Paul P. Mealing

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Sunday, 15 March 2009

The problems with fundamentalism

It’s a sad indictment that I should feel it necessary to write this post, but the blogosphere, at least considerable sections of it, are full of it. Notice the use of the plural, though there is one specific problem that compounds all the others – it’s called intolerance. Not that long ago, in the land I inhabit, we had our own brush with intolerance that had ramifications right across the nation and across the political spectrum – she was called Pauline Hanson.

I’ve always had a tendency to analyse, even when the issues are emotive and personal. What I found interesting about the Pauline Hanson phenomenon is that she created intolerance in people like myself who are normally tolerant. Pauline Hanson taught me that I’m intolerant of intolerance. Pauline, a fish and chip shop proprietor, who became a parliamentarian, created a political storm that pretty well divided a country and even divided families. The link with fundamentalism is that fundamentalists, like Pauline Hanson, create intolerance on both sides.

This is why someone like Richard Dawkins, with whom I share many of his arguments, not only shows contempt for anyone with religious beliefs but contempt for anyone who is tolerant of people with religious beliefs (just read his introduction to the paperback edition of The God Delusion). So, whilst I support Dawkins in his fight against religious fundamentalism completely, I don’t support his fight against religion per se at all. I don’t agree with a black and white view of the world, that he tends to portray, which is divided between atheists and religious fundamentalists, and therefore one must take one side or the other. I wish to lay out my slate that there is a world that can include atheists and religious believers. My role models for this perspective are Karen Armstrong and the Dalai Lama.

I write a lot about science and mathematics on this blog, but almost every essay includes an aside to explain why the mysteries of the universe cannot be resolved by the invocation of God. It seems to me that many people don’t appreciate that a philosophical argument that uses science to support it, doesn’t necessarily turn it into a scientific argument. I believe that even Dawkins makes this error when he introduces the anthropic principle, in concert with the concept of the multiverse, as if it’s a scientific argument rather than a philosophical argument supported by both known and speculative science (The God Delusion). There is nothing wrong with Dawkins’ argument – it’s philosophical in the same way that Paul Davies produces an alternative philosophical argument in The Goldilocks Enigma, only, with Davies, one is more aware that it is philosophical. I make this distinction because many fundamentalists don’t seem to appreciate that a philosophical argument that includes scientific evidence or a mathematical proof is not of itself a scientific or mathematical proof. There are no philosophical proofs in my view (refer my Mar.08 post: What is philosophy?).

But I’m getting off the track before I’ve even started. If one reads a lot of science, like I do, then one sees a history of investigation at many levels where the solution of one mystery reveals other mysteries that we didn’t even know existed. I contend therefore, that it’s quite possible, even reasonable to assume, that we will never know all the mysteries of the natural universe, let alone resolve them. It is for this reason that any sceptic of science, which includes all religious fundamentalists that I’ve read or heard or argued with, can find a hole in any area of science, which they believe they can exploit.

It follows, according to their logic, that the answer to any mystery, still unresolved by science, can therefore be found in the Bible, as if the Bible has provided all the information we currently have on the natural world. Therefore the Genesis explanation, of man being made from dirt and woman from a man’s rib, overturns all the scientific evidence of biological evolution discovered in the last 2 centuries. ID and creationism are not about studying science, despite the camouflage rhetoric to the contrary, they are about proving that the Bible is true. For Christian fundamentalists, the Bible is the only source of truth in the earthly world. Despite all the discoveries of science, especially in the last 500 years, any conflict with biblical scripture, whether apparent or real, rules science invalid. It is on this battle-line that I firmly side with Dawkins.

Mathematics and physics are my private passion, and I’m currently reading about Paul Dirac’s discovery of an equation that didn’t just predict anti-matter but insisted upon its existence. In 1928, Dirac took the recently formed Schrodinger equations of quantum mechanics and Einstein’s equations of special relativity, and in resolving their apparent dichotomy, not only justified evidence already known yet unexplained (the magnetic moment of electrons), but predicted the electron’s anti-particle, the positron. This is an intellectual achievement that is monumental in its consequences, comparable to Einstein’s equation: E= mc2. There is nothing in the Bible to compare with this. Imagine if the Bible told us that God created anti-matter alongside matter. On the contrary, the Bible tells us about a global flood that is physically impossible, a woman turned into salt, a child born from a woman who never had sexual intercourse, and I think the sun stops at some point, which was a particular point of contention that the Catholic Church had with Galileo in 1633 (ref: Livio, see previous post).

