Paul P. Mealing

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Showing posts with label Religion. Show all posts
Showing posts with label Religion. Show all posts

Sunday 19 March 2017

The importance of purpose

A short while ago, New Scientist (Issue: 28 January 2017) had on its cover the headline, The Meaning of Life. On reading the article, titled Why am I here? (by Teal Burrell, pp. 30-33) it was really about the importance to health in finding purpose in one’s life. I believe this is so essential that I despair when I see hope and opportunity deliberately curtailed as we do with our treatment of refugees. It’s criminal – I really believe that – because it’s so fundamental to both psychological and physical health. As someone who often struggled to find purpose, this is a subject close to my heart.

As the article points out, for many people, religion provides a ‘higher purpose’, which is really a separate topic, but not an unrelated one. The author also references Viktor Frankl’s famous book, Man’s Search for Meaning (very early in the piece), which I’ve sometimes argued is the only book I’ve read that should be compulsory reading. The book is based on Frankl’s experience as a holocaust survivor, but ultimately led to a philosophy and a psychological method (for want of a better term) that he practiced as a psychologist.

I’ve also read another book of his, The Unconscious God, where he argues that there are 3 basic ways in which we find purpose or meaning in our lives. One, through a relationship; two through a project; and three through dealing with adversity. This last seems paradoxical, even oxymoronic, yet it is the premise of virtually every work of narrative fiction that all of us (who watch cinema or TV) imbibe with addictive enthusiasm. I’ve long argued that wisdom doesn’t come from achievements or education but dealing with adversity in our lives, which is impossible to avoid no matter who you are. It makes one think of Socrates' (attributed) famous aphorism: The unexamined life is not worth living. If we think about it, we only examine our lives when we fail. So a life without failure is not really much of a life. The corollary to this is that risk is essential to success and to gaining maturity in all things.

Humans are the most socially complex creatures on the planet – take language. I’ve recently read a book, Cosmo Sapiens; Human Evolution from the Origin of the Universe, by John Hands. It’s as ambitious as its title suggests and it took him 10 years to complete: very erudite and comprehensive, Hands challenges science orthodoxies without being anti-science. But his book is not the topic of this post, so I won’t distract you further. One of his many salient points is that humans are unique, not the least because of our ability for self-reflection. He contends that we are not the only species with the ability to ‘know’, but we are the only species who ‘know that we know’ (his words) or think about thinking (my words). The point is that cognitively we are distinct from every other species on the planet because we can consider and cogitate on our origins, our mortality and our place in the overall scheme of things, in ways that other species can’t possibly think about.

And language is the key attribute, because, without it, we can’t even think in the way that we all take for granted; yet it's derived from our social environment (we all had to be taught). I understand that children isolated from adults can develop their own language, but, even under these extremely rare circumstances, it requires social interaction to develop. This is a lengthy introduction to the fact that all of us require social interaction (virtually from birth) to have a meaningful life in any way, shape or form. We spend a large part of our lives interacting with others and, to a very large extent, the quality of that interaction determines the quality of our lives.

And this is a convoluted way of reaching the first of Frankl’s ‘ways of finding meaning’: through a relationship. For most of us this implies a conjugal relationship with all that entails. For many of us, in our youth, there is a tendency to put all our eggs in that particular basket. But with age, our perspective changes with lust playing a lesser role, whilst more resilient traits like friendship, reliance and trust become more important, even necessary, in long term relationships, upon which we build something meaningful for ourselves and others. For many people, I think children provide a purpose, not that I’ve ever had any, but it’s something I’ve observed.

I know from personal experience, that having a project can provide purpose, and for many people, myself included, it can seem necessary. We live in a society (in the West, anyway) where our work often defines us and gives us an identity. I think this has historical roots. Men, in particular, were defined by what they do, often following a family tradition. This idea of a hereditary role (for life) is not as prevalent as it once was, but I suspect it snuffed out the light of aspiration for many. A couple of weeks ago I saw David Stratton; a Cinematic Life, followed by a Q&A with the man himself. David, who is about a decade older than me, came to Australia and made a career as a film critic, becoming one of the most respected, not only in Australia, but in the world. However, the cost was the bitter disappointment expressed by his father for not taking over the family grocery business back in England. Women, on the other hand, were not allowed the luxury of finding their own independent identity until relatively recently in Western societies. It’s the word ‘independent’ that was their particular stumbling block, because, even in my postwar childhood, women were not meant to be independent of a man.

The movie, Up in the Air, starring George Clooney, which I reviewed back in 2010, does a fair job of addressing this issue in the guise of cinematic entertainment. To illustrate my point, I’ll quote from my own post:

The movie opens with a montage of people being sacked (fired) with a voice-over of Clooney explaining his job. This cuts to the core of the movie for me: what do we live for? For many people their job defines them – it is their identity, in their own eyes and the eyes of their society. So cutting off someone’s job is like cutting off their life – it’s humiliating at the very least, suicidally depressing at worst and life-changing at best.

So purpose is something most of us pursue, either through relationships within our family or through our work or both. But many of you will be asking: is there a higher purpose? I can’t answer that, but I’ll provide my own philosophical slant on it.

Socrates (again), who was forced to take his own life (as a consequence of a democratic process, it should be noted) supposedly said, in addition to the well-worn trope quoted above: 'Whether death is a door to another world or an endless sleep, we don’t know'. And I would add: We are not meant to know. I’m agnostic about an afterlife, but, to be honest, I’m not expecting one, and I’ve provided my views elsewhere. But there is a point worth making, which is that people who believe that their next life is more important than the one they’re currently living often have a perverse, not to say destructive, view on mortality. One only has to look at suicide bombers who believe that their death is a ticket to Paradise.

Having said all that, it’s well known that people with religious beliefs can benefit psychologically in that they often live healthy and fulfilling lives (as the New Scientist article, referenced in the introduction, attests). Personally, I think that when one reaches the end of one’s life, they will judge it not by their achievements and successes but by the lives they have touched. Purpose can best be found when we help others, whether it be through work or family or sport or just normal everyday interactions with strangers.

Sunday 6 November 2016

Dr Strange; a surprisingly philosophical movie

I have to admit I wouldn’t have gone to see this based on the trailer, as it just appeared to be a special effects spectacular, which is what you expect from superhero movies. And it seemed very formulaic - an apprentice, a mentor, a villain who wants to destroy the world - you know the script. What changed my mind was a review by Stephen Romei in the Australian Weekend Review (29-30 Oct. 2016), who gave it 3.5 stars, and re-reading it, gives a lot of the plot away. I’ll try not to do that here, but I’m not promising.

Dr Stephen Strange is played by Benedict Cumberbatch, who is much better cast here than in The Imitation Game, which I thought was a travesty. As an aside, The Imitation Game was an insult to the real Alan Turing, but I don’t believe that was Cumberbatch’s fault. I blame the director, writers and producers, who, knowing the audience’s ignorance, gave them the caricature of genius that they expected the audience wanted to see.

Cumberbatch’s Dr Strange is a self-obsessed, egotistical, unapologetically self-promoting brain surgeon. He’s never known failure and that’s an important psychological point in my view. The first subliminal philosophical reference in this movie is the well-worn trope: the unexamined life is not worth living. This is pretty much the theme or premise of every story ever told. The point is that no one examines their life until they experience failure, and, of course, Strange faces failure of a catastrophic kind. Otherwise, there’d be no movie.

He then goes on a mystical journey, which many of us may have done at an intellectual level, but can only be done viscerally in the world of fiction. I should point out that I went through a prolonged ‘Eastern philosophy’ phase, which more or less followed on from the ‘Christian’ phase of my childhood. I’m now going through a mathematical phase, as anyone reading this blog could not have failed to notice.

Anyway, Strange’s journey is distinctly Eastern, which is the antithesis of his medical-science background. But he is introduced to an ‘astral’ or ‘spirit’ dimension, and there is a reference to the multiverse, which is a current scientific trope, if I may re-use that term in a different context. I don’t mind that ‘comic book’ movies allude to religious ideas or even that they mix them with science, because one can do that in fiction. I’ve done it myself. The multiverse is an allusion to everything that we don’t know scientifically (even in science) and is the current bulwark against metaphysics. Employing it in a fantasy movie to enhance the fantasy element is just clever storytelling. It embodies the idea, that is still very current in the East, that science cannot tell us everything.

There are 2 mythological references in the movie, including one biblical one. At one point the villain, Kaecilius (played by Mads Mikkelsen) attempts to seduce Strange to the ‘dark side’, which is very reminiscent of Satan’s attempt to seduce Jesus in the desert. I’ve always liked that particular biblical story, because it represents the corruption of power and status over the need to serve a disenfranchised public. In other words, it is an appeal to ego over the need to subordinate one’s ego for a greater good.

One of the themes of the story is mortality and immortality; something I’ve explored in my own fiction, possibly more explicitly. We live in a time where, as Woody Allen once explained in literary terms, we ‘suspend disbelief’ that we are going to live forever. We tend to avoid, in Western culture, any reference to mortality, yet it is an intrinsic part of life. We all eventually get there but refuse to face it until forced to. This is actually addressed in this movie, quite unexpectedly, as we don’t expect lessons in philosophy in a superhero movie.

Last but not least, there is a subtle but clever allusion to Camus’ famous retelling of the Greek Sisyphus myth (look it up), not something your average cinema audience member would be expected to know. It is embedded in one of those plot devices that I love: where the hero uses an unexpected ‘twist’, both literally and figuratively, and where brain defeats overwhelming force.

Friday 6 May 2016

Is morality objective?

This is another 'Question of the Month' from Philosophy Now (Issue 113, April/May 2016).

There is a constraint on length (400 words) otherwise I'd elaborate more. I have addressed this issue before regarding a specific case, which I cite in my essay below.


There are two types of morality that co-exist virtually everywhere and at all times, yet they are, for the most part, poles apart. They are morality in theory and morality in practice and they align with objective morality and subjective morality respectively. I will demonstrate what I mean by example, but first I will elaborate on morality as it is practiced. For most people morality stems from cultural norms.

