forms’. I don’t wish to get too esoteric about this, so I will present the same idea in a more prosaic context. I’ve said elsewhere that the success of science is a direct consequence of a continuing dialectic between theory and experiment, or theory and observation. This is exactly the same thing that I believe Kant was talking about, keeping in mind that he lived in the time following Newton when it was believed we all existed in a clockwork universe.

My own particular take on this is that mathematics is the principal medium that allows this dialectic to occur. Without mathematics our comprehension of the universe (the entire natural world in fact) would be limited in the extreme. This realisation, in Western philosophy at least, began with Pythagoras, was given impetus by Galileo, Kepler, Newton and Leibniz (along with many others), but only found it’s true significance in the 20th century, with Einstein (following Maxwell), along with Bohr, Schrodinger, Heisenberg and all those who have contributed since. Chaitin’s book, as I’ve already said, is effectively about epistemology and, in particular, the epistemology of science and mathematics. In fact, Chaitin’s entire thesis is that they are more closely related than we tend to think, but I’m getting ahead of myself.

Firstly, I need to share with you Chaitin’s excitement, and sense of historical significance, that he finds in Godel’s Incompleteness Theorem of 1931. Before this theorem, and even after it, mathematicians have believed that mathematics is inherently axiomatic (going back to Euclid, another Greek), which is its strength and its claim to objective truth. But even before Godel, as Chaitin points out, Georg Cantor and Bertrand Russell had already shown that mathematical certainty could be a chimera. Cantor is best known for his ‘diagonal method’ of showing why there are more ‘real numbers’ than ‘rationals’ (Penrose gives a good exposition in The Emperor’s New Mind). Turing, by the way, employed Cantor’s diagonal method in the most critical step of his ‘halting problem’ proof, so it has far-reaching consequences.

Over a hundred years ago, Cantor postulated the idea of infinite sets (transfinite numbers), which was such a radical and controversial idea for its time, that, according to Chaitin, Cantor suffered a breakdown as a result of the criticism and was never given a position in a first rate institution. Being ahead of your time can sometimes be a career stopper, no matter what your achievements. These days, Cantor is regularly referred to in mathematical texts on number theory.

Godel gave a proof, that took the whole mathematical world by surprise, that the so-called axiomatic method was flawed, or, at the very least, could not be unconditionally relied upon. Effectively, Godel’s proof and Turing’s, which is even more demonstrative, says that, no matter what formal mathematical system you have, based on a set of known axioms, there is always the possibility of mathematical ‘truths’ that cannot be derived from these axioms. So the method of determining mathematics that we have all relied upon since the concept of numbers was derived, is not so deterministic after all. Now, as Chaitin points out, despite the absolute shock this conclusion created, people have largely carried on as if it never happened. Many people see it as an esoteric anomaly that has no bearing on real mathematical problems, but, as Chaitin points out, that is not the case.

The best example would be Reimann’s hypothesis and the Zeta function. There have been some excellent books written on this subject (Prime Obsession by John Derbyshire, The Music of the Primes by Marcus du Sautoy and Stalking the Reimann Hypothesis by Dan Rockmore are three I enjoyed reading). I won’t elaborate, except to say that it is a convoluted and intriguing journey into the mathematical realm, and it is to do with the distribution of primes, but it’s the perfect example. It’s the perfect example because computer programmes (Turing machines) have calculated it to be correct to astronomical magnitudes, but there is still no proof. It demonstrates perfectly the so-called ‘halting problem’ because if the programme halts the hypothesis is false, and if the hypothesis is correct, then the programme will never stop (unless instructed to of course). But more than this, most mathematicians accept it as true, despite the lack of a ‘formal’ proof, and it is now used as an ‘axiom’ for other mathematical proofs, albeit conditionally. And this is what Godel said, that there can be an axiom, or axioms, outside the formal system you are using that can be the basis of newly discovered mathematical ‘truths’. Another, more readily comprehended example, also given in Chaitin’s book, is Goldbach’s conjecture: all even numbers above 2 are the sum of 2 primes. (You can check this for yourself with the first 10 even numbers, remembering that 1 is not considered a prime.) A relatively simple computer programme can be written to check this, but, again, it only stops if the conjecture is wrong. (This has been checked to 10 raised to the power of 14, 1 with 14 zeros after it).

