Cycles of Time, subtitled An Extraordinary New View of the Universe, is a very recent book by Roger Penrose; so recent that I pre-ordered it. Anyone who has followed my blog over the last few years will know that I’m a big fan of Penrose. Along with Paul Davies and Richard Feynman, I think he’s one of the top physics writers for laypeople ever. John Gribbin and James Gleick are also very good but not quite in the same league in my opinion. Davies, Feynman and Penrose all have different strengths so comparisons are not entirely fair. Feynman was the great communicator of some of the most esoteric theories in physics and if you want to grasp the physics, he’s the best. Davies is, in my view, the best philosophical writer and also covers the widest field: covering topics like astrophysics, the origin of life, cosmology, chaos theory, the nature of time and in The Goldilocks Enigma the meaning of life, the universe and everything.
Penrose is actually a mathematician and made significant contributions to tessellation (tiles, map boundaries etc), but he’s also won at least one award in physics (1988 Wolf Prize jointly with Stephen Hawking) and his dissertations on the subject of consciousness reveal him as an erudite and compelling polymath.
My favourite book of his is The Emperor’s New Mind(1989) where he first tackled the subject of consciousness and challenged the prevailing view that Artificial Intelligence would herald in a new consciousness equivalent to or better than our own. But the book also covers almost the entire field of physics, argues cogently for a Platonic view of mathematics, explains the role of entropy on a cosmic scale, and devotes an entire chapter to the contingent nature of ‘truth’ in science. A must-read for anyone who thinks we know everything or are on the verge of knowing everything.
Now I’m the first to admit that I can quickly get out of my depth on this topic, and I can’t defend all the arguments that Penrose delivers, because, quite frankly, I don’t understand all the physics that lay behind them, but he’s one of the few people, with the relevant intellectual credentials, who can challenge the prevailing view on our universe’s origins and not lose credibility in the process.
For a start, reading this book makes one realise how little we do know and how speculative some of our theories are. Many commentators treat theoreticians who challenge string theory, and its latest incantation, M theory, as modern-day luddites, which is entirely unfair considering that string theory has no experimental or observational successes to its name. In other words, it’s a work of mathematical genius that may or may not reflect reality. Penrose’s CCC (Conformal Cyclic Cosmology) is also a mathematically consistent theory with no empirical evidence to either confirm or deny it. (Penrose does suggest avenues of enquiry to rectify that however.)
I first came across CCC in a book, On Space and Time (2008), a collection of ‘essays’ by people like Alain Connes, Shahn Majid, Andrew Taylor and of course Sir Roger Penrose. It also included John Polkinghorne and Michael Heller to provide a theological perspective. Personally, I think it would have been a better book if it stuck to the physics, because I don’t think metaphysical philosophies are any help in understanding cosmology, even though one could argue that mathematical Platonism is a metaphysical philosophy. I don’t mind that people want to reconcile scientific knowledge with their personal religious beliefs, but it’s misleading to imply that religion can inform science. And science can only inform religion if one conscientiously rejects all the mythology that religions seem to attract and generate. Putting that personal caveat aside, I can highly recommend this book, edited by Shahn Majid, for an overview of current thinking on cosmology and all the mysteries that this topic entails. This is true frontier-science and that perspective should never be lost in any such discussion.
Getting back to Penrose, his latest book tackles cosmology on the grandest scale from the universe’s Big Bang to its inevitable demise. Along the way he challenges the accepted wisdom of inflation amongst other prevailing ideas. He commences with a detailed description of entropy because it lies at the heart of the conundrum as he sees it. It’s entropy that makes the Big Bang so very special, and he spends almost half the book on expounding why.
Penrose describes specific aspects of time that I referred to in a post last year (The enigma we call time, July 2010). He gives the same example I did of an egg falling off a table demonstrating the inherent relationship between entropy (the 2nd law of thermodynamics) and the arrow of time we are all familiar with. He even cites a film running backwards showing an egg reconstituting itself and rising from the floor as an example of time reversal and a violation of the 2nd law of thermodynamics acting simultaneously, just as I did. He also explains how time doesn’t exist without mass, because for photons (light rays), which are massless, time is always zero.
