I’ve just read John D. Barrow’s Pi in the Sky, published in 1992, and hard to get, as it turns out. I got a copy through Amazon UK, who had one in stock, and it’s old and battered but completely intact and legible, which is the main thing.
Those of you who regularly read my blog (not many of you, I suspect) will know that I’ve read lots of Barrow’s books, possibly The Book of Universes is the best, which I reviewed in May 2011.
Pi in the Sky is a very good title because it alludes to the Platonist philosophy of mathematics that seems to dominate both mathematics and physics as it’s practiced, in contrast to how many of its practitioners would present it. Barrow points out, both in his introduction and his concluding remarks (after 250+ pages), that Platonism has religious and mystical connotations that are completely at odds with both mathematics and science as disciplines.
He points out that there is a divide between mathematicians and physicists and economists and sociologists in the way they approach and view mathematics. For the economist and sociologist, mathematics is a tool that humans invented and developed, which can be applied to a range of practical applications like weather forecasting, economic modelling and analysis of human behaviours.
On the other hand, pure mathematicians and physicists see an ever-increasing complex landscape that has not only taken on an existence of its own but is becoming the only means available to understanding the most secret and fundamental features of the universe, especially at the extremities of its scale and birth.
This is an ambitious book, with barely an equation in sight, yet it covers the entire history of mathematics from how various cultures have represented counting (both in the present and the ancient past) to esoteric discussions on Godel’s theorem, Cantor’s transfinite sets and philosophical schools on ‘Formalism’, ‘Constructivism’, ‘Intuitionism’ and ‘Inventism’. Naturally, it covers the entire history of Platonism from Pythagoras to Roger Penrose. It’s impossible for me to go into any detail on any of these facets, but it needs to be pointed out that Barrow discusses all these issues in uncompromising detail and seems to pursue all philosophical rabbits down their various warrens until he’s exhausted them.
He makes a number of interesting points, but for the sake of brevity I will highlight only a couple of them that I found compelling:
‘Once an abstract notion of number is present in the mind, and the essence of mathematics is seen to be not the numbers themselves but the collection of relationships that exists between them, then one has entered a new world.’
This is a point I’ve made myself, though I have to say that Barrow has a grasp of this subject that leaves me well behind in his wake, so I’m not claiming any superior, or even comparable, knowledge to him. It’s the relationships between numbers that allows algebra to flourish and open up doors we would never have otherwise discovered. It is the interplay between ingenious human invention and the discovery of these relationships that creates the eternal philosophical debate (since Plato and Aristotle, according to Barrow): is mathematics invented or discovered?
One cannot discuss this aspect of mathematics without looking at the role it has played in our comprehension of the natural world: a subject we call physics. Nature’s laws seem to obey mathematical rules, and many would argue that this is simply because we need to quantify nature in order to study it, and once we quantify something mathematics is automatically applied. This quantification includes, not just matter, but less obvious quantifiable entities, like heat, gravity, electromagnetism and entropy. However, as Barrow points out, the deeper we look at nature the more dependent we become on mathematics to comprehend it, to the point that there is no other means at our disposal. Mathematics lies at the heart of our most important physical theories, especially the ones that defy our common sense view of the world, like quantum mechanics and relativity theory.
The point is that these so-called ‘laws’ are all about ‘relationships’ between physical entities that find analogous mathematical ‘relationships’ that have been discovered ‘abstractly’, independently of the physics. There may not be a Platonic realm with mathematical objects like triangles and the like but the very peculiar relationships which constitute the art we call mathematics have sometimes found concordant relationships in what we call the ‘laws of nature’. It is hard for the physicist not to believe that these ‘mathematical’ relationships exist independently of our minds and possibly the universe itself, especially since this mathematical ‘Platonic’ universe seems to contain relationships that our universe (the one we inhabit) does not.