Now, strictly speaking, what I have just described isn’t the halting problem, but a consequence of it. What Turing said (proved, in fact) is that there is no way of knowing if a programme will halt or not for a particular theorem. If we knew that, then, obviously, we would be able to say in advance if these conjectures were true or false.

Chaitin makes the comparison between this discontinuity of axioms and physics. He gives the example of Maxwell’s equations having no basis in Newton’s equations, yet forming an ‘axiom’ for Einstein’s equations of relativity. Likewise, quantum mechanics has no basis in either Newtonian mechanics or Einstein’s relativity, but has become a new ‘axiom’ for future theories (Thomas Kuhn calls them paradigms). Chaitin argues, that not only does this demonstrate that mathematics and physics are more closely related than we consider, but that there is good reason to suggest that mathematics should be done more like physics, where new axioms may not have to rely on previous ones. Chaitin calls this proposed methodology ‘quasi-empiricism’, a term coined by Imre Lakatos.

Chaitin goes even further on this subject, and claims that the similarity between physics and mathematics lies at their base, which is randomness. In fact, Chaitin claims that this is his major contribution to mathematics, arising from his invention of the term ‘Ω’ (Omega), though he calls it a discovery, to designate the probability of a programme ‘halting’, otherwise known as the ‘halting probability’. I won’t elaborate too much on this, so, if you want to know more, you will need to read his book. For Chaitin, ‘Ω’ is the logical extension of Godel’s and Turing’s landmark theories, and proof of mathematics’ inherent irreducibility (his term). The significance of this ‘discovery’, according to Chaitin, is that it’s proof that there is no mathematical ‘theory of everything’ (TOE) – no all encompassing meta-mathematical theory. But he sees this as liberating. To quote: ‘Ω shows that one cannot do mathematics mechanically and that intuition and creativity are essential.’

Another person who discusses these issues (raised by Godel and Turing) in devoted detail, is Roger Penrose (The Emperor’s New Mind), but in the context of Platonism. Penrose is a self-confessed ‘Platonist’, meaning he believes that mathematics exists in an independent realm to the human mind. This is a contentious viewpoint (I discuss it from a different perspective in my Sep.07 posting: Is mathematics invented or discovered?). Chaitin says very little on this question (see below), but quotes Godel, who was a ‘Platonist’, and Einstein, who was not. Paul Davies, who writes an excellent foreword to Chaitin’s book, makes the case, in a couple of books, (The Mind of God and The Goldilocks Enigma) that mathematics ‘shadows’ the natural world, but doesn’t call himself a Platonist. Stephen Hawking, who famously worked with Penrose on singularities and black holes, doesn't share his colleague's philosophical viewpoint at all, and calls himself an 'unashamed reductionist' and a 'positivist'. Most philosophers dismiss the notion of Plato’s forms, but mathematics is an area where it persists. I dislike the term but I agree with the philosophical premise: mathematics has an independent existence to human thought. Plato’s forms originally applied to everything, not just mathematics, so somewhere there was a perfect world (like heaven) and Earth was merely a facsimile of it. This is similar to some people’s interpretation of Taoism, but it’s not mine. But this brings me to the subject alluded to in the title of this posting: mathematics is arguably the only evidence we have of a transcendental, or metaphysical, realm.