The prevailing view, according to almost everything I read on this subject via science magazines, is that we live in a multiverse where universes pop out like exploding bubbles, of which the Big Bang and its consequent ‘inflation’ was just one. In the Christmas/New Year edition of New Scientist (25 December 2010/1 January 2011, p.9) there is an article that claims we may have ‘evidence’ of ‘bruising’ in the CMB (Cosmic Microwave Background) resulting from ‘collisions’ with other universes. (The cosmic background radiation was predicted by the Big Bang and discovered purely by accident, which makes it the best evidence we have that our universe did indeed begin with the Big Bang.)
Some people also believe there is an asymmetry to the universe, implying there is an ‘axis’, which would be consistent with us being ‘joined’ to a ‘neighbouring universe’. But be careful with all these speculative scenarios fed by inexplicable and potentially paradigm-changing observations – they just confirm how little we really know.
The multiverse in conjunction with the ‘anthropic principle’ appears to be the most widely accepted explanation for the how, why and wherewithal of our hard-to-believe existence. Because we live in possibly the only universe of an infinite number then naturally it is the only universe we have knowledge of. If all the other universes, or almost all, are uninhabitable then no one will ever observe them. Ergo we observe this universe because it’s the one that produced life, of which we are the ultimate example.
Paul Davies, in The Goldilocks Enigma, spends a page and a half discussing both the virtues and pitfalls of the multiverse proposition. In particular, he discusses what he calls ‘...the extreme multiverse model proposed by Max Tegmark in which all possible worlds of any description really exist…’ In other words, whatever mathematics allows can exist. Quoting Davies again: ‘The advantage of the extreme multiverse is that it explains everything because it contains everything.’ However, as he also points out, because it explains everything it virtually explains nothing. As someone else, a theologian (I can’t remember who), once pointed out, in a discussion with Richard Dawkins, it’s no more helpful than a ‘God-of-the-gaps’ argument, which also explains everything and therefore ultimately explains nothing.
Stephen Hawking has also come out with a new book with Leonard Mlodinow titled The Grand Design, which I haven’t read but read reviews of, in particular Scientific American. Someone in America (Dale, who has a blog, Faith in Honest Doubt) put me onto a radio podcast by some guys under the name, Reasonable Doubts, who ran a 3-part series on Buddhism. At the end of one of their programmes they took Hawking to task for making what they saw as the absurd claim that the universe could be ‘something from nothing’.
I left a comment on their blog that this was not a new idea:
I'm not sure why you got in a tiz about Hawkings' position, though I haven't read his latest book, but I read an editorial comment in Scientific American under the heading, Hawking vs God. The idea that the universe could be 'something for nothing' is not new. Paul Davies discussed it over 20 years ago in God and the New Physics (1983) in a chapter titled: Is the universe a free lunch? He says almost exactly what Hawking is credited with saying (according to Scientific American): the universe (according to the 'free lunch' scenario) can account for itself, the only thing that is unaccountable are the laws of nature that apparently brought it about. Davies quotes physicist, Alan Guth: "It's often said that there is no such thing as a free lunch. The universe, however, is a free lunch."
Davies, Hawking and Penrose are not loonies – they are all highly respected physicists. We’ve learned from Einstein and Bohr that nature doesn’t obey rules according to our common sense view of the world, and, arguably, the universe’s origin is the greatest of all unsolved mysteries. Why is there something instead of nothing? And is there any reason to assume that there wasn’t nothing before we had something?
What, may you ask, has any of this to do with Penrose’s CCC theory? It’s just a detour to synoptically describe the intellectual landscape that his theory inhabits.
As I alluded to earlier, Penrose focuses on the biggest conundrum in the universe, being entropy, and how it makes the Big Bang so ultra-ultra special. Few discussions I’ve read on cosmology even mention the role of entropy, yet it literally drives the entire universe’s evolution – Paul Davies doesn’t shy away from it in God and the New Physics - but otherwise, only Penrose puts it centre stage from my reading experience.
Both Davies and Penrose discuss it in terms of ‘phase space’ which is really hard to explain and really hard to envisage without thinking about dimensional space. But effectively the equation for entropy is the logarithm of a volume of phase space multiplied by Boltzmann’s constant: S = k log(V). The use of a logarithm allows one to differentiate between entropies in a dynamic system. Significantly, one can only ‘take away’ entropy by adding it to somewhere else that’s external to the ‘closed’ environment one is studying. The most obvious example is a refrigerator that keeps cold by dumping heat externally to the ambient air in a room (the fridge loses entropy by adding it externally). As Penrose points out, the only reason the Sun’s energy is ‘useful’ to us is because it’s a ‘locally’ hot spot in an otherwise cold space. If it was in thermal equilibrium with its environment it would be useless to Earth. ‘Work’ can only be done when there is an imbalance in energy (usually temperature) between a system and its environment.