So while Christian fundamentalists want equal time to teach ID or creationism, or whatever they want to call it, in a science class alongside evolution, someone should point out to them the discrepancies between biblical myths and scientific theories, as well as the criteria involved (refer my Nov.07 post, Is evolution fact? Is creationism myth?).

My point is that yes, there are lots of questions still unsolved in science, including questions inherent in evolutionary theory, but the successes of science far outweigh any explanation of the natural world found in any religious text, so there is no logic, and absolutely no justification, in replacing science with a biblical account in any area of the sciences at all.

I contend that there are questions science can’t answer. Philosophical questions on why humans look for meaning in their lives or the resolution of moral dilemmas. This latter issue leads to the argument, that I’ve heard from a number of religious fundamentalists, that without a belief in God one is a moral relativist. I find this a truly bizarre conclusion and it’s always presented as if it’s self-evident – there can be no alternative. You either believe in God and have morals or you don’t believe in God and you’re amoral. They should read Hugh Mackay’s book, Right & Wrong; how to decide for yourself, which is the best book on the subject I’ve read.

There are a number of ways of looking at morality. For a start, you can read a book that prescribes everything you do, from how to treat slaves to whether you should eat pork, and what you can do on what days of the week, and also throws in 10 solid statements, or rules, on how to get along with your fellow man. But there are other approaches, like a meta-philosophical approach, attempted by people like John Stuart Mill, and before him, some ancients like Plato and Aristotle, and even a Chinese bloke called Confucius. Then there’s Hugh Mackay’s approach where you look at every situation on its merits and decide for yourself. No, that’s not moral relativism. Moral relativism is where you accept whatever any culture decides for itself, which may include cultural practices like the mutilation of girls’ genitalia at puberty, or the public beating of someone for selling meat on the wrong day of the week, or a woman having to be sacrificed at her husband’s funeral. That’s moral relativism; atheism is rarely a factor at all.

Then there is your conscience: one of the most misunderstood but most manipulated characteristics of human nature. Religious fundamentalists may tell you, or imply, that your conscience is God whispering in your ear, but in reality, your conscience is conditioned by your culture and your upbringing. Freud called it the super-ego. Your conscience is what made you feel guilty about masturbating when you were an adolescent – not God whispering in your ear at all, though it can be made to feel that way.

Hugh Mackay explains the dangers of taking your morals from God, because once you believe that, you can justify any action, like flying a fully loaded aeroplane into an occupied building. That is not an isolated example – just look at the Crusades, the Inquisition, and any number of atrocities justified in the name of God. Mackay is not anti-religion by any means, and explains that religion is more about finding meaning in your life.

Dawkins, if I read him correctly, is contemptuous of people finding meaning through religion. But according to Dawkins, we are just ‘gene-replicating organisms’, therefore any intellectual ruminations concerning our raison d’etre must be a waste of time. No, he’s never said that, but it’s the only logical conclusion: we live for our genes; they don’t exist for our benefit. So, I do see a role for religion, which makes me a bit of a weirdo. But at least I can acknowledge that my religion is nothing special compared to anyone else’s. You see, I grew up in a culture where religion was considered something very personal, like your most intimate thoughts, so you never discussed it unless you were invited to. I also realised that if everyone followed that precept then people with different religious views could get along just fine. In fact, I contend that everyone’s religious point of view is unique to them, so why should I intrude or insist that mine is better?

But this in itself begs another question: why do I argue with fundamentalists? Because fundamentalists believe the exact opposite to this: that everyone should believe the same thing, which is exactly what they believe, and, what’s more, they have the text to prove it. But this text, when taken literally, conflicts with current scientific thinking, so now we have scientists in opposition to all religious belief. As I said or alluded to at the beginning: intolerance breeds intolerance to itself.

Monday, 2 March 2009

The Unreasonable Effectiveness of Mathematics


This is a quote from Physics Nobel Laureate Eugene Wigner, and it appears in the first sentence on the front fly leaf cover of Mario Livio’s book, Is God a Mathematician? 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).

I use Wigner’s quote as the title of this post, rather than the title of Livio’s book, because it’s the quote that he keeps returning to and attempting to address, rather than any real attempt to address the question on the cover of his book.

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 shouts 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: 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.)