Interestingly, people on both sides of this argument present Godel’s famous Incompleteness Theorem as supporting their philosophical point of view. Chaitin himself says, ‘[Godel’s theorem] exploded the normal Platonic view of what math is all about’, without elaborating on what he means by ‘normal Platonic view’ in this context. Russell, according to one account I read, was derisively disappointed when he met Godel and discovered he was unashamedly a Platonist. Many people I’ve met, philosophers in particular, believe that Russell and Wittgenstein settled this question for good, but I’m not sure that many physicists would agree. I once had a conversation with a philosophy lecturer, whom I greatly respected, who asked me if I thought that mathematics done by some hypothetical inhabitants in the constellation Andromeda would be the same as mathematics done by us on Earth. I answered: Of course; to which he responded: But you’re assuming that Andromedans would use base 10 arithmetic. I said that this is like saying that a tiger in China is not a tiger because it is called something else in Chinese. I used this analogy because he had used it himself to make an epistemological point earlier in the discussion. Unfortunately, he just assumed that I didn’t know what I was talking about, and I never got the opportunity to enlighten him further.

Using the same hypothetical, Chaitin quotes Stephen Wolfram (A New Kind of Science), whom I haven’t read, who argues, and gives examples, of mathematics that might be different to what we are familiar with. But I would suggest, that unless the laws of the universe are significantly different on another planet, then the mathematics any inhabitants developed would be the same as ours. Because, as Davies and Penrose point out, mathematics and the natural world are married in a way that is inescapable to anyone who explores them deeply enough. Even on our own planet, different cultures developed mathematical ideas independently but were ultimately convergent. So whilst I agree that mathematics may be a boundless realm, its marriage to the natural world suggests inevitable avenues of investigation and discovery.

Penrose, in particular, argues a very strong case for Platonism. In The Emperor’s New Mind, he spends an entire chapter on the Mandelbrot set (with a detour to Cantor, Euler and Gauss) and presents it as an exemplar of Platonist mathematics. The entire Mandelbrot set exists only in an infinite realm so that no one will ever see it in its entirety, yet it is generated by a simple algorithm or formula. (This leads to a discussion on complexity, which is also a key theme in Chaitin’s book, but I will return to complexity in a moment.) For Penrose, the Mandelbrot set is evidence that something can only exist in a mathematical realm that we only get a glimpse of – this is a very profound idea. (To get a glimpse, check the following link: Mandelbrot Set ) Is this different to any other work of art? Well, Penrose makes the same analogy, but the fundamental difference is that mathematics doesn’t manifest itself as a ‘unique’ or ‘one-off’ creation, as works of art do. (Someone else could have discovered Reimann’s geometry or Schrodinger’s equations, but no one else could have created Beethoven’s symphonies or Bach’s Brandenburg concertos). And it is difficult to escape the connection between mathematics and the natural world, the Mandelbrot set notwithstanding.

In any discussion on mathematics, including Chaitin's, one cannot escape infinity – it infiltrates all attempts to capture it and tie it down. It’s also what makes it elusive (take the Reimann hypothesis) and boundless in every sense (look at Π and e). It’s what takes it outside human experience and makes it ‘magical’ (like the calculus). In Euler’s famous equation, infinities abound, yet it’s a simple relationship between e, Π, i, 1 and 0 (where i is the square route of minus 1). Feynman called it ‘the most remarkable formula in math’ when he thought he had ‘discovered’ it a month before his 15th birthday. ( See link: Euler's Equation ) To appreciate the complexity that lies behind this simple equation, and the way it ties together so many branches of mathematics, you need to go to Euler's Formula.

For Penrose, it’s almost religious:

‘The notion of mathematical truth goes beyond the whole concept of formalism [this is Godel’s theorem in a nutshell]. There is something absolute and “God-given” about mathematical truth. This is what mathematical Platonism… is. Any particular formal system has a provisional and “man-made” quality about it… Real mathematical truth goes beyond mere man-made constructions.’

Strong words indeed. This has been a lengthy treatise, but not one that is especially decisive or well-argued. I have hardly touched the subject of complexity, which is a key component of Chaitin’s thesis, indeed his life’s work. One of the points he makes is that mathematical complexity may provide a key to understanding biological evolution – after all, DNA is the world’s most extraordinary piece of software. Complexity, as described by Chaitin, is effectively the difference in the length of an algorithm (in bits) to the length of the results it produces (he defines it in a logarithmic expression). The Mandelbrot set is a good example, because a very short algorithm can produce an extraordinarily detailed and complex picture of infinite proportions via a computer. DNA is, in effect, a very small molecular structure that can produce extremely complex and diverse organic entities that have life (ad infinitum it would appear); so I would argue that it’s more than just an analogy. (Chaitin makes the point that, with its 4 bases, human DNA contains 6 trillion bits of information; 6 followed by 9 zeros.)