Many people rely on their conscience to determine their moral compass but one’s conscience is a social construct largely determined by one’s upbringing in whatever society one was born into. For example, in some societies, one can be made to feel guilty about the most natural impulses, like masturbation. Guilt and sex have been associated over generations but it is usually one-sided. Women are often forced to carry the greater burden of guilt and homosexuals can be forced to feel criminal. Both these examples illustrate how cultural norms determine the morality one was inculcated with from childhood.

In some societies there are cultural clashes, usually generational, where the same moral issue can inflame antithetical attitudes. For example, in India in December 2012, a young woman, Jyoti Singh, a recently graduated medical student, was raped and murdered on a bus after she went and saw a movie with her boyfriend. A documentary by British filmmaker, Leslee Udwin, revealed the cultural schism that exists in India over this issue. Some believed (including the lawyers representing the gang who committed the crime) that the girl was responsible for her own fate, whereas others campaigned to have rape laws strengthened. This demonstrates most starkly how culture determines moral values that become normative and then intransigent.

In many cultures it is taught that God determines moral values, and these are often the most prescriptive, oppressive, misogynistic and sometimes brutal examples of enforced cultural mores. People who practice this often claim that theirs is the only true objective morality, but, in truth, when one invokes God to rationalise one’s morality, anything, including the most savage actions, can be justified.

On the other hand, morality in theory is very simple: it is to treat everyone the same and give everyone the same rights, be they men, women, homosexuals, people of different faith or different skin colour. One only has to look at the treatment of refugees to realise how even the most liberal societies struggle with this precept.

Monday 14 March 2016

Argument, reason and belief

Recently in New Scientist (5 March 2016) there was a review of a book, The Persuaders: The Hidden Industry that Wants to Change Your Mind by James Garvey (which I must read), which tackles the issue of why argument by reason often fails. I’ve experienced this first hand on this blog, which has led me to the conclusion that you can’t explain something to someone who doesn’t want it explained. The book referenced above is more about how propaganda works, apparently, but that is not what I wish to discuss.

In the same vein, I’ve recently watched a number of YouTube videos covering excerpts from debates and interviews with scientists on the apparent conflict between science and religion. I say apparent because not all scientists are atheists and not all theologians are creationists, yet that is the impression one often gets from watching these.

The scientists I’ve been watching include Richard Dawkins, Neil deGrasse Tyson, Bill Nye (aka the science guy) and Michio Kaku. I think Tyson presents the best arguments (from the small sample I watched) but Michio Kaku comes closest to presenting my own philosophical point of view. In one debate (see links at bottom) he says the ‘God question’ is ‘undecidable’ and predicts that, unlike many scientific questions of today, the God question will be no further advanced in 100 years time than it is in the current debate.

The issue, from my perspective, is that science and religion deal with completely different things. Science is an epistemology – it’s a study of the natural world in all its manifestations. Religion is something deeply personal and totally subjective, and that includes God. God is something people find inside themselves which is why said God has so many different personalities and prejudices depending on who the believer is. I’ve argued this before, so I won’t repeat myself.

At least 2 of the scientists I reference above (Dawkins and Tyson) point out something I’ve said myself: once you bring God into epistemology to explain some phenomenon that science can’t currently explain, you are saying we have come to the end of science. History has revealed many times over that something that was inexplicable in the past becomes explicable in the future. As I’ve said more than once on this blog: only people from the future can tell us how ignorant we are in the present. Tyson made the point that the apposite titled God-of-the-Gaps is actually a representation of our ignorance – a point I’ve made myself.

This does not mean that God does not exist; it means that God can’t help us with our science. People who argue that science can be replaced with Scripture are effectively arguing that science should be replaced by ignorance. The Old Testament was written by people who wanted to tell a story of their origins and it evolved into a text to scare people into believing that they are born intrinsically evil. At least that’s how it was presented to me as a child.

Of all the videos I watched, the most telling was an excerpt from a debate between Bill Nye (the science guy) and Ken Ham (the architect of the Creation Museum in Petersburg, Kentucky). Ham effectively argued that science can only be done in the present. So-called historical science, giving the age of the Earth or the Universe, or its origins, cannot be determined using the same methods we use for current scientific investigations. When asked if any evidence could change his beliefs, he said there was no such evidence and the Bible was the sole criterion for his beliefs.

And this segues back into my introduction: you cannot explain something to someone who doesn’t want it explained. When I argue with someone or even present an argument on this blog, I don’t expect to change people’s points of view to mine; I expect to make them think. Hence the little aphorism in the blog’s title block.

One of the points made in the New Scientist review, referenced in my opening, is that people rarely if ever change their point of view even when presented with indisputable evidence or a proof. This is true even among scientists. We all try to hang on to our pet theories for as long as possible until they are no longer tenable. I’m as guilty of this as anyone, even though I’m not a scientist.

One of the things that helps perpetuate our stubbornness is confirmation bias (mentioned by New Scientist) whereby we tend to only read or listen to people whom we agree with. We do this with politics all the time. But I have read contrary points of view, usually given to me by people who think I’m biased. I’ve even read C.S. Lewis. What I find myself doing in these instances is arguing in my head with the authors. To give another example, I once read a book by Colin McGinn (Basic Structures of Reality) that only affirmed for me that people who don’t understand science shouldn’t write books about it, yet I still read it and even wrote a review of it on Amazon UK.

There is a thing called philosophy and it’s been married to science for many centuries. Despite what some people claim (Richard Dawkins and Stephen Hawking to mention 2) I can’t see a divorce any time soon. To use a visual metaphor, our knowledge is like an island surrounded by a sea of unsolved mysteries. The island keeps expanding but the sea is infinite. The island is science and the shoreline is philosophy. To extend the metaphor, our pet theories reside on the beach.

Noson Yanofsky, a Professor of Computer and Information Science in New York, wrote an excellent book called The Outer Limits of Reason, whereby he explained how we will never know everything – it’s cognitively and physically impossible. History has demonstrated that every generation believes that we almost know everything that science can reveal, yet every revelation only reveals new mysteries.

This is a video of Michio Kaku and Richard Dawkins, amongst others, giving their views on science, God and religion.

This is a short video of Leonard Susskind explaining 2 types of agnosticism, one of which he seems to concur with.

Tuesday 2 February 2016

Creation Science: a non sequitur

A friend of mine – someone whom I’d go to for help – leant me a ‘Creation’ magazine to prove that there are creationists who are real scientists. And, I have to admit, my friend was right: the magazine was full of contributors who had degrees in science, including one who has a PhD and honours and works at a run-of-the-mill university; but who wrote the following howler: ‘Cosmology is unscientific because you can’t do an experiment in cosmology.’ I wonder if said writer would be willing to say that to Australian Nobel Prize winner, Brian Schmidt. Only humans can be living contradictions.

Creation science is an epistemological contradiction – there’s no such thing – by definition. Science does not include magic – I can’t imagine anyone who would disagree with that, but I might be wrong. Replacing a scientific theory with supernaturally enhanced magic is anti-science, yet creationists call it science – as the Americans like to say: go figure.

The magazine was enlightening in that the sole criterion for these ‘scientists’ as to the validity of any scientific knowledge was whether or not it agreed with the Bible. If this was literally true, we would still be believing that the Sun goes round the Earth, rather than the other way round. After all, the Book of Joshua tells us how God stopped the Sun moving in the sky. It doesn’t say that God stopped the Earth spinning, which is what he would have had to do.

One contributor to the magazine even allows for ‘evolution’ after ‘creation’, because God programmed ‘subroutines’ into DNA, but was quick to point out that this does ‘not contradict the Bible’. Interesting to note that DNA wouldn’t even have been discovered if all scientists were creationists (like the author).

Why do you think the ‘Dark Ages’ are called the dark ages? Because science, otherwise known as ‘natural philosophy’, was considered pagan, as the Greeks’ neo-Platonist philosophy upon which it was based was pagan. Someone once pointed out that Hypatia’s murder by a Christian mob (around 400AD) signalled the start of the dark ages, which lasted until around 1200, when Fibonacci introduced the West to the Hindu-Arabic system of numbers. In fact, it is the Muslims who kept that knowledge in the interim, otherwise it may well have been lost to us forever.

So science and Christianity have a long history of contention that goes back centuries before Copernicus, Galileo and Darwin. If anything, the gap has got wider, not closer; they’ve only managed to co-exist by staying out of each other’s way.

There are many religious texts in the world, a part of our collective cultural and literary legacy, but none of them are scientific or mathematical texts, which also boast diverse cultural origins. It is an intellectual conceit (even deceit) to substitute religious teaching for scientifically gained knowledge. Of course scientifically gained knowledge is always changing, advancing, being overtaken and is never over. In fact, I would contend that science will never be complete, as history has demonstrated, so there will always be arguments for supernatural intervention, otherwise known as the ‘God-of-the-Gaps’. Godel’s Incompleteness theorem infers that mathematics is a never-ending epistemological mine, and I believe that the same goes for science.

Did I hear someone say: what about Intelligent Design (ID)? Well, it’s still supernatural intervention, isn’t it? Same scenario, different description.

Religion is not an epistemology, it’s a way of life. Whichever way you look at it, it’s completely subjective. Religion is part of your inner world, and that includes God. So the idea that the God you’ve found within yourself is also the Creator of the entire Universe is a non sequitur. Because everyone’s idea of God is unique to them.

Tuesday 15 December 2015

The battle for the future of Islam

There are many works of fiction featuring battles between ‘Good’ and ‘Evil’, yet it would not be distorting the truth to say that we are witnessing one now, though I think it is largely misconstrued by those of us who are on the sidelines. We see it as a conflict between Islam and the West, when it’s actually within Islam itself. This came home to me when I recently saw the biographical movie, He Named Me Malala (pronounce Ma-la-li, by the way).