In 2010, or thereabouts, I read Marcus du Sautoy’s excellent book, Finding Moonshine, which is really all about dimensions. The most fantastical part of this book was the so-called ‘Atlas’, which was a project largely run by John Conway with a great deal of help from others (in the 1970s), which compiled all 26 ‘sporadic groups’ that I won’t attempt to explain or define. Part of the compilation included a mathematical object called the ‘Monster’ which existed in 196,883 dimensions. Then a friend and colleague of Conway’s, John Mackay, discovered a most unusual and intriguing connection between ‘The Monster’ and another mathematical entity called a ‘modular function’ in number theory, even though it first appeared as an apparent ‘coincidence’ - as no reason could be conceived - but a sequence in the modular function could be matched to the sequence of ‘dimensions’ in which the Monster could exist.
I’m only telling snippets of this story – read du Sautoy’s book for the full account – but it exemplifies how completely unforeseen and unlikely connections can be found in disparate fields of mathematics. The more we explore the world of mathematics, the more it surprises us with relationships we didn’t foresee; it’s hard to ignore the likelihood that these relationships exist independently of our discovering them.
Because the only mathematics we know is a product of the human mind, it can be, and often is, argued that without human intelligence it wouldn’t exist. But no one presents that argument concerning other areas of human knowledge like the laws of physics, where experimentation can validate or refute them. However, no one denies that mathematics contains ‘truths’ that are even more unassailable than the physics we observe. And herein lies the rub: these ‘truths’ would still be true even without our knowledge of them.
This brings me to the second insight Barrow made that caught my attention:
He points out that our mathematical theories describing the first three minutes of the Universe predict specific ratios of the earliest ‘heavier’ elements: deuterium, 2 isotopes of helium and lithium, which are 1/1000, 1/1000, 22 and 1/100,000,000 respectively; with the remaining (roughly 78% ) being hydrogen. And this has been confirmed by astronomical observations. He then makes the following salient point:
‘It confirms that the mathematical notions that we employ here and now apply to the state of the Universe during the first three minutes of its expansion history at which time there existed no mathematicians… This offers strong support for the belief that the mathematical properties that are necessary to arrive at a detailed understanding of events during those first few minutes of the early Universe exist independently of the presence of minds to appreciate them.’
As Barrow points out more than once, not all conscious entities have a knowledge of mathematics – in fact, it’s a specialist esoteric discipline that only the most highly developed societies can develop, let alone disseminate. Nevertheless, mathematics has provided a connection between the human mind and the machinations of the Universe that even the Pythagoreans could not have envisaged. I’ve said this before and Marcus du Sautoy has said something similar: it’s like a code that only a suitably developed intelligent species can decipher; a code that hides the secret to the Universe’s origins and its evolvement. No religion I know of can make a similar claim.
Monday 6 October 2014
Monday 25 August 2014
Climate Change is a psychological problem
In last week’s issue of New Scientist (16 August 2014, pp. 24-25), George Marshall wrote a mostly pessimistic opinion piece about the acceptance of human-initiated climate change by the general public. Marshall is founder of the ‘Climate Outreach and Information Network in Oxford, UK,' and author of a book, Don’t Even Think About It; Why our brains are wired to ignore climate change, which is about to be published. This alone will stop many climate change sceptics from reading his article let alone his book.
Basically, he argues that it’s human nature to place more importance on short term pain over long term gain. In other words, we are reluctant to make sacrifices or accept short term costs in favour of long term goals that won’t be seen in our own lifetime and which no one can definitively quantify. Politicians don’t have the political will to overcome the collective inertia or risk election over an issue that many can’t perceive as current or relevant to their own lives. In Australia, and, I suspect elsewhere, this has become an emotionally charged issue with people sending threatening emails to scientists, and claiming that there is some global academic conspiracy to maintain funding and jobs for climate scientists who would otherwise be out of a job if climate change didn’t exist. Such irrationality merely demonstrates how reason is the first casualty when public opinion attempts to overturn peer-reviewed science.
In last week’s episode of ABC’s weekly programme, Q&A, the issue came up and Heather Ridout, a highly respected Australian business woman, currently head of AustralianSuper and a Board member for the Reserve Bank of Australia, seems an unlikely advocate for action on Climate Change, given those credentials, yet argued that the scientific argument is well and truly over and it’s time we accepted the scientific status quo instead of challenging it with spurious and contrary viewpoints that are given the same weight as globally accepted scientific opinion.