Perhaps there is another level of complexity behind DNA in the same way that quantum mechanics exists behind classical physics. No one can anticipate what we will find. When Darwin hypothesised about evolution, no one would have predicted genes, let alone DNA. And when Newton proposed gravity no one would have predicted relativity theory, let alone quantum mechanics. We think, just like they did, that we’ve discovered everything there is to discover, but we haven’t.

This essay only scratches the surface of Chaitin’s multi-layered thesis, so, if it stimulates you, read his book. My favourite chapter is titled On the intelligibility of the universe, where he liberally quotes great minds like: Einstein, Feynman and Born; all ruminating on the theoretical component of the dialectic of science that I referred to earlier.

Does Chaitin believe in a mathematical transcendental realm? Well, he certainly believes in a metaphysical approach, subscribing to a “digital philosophy” (his quotation marks), along with Edward Fredkin and Stephen Wolfram. He calls it a ‘neo-Pythagorean vision of the world’, where ‘God is not a mathematician’, but ‘a computer programmer.’ But he adds the following caveat: this is a new viewpoint, and it will be interesting to see how far it takes us.

Personally, whilst I don’t have the intellectual abilities of these people, and therefore I can’t challenge their premise, I believe there is more to the universe than algorithms. For a start, I don't believe the human mind runs on algorithms, despite what some cognitive psychologists might think (on that point I agree with John Searle and Roger Penrose).

So Chaitin argues that most real numbers are uncomputable and this makes mathematics infinitely complex (if a number can't be calculated there is no formula or algorithm for it, which makes it infinitely complex by Chaitin's own mathematical definition of complexity, though he credits Leibniz with the original idea). Also, I accept his argument that there is no overall meta-mathematical theorem - no TOE for mathematics - because that is the essence of Godel's and Turing's proofs. I agree with his statement that intuition and creativity are essential, because history has demonstrated that beyond dispute. I would not be surprised if, as he speculates, mathematics gives us an unexpected insight into biology and evolution, though, obviously, I've no idea how it might happen. And, as I have said elsewhere, I believe it is our knowledge of mathematics that will determine the limits of our knowledge of the physical universe and the natural world. In my opinion, this was Pythagoras's great paradigmatic insight and his legacy to philosophy and science.

Mathematics can take us into worlds that we don’t normally perceive: higher dimensions, complex planes, infinite series and infinitesimal intervals – but in the world we live in, it continues to uncover riches and mysteries beyond our imagination.

You may also want to read my post on The Laws of Nature (Mar.08).

Is evolution fact? Is creationism myth?

Most people reading this already have preconceived answers, but they would be pushed to defend them beyond: 150 years of scientific investigation can’t be wrong, or the Bible is the ‘Word of God’. At the heart of this, however, lies another question altogether: what constitutes truth? In fact, it was tempting to title this essay, What is truth? But I wished the topic to be more specific. Truth is often subjective, and objective truth only becomes apparent over time. Truth usually requires longevity in our cognitive world to gain validity. But truth can also be found in myth in the form of allegory. To give a biblical example, the story of the good Samaritan is a parable, but many would argue it contains a profound truth about human nature. Is the Genesis story also allegorical? I will return to this point later.

To bring the discussion back to the topic at hand, one needs to ask another question: are there any scientific facts? Many philosophers, perhaps most, would argue that the answer is no. They would say that all scientific ‘facts’ or ‘truths’ are contingent, meaning tomorrow (any tomorrow) we may find evidence to the contrary, no matter what we’ve observed in the past. For example, we all assume the sun will rise tomorrow, but it may not, and certainly one day it will not. This is an extreme example, but let’s look at the same example in another way. Does the earth go around the sun or does the sun go around the earth? One of these is true and the other false, which means, that as far as I’m concerned, the one that is true is a ‘fact’.