Malala is well known as the 14 year old Pakistani school girl, shot in the head on a school bus by the Taliban for her outspoken views on education for girls in Pakistan. Now 18 years old (when the film was made) she has since won the Nobel Peace Prize and spoken in the United Nations, as well as having audiences with world leaders, like Barak Obama. In a recent interview with Emma Watson (on Emma’s Facebook page) she appeared much wiser than her years. In the movie, amongst her family, she behaves like an ordinary teenager with ‘crushes’ on famous sports stars. In effect, her personal battle with the Taliban represents in microcosm a much wider battle between past and future that is occurring on the world stage within Islam. A battle for the hearts and minds of Muslims all over the world.

IS or ISIS or Daesh has arisen out of conflicts between Shiites and Sunnis in both Iraq and Syria, but the declaration of a Caliphate has led to a much more serious, even sinister, connotation, because its followers believe they are fulfilling a prophecy which will only be resolved with the biblical end of the world. I’m not an Islamic scholar, so I’m quoting from Audrey Borowski, currently doing a PhD at the University of London, who holds a MSt (Masters degree) in Islamic Studies from Oxford University. She asserts: ‘…one of the Prophet Muhammad’s earliest hadith (sayings) locates the fateful showdown between Christians and Muslims that heralds the apocalypse in the city of Dabiq in Syria.’

“The Hour will not be established until the Romans (Christians) land at Dabiq. Then an army from Medina of the best people on the earth at that time… will fight them.”

She wrote an article of some length in Philosophy Now (Issue 111, Dec. 2015/Jan. 2016) titled Al Qaeda and ISIS; From Revolution to Apocalypse.

The point is that if someone believes they are in a fight for the end of the world, then destroying entire populations and cities is not off the table. They could resort to any tactic, like contaminating water supplies of entire cities or destroying food crops on a large scale. I alluded in the introduction that this apocalyptic ideology, in a fictional context, represents a classic contest between good and evil. From where I (and most people reading this blog) stand, anyone intent on destroying civilization as we know it, would be considered the ultimate evil. 

What is most difficult for us to comprehend is that the perpetrators, the people ‘on the other side’ would see the roles reversed. Earlier this year (April 2015), I wrote a post titled Morality is totally in the eye of the beholder, where I explained how two different cultures in the same country (India) could have completely opposing views concerning a crime against a young woman, who was raped and murdered on a bus returning from seeing a movie with her boyfriend. One view was that the girl was the victim of a crime and the other view was that the girl was responsible for her own fate.

Many people have trouble believing that otherwise ordinary people, who commit evil acts in the form of atrocities, would see themselves as not being evil. We have an enormous capacity to justify to ourselves the most heinous acts, and no where is this more evident, than when one believes they are performing the ‘Will of God’. This is certainly the case with IS and their followers.

Unfortunately, this has led to a backlash in the West against all Muslims. In particular, we see both in social media and mainstream media, and even amongst mainstream politicians, a sentiment that Islam is fundamentally flawed and needs to be reformed. It seems to me that they are unaware that there is already a battle happening within Islam, where militant bodies like IS and Boko Haram and the Taliban represent the worse and a young schoolgirl from Pakistan represents the best.

Ayaan Hirsi Ali (whom I wrote about in March 2011), said when she was in Australia many years ago, that Islam was not compatible with a secular society, which is certainly true if Islamists wish to establish a religious-based government. There is a group, Hizb ut-Tahrir, who is banned in most Western countries, but not UK or Australia, and whose stated aim is to form a caliphate and whose political agenda, including the introduction of Sharia law, would clearly conflict with Australian law. But the truth is that there are many Muslims living an active and productive life in Australia, whilst still practising their religion. A secular society is not an atheistic society, yet is religiously nondependent by definition. In other words, there is room for variety in religious practice and that is what we see. Extremists of any religious persuasion are generally not well received in a pluralist multicultural society, yet that is the fear that is driving the debate in many secular societies.

Over a year ago (Aug 2014) I wrote a post titled Don’t judge all Muslims the same, based on another article I read in Philosophy Now (Issue 104, May/Jun 2014) by Terri Murray (Master of Theology, Heythrop College, London) who made a very salient point differentiating cultural values and ideals from individual ones.  In particular, she asserted that an individual’s rights overrules the so-called rights of a culture or a community. Therefore, misogynistic issues like female genital mutilation, honour killings, child marriage, all of which are illegal in Australia, are abuses of individual rights that may be condoned, even considered normal practice, in some cultures.

Getting back to my original subject matter, like the case of the Indian girl (a medical graduate) who was murdered for going on a date, this really is a battle between past and future. IS and the Taliban and their variant Islamic ideologies represent a desire to regain a past that has no relevance in the 21st Century – it’s mediaeval, not only in concept but also in practice. One of the consequences of the Internet is that it has become a vehicle for both sides. So young women in far off countries are learning that there is another world where education can lead to a better life. And this is the key: education of women, as Malala has brought to the world’s attention, is the only true way forward. It’s curious that women are what these regimes seem to fear most, including IS, whose greatest fear is to be killed by a female Kurdish warrior, because then they won’t get to Paradise.

Saturday 14 November 2015

The Unreasonable Effectiveness of Mathematics

I originally called this post: Two miracles that are fundamental to the Universe and our place in it. The miracles I’m referring to will not be found in any scripture and God is not a necessary participant, with the emphasis on necessary. I am one of those rare dabblers in philosophy who argues that science is neutral on the subject of God. A definition of miracle is required, so for the purpose of this discussion, I call a miracle something that can’t be explained, yet has profound and far-reaching consequences. ‘Something’, in this context, could be described as a concordance of unexpected relationships in completely different realms.

This is one of those posts that will upset people on both sides of the religious divide, I’m sure, but it’s been rattling around in my head ever since I re-read Eugene P. Wigner’s seminal essay, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. I came across it (again) in a collection of essays under the collective title, Math Angst, contained in a volume called The World Treasury of Physics, Astronomy and Mathematics edited by Timothy Ferris (1991). This is a collection of essays and excerpts by some of the greatest minds in physics, mathematics and cosmology in the 20th Century.

Back to Wigner, in discussing the significance of complex numbers in quantum mechanics, specifically Hilbert’s space, he remarks:

‘…complex numbers are far from natural or simple and they cannot be suggested by physical observations. Furthermore, the use of complex numbers in this case is not a calculated trick of applied mathematics but comes close to being a necessity in the formulation of the laws of quantum mechanics.’

It is well known, among physicists, that in the language of mathematics, quantum mechanics not only makes perfect sense but is one of the most successful physical theories ever. But in ordinary language it is hard to make sense of it in any way that ordinary people would comprehend it.

It is in this context that Wigner makes the following statement in the next paragraph following the quote above:

‘It is difficult to avoid the impression that a miracle confronts us here… or the two miracles of the existence of laws of nature and of the human mind’s capacity to divine them.’

Hence the 2 miracles I refer to in my introduction. The key that links the 2 miracles is mathematics. A number of physicists: Paul Davies, Roger Penrose, John Barrow (they’re just the ones I’ve read); have commented on the inordinate correspondence we find between mathematics and regularities found in natural phenomena that have been dubbed ‘laws of nature’.

The first miracle is that mathematics seems to underpin everything we know and learn about the Universe, including ourselves. As Barrow has pointed out, mathematics allows us to predict the makeup of fundamental elements in the first 3 minutes of the Universe. It provides us with the field equations of Einstein’s general theory of relativity, Maxwell’s equations for electromagnetic radiation, Schrodinger’s wave function in quantum mechanics and the four digit software code for all biological life we call DNA.

The second miracle is that the human mind is uniquely evolved to access mathematics to an extraordinarily deep and meaningful degree that has nothing to do with our everyday prosaic survival but everything to do with our ability to comprehend the Universe in all the facets I listed above.

The 2 miracles combined give us the greatest mystery of the Universe, which I’ve stated many times on this blog: It created the means to understand itself, through us.

So where does God fit into this? Interestingly, I would argue that when it comes to mathematics, God has no choice. Einstein once asked the rhetorical question, in correspondence with his friend, Paul Ehrenfest (if I recall it correctly): did God have any choice in determining the laws of the Universe? This question is probably unanswerable, but when it comes to mathematics, I would answer in the negative. If one looks at prime numbers (there are other examples, but primes are fundamental) it’s self-evident that they are self-selected by their very definition – God didn’t choose them.

The interesting thing about primes is that they are the ‘atoms’ of mathematics because all the other ‘natural’ numbers can be determined from all the primes, all the way to infinity. The other interesting thing is that Riemann’s hypothesis indicates that primes have a deep and unexpected relationship with some of the most esoteric areas of mathematics. So, if one was a religious person, one might suggest that this is surely the handiwork of God, yet God can’t even affect the fundamentals upon which all this rests.

Addendum: I changed the title to reflect the title of Wigner's essay, for web-search purposes.

Sunday 13 September 2015

Physics, mathematics, the Universe - is Reason its raison d'être?

I’ve just read Paul Davies’ The Mind of God: Science & The Search for Ultimate Meaning, published in 1992, so a couple of decades old now. He wrote this as a follow-up to God and the New Physics, which I read some years ago. This book is more philosophical and tends to deal with cosmology and the laws of physics – it’s as much about epistemology and the history of science as about the science itself. Despite its age, it’s still very relevant, especially in regard to the relationship between science and religion and science and mathematics, both of which he discusses in some depth.

Davies is currently at The University of Arizona (along with Lawrence Krauss, who wrote A Universe from Nothing, amongst others), but at the time he wrote The Mind of God, Davies was living and working in Australia, where he wrote a number of books over a couple of decades. He was born and educated in England, so he’s lived on 3 continents.