Marshall opens his article with a quote from Daniel Kahneman, who won the 2002 Nobel Prize for economics: “…I am deeply pessimistic, I really see no path to success on climate change.” To quote Marshall, Kahneman won the prize ‘for his research on the psychological biases that distort rational decision making.’ In particular, he coined the term “loss aversion”, which is effectively the point I made in the opening of the second paragraph: reluctance to accept short term pain for a long term gain of uncertain magnitude.
Kahneman also talks about “assimilation bias”, which is our ability to make information fit our personal prejudices, which is why people on opposing sides of the political spectrum can have such contradictory views over the same issue, like climate change. The problem with all this, as Marshall expounds, is that, politically, it is much easier to postpone the problem than deal with it now. The easy way out for politicians, is to give it lip service whilst pursuing policies that actually do nothing to address it. This is exactly what our current political leadership is doing in Australia, and I believe it’s happening elsewhere as well.
What I find interesting, in light of the psychological dimension that both Marshall and Kahneman propound, is how the issue seems to fall on the 'right' and 'left' of the political divide. In Australia, a conservative politician lost the leadership of his own party (by 1 vote) when he put climate change on the line, which was very brave, but changed the political landscape in Australia dramatically for the last 3 election terms.
It is the ‘right’ of politics that sees climate change as a furphy and it is the ‘left’ that sees it as one of the foremost challenges of the 21st Century, for the entire world. If one examines politics historically, it is the ‘liberal’ politicians who have led social reforms in areas of equality and social justice that have, in later generations, become mainstream. I predict that this also applies to climate change, where ‘liberal’ politicians are once more showing leadership on a socially contentious issue, that will, in later generations, be accepted as the status quo, as the scientific community has already done.
Basically, he argues that it’s human nature to place more importance on short term pain over long term gain. In other words, we are reluctant to make sacrifices or accept short term costs in favour of long term goals that won’t be seen in our own lifetime and which no one can definitively quantify. Politicians don’t have the political will to overcome the collective inertia or risk election over an issue that many can’t perceive as current or relevant to their own lives. In Australia, and, I suspect elsewhere, this has become an emotionally charged issue with people sending threatening emails to scientists, and claiming that there is some global academic conspiracy to maintain funding and jobs for climate scientists who would otherwise be out of a job if climate change didn’t exist. Such irrationality merely demonstrates how reason is the first casualty when public opinion attempts to overturn peer-reviewed science.
In last week’s episode of ABC’s weekly programme, Q&A, the issue came up and Heather Ridout, a highly respected Australian business woman, currently head of AustralianSuper and a Board member for the Reserve Bank of Australia, seems an unlikely advocate for action on Climate Change, given those credentials, yet argued that the scientific argument is well and truly over and it’s time we accepted the scientific status quo instead of challenging it with spurious and contrary viewpoints that are given the same weight as globally accepted scientific opinion.
Marshall opens his article with a quote from Daniel Kahneman, who won the 2002 Nobel Prize for economics: “…I am deeply pessimistic, I really see no path to success on climate change.” To quote Marshall, Kahneman won the prize ‘for his research on the psychological biases that distort rational decision making.’ In particular, he coined the term “loss aversion”, which is effectively the point I made in the opening of the second paragraph: reluctance to accept short term pain for a long term gain of uncertain magnitude.
Kahneman also talks about “assimilation bias”, which is our ability to make information fit our personal prejudices, which is why people on opposing sides of the political spectrum can have such contradictory views over the same issue, like climate change. The problem with all this, as Marshall expounds, is that, politically, it is much easier to postpone the problem than deal with it now. The easy way out for politicians, is to give it lip service whilst pursuing policies that actually do nothing to address it. This is exactly what our current political leadership is doing in Australia, and I believe it’s happening elsewhere as well.
What I find interesting, in light of the psychological dimension that both Marshall and Kahneman propound, is how the issue seems to fall on the 'right' and 'left' of the political divide. In Australia, a conservative politician lost the leadership of his own party (by 1 vote) when he put climate change on the line, which was very brave, but changed the political landscape in Australia dramatically for the last 3 election terms.