Now, 400 years ago, this very question was a huge issue: cost Galileo his job, almost his life. 400 years is not that long ago, if one considers that Western philosophy and science started with the Ancient Greeks about 2500 years ago, and astronomy had been practiced by a number of cultures well before then. But even 400 years ago, the answer to one of these questions was still a fact. Either the earth went around the sun, or it didn’t; there was nothing contingent about it. It didn’t go around the sun today and do something different tomorrow, or next year, or next millennium. It’s just that, at the time, it was still a disputable fact. It was a fact awaiting proof, if you like, which eventually came from Johannes Kepler using Tycho Brahe’s observations. Now, in case you think the Church was just being bloody-minded (which they were), the Vatican’s astronomer had a very good argument to counter Galileo. He said that if the earth went round the sun as Galileo claimed then why didn’t we observe a parallax shift against the distant stars over a one year period? The reason was that the stars were much further away than anyone could possibly imagine, and so the necessary parallax adjustment wasn't observable with the instruments of the day. It’s a bit like the argument Columbus had convincing people that if he sailed far enough west he would eventually encounter Asia. The boffins of their time knew his calculations were incorrect and he would only be half way there, which is why they were against his mission, not because they thought the earth was flat.

The reason I’ve spent so much time on this one topic is because it’s a similar situation of religion versus science, though, arguably, evolutionary theory is in a stronger position today than Galileo’s position was 400 years ago, because the arguments against Galileo were not as ignorant as people think, and Galileo was up against a 1400 year old theory (Ptolemy's). So are there any scientific truths? The only truth in science is that whatever we’ve discovered, there always remains some mystery still to be solved. In other words, science is an endeavour of endless depth and mystery, so there appears to be no ultimate truth as some would like to find it.

The best book I’ve read on science is Roger Penrose’s The Emperor’s New Mind for a number of reasons, not least because it’s pitched at a level I can readily comprehend. Penrose provides the best exposition on entropy I’ve read, including its cosmological significance, as well as a philosophy of mathematics very similar to mine (see my post: Is mathematics invented or discovered?) But Penrose also provides an entire chapter on what constitutes a successful scientific theory. Penrose provides 3 categories for theories: TENTATIVE, USEFUL, and SUPERB (the capitalisation is his) which he then discusses in depth. I won’t repeat his discussion here, but it illustrates how theories evolve, with TENTATIVE and USEFUL being more contingent, and SUPERB being supremely successful over time. Interestingly, he includes Newton’s dynamics as a SUPERB theory even though it was overtaken by Einstein’s relativity theory. This is because many aspects of Newton’s theory, including the inverse square law for gravity, still apply under Einstein’s theory. Even if Einstein’s theory is overtaken, one would expect that many aspects, like the observed relativistic effects on time, would remain in any new theory. In effect, he is saying that a SUPERB theory, though it must satisfy the highest standards, does not explain everything. Outside of physics, Penrose argues that only Darwin’s and Wallace’s theory of natural selection comes closest to his idea of a SUPERB theory. Note that the theory of natural selection does not encompass evolutionary theory totally – there are other biological components to the theory that neither Darwin nor Wallace could have known about.

Science is a dynamic enterprise – we have never known the answers to all the mysteries that it uncovers, but what we do know is that future generations unlock secrets we can only speculate about. This is what has made science the most successful enterprise undertaken by humankind: a continous dialectic between existing knowledge and future discoveries. And this dialectic is epitomised in the case of Darwin’s acclaimed theory of evolution. When he proposed the theory he had no idea how traits were passed on from one generation to another, let alone how they could change or ‘mutate’. Everything we have discovered since has only confirmed the theory. We have discovered not only the mechanism of passing on traits (genes) but the message itself (DNA). DNA has allowed us to place every organism on earth in its correct evolutionary relationship to every other organism. DNA is the most compelling evidence yet that all life forms on earth have a common ancestor. (We share over 98% of our DNA with chimpanzees, and 63% with mice.) It’s not just simply that everything we have found ‘fits’ the theory, but if the theory was false, then the evidence would have told us that as well. In other words, the evidence is far from neutral. And, going back to the analogy with Galileo’s defence of Copernicus’s theory, it’s either true or it’s false: you can’t say evolution works some of the time or only works with some species and not others. It’s either true or false – it’s either a fact or it’s not – just like, in Galileo’s time, the earth went round the sun or it didn’t.