Davies is often quoted out of context by Christian fundamentalists, giving the impression that he supports their views, but anyone who reads his books knows that’s far from the truth. When he first arrived in America, he was sometimes criticised on blogs for ‘promoting his own version of religion’, usually by people who had heard of him but never actually read him. From my experience of reading on the internet, religion is a sensitive topic in America on both sides of the religious divide, so unless your views are black or white you can be criticised by both sides. It’s worth noting that I’ve heard or read Richard Dawkins reference Davies on more than a few occasions, always with respect, even though Davies is not atheistic.

Davies declares his philosophical position very early on, which is definitely at odds with the generally held scientific point of view regarding where we stand in the scheme of things:

I belong to the group of scientists who do not subscribe to a conventional religion but nevertheless deny that the universe is a purposeless accident… I have come to the point of view that mind – i.e., conscious awareness of the world – is not a meaningless and incidental quirk of nature, but an absolute fundamental facet of reality. That is not to say that we are the purpose for which the universe exists. Far from it. I do, however, believe that we human beings are built into the scheme of things in a very basic way.

In a fashion, this is a formulation of the Strong Anthropic Principle, which most scientists, I expect, would eschew, but it’s one that I find appealing, much for the same reasons given by Davies. The Universe is such a complex phenomenon, its evolvement (thus far) culminating in the emergence of an intelligence able to fathom its own secrets at extreme scales of magnitude in both space and time. I’ve alluded to this ‘mystery’ in previous posts, so Davies’ philosophy appeals to me personally, and his book, in part, attempts to tackle this very topic.

Amongst other things, he gives a potted history of science from the ancients (especially the Greeks, but other cultures as well) and how it has largely replaced religion as the means to understand natural phenomena at all levels. This has resulted in a ‘God-of-the-Gaps’, where, epistemologically, scientific investigations and discoveries have gradually pushed God out of the picture. He also discusses the implications of a God existing outside of space and time actually creating a ‘beginning’. The idea of a God setting everything in motion (via the Big Bang) and then watching his creation evolve over billions of years like a wound up watch (Davies’ analogy) is no more appealing than the idea of a God who has to make adjustments or rewind it occasionally, to extend the metaphor.

In discussing how the scientific enterprise evolved, in particular how we search for the cause of events, reminded me of my own attraction to science from a very early age. Children are forever asking ‘why’ and ‘how’ questions – we have a natural inclination to wonder how things work – and by the time I’d reached my teens, I’d realised that science was the best means to pursue this.

Davies gives an example of Newton coming up with mathematical laws to explain gravity that not only provided a method to calculate projectiles on Earth but also the orbits of planets in the solar system. Brian Cox in a documentary on Gravity, wrote the equation down on a piece of paper, borrowing a pen from his cameraman, to demonstrate how simple it is. But Newton couldn’t explain why everything didn’t simply collapse in on itself and evoked God as the explanation for keeping the clockwork universe functioning. So Newton’s explanation of gravity, albeit a work of genius, didn’t go far enough.

Einstein then came up with his theory that gravity was a consequence of the curvature of space-time caused by mass, but, as Cox points out in his documentary, Einstein’s explanation doesn’t go far enough either, and there are still aspects of gravity we don’t understand, at the quantum level and in black holes where the laws of physics as we know them break down. As an aside, it’s the centenary year of Einstein publishing his General Theory of Relativity and I’ve just finished reading a book (The Road to Relativity by Hanoch Gutfreund and Jurgen Renn) which goes through the original manuscript page by page explaining Einstein’s creative process.

But back to Newton’s theory, I remember, in high school, trying to understand why acceleration in a gravitational field was the same irrespective of the mass of the body, and I could only resort to the mathematics to give me an answer, which didn’t seem satisfactory. I can also remember watching a light plane in flight over our house and seeing it side-slipping in the wind. In other words, the direction of the nose was slightly offset to its direction of travel to counter a side wind. I remember imagining the vectors at play and realising that I could work them out with basic trigonometry. It made me wonder for the first time, why did mathematics provide an answer and an explanation – what was the link between mathematics, a product of the mind, and a mechanical event, a consequence of the physical world?

I’ve written quite a lot on the topic of mathematics and its relationship to the laws of nature; Davies goes into this in some depth. It is worth quoting him on the subject, especially in regard to the often stated scepticism that the laws of nature only exist in our minds.

Sometimes it is argued that laws of nature, which are attempts to capture [nature’s] regularities systematically, are imposed on the world by our minds in order to make sense of it… I believe any suggestion that the laws of nature are similar projections of the human mind [to seeing animals in the constellations, for example] is absurd. The existence of regularities in nature are a mathematical objective fact… Without this assumption that the regularities are real, science is reduced to a meaningless charade.

He adds the caveat that the laws as written are ‘human inventions, but inventions designed to reflect, albeit imperfectly, actually existing properties of nature.’ Every scientist knows that our rendition of nature’s laws have inherent limitations, despite their accuracy and success, but quite often they provide new insights that we didn’t expect. Well known examples are Maxwell’s equations predicting electromagnetic waves and the constant speed of light, and Dirac’s equation predicting anti-matter. Most famously, Einstein’s special theory of relativity predicted the equivalence of energy and mass, which was demonstrated with the detonation of the atomic bomb. All these predictions were an unexpected consequence of the mathematics.

Referring back to Gutfreund’s and Renn’s book on Einstein’s search for a theory of gravity that went beyond Newton but was consistent with Newton, Einstein knew he had to find a mathematical description that not only fulfilled all his criteria regarding relativistic space-time and the equivalence of inertial and gravitational mass, but would also provide testable predictions like the bending of light near massive stellar objects (stars) and the precession of mercury’s orbit around the sun. We all know that Riemann’s non-Euclidian geometry gave him the mathematical formulation he needed and it’s been extraordinarily successful thus far, despite the limitations I mentioned earlier.

Davies covers quite a lot in his discussion on mathematics, including a very good exposition on Godel’s Incompleteness Theorem, Turing’s proof of infinite incomputable numbers, John Conway’s game of life with cellular automata and Von Neuman’s detailed investigation of self-replicating machines, which effectively foreshadowed the mechanics of biological life before DNA was discovered.

In the middle of all this, Davies makes an extraordinary claim, based on reasoning by Oxford mathematical physicist David Deutsch (the most vocal advocate for the many worlds interpretation of quantum mechanics and a leader in quantum computer development). Effectively, Deutsch argues that mathematics works in the real world (including electronic calculators and computers) not because of logic but because the physical world (via the laws of physics) is amenable to basic arithmetic: addition, subtraction etc. In other words, he’s basically saying that we only have mathematics because there are objects in our world that we can count. In effect, this is exactly what Davies says.

This is not the extraordinary claim. The extraordinary claim is that there may exist universes where mathematics, as we know it, doesn’t work, because there are no discrete objects. Davies extrapolates this to say that a problem that is incomputable with our mathematics may be computable with alternative mathematics that, I assume, is not based on counting. I have to confess I have issues with this.

To start from scratch, mathematics starts with numbers, which we all become acquainted with from an early age by counting objects. It’s a small step to get addition from counting but quite a large step to then abstract it from the real world, so the numbers only exist in our heads. Multiplication is simply adding something a number of times and subtraction is simply taking away something that was added so you get back to where you started. The same is true for division where you divide something you multiplied to go backwards in your calculation. In other words, subtraction and division are just the reverse operations for addition and multiplication respectively. Then you replace some of the numbers by letters as ‘unknowns’ and you suddenly have algebra. Now you’re doing mathematics.

The point I’d make, in reference to Davies’ claim, is that mathematics without numbers is not mathematics. And numbers may be to a different base or use different symbols, but they will all produce the same mathematics. I agree with Deutsch that mathematics is intrinsic to our world – none of us would do mathematics if it wasn’t. But I find the notion that there could hypothetically exist worlds where mathematics is not relevant or is not dependent on number, absurd, to use one of Davies’ favourite utterances.

Earlier in the book, Davies expresses scepticism at the idea that the laws of nature could arise with the universe – that they didn’t exist beforehand. In other words, he’s effectively arguing that they are transcendent. Since the laws are firmly based in mathematics, it’s hard to argue that the laws are transcendent but the mathematics is not.

I have enormous respect for Davies, and I wonder if I’m misrepresenting him. But this is what he said, albeit out of context:

Imagine a world in which the laws of physics were very different, possibly so different that discreet objects did not exist. Some of the mathematical operations that are computable in our world would not be so in this world, and vice versa.

Speaking of mathematical transcendence, he devotes almost an entire chapter to the underlying mystery of mathematics’ role in explicating natural phenomena through physics, with particular reference to mathematical Platonists like Kurt Godel, Eugene Wigner and Roger Penrose. But it’s a quote from Richard Feynman, who was not a Platonist as far as I know, that sums up the theme.

When you discover these things, you get the feeling that they were true before you found them. So you get the idea that somehow they existed somewhere… Well, in the case of physics we have double trouble. We come across these mathematical interrelationships but they apply to the universe, so the problem of where they are is doubly confusing… Those are philosophical questions that I don’t know how to answer.

Interestingly, in his later book, The Goldilocks Enigma (2006), Davies distances himself from mathematical Platonism and seems to espouse John Wheeler’s view that both the mathematics and the laws of nature emerged ‘higgledy-piggledy’ and are not transcendent. He also tackles the inherent conflict between the Strong Anthropic Principle, which he seems to support, and a non-teleological universe, which science virtually demands, but I’ll address that later.

Back to The Mind of God, he discusses in depth one of the paradigms of our age that the Universe can be totally understood by algorithms leading to the possibility that the Universe we live in is a Matrix-like computer simulation. Again, referring to The Goldilocks Enigma, he discounts this view as a variation on Intelligent Design. Towards the end of Mind of God, he discusses metaphysical, even mystical possibilities, but not as a replacement for science.

But one interesting point he makes, that I’ve never heard of before, was proposed by James Hartle and Murray Gellmann, who claim:

…that the existence of an approximately classical world, in which well-defined material objects exist in space, and in which there is a well-defined concept of time, requires special cosmic initial conditions.