It is the ‘right’ of politics that sees climate change as a furphy and it is the ‘left’ that sees it as one of the foremost challenges of the 21st Century, for the entire world. If one examines politics historically, it is the ‘liberal’ politicians who have led social reforms in areas of equality and social justice that have, in later generations, become mainstream. I predict that this also applies to climate change, where ‘liberal’ politicians are once more showing leadership on a socially contentious issue, that will, in later generations, be accepted as the status quo, as the scientific community has already done.
Sunday 17 August 2014
Woody Allen’s Magic in the Moonlight
I’ve just seen this movie at NOVA (yes, I’ll give them a plug for Melbournians). In Australia, we are very fortunate in that we have art-house multiplexes, as well as commercial ones. Not all movies are made for teenagers (in particular teenage boys): there are lots of good movies from all over the world made with adults in mind. And Melbourne art-house cinemas are evidence that there is an audience for them, at least in Melbourne. Does that make me a cultural snob? Probably.
About 15 years ago, I was working on an engineering project in the ‘bush’, in north-east Victoria, living in Benalla, which is about 2.5 hrs from Melbourne. About 10 minutes outside of Benalla was a ’one-horse’ town called Swanpool – one of those towns you’d miss if you blinked – I don’t even think it had a pub. But it had a public hall that some locals had converted into a cinema. The seats were cheap and you came rugged up (Benalla is frosty in winter) and brought your own coffee mug to get a cheaper cup of coffee. The point of this little sojourn is that on Saturday nights they screened blockbusters but on Friday nights they screened art-house movies (usually foreign). I saw the Cuban film about homosexuality, Strawberry and Chocolate and the French surrealist film, The City of Lost Children, amongst many others. I remember sending an email to an ex-pat friend living in California that art-house cinema was alive and well in country Victoria.
Woody Allen is going through a European phase, and Magic in the Moonlight is no exception, set on the Cote d’Azur in France. Amongst his more recent films, I think To Rome With Love failed to hit the mark, but Midnight in Paris was a work of genius. I also enjoyed You’ll Meet a Tall Dark Stranger, even though it didn’t get good reviews; I liked it for Allen’s ability to put up a mirror to our humanly flaws, and loved it for the Faustian twist in its tail.
Which brings me to Magic in the Moonlight, starring British acting icon, Colin Firth. It’s masterly economical in the way Allen leads us through the narrative, referencing the next scene in its predecessor, so that the story flows without any intellectual or logical hurdles to deal with. And yes, it’s predictable but we don’t know how it will be resolved, so that sort of predictability is welcome, especially when the resolution is both logical and a surprise, as it is in this film. The resolution of the romantic dimension is less a surprise but it’s treated in an unusual and humourous fashion.
But the reason I’m writing about this particular Allen film is because it has a philosophical dimension. Colin Firth’s character, ‘Stanley Crawford’, is a sceptic in the tradition of James Randi, and he meets his match in ‘Sophie Baker’ (Emma Stone), an American ‘psychic’, and the rest I won’t tell you. In fact, I haven’t told you any more than you can deduce from the trailer. The point is that Allen plays with his audience, knowing they will take sides in this philosophical-oriented debate: is there something beyond the world we can see? In effect, he tackles the divide between the hard-nosed scientists and empiricist philosophers and the romantic idealists who believe or like to believe that life holds more meaning than the short span of our years.
About 15 years ago, I was working on an engineering project in the ‘bush’, in north-east Victoria, living in Benalla, which is about 2.5 hrs from Melbourne. About 10 minutes outside of Benalla was a ’one-horse’ town called Swanpool – one of those towns you’d miss if you blinked – I don’t even think it had a pub. But it had a public hall that some locals had converted into a cinema. The seats were cheap and you came rugged up (Benalla is frosty in winter) and brought your own coffee mug to get a cheaper cup of coffee. The point of this little sojourn is that on Saturday nights they screened blockbusters but on Friday nights they screened art-house movies (usually foreign). I saw the Cuban film about homosexuality, Strawberry and Chocolate and the French surrealist film, The City of Lost Children, amongst many others. I remember sending an email to an ex-pat friend living in California that art-house cinema was alive and well in country Victoria.
Woody Allen is going through a European phase, and Magic in the Moonlight is no exception, set on the Cote d’Azur in France. Amongst his more recent films, I think To Rome With Love failed to hit the mark, but Midnight in Paris was a work of genius. I also enjoyed You’ll Meet a Tall Dark Stranger, even though it didn’t get good reviews; I liked it for Allen’s ability to put up a mirror to our humanly flaws, and loved it for the Faustian twist in its tail.