Richard Feynman notably won a Nobel Prize for his groundbreaking work on QED (quantum electrodynamics), and worked at Los Alamos on the Manhattan Project (the development of the atomic bomb in WWII). Most famously, he demonstrated on television how the Challenger shuttle failed: using a clamp, a pair of pliers and a pitcher of iced water he showed how the shuttle's O-rings lost elasticity under freezing conditions. He was not only one of the truly great physicists of his generation, but also one of the great teachers of science. In a book of his lectures on relativity theory, Six Not-So-Easy Pieces, he describes how the amino acid, L-alanine, is only found in life in a left-handed form, while it exists equally in right-handed and left-handed forms outside of life (the right-handed version is called D-alanine). Using a combination of irrefutable logic and brilliantly realised imagery, he explains how this could only come about if all existing life forms have a common origin. Paul Davies makes the same point, less eloquently perhaps, but no less persuasively, in his book, The Origin of Life.

This does not mean we understand everything we need to know about evolution. Quite the contrary: the biggest conundrum still to be resolved is how did the first DNA come about (refer Davies). Any ideas on this are very speculative – still very much in the TENTATIVE mode to use Penrose’s nomenclature. And this leads us to Intelligent Design (ID). When it comes to an exercise in complexity, DNA takes the cake, and according to the ID advocates, complexity stops evolution in its tracks. (For a brief discussion on complexity, including its role in DNA, see my later post: Is mathematics evidence of a transcendental realm?) Using the ID argument, DNA could have only been ‘designed’ by some ‘intelligent’ entity, a Creator or God, and evolution did the rest, or, evolution never happened. If we take the second argument first: evolution never happened; then genes, DNA and natural selection are irrelevant to nature, except for sexual reproduction. Speciation never occurred, which means everything was created all at once, or God came along every now and then, as was his whim, to create some new species. He manipulated the DNA so as to create new species whenever he wanted. Not only does this not ring true, it’s not accounted for in the Bible either (I'm leaving the biblical interpretation to last). Taking the first argument that God created DNA and let evolution do the rest, one is effectively saying that science can no longer answer any further questions on this: we have come to the end of science; only God can explain the origin of life.

Personally, I have no problem with admitting that we don’t know everything, but I would like to point out that history demonstrates continuously that only future generations can tell us how ignorant the current generation is. So I expect, that at some point in the future, the origin of DNA will be explained – in fact, I’m quite confident, even though I’ve no idea how.

The biblical interpretation, of course, does away with all of this nonsense: there is nothing to explain. And this brings me to Karl Popper, who instigated the proviso that a scientific theory needed to be able to generate falsifiable hypotheses. He did this to eliminate pseudo-scientific theories, which can explain everything no matter what we find, and his particular target at the time was Freud. In other words, a scientific theory needs to be put at risk. If you can’t prove it wrong then it’s purely speculative. Creationism is a pseudo-science in that it’s always right no matter what the evidence says. If we find something in nature then that’s the way God created it – all questions answered.

Now some people argue that evolution, on the basis of this criterion, is also a pseudo-science, because no one can observe it in progress. Well, natural selection is observed all the time, but no one can observe evolution en masse for even a fraction of the history of the planet. However, evolution can generate a number of hypotheses that can be proved false. The most obvious would be to find fossils of the same species in completely different geological time zones, or to find fossils out of sequence in the same line. With advances in DNA the most critical test is to find genetic relationships between species that contradict the fossil record. So the claim that evolution can’t be falsified is a nonsense.