In other words, they’re saying that the Universe would be a purely quantum world with everything in superpositional states (nothing would be fixed in space and time) were it not for ‘the special quantum state in which the universe originated.’ James Hartle developed with Stephen Hawking the Hawking-Hartle model of the Universe where time evolved out of a 4th dimension in a quantum big bang. It may be that Hartle’s and Gellmann’s conjecture is dependent on the veracity of that particular model. The link between the two ideas is only alluded to by Davies.

Apropos to the book’s title, Davies spends an entire chapter on ‘God’ arguments, in particular cosmological and ontological arguments that require a level of philosophical nous that, frankly, I don’t possess. Having said that, it became obvious to me that arguments for God are more dependent on subjective ‘feelings’ than rational requirements. After lengthy discussions on ‘necessary being’ and a ‘contingent universe’, and the tension if not outright contradiction the two ideas pose, Davies pretty well sums up the situation with this:

What seems to come through such analyses loud and clear is the fundamental incompatibility of a completely timeless, unchanging, necessary God with the notion of creativity in nature, with a universe that can change and evolve and bring forth the genuinely new…


In light of this, the only ‘God’ that makes sense to me is one that evolves like ‘Its’ creation and, in effect, is a consequence of it rather than its progenitor.

One of the points that Davies makes is how the Universe is not strictly deterministic or teleological, yet it allows for self-organisation and the evolvement of complexity; in essence, a freedom of evolvement without dictating it. I would call this pseudo-teleological and is completely consistent with both quantum and chaotic events, which dominate all natural phenomena from cosmological origins to the biological evolution of life.

This brings one back to the quote from Davies at the beginning of this discussion that the universe is not a meaningless accident. Inherent in the idea of meaningfulness is the necessary emergence of consciousness and its role as the prime source of reason. If not for reason the Universe would have no cognisance of its own existence and it would be truly ‘purposeless’ in every way. It is for this reason that people believe in God, in whatever guise they find him (or her, as the case may be). Because we can find reason in living our lives and use reason to understand the Universe, the idea that the Universe itself has no reason is difficult to reconcile.

Thursday 3 September 2015

Ruminations on The Sparrow (SF novel by Mary Doria Russell, 1996)

Russell is a paleoanthropologist and so is one of the characters in her book (Anne) whom one thinks may represent the author’s world view, especially concerning religion and God. Anne is basically a good natured and tolerant sceptic.

Whether Anne is representative of the author’s point of view or not, I found Russell’s ideas of God, as expressed explicitly by the main character, Emilio Sandoz, a Jesuit (but also implicitly by others) to be old-fashioned, even anachronistic. The idea of God as a father figure and we being ‘His’ children is one I rejected in my teens, especially after reading Camus’ The Plague (La Peste).  So, in some ways, I think Russell is applying the same literary devices as Camus (pointless and undeserved human suffering) to challenge this particular version of God that many of us grew up with.

At one point the character, Anne, asks Emilio if it’s alright for her to ‘hate God’. Towards the end of the novel, another Jesuit priest proposes the idea (not original, I suspect) that God had to make room for the existence of the Universe by removing Himself, which is really a Deistic version of God that one sometimes finds appealing to scientists, because such a God would be non-interventionist. If one takes this to its logical conclusion, there is no reason for this God to have empathy or be the anthropomorphic version we are familiar with from the Bible.

The interesting point is that people sometimes ‘find God’ in the midst of their own suffering. I think of Viktor Frankl (an Auschwitz survivor) who wrote Man’s Search for Meaning and The Unconscious God, who argued that a person can find meaning through adversity. But this supports my own view that God is something that people find within themselves and is not dependent on making God responsible for whatever happens in the world.

As Russell’s novel makes clear, if one makes God responsible for everything that happens, then He’s responsible for the suffering as well as the triumphs of the human spirit. At the start of the story’s journey, the protagonists believe that everything they’re doing is part of God’s plan – it’s meant to be – but at the end, this premise is effectively negated.

One of the attractions of Sci-Fi for me, even when I was quite young, is that it allows what-if scenarios, alternative societies. I would suggest that Frank Herbert and Ursula Le Guin were particularly adept at rendering alternative social structures. Russell’s alien society is particularly well thought through and makes one consider how it may have evolved on Earth had other hominids (like Neanderthals) survived into an agricultural world. As it is, we were (and still are) very good at exploiting economically weaker sectors of our societies, at all levels, from global to local.

There is no clear resolution, at least for me, to the ‘God question’, which is a central theme of her book. One can end up ‘hating’ God, if one follows the logical conclusion from the book’s premise to its confounding end, but I believe that the characters in the story are simply following an antiquated version of God.

P.S. I should point out that this book won the 1998 Arthur C. Clarke Award.

Friday 26 June 2015

Some ruminations on a debate about the existence of God

I came across this debate on YouTube between Sye Ten Bruggencate and Matt Dillahunty (31 May 2014): “Is it Reasonable to Believe that God Exists?” I’ve come across Sye before and even argued with him on Stephen Law’s blog (or attempted to) a few years back; probably more than a few years, actually. He’s a self-described presuppositionist and a member of the Associate Reformed Presbyterian Church, who lives in Ontario, while Matt is a former Christian and now hosts a cable TV show, The Atheist Experience, based in Austin, Texas.

The debate is close to 2 hrs, including questions from the audience, which is followed by the participants’ ‘summing up’. I watched the entire debate partly because I was curious how Matt would handle Sye, who’s debating style is to make unsupported assertions then try and put the burden of proof, or disproof, onto his opponent. To give an example from my own experience: he once asked me to provide evidence that God had not made himself manifest to humankind (I’m paraphrasing from memory). I said I can’t provide evidence of something that didn’t happen, not happening. And his response was that it was my assertion therefore I had to prove it.

I was impressed by Matt’s temperament as well as his arguments, where he was very careful and precise whilst not being difficult to follow, even though he spoke quickly to ensure he stayed within the time limits imposed. Both of them were well prepared and had obviously researched each other’s positions. Sye cleverly used video excerpts of Matt to not only pre-empt Matt’s arguments but to support his own counter-arguments. Matt used humour in combination with rigid logic and precise language.

Sye’s argument was simplistic in the extreme: “It’s reasonable to believe that which is true; it’s true that God exists; therefore it’s reasonable to believe that God exists.” In his summing up Matt called it ‘kindergarten theology’ and ‘kindergarten philosophy’.

One of Sye’s key points of argument (which I’ve seen him use before) is to claim that his opponent can only argue from his (Sye’s) world view, and his world view is provided by God. He argues that any other world view is ‘absurd’, and in Matt’s case, Matt could, by his own admission, be a ‘brain in a vat’. However, Matt clarifies this by saying that he doesn’t believe he’s a brain in a vat, but it’s a well known philosophical conundrum that this can’t be proven. I first came across this in Stephen Law’s Philosopher’s Gym about 12 years ago, before I discovered him on his blog. In the debate, this logically led to a discussion on solipsism, which, Matt argued, can’t be proved to be false.

I’ve discussed this before, and, whilst all of us believe that everyone else we meet is not a figment of our imagination, there is one situation, which we have all experienced, where this is actually true. Neither Sye nor Matt mentioned this but that situation is a dream. A dream is solipsistic. So how do we know that we’re not in a dream. Because we have shared memories when we’re not in a dream. If I have a dream that includes someone I know, then when I next meet them in real life, they have no memory of that interaction, only I do. So unless one’s entire life is a dream then solipsism is a non sequitur if we have shared experiences that we can both remember.

One of the things that came out of this debate for me, and which Matt touched on briefly, is that if you have no common ground to begin with then you really can’t debate a subject. Specifically, Matt pointed out that he and Sye had different definitions of truth, which logically means that they would never be able to agree on whether something was true or not. I realised that it would be pointless for me to engage in an argument with someone whose entire world view is premised on fiction: a book of mythological stories. Sye argues that everyone knows that God exists, including babies (when Matt specifically asked him). No one can argue with that and Sye knows it, which is why he claims he’s unbeatable when it comes to arguments about the existence of God.

Matt argues that knowledge is a subset of beliefs, which I hadn’t considered before, and truth is based on evidence. Sye responded that evidence is something you take into a court and you become the judge but you can’t judge God. But if you don’t believe in God then that argument is irrelevant and without a God who actually intervenes in the assessment, one must use one’s own intellect to judge the evidence, which is what we all do all the time otherwise we wouldn’t be able to live.

So Sye’s basis for truth is God, which is revealed in scripture, and my basis for objective truth is mathematics, so we couldn’t be further apart. Sye would argue that I need his world view to believe that, because mathematics wouldn’t exist without God.  However, I would argue that mathematics trumps God because even God can’t change a prime number to a non-prime number or vice versa or change the value of Pi or make 2 + 2 = 5.  If Sye was to respond that God is mathematics then I might agree with him, but that has nothing to do with scripture.


Addendum: I've given this some more thought, plus I've watched the entire debate again. I believe I can challenge Sye's world view. Notice I say 'challenge' because that's the best one can do; I don't believe I can get him to change his world view any more than I believe he could get me to change mine.

Just to clarify my own position, I'm not anti-theist per se (as I've explained elsewhere); I believe God is something that people find within themselves, but that's another argument for another time.

My challenge is to do with my last paragraph of my original post, because I believe that mathematics gives us the only transcendental truths we know, whilst acknowledging that not everyone agrees with that position. By transcendental, I mean that mathematical truths exist independently of the human mind and even the universe. As someone once joked: If tomorrow the universe ceased to exist, the only part of science one could continue to do would be mathematics (that’s me paraphrasing John Barrow quoting Dave Rusin). I've discussed this position elsewhere.

My challenge to Sye is that mathematics even transcends God, for the reasons I pointed out in that closing paragraph. God can't change mathematics any more than we can: he can't make 2 + 2 = 5, amongst even more esoteric mathematical concepts like changing primes. If God can't change them, then logically they are independent of God. So I have a means of finding 'truths' that transcend God, therefore I don't need God in order for them to be true. What's more, mathematics provides 'truths' that anyone with the requisite intellectual ability can discover, without reference to any religious scripture or any divine revelation.

