I apologise in advance to overseas readers (outside Australia) who can’t view this, but this interview on ABC’s Lateline current affairs programme on Thursday (8 Oct) was a standout. Emma Alberici, a well respected television journalist and previous foreign correspondent with ABC’s European bureau, interviews, or attempts to interview, Wassim Doureihi, member of Hizb ut-Tahir; an organisation which has been banned in many countries, but not Australia or the UK. This link gives a good summary of that interview, but it’s also ABC, so maybe unavailable outside Oz.
A lecture was held by the group’s Arabic spokesperson, Ismail Al-Wahwah, at Lakemba, Sydney last night, which, according to the SMH and Guardian (links), was not much different in rhetoric to Doureihi’s diatribe a few days earlier. Basically, they claim the current situation in Iraq is a direct consequence of America’s, and its allies’, involvement in that conflict, as well as earlier conflicts involving Muslims. And that, apparently, justifies everything that IS does. Though Doureihi never actually condones IS, he went to extraordinary lengths to avoid discussing their actions and/or strategy when talking to Alberici, which frustrated her enormously.
There are a couple of issues I wish to address: firstly, the sheer distortion in Dourheihi’s argument that doesn’t match the evidence; and secondly, the possible motivation behind people’s desire to join this ‘fight’ and how they manage to justify its atrocities.
Doureihi repeatedly asserted that the current conflict in Iraq is all about foreign occupation. But there is no foreign occupation in Iraq at present – the current Western forces have been invited by the Iraqi democratically elected government (as Alberici pointed out) – and IS arose in Syria, where there is no Western intervention at all, and moved into Iraq before the West got involved. Besides, IS are not attacking a foreign occupation in Iraq (the Westerners they behead are not military personnel); they are attacking people who have lived there for generations, mainly Kurds and Yazidi. In fact, they are committing genocide against these people, which has nothing to do with any foreign occupation.
One can argue about the wisdom of the West’s intervention in Iraq under Bush, especially considering the legerdemain of the so-called WMDs (Weapons of Mass Destruction) that never existed, and its woefully poor execution under Cheney and Rumsfeld. But you have to draw a very long bow to argue that IS have entered Iraq to right the wrongs of that misadventure, when they kill all males who won’t convert to Islam and sell all their women into slavery.
A few years back, I read The Islamist by Ed Hussain, who was radicalised in Great Britain, as a student, before becoming disillusioned and returning to a more moderate position on Islam. It’s an insightful book in that it distinguishes between the religion of Islam as practiced by many Muslims living in secular societies and the political ideology of extremists who want to reshape the world into a totalitarian Islamic state. Hussain believed, at the time, the entire world would inevitably become a ‘Caliphate’, not least because it was ‘God’s Will’. What turned Hussain around was when a student was stabbed to death by a member of his own group. Hussain suddenly realised he wanted no part of an organisation that saw killing non-adherents as part of its creed.
When IS first declared itself a caliphate, an Australian academic (I can’t recall his name or his department) made the observation, in regard to Muslims in Indonesia, that just the idea of a caliphate would have enormous appeal that many would find hard to resist. In other words, many see this as some sort of Islamic nirvana, a new ‘world order’, where all wrongs will be made right and all peoples will be made to see and understand God’s wisdom and be guided by it through Sharia law. Naturally, this is anathema to anyone living in a Western democratic secular society, and is seen as turning back the clock centuries, before the Enlightenment and before the European renaissance and before modern scientific relevations, not to mention undoing generations of women’s independence of men, whether sexually, financially or educationally.
And this is the nexus of this conflict: it’s a collision of ideas and ideals that has no compromise. IS and its ilk, the Taliban in Afghanistan and Boko Haram in Africa, are fighting against the 21st Century. They know as well as we do, that there is no place for them, politically, in the world’s global future, and they can only rail against this by killing anyone who does not agree with their vision, and committing all women to marital slavery.
Finally, there is a comment by an Australian Islamist fighting in Syria, who believes that IS’s tactics of beheading journalists and aid workers is justified because their deaths are insignificant compared to the hundreds of innocent people (including children) killed by Western sponsored air raids. If these deaths can ‘blackmail’ America and its allies into not killing innocents then it is worth it, according to him.
David Kilcullen, an Australian expert on Afghanistan and a former adviser to Condoleezza Rice during the Bush administration, is one of the few who argued against drone strikes in Pakistan because they would ‘recruit’ jihadists. The abovementioned apologist for IS would suggest that such a belief was justified.
However, IS don’t just behead Westerners; it’s one of their psychological tactics against anyone who doesn’t convert to their specific brand of Islam. It’s meant to horrify and terrorise all their enemies, whoever they might be, and it succeeds.
Contrary to popular belief and popular crime thrillers, most people who perform evil acts, as perceived by most societies, don’t believe that what they are doing is evil and can always find a way to justify it. No where is this more acute than when the perpetrators believe that they have ‘God on their side’.
Sunday, 12 October 2014
Monday, 6 October 2014
Mathematics as religion
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.
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.
Subscribe to:
Posts (Atom)