The biblical interpretation is that all species were created everywhere in the world all at once. All the millions of species in the Amazon, all the weird and wonderful species that Darwin found on Galapagos, all the marsupials in Australia, all the dinosaurs, trilobites and millions of other species that have disappeared, but, strangely, only one race of humankind. All of these, of course, were also picked up in Noah’s ark and redistributed afterwards. At the same time, God created all the galaxies and all the light rays and all the quasars and all the neutrinos traveling through space – all within a 6 day period. The other interpretation is that all the scientific discoveries of the last century are completely fraudulent and none of these things exist, or not in the way we interpret them. Creationism not only does away with evolution but most of modern scientific knowledge, and certainly all of cosmology. I've argued with a number of creationists who claim they are not anti-science, only anti-evolution, but they seem unaware that their very claims of creationism make it impossible for them to be one without the other.

As recently witnessed in the 'Climate Change' debate, someone with a little knowledge can easily convince someone with no knowledge that they are right, even though a third person with a lot more knowledge can demonstrate that they are both wrong. I find it's the same with the Creationism/Evolution debate, even though it's really a debate about religion versus science, or, as I like to point out, myth versus science (see below). One of the favourite arguments of anti-evolutionists, is that evolution defies the second law of thermodynamics, also known as entropy. Both Roger Penrose (The Emperor's New Mind) and Paul Davies (The Origin of Life) provide excellent explanations of why this is a fallacy. But, without going into these arguments, I would like to give an everyday, millions of times repeatable, example of why the argument is false. Basically, the antagonists claim that entropy doesn't allow simple entities to develop into complex ones. A good example of entropy is breaking an egg and making an omelette (refer Penrose). It's impossible to take the omelette and get the egg back as it was before you started. In fact, Penrose points out that entropy is the only law in physics that really prohibits time from running backwards. Both quantum mechanics and relativity allow time reversal, mathematically speaking. Entropy says that everything goes from order to disorder, but there's a catch, which is energy. If you add nett energy you can go from disorder to order as we witness all the time. Now, the everyday example is every living organism on the planet, including each and every one of us. We all started out as simple cellular organisms (zygotes in the case of humans) and develop into extremely complex multi-cellular organisms without breaking the second law of thermodynamics. And it happens everyday, as it has done for millions of years, with swarms upon swarms of living entities all over the planet.

Ken Ham is an Australian, the same age as me as it turns out, who started www.answersingenesis.com and built the ‘Creation Museum’ in Kentucky. His entire premise is that humans are fallible but God is not, therefore the ‘Word of God’, the Bible, is the only criterion for validating a scientific theory. On his web site, I once submitted the following question: Since the time of Pythagoras (500 BC) to the present day, tell me one scientific discovery that arose from studying the scriptures? I never got a response, even though it was submitted over 2 years ago. The Bible tells us nothing about science: nothing about DNA, about the constant speed of light, about Euler’s famous equation or Einstein’s (E=mc2) or his theory of gravity; so why would it tell us anything about evolution or natural selection or genetics. The Bible was never written as a scientific text, even though people like Pythagoras, Euclid and Archimedes had already lived before the New Testament was written. So even the scientific knowledge of the day was not included.

Personally, I see the Bible as a book full of stories. A story, any story, can contain profound truths, but that doesn't mean the story itself is true, and that's how I see the Bible.

The Bible is full of mythical events: Jonah eaten by a whale, Moses parting the Red Sea, Lot's wife turned into a pillar of salt and Jesus walking on water; are amongst the best known, and there are myriad others. But the Genesis story is arguably the most mythical story of them all. In Genesis you have a man being made out of dirt, a woman made from a man’s rib, a serpent who speaks and a piece of fruit, that, when ingested, makes people genetically inherently evil. Not to mention that, afterwards, God punishes the snake by making it forever legless. It’s a story full of mythical elements, so what does it all mean? Myths can be interpreted a number of ways, but my interpretation of the Genesis myth is that it contains a fundamental truth: that no one can go through life without having to deal with evil at some level. Evil is a part of our human nature but that doesn’t mean I believe we are born evil. Evil arises from a set of conditions, usually social, that turns human against human. Any one of us can become evil, given the circumstances, but it’s not because of our biblical origins, it’s because of our evolutionary heritage (I discuss this in detail in my posting on Evil).