Thursday 11 June 2015

The fine-tuned Universe

I’ve discussed this before in relation to John D. Barrow’s revelations concerning the fine structure constant, amongst other things, in his excellent book, The Constants of Nature. A recent episode of Catalyst, called Custom Universe also raised this issue, plus the latest issue of New Scientist (6 June 2015, pp.37-39) explaining the extraordinary fine difference in mass between neutrons and protons (that can’t be explained with our current knowledge of physics) and, in particular, the consequences of small variations to that difference.

In other words, the stability of atoms, including the prototype atom, hydrogen, is dependent on the neutron being slightly heavier than the proton by 0.14% (the neutron is 939.6 Mev and the proton is 938.3 Mev). Making the difference much bigger would result in more complex atoms becoming impossible to create and much smaller would have converted all hydrogen atoms into inert helium, therefore no fusion in stars and no other atoms. Smaller still or making protons heavier than neutrons would have resulted in protons decaying into neutrons and therefore no atoms at all.

This is just one of many examples of fine-tuning in our universe that makes the evolution of complex life forms, and therefore intelligent life, possible. And, of course, we still don’t know why matter outweighed anti-matter in the early stages of the universe by 1 billion and 1 to 1 billion, otherwise the universe would be just radiation and nothing else.

The standard answer to this is the multiverse, which postulates that there exists up to an infinite number of alternative universes, and, logically, we must exist in the one universe that allows intelligent life, like us, to evolve. Brian Cox (in Human Universe) uses the analogy of a lottery. When we buy a lottery ticket the chances of winning is some astronomical number, and in our individual lifetimes, very few of us ever win. However, as Cox points out, someone wins every time, and that’s the same with the multiverse. We win because we are in it and all the others that don’t win are unknown and unknowable because no consciousness can evolve in them to find out. This is known as the weak Anthropic Principle, which I’ve discussed elsewhere.

What many people don’t realise is that if there is an infinite number of universes then there must be an infinite number of you and me, because, in an infinite amount of space and time, anything that can happen once must happen an infinite number of times – a mathematical truism.

But many see the multiverse as a cop-out, because it explains everything and nothing. It says all things are possible therefore we are possible, problem solved. It provides an answer with no explanation. And, at its extreme interpretation, it says that everything is possible an infinite number of times.

Max Tegmark advocates this extreme interpretation in his book, Our Mathematical Universe, where he postulates up to 4 levels of multiverses, including the quantum multiverse. In fact, Tegmark conjured up a thought experiment, whereby if you die you just find yourself in an alternative quantum universe, and therefore you are effectively immortal. To take this to its logical conclusion, there must exist a universe where everyone lives forever, therefore we all eventually find Heaven, or at least, its mathematically plausible equivalent.

Equally relevant to this topic, is the issue of biological evolution, and I’ve just finished reading an excellent book on this subject, Life Ascending; The Ten Great Inventions of Evolution by Nick Lane. Now many people (including Richard Dawkins, I imagine) will take issue with the word ‘invention’ and ‘evolution’ appearing in the same sentence, let alone on the cover of a book. But I doubt Dawkins would take issue with any of the material between the covers, even in the places where his name is cited. Lane, of course, is aware of some people’s sensitivity to the word ‘invention’ in this context, and is quick to explain he’s not referring to a ‘creator’ but to the extraordinary inventiveness inherent in the process of natural selection. In the same way, and for the same reasons, I have no problem in appropriating the word ‘design’ when discussing evolution because natural selection is nature’s design methodology and its more significant ‘inventions’ are the subject of the book, hence the totally apposite title.

Lane structures the book into 10 chapters that cover his ‘ten inventions’: 1) The Origin of Life; 2) DNA; 3) Photosynthesis; 4)The Complex Cell; 5) Sex; 6) Movement; 7) Sight; 8) Hot Blood; 9)Consciousness; 10) Death.

I have to say that this is the best book on evolution that I’ve read, not least because Lane has such a commanding knowledge of his subject and a very accessible style of prose. Lane is a biochemist by training and it’s his ability to explain what happens at a molecular level that gives the book so much intellectual weight. He appears up to date on all the latest discoveries and provides historical context everywhere; so we learn how theories have developed, sometimes stalled, sometimes been disproved and sometimes yet to be confirmed. Anyone who studies science, at whatever level, appreciates that we never know everything and we never will, but that we are constantly uncovering newly discovered nature’s secrets that would astound the likes of Darwin and his contemporaries with their depth and ingenuity.

All the chapters contain information that I wasn’t aware of previously, but the first two chapters are probably the most revelatory and the most enthralling. One suspects that it’s at this level that Lane is most intrigued and therefore most knowledgeable on all the latest developments. I won’t go into details, but he provides the best arguments I’ve come across on how life, at its simplest form, may have evolved from pure chemistry. In light of the title of this post, I was struck on more than one occasion on how just the right elements or combination of factors arose to produce the forebears of life as we now know it.

This is all good grist for those who believe we have a special destiny, and that there is the ‘hand’ of some immaterial force behind it all. The other extreme is to be dismissive of this view as ‘weak-minded’ and ‘unintelligent’, yet I find the idea that our existence is an accident that should never have happened equally absurd and, dare-I-say-it, unintelligent. My own view, that I’ve expressed elsewhere, is that the Universe is brim-full of purpose yet that purpose has evolved with no plan or blueprint in sight, no pre-destined goal, just a set of laws that have allowed it all to happen.

If there is a ‘creator’, then ‘he’, ‘she’ or ‘it’ works in a very strange fashion, certainly not in the manner that creationists and ID advocates would have us believe, because the ‘design’ has been done piece-meal with many wrong turns, much trial and error and many catastrophes on a grand scale, of which we could easily become one ourselves. In comparison to the epic story of life, we are like mayflies, existing for less than a day, thus far – it’s a sobering thought.

In regard to the ridiculous debate on religion versus science, it is worth quoting Lane himself from the last paragraph of his book.

I think the picture painted here in this book is true. Life most surely evolved, along the lines described here. That is not dogma, but evidence tested in reality and corrected accordingly. Whether this grand picture is compatible with faith in God, I do not know. For some people, intimately acquainted with evolution, it is; for others, it is not.

Addendum: This is a YouTube interview with physicist, Leonard Susskind, who discusses the fine-tuned universe on Closer to Truth, which appears to be a series of interviews with well known scientists and philosophers giving us their interpretation of philosophical cum scientific conundrums.

Susskind, not surprisingly, delivers a very compelling argument for the multi-verse, or, as he calls it, the mega-verse, and, in so doing, references String or M Theory as supporting this view. Personally, I'm a bit of a sceptic of String theory and its many variations, as it reminds me of Ptolemy's epicycles, but I may well be proven wrong in the near or far future. Only time will tell.

But what struck me as I listened to Lenny's argument, was that, even if it's true, it still means that our universe is very special, amongst all the possibilities. However, as I pointed out in my main post, if there are an infinite number of universes then it's not special at all.

Sunday 1 March 2015

Chaos – nature’s preferred means of evolution and dynamics

Ian Stewart is a highly respected mathematician and populariser of mathematics. He has the rare ability to write entire books on the esoteric side of mathematics with hardly an equation in sight. The ‘new edition’ of Does God Play Dice? has the subtitle, The New Mathematics of Chaos, and that’s what the book is all about.  The first edition was published in 1989, the second edition in 1997, so not that new any more. Even so, he gave me more insights and knowledge into the subject than I knew existed. I’d previously read Paul Davies’ The Cosmic Blueprint, which does a pretty good job, but Stewart’s book has more depth, more examples, more explanations and simply more information. In addition, he does this without leaving me feel stranded in the wake of his considerable intellect.

For a start, Stewart puts things into perspective, by pointing out how chaos pervades much of the natural world – more so than science tends to acknowledge. In physics and engineering classes we are taught calculus and differential equations, which, as Stewart points out, are linear, whereas most of the dynamics of the natural world are non-linear, which make them ripe for chaotic analysis. We tend to know about chaos through its application to systems like weather, fluid turbulence, population dynamics yet its origins are almost purely mathematical. Throughout the book, Stewart provides numerous examples where the mathematics of chaos has been applied to physics and biology.

Historically, he gives special attention to Poincare, whom he depicts almost as the ‘father of chaos’ (my term, not his) which seems appropriate as he keeps returning to ‘Poincare sections’ throughout the book. Poincare sections are hard to explain, but they are effectively geometrical representations of periodic phenomena that have an ‘attractor’.  That’s an oversimplification, but ‘attractors’ are an important and little known aspect of chaos, as many chaotic systems display an ability to form a stable dynamical state after numerous iterations, even though, which particular state is often unpredictable. The point is that the system is ‘attracted’ to this stable state. An example, believe it or not, is the rhythmic beat of your heart. As Stewart explains, ‘the heart is a non-linear oscillator’.

Relatively early in the book, he provides an exposition on ‘dynamics in n-space’. Dimensions can be used as a mathematical concept and not just a description of space, which is how we tend to envisage it, even though it’s impossible for us to visualise space with more than 3 dimensions. He gives the example of a bicycle, something we are all familiar with, having numerous freedoms of rotation, which can be mathematically characterised as dimensions. The handle bars, each foot pedal as well as the wheels all have their own freedom of rotation, which gives us 5 at least, and this gives 10 dimensions if each degree of freedom has one variable for position and one for velocity.

He then makes the following counter-intuitive assertion:

What clinches the matter, though, is the way in which the idea of multi-dimensional spaces fit together. It’s like a 999-dimensional hand in a 999-dimensional glove.

In his own words: ‘a system with n degrees of freedom – n different variables – can be thought of as living in n-space.’ Referring back to the bicycle example, its motion can be mathematically represented as a fluid in 10 dimensional space.