Which brings me to Magic in the Moonlight, starring British acting icon, Colin Firth. It’s masterly economical in the way Allen leads us through the narrative, referencing the next scene in its predecessor, so that the story flows without any intellectual or logical hurdles to deal with. And yes, it’s predictable but we don’t know how it will be resolved, so that sort of predictability is welcome, especially when the resolution is both logical and a surprise, as it is in this film. The resolution of the romantic dimension is less a surprise but it’s treated in an unusual and humourous fashion.
But the reason I’m writing about this particular Allen film is because it has a philosophical dimension. Colin Firth’s character, ‘Stanley Crawford’, is a sceptic in the tradition of James Randi, and he meets his match in ‘Sophie Baker’ (Emma Stone), an American ‘psychic’, and the rest I won’t tell you. In fact, I haven’t told you any more than you can deduce from the trailer. The point is that Allen plays with his audience, knowing they will take sides in this philosophical-oriented debate: is there something beyond the world we can see? In effect, he tackles the divide between the hard-nosed scientists and empiricist philosophers and the romantic idealists who believe or like to believe that life holds more meaning than the short span of our years.
Sunday 10 August 2014
Don’t judge all Muslims the same
In Philosophy Now (Issue 102, May/June 2014), Terri Murray (Master of Theology, Heythrop College, London) wrote an essay titled, Is Judging Islamic Culture Possible? Now I’ve touched on this topic before in various guises, but it’s perhaps more relevant than ever with the rise of ISIS or IS (Islamic State) with its self-appointed Caliphate and its barbaric treatment of anyone who won’t follow its dictates.
Murray’s article is lengthy and well-argued, so it’s a bit unfair to distill her arguments into succinct sound-bytes, as I’m about to do. Basically, Murray delineates between what she calls ‘liberal multiculturalism’ and ‘pluralist multiculturalism’: where she contends the former (of which she claims to belong) puts the rights of the individual above cultural identity; and the latter where cultural identity holds sway over individual liberty. That’s the gist of her argument, but, in particular, she compares this with feminism and LBGT rights, both of which she’s been an outspoken advocate of, or so she tells us, and I have no reason to disbelieve her.
But she also refers to the ‘pluralist multiculturalists’ as ‘relativists’, and much of her argument revolves around this, contextually. In effect, the moral or cultural relativists argue that we in the West are not in a position to criticise other cultures and Islamic culture in particular – political correctness gone mad, is how many conservatives and some liberals would put it.
Murray lives in England and I live in Australia, where cultural sensitivities are not dissimilar but not exactly the same. I both work and socialise with Muslims, some of whom I consider very good friends, which naturally colours my own perceptions and opinions, but that’s not the issue. In a post last year (Aug. 2013), I argued that there was no such thing as moral relativism, whereas Murray’s argument effectively hinges on that idea. I argued that no one can hold a moral standpoint on an issue that covers every perceived view – it’s impossible – so what she’s talking about is tolerance, as she acknowledges herself. But I’ve also argued elsewhere that the limit of tolerance is intolerance by others. Like many so-called liberals, I’m intolerant of intolerance, and that is the guiding criterion when it comes to judging Islam or variants of Islam or any other cultural practice.
Moral values, as practiced, are invariably subjective, and arise from cultural or social norms that we are exposed to from our earliest cognitive years. But in our teens and early twenties, our so-called ‘formative’ years, we can undergo changes in attitudes and beliefs and often challenge the views we were brought up with. It is my belief that many members of IS, especially those from a Western background, fall into this category. Why they are attracted to this ideology, I can neither imagine nor understand, but we know it’s happening. The point is that while many of us find their behaviour abhorrent in the worst possible way, they believe the opposite and claim that it is our lifestyle that is sinful and against the laws of ‘God’, which is how they justify what they do. As I’ve said before, when you take your morals from ‘God’ you can justify any atrocity.