Many people interpret the Genesis story as ‘original sin’, which is a fundamental concept in Christianity. Because we all have original sin, only Jesus can save us from eternal damnation. This requires an extension of the myth to include Satan and a place called hell in the afterlife. I have a serious problem with the concept of ‘original sin’, not only because of all these mythical extensions, but because it’s a most pessimistic view of humanity, and I strongly disagree with the idea of teaching children that they are born evil. But as a means of psychological control over large sections of a population, it’s brilliant, and the Church exploited it for centuries.

Coming back to the discussion at hand, I don’t believe you can credibly replace a valid scientific theory with a myth. I’ve said elsewhere that science and religion can’t answer each other’s questions (I discuss this in my posting: Does the Universe have a Purpose?). Many people, on both sides of the argument, disagree with this. They claim that they absolutely overlap, but I counter that they only overlap if you insist on it. Science is the study of natural phenomena in all its manifestations. Religion, on the other hand, is an internal experience, and this creates a fundamental epistemological divide that people seem to overlook in this debate.

One of the fundamental criterion for the success of a scientific experiment is that it has to be replicable – it can’t be a one off. This means that anyone doing the same experiment under the same conditions should get the same result. Without this predictability science would be useless, both as an enterprise for discovery and as a fount for new technology. Having said that, it’s the unpredictable events, and the inexplicable ones, that lead to new theories, often dramatically, as expounded upon by Thomas Kuhn in his treatise on 'scientific revolutions'.

In the case of religion, however, any experience is unique to the person who has it. And this includes God, because God is an experience. The only manifestation of God that we know of is an internal one, albeit, it may feel like an external connection. And that experience is unique to that person. This means there are no religious truths, except at a very individual and intimate level. This creates a contradiction between personal religious experience and institutionalised religions that insist that everyone’s religious experiences must be the same, or of the same type (see my post on Religion). It’s when we attempt to rationalise these experiences, usually in the context of our cultural background, that we claim they are an ultimate truth. I contend that there is only one objective religious truth: we don’t know. Anything else is a dishonesty to the self, ‘mauvaise foi’, to quote Sartre.

People have a habit of confounding what they believe with what they know. When I studied philosophy, I was told that there are things that you know and things that you believe, and what you believe is contingent on what you know, but not the converse. (The Dalai Lama makes a similar point in his book on science and religion, The Universe in a Single Atom) When it comes to religion, I don’t expect anyone else to believe what I believe, because my experience is unique, and so is everyone else’s.

Footnote: The Dalai Lama was a good friend of, and heavily influenced by, the renowned physicist, David Bohm, who also worked on the Manhattan Project. David Bohm lived in exile in England following his refusal to testify in the McCarthy senate hearings. The Dalai Lama said it was something they had in common, ironically, by polar opposite political forces: one communist and one anti-communist. Late in his life, Bohm wrote a philosophical book called Wholeness and the Implicate Order. In it, he speculates (amongst other things) that quantum mechanics may be the manifestation of our universe being a 3 dimensional projection of a higher spacial dimensional world.

Addendum: I argue continuously that ignorance is the greatest enemy of the 21st Century. A view also shared by the Dalai Lama apparently, who said: 'ignorance is one of the 3 poisons of the mind.' Stephen J. Gould once made the point that this particular debate is very parochially American. The rest of the Western world appears to be less confused about the roles of religion and science, especially in education, and, for the most part, moved on from this debate generations ago. There is nothing wrong in admitting ignorance - in fact, it is to be commended - but passing on ignorance under the guise of education is inexcusable, and a serious backward step. At a very early stage in my education (adolescence), I realised that real knowledge comes from knowing how much one doesn't know.