Stewart then evokes a theorem, discovered in the 19th Century by Joseph Liouville, that if the system is Hamiltonian (meaning there is no friction) then the fluid is incompressible. As Stewart then points out:

…something rather deep must be going on if the geometric picture turns dynamics not just into some silly fluid in some silly space, but renders it incompressible (the 10-dimensional analogue of ‘volume’ doesn’t change as the fluid flows).

The reason I’ve taken some time to elaborate on this, is that it demonstrates the point Stewart made above – that an abstract n-dimensional space has implications in reality –  his hand-in-glove analogy.

Again, to quote Stewart:

I hope this brings you down to Earth with the same bump I always experience. It isn’t an abstract game! It is real!

Incompressibility is such a natural notion, it can’t be coincidence. Unless you agree with Kurt Vonnegut in Cat’s Cradle, that the Deity made the Universe as an elaborate practical joke.


The point is that the relationships we find between mathematics and reality are much more subtle than we can imagine, the implication being that we’ve only scratched the surface.

Anyone with a cursory interest in chaos knows that there is a relationship between chaos and fractals, and that nature loves fractals. What a lot of people don’t know is that fractals have fractional dimensions (hence the name) which can be expressed logarithmically. As Stewart points out, the relationship with chaos is that the fractal dimension ‘turns out to be a key property of an attractor, governing various quantitative features of the dynamics.’

I won’t elaborate on this as there are more important points that Stewart raises. For a start, he spends considerable time and space pointing out how chaos is not synonymous with randomness or chance as many people tend to think. Chaos is often defined as deterministic but not predictable which reads like a contradiction, so many people dismiss it out-of-hand. But Stewart manages to explain this without sounding like a sophist.

It’s impossible to predict because all chaotic phenomena are sensitive to the ‘initial conditions’. Mathematically, this means that the initial conditions would have to be determined to an infinitesimal degree, meaning an infinitely long calculation. However the behaviour is deterministic in that it follows a path determined by those initial conditions which we can’t cognise. But in the short term, this allows us to make predictions which is why we have weather forecasts over a few days but not months or years and why climate-forecast modelling can easily be criticised. In defence of climate-forecast modelling, we can use long term historical data to indicate what’s already happening and project that into the future. We know that climate-related phenomena like glaciers retreating, sea temperature rise and seasonal shifts are already happening.

This short term, long term difference in predictability varies from system to system, including the solar system. We consider the solar system the most stable entity we know, because it’s existed in its current form well before life emerged and will continue for aeons to come. However, computer modelling suggests that its behaviour will become unpredictable eventually. Jacque Laskar of the Bureau des Longitudes in Paris has shown that ‘the entire solar system is chaotic’.

To quote Stewart:

Laskar discovered… for the Earth, an initial uncertainty about its position of 15m grows to only 150m after 10 million years, but over 100 million years the error grows to 150 million kilometres.

So while chaos is 'deterministic', it's computably indeterminable, which is why it's 'unpredictable'. I've written another post on that specific topic.

In the last chapter, Stewart attempts to tackle the question posed on the front cover of his book. For anyone with a rudimentary knowledge of physics, this is a reference to Einstein’s famous exhortation that he didn’t believe God plays dice, and Stewart even cites this in the context of the correspondence where Einstein wrote it down.

Einstein, of course, was referring to his discomfort with Bohr’s ‘Copenhagen interpretation’ of quantum mechanics; a discomfort he shared with Erwin Schrodinger. I’ve written about this at length elsewhere when I reviewed Louisa Gilder’s excellent book, The Age of Entanglement. Stewart takes the extraordinary position of suggesting that quantum mechanics may be explicable as a chaotic phenomenon. I say extraordinary because, in all my reading on this subject, no one has ever suggested it and most physicists/philosophers would not even consider it.

I have come across some physicist/philosophers (like David Deutsch) who have argued that the ‘many worlds’ interpretation of quantum mechanics can, in fact, explain chaos. A view which I’m personally sceptical about.

Stewart resurrects David Bohm’s ‘hidden variables’ interpretation, preferred by Einstein, but generally considered disproved by experiments confirming Bell’s Inequality Theorem. It’s impossible for me to do justice to Stewart’s argument but he does provide the first exposition of Bell’s theorem that I was able to follow. The key is that the factors in Bell’s Inequality (as it’s known) refer to correlations that can be derived experimentally. The correlations are a statistical calculation (something I’m familiar with) and the ‘inequality’ tells you whether the results are deterministic or random. In every experiment performed thus far, the theorem confirms that the results are not deterministic, therefore random.

Stewart takes the brave step of suggesting that Bell’s Inequality can be thwarted because it relies on the fact that the results are computable. Stewart claims that if they’re not computable then it can’t resolve the question. He gives the example of so-called ‘riddled basins’ where chaotic phenomena can interact with ‘holes’ that allow them to find other ‘attractors’. Again, an oversimplification on my part, but as I understand it, in these situations, which are not uncommon according to Stewart, it’s impossible to ‘compute’ which attractor a given particle would go to.

Stewart argues that if quantum mechanics was such a chaotic system then the results would be statistical as we observe. I admit I don’t understand it well enough to confer judgement and I have neither the mathematical nor physics expertise to be a critical commentator. I’ll leave that to others in the field.

I do agree with him that the wave function in Schrodinger’s equation is more than a ‘mathematical fiction’ and it was recently reported in New Scientist that a team from Sydney claim they have experimentally verified its reality. But I conjecture that ‘Hilbert space’, which is the abstract space where the wave function mathematically exists, may be what’s real and we simply interact with it, but there is no more evidence for that than there is for the ‘multiple universes’ that is currently in favour and gaining favour.

Towards the very end of the book, Stewart hypothesises on how different our view of quantum mechanics may be today if chaos theory had been discovered first, though he’s quick to point out the importance of computers in allowing chaos to be exploited. But he makes this interesting observation in relation to the question on the cover of his book:

Now, instead of Einstein protesting that God doesn’t play dice, he probably would have suggested that God does play dice. Nice, classical, deterministic dice. But – of course – chaotic dice. The mechanism of chaos provides a wonderful opportunity for God to run His universe with deterministic laws, yet simultaneously to make fundamental particles seem probabilistic.

Of course, in the real world, dice are chaotic because the outcome of a throw is subject to the sensitivity of the initial conditions, which is the throw itself. The same with a coin toss. So each throw has its own initial conditions, which creates the randomness from throw to throw that we observe.

Of course, both Stewart’s and Einstein’s reference to a Deity is tongue-in-cheek, but I’ve long thought that chaos provides the ideal mechanism for a Deity to intervene in the Universe. Having said that, I don’t believe in Divine intervention, because it assumes that God has a plan that 'He' needs to keep interfering with. I prefer to think that God is simply the laws of the Universe (a la Einstein’s God) and they will run their course.

Chaos may be 'deterministic' but you can't rerun a chaotic phenomenon and get the same result - that's how chaos was discovered. The Universe obeys 'strange attractors', which provides stability to some systems while still being ultimately unpredictable. We don't know enough to know why the Universe turned out the way it did. Every age has its own sphere of ignorance, but chaos suggests that the future cannot be ultimately known. In other words, there appears to be a limit to what it's possible to know and not just a limit dependent on our cognitive abilities.

Saturday 10 January 2015

That Mystery of Mysteries

I read an interesting article in the latest issue of Philsophy Now (Issue 105, Nov/Dec 2014) by Toni Vogel Cary titled, That Mystery of Mysteries, about the 2 centuries old debate regarding the theory of evolution and God-manipulated speciation. Toni Vogel Carey is introduced as ‘a philosophy professor in a former life, has written for twenty years… and serves on the US advisory board of Philosophy Now.’

She presents some interesting statistics that suggest ignorance in science this century is increasing rather than decreasing. For example: ‘In Great Britain, few besides evangelicals paid attention to creationism before 2002. But by 2006, a BBC poll showed that 4 out of 10 in the UK thought religious alternatives to Darwin’s theory should be taught as science in schools.’

She then gives equally scary anecdotes for the former Eastern European block countries, where, for example: ‘In 2006, Poland’s minister for education repudiated the theory of evolution, and his deputy dismissed it as “a lie”.’

She gives other examples, from various countries and educational institutions that should ring alarm bells for anyone interested in providing scientific tuition to future generations. Towards the end of her lengthy discussion that goes back to Herschel, Lyell and Darwin (of course), she cites a recent publication by Thomas Nagel, titled Mind & Cosmos (2012) (which I haven’t read, it must be stated) where ‘Nagel argues for “natural teleology”, a view of nature as forward-looking and purposeful, yet secular rather than deistic or theistic.’ And herein lies the rub: it is very difficult for us to believe that something like us (humans) could not be the consequence of some ‘cosmic plan’ (That Mystery of Mysteries), the why and wherefore we have speculated about ever since we gained the ability to think and imagine in a way that no other species can even cognise.

At the risk of going off on a complete tangent, I wish to reference an excellent BBC doco I saw recently called Apeman – Spaceman, the first of a 5 part series, Human Universe, presented by that cross between David Attenborough and a failed rock star, Brian Cox. Cox starts his programme, in a very Attenborough-like moment, attempting to cosy up to some baboons who live in the highlands of Ethiopia. Though not our closest relative and not even true baboons, Cox explains that, amongst the higher primates, they have the most complex social behaviours, second only to humans, and can even string together a series of vocalisations, thus combining sounds that have different meanings individually.

The point of this explication is to demonstrate the humungous gap that exists between humans and all other species on the planet, cognitively. One really cannot overstate this point, as many people prefer to believe that there is nothing ‘special’ about humans at all. But as Cox states explicitly, we are ‘unique’, certainly on planet Earth and possibly in the entire universe. We are unique because we are the only species that can speculate about, let alone comprehend, our place in the much larger scheme of things. It is from this unique cognitive vantage point that both religion and science arose.