But more significantly, to decrease the entropy in a ‘closed’ system (like a refrigerator or Earth) there must be an increase in entropy externally. So ultimately the entire universe’s entropy must always be increasing. The corollary to that is that the universe must have started with a very small entropy indeed, and that is what makes the Big Bang so very special. In fact Penrose calculates the ultimate phase space volume of the entire universe as e raised to the power of 10 raised to the power of 123, (e10)123, or, if it’s easier to comprehend, take 10 raised to the power of 10 (10 plus 10 noughts) raised to the power of 123 (10 x 123 noughts). So That’s 1 with 123 x 10 noughts after it. To reverse this calculation, it means that the precision of the big bang to create the universe that we live in is one part in 10 to the 10 to 123, (1-10)-123. So that’s a precision of 0.00…(123x10 0’s)1.
Penrose takes the universe in its current state and extrapolates it back to its near-origin at the so-called inflationary stage between 10-35 and 10-32 seconds from its birth. He also extrapolates it into its distant future, making some assumptions, and finding that the two states are ‘conformally’ equivalent. One of his key assumptions is that the universe is inherently hyperbolic so it has a small but positive cosmological constant. This means that the universe will always expand and never collapse back onto itself. Penrose provides good arguments, that I won’t attempt to replicate here, that a ‘Big Bounce’ scenario could not produce the necessary entropic precision that we appear to need for the Big Bang. In other words, it would be a violation of the 2nd law of thermodynamics.
Penrose’s future universe assumes that the universe would consist entirely of black holes, many of which exist at the centre of all known galaxies. As these black holes become ‘hotter’ than the space that surrounds them, they will evaporate through Hawking radiation, so that eventually the entire universe will be radiation in the form of electromagnetic waves and gravitons. Significantly there will be virtually no mass therefore no clocks, and, from what I can understand, that’s what makes the universe conformal. It will have a ‘conformal boundary’. Penrose’s bold hypothesis is that this conformal boundary will become the conformal boundary that we envisage at the end of the inflationary period of our universe. Hence the death of one universe becomes the birth of the next.
What of the conundrum of the 2nd law of thermodynamics? Penrose spends considerable time discussing whether or not information is lost in black holes, which is a contentious point. Hawking once argued that information was lost, but now argues otherwise. Penrose thinks he should have stuck to his guns. Many scientists believe it’s a serious flaw in cosmological thinking to consider that information could be lost in black holes. Many scientists and philosophers argue that ‘everything’ is information, including us. There’s an argument that teleportation is theoretically achievable, even on a macro scale, because everything is just information at base. I’ve never been convinced of that premise, but leaving that aside, I think that information could be lost in black holes and so does Penrose. If this is true then all information regarding our universe will no longer exist after all the black holes evaporate, and, arguably, entropy will be reset, along with time. I’ve simplified this part of Penrose’s treatise, so I may not be doing him justice, but I know that the loss of information through multiple black hole evaporation is crucial to his theory.
When I first came across this thesis in On Space and Time I admit that it appealed to me philosophically. The idea that the end of the universe could be mathematically and physically equivalent to its beginning, and therefore could recycle endlessly is an intellectually attractive idea. Nature is full of beginnings and endings on all sorts of scales, why not on the cosmological scale? Infinity is the scariest concept there is if you think about it seriously – the alternative is oblivion, nihilism effectively. We have a life of finite length that we are only aware of while we are living it, yet we know that existence goes on before we arrive and after we’re gone. Why should it be any different for the universe itself?
I admit I don’t understand all the physics, and there still seems to be the issue of going from a cold universe of maximum entropy to a hot universe of minimum entropy, yet Penrose seems to believe that his ‘conformal boundary’ at both ends allows for that eventuality.
Sunday, 16 January 2011
Saturday, 8 January 2011
It's women who choose, not men
Not so recently, I told someone I had a blog and it was called Journeyman Philosopher and they couldn’t stop themselves from laughing. I said, ‘Yes, it is a bit wankerish.’ Especially for an Aussie. But I’m not and never will be the real thing – a philosopher, that is – yet I practice philosophy, by attempting to emulate the credo I have inscribed at the top. The truth is that none of us, who value knowledge for its own sake, ever stop learning