The danger, as I see it, is in taking a polarised view. Murray is arguing against one of those polarised views: that we must accept and tolerate all manifestations of Islam irrespective of its consequences on individuals. Even forgetting about IS for the moment (Murray’s article was written prior to IS’s rise to dominance in Syria and Iraq), issues like female genitalia mutilation and honour killings are examples where the rights of individuals trump cultural tolerance and sensitivity, as Murray points out. But there is another form of polarisation that is equally dangerous and far more likely, which is to brand all Muslims with the same brush. We already see this with religious commentators like Richard Dawkins and Sam Harris, both of whom attack all kinds of religion and argue that moderate religious believers somehow support fundamentalism, which is simplistic, divisive and plain wrong. No one suffers under militant Islam more than moderate Muslims as we are currently witnessing in Iraq, but also Indonesia and other countries. To alienate moderate Muslims in a ‘war’ against Islamic extremists is a huge mistake. In Australia, at least, politicians and strategists seem to be very aware of this dimension to the issue, at least, locally.
Murray’s article is lengthy and well-argued, so it’s a bit unfair to distill her arguments into succinct sound-bytes, as I’m about to do. Basically, Murray delineates between what she calls ‘liberal multiculturalism’ and ‘pluralist multiculturalism’: where she contends the former (of which she claims to belong) puts the rights of the individual above cultural identity; and the latter where cultural identity holds sway over individual liberty. That’s the gist of her argument, but, in particular, she compares this with feminism and LBGT rights, both of which she’s been an outspoken advocate of, or so she tells us, and I have no reason to disbelieve her.
But she also refers to the ‘pluralist multiculturalists’ as ‘relativists’, and much of her argument revolves around this, contextually. In effect, the moral or cultural relativists argue that we in the West are not in a position to criticise other cultures and Islamic culture in particular – political correctness gone mad, is how many conservatives and some liberals would put it.
Murray lives in England and I live in Australia, where cultural sensitivities are not dissimilar but not exactly the same. I both work and socialise with Muslims, some of whom I consider very good friends, which naturally colours my own perceptions and opinions, but that’s not the issue. In a post last year (Aug. 2013), I argued that there was no such thing as moral relativism, whereas Murray’s argument effectively hinges on that idea. I argued that no one can hold a moral standpoint on an issue that covers every perceived view – it’s impossible – so what she’s talking about is tolerance, as she acknowledges herself. But I’ve also argued elsewhere that the limit of tolerance is intolerance by others. Like many so-called liberals, I’m intolerant of intolerance, and that is the guiding criterion when it comes to judging Islam or variants of Islam or any other cultural practice.
Moral values, as practiced, are invariably subjective, and arise from cultural or social norms that we are exposed to from our earliest cognitive years. But in our teens and early twenties, our so-called ‘formative’ years, we can undergo changes in attitudes and beliefs and often challenge the views we were brought up with. It is my belief that many members of IS, especially those from a Western background, fall into this category. Why they are attracted to this ideology, I can neither imagine nor understand, but we know it’s happening. The point is that while many of us find their behaviour abhorrent in the worst possible way, they believe the opposite and claim that it is our lifestyle that is sinful and against the laws of ‘God’, which is how they justify what they do. As I’ve said before, when you take your morals from ‘God’ you can justify any atrocity.
The danger, as I see it, is in taking a polarised view. Murray is arguing against one of those polarised views: that we must accept and tolerate all manifestations of Islam irrespective of its consequences on individuals. Even forgetting about IS for the moment (Murray’s article was written prior to IS’s rise to dominance in Syria and Iraq), issues like female genitalia mutilation and honour killings are examples where the rights of individuals trump cultural tolerance and sensitivity, as Murray points out. But there is another form of polarisation that is equally dangerous and far more likely, which is to brand all Muslims with the same brush. We already see this with religious commentators like Richard Dawkins and Sam Harris, both of whom attack all kinds of religion and argue that moderate religious believers somehow support fundamentalism, which is simplistic, divisive and plain wrong. No one suffers under militant Islam more than moderate Muslims as we are currently witnessing in Iraq, but also Indonesia and other countries. To alienate moderate Muslims in a ‘war’ against Islamic extremists is a huge mistake. In Australia, at least, politicians and strategists seem to be very aware of this dimension to the issue, at least, locally.
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