If there is any one thing that defines humanity as a species it is surely curiosity. It is curiosity that has led us into space (the focus of Cox’s first episode) but also led us on an intellectual trail uncovering such wonders as mathematical calculus, nuclear physics, the human genome and every scientific discovery since we first grasped the art of writing down our thoughts so future generations could build an unassailable cumulative knowledge that has given us computers, air travel, smart phones and all the mod-cons we take for granted in Western societies the world over.

And this exceptional evolutionary ‘success’ also creates a paradox in popular Western thinking as Carey’s discussion exposes. Whilst we all accept the benefits that science has provided for us, without even thinking about them most of the time, many of us can’t accept that science has also provided an explanation for how Earthly species have developed, changed, evolved, gained ascendency and become extinct.

I believe there are 2 reasons for this. Firstly, scientific knowledge is always contingent on future discoveries. This means we never know everything, and, what’s more, we never will. There are limits to what we can know as I’ve discussed in another post. So how do I know that evolution is true? Because the biological knowledge that underpins the human genome project (DNA) also underpins the theory of evolution, completely unknown and unforeseen in Darwin’s time. This is a well documented and carefully studied case where future discoveries enhanced a contentious scientific theory beyond its originators’ (Darwin’s and Wallace’s) wildest imaginings.

But there is still a lot we don’t know about evolution: for example, how did DNA evolve and how did it originate? Did it come from outer space? In response, creationist and ID advocates can provide glib answers that, if taken seriously, close off any further avenues of investigation; effectively stemming the very curiosity that has given us what we have learned to date.

The second reason is that our intuition and common sense can let us down when it comes to scientific knowledge. There are 2 well-known examples: Einstein’s theories of relativity and quantum mechanics. Relativity theory tells us that clocks run slower when they travel faster (relative to another clock) and clocks run faster in lower gravity (like on satellites as opposed to ground level, Earth). Intuition and common sense tell us that this can’t be true, yet the GPS in your mobile phone or in the Sat-Nav of your car depend on relativity for their accuracy.

Quantum mechanics tells us that a particle can exist in superposition with itself: an electron can go through 2 slits at once and interfere with itself on the other side, though if we try and determine which slit it goes through then it will only go through one of them. Yet quantum mechanics is not only the most empirically successful theory in the entire history of science, it underpins every electronic device you use, from TVs to computers to washing machines.

As I’ve stated many times on this blog in a variety of contexts, the biggest mystery of the universe is that it created the means to understand itself, through us. As I’ve also stated, more recently, the biggest difference between religion and science is that religion maintains the universe is teleological and science tells us that it’s not. So how do I reconcile this? Basically, I argue that ‘purpose’ has evolved, meaning there was no pre-ordained plan. It’s like God really did cast a set of dice and allowed the universe to find its own purpose. Einstein famously said, "God does not play with dice", but chaos and quantum theory suggest otherwise.

Addendum: This is a related post that I wrote a few years back, where, in the final paragraph, I come to a similar conclusion.

Friday 5 December 2014

Theory, knowledge and truth

Bear with me while I give a little backstory. Julia Zemiro, the effervescent host of RocKwiz (a brilliant show for those who are missing out) has made a TV series called ‘Home Delivery’ where she takes a celebrity (all comedians, either UK or Oz) back to their home town. In a recent episode she took Ruth Jones, an award-winning UK comedienne back to her home town in Wales. As part of the tour, she visited her church where a number of events in her life took place, apparently.

Given the context, Julia asked her if she was a ‘believer’. I thought Jones’ answer so candid and honest, it’s worth repeating. She said she believes there is something ‘greater than us’ but we really ‘have no idea’. Maybe not her exact words but certainly her sentiment. It was the admission of ignorance and humility that struck me – so different to any theological statement one cares to hear. And I realised, by the sheer contrast implicit in her statement, why I have such an issue with the Church; well, any church, basically. Because they all claim to know what they can’t possibly know and preach it with the absolute certainty that dogma requires.

And despite what they all claim, there is no text anywhere in the world that can tell us what, if any, greater purpose there is. Now, I’m not opposed to the idea that there could be a greater purpose and I have no problem with people believing that (like Ruth Jones). I only have a problem when they claim to know what that purpose is and what one must do (in this life) to achieve it.

When I was a philosophy student, a lecturer made the salient point that there are things one believes and things one knows and it’s important to keep in mind that what one believes should be contingent upon what one knows and not the converse. This is perfectly logical, even common sense, yet it’s extraordinary the mental gymnastics some people will perform to maintain a contrary position. To give an example, I read an account where William Lane Craig, in a conversation with the author of a Christian text, defended his belief that Mary conceived Jesus without having sex.

And this brings me to the fundamental epistemological divide that exists between science and religion, as we see it discussed and abused in the so-called Western world. Because science is essentially about knowledge, about what we know as opposed to what we might speculate and philosophise about, even though the boundaries sometimes get a bit blurred.

The success of science, over a period of 2500 years, if one wants to go back to Thales and Pythagoras, has arisen from a combination of theory, mathematics and empirical evidence. Now, whilst there is not a lot of mathematics in the biological sciences, it’s the discovery of DNA, with its inherent ‘software-like’ code that underpins all of biology and evolutionary theory in particular. And like the other disciplines of science, mathematics (in the form of knot theory) is informing us as to how DNA actually manages to function.

But out of that triumvirate, it is empirical evidence that ultimately holds sway. We can find truth in mathematics independently of any physical parameters, but when we apply our mathematics to physical theories, only physical evidence tells us if the theory is true. An example is string theory, which is a mathematical model of the universe predicting up to 11 dimensions, yet, whilst no evidence can be found to confirm it, it really does remain just a theory. Whereas Einstein’s theories of relativity (the special and general theory) are proven facts, as is quantum mechanics. Evolution, I would argue, is also a fact, simply because the evidence that proves it’s true could just as readily prove it’s wrong (the evidence is not neutral). So theories can be facts and not ‘just a theory’.

But all scientific knowledge is contingent on future knowledge which is how it has evolved. For example, Newton’s theories were overtaken by Einstein’s theories, yet the equations governing relativity theory reduce to Newton’s equations when relativistic effects are negligible. As someone once pointed out (John Worrall, London School of Economics, 1989) it’s the mathematics that survives from one physical theory to the next that informs us what aspect of the original theory was true. Again, referring to Newton and Einstein, gravity obeys an inverse square law in both their theories.

As I’ve described on another post when I reviewed Noson S. Yanofsky’s excellent book, The Outer Limits of Reason, there are limits to knowledge at all levels. So science acknowledges that it’s impossible to know everything, yet there is every reason to believe that our knowledge will increase for as long as humanity can survive. At the end of my last post, I pointed out that an implication of Godel’s Incompleteness Theorem is that mathematics is infinite, which means that there is no end to what we can discover.

So where does philosophy sit and where does religion sit amongst all this scientific knowledge? Well, I would suggest that there is an interface between science and philosophy that will always exist because philosophy quests for answers that are currently beyond our reach, some of which, like multiverses and Artificial Intelligence, may be resolved or may not.

A few years back, I said that religion is the mind’s quest to find meaning for its own existence, and I think that this is a perfectly logical and healthy thing for a mind to do. But religion, as it has evolved culturally, is full of mythology dressed up as truth. That is not to say that the figures who feature prominently in these religions are necessarily fictional, but the stories that have arisen in their wake are mythological in content. People like Jesus, Mohammed, Buddha, even Confucius, never wrote anything down so we are left with their ‘sayings’ (Mohammed was illiterate, which is why the Quran is probably in verse). But myth is very hard to shake once it takes hold in the collective consciousness of a population, and once it becomes ‘religion’ it becomes heretical to even question it.

Unfortunately, much of the debate between science and religion stems from what people think constitutes truth. Truth can exist in fiction, but in the form of life-lessons rather than narrative facts. When people believe that a narrative containing mythical elements is true, they will often argue that the mythical elements really happened by giving them supernatural attributes (like the example provided by Craig above). This is anathema to a scientifically trained mind and as far from any truth they would care to entertain.

So when people use the Bible as a criterion for scientific truth, it is certain to create conflict. Four hundred years ago, Galileo was threatened with torture by the Vatican for proposing that the Earth went round the Sun instead of the converse, as was then believed. The Vatican’s contention was that this contradicted a passage in the Bible that claims that God stopped the Sun moving in the sky. Now, we all know (thanks to pure science) that God could not have stopped the sun moving in the sky because the sun doesn’t move at all relative to the Earth’s orbit.

Yet still, in the 21st Century, we have people (like Ken Ham) claiming that the book of Genesis, which is full of mythological events like a snake that talks and a woman made from a man’s rib and a man made from dirt and a piece of fruit that turns people evil, nevertheless overrules all of modern science. I apologise on behalf of all Australia for unleashing Ken Ham onto the modern world, where he clearly doesn’t belong.

I once posted a question on his website asking for the nomination of one scientific discovery in the past 2500 years that has been made from studying the Scriptures. Not surprisingly, I never received a reply.

A few hundred years before Christ was born, Euclid, who was Librarian at the famous Library of Alexandria, wrote his seminal text, The Elements. This is arguably one of the most important texts ever written, certainly more important than any religious text as it contains real transcendental truths in the form of mathematical proofs. Mathematics is the only knowledge we have that transcends the Universe. As John Barrow quipped in one of his many books (citing Dave Rusin): Mathematics is the only part of science you could continue to do if the Universe ceased to exist.

It is hard to go past mathematics if you want truths, especially truths that are independent of humanity and the Universe itself. Of course, not everyone agrees with this Platonic sentiment, but it’s hard to avoid when one considers that there are an infinite number of primes that we can’t possibly know or an infinite string of digits in pi that we know must exist yet can’t possibly cognise. Mathematics is transcendent simply because it embraces infinity on so many levels.

To quote Barrow again, in a slightly more serious tone:

Mathematics is part of the world, and yet transcends it. It must exist before and after the Universe. Most scientists and mathematicians… work as though there were an unknown realm of truth to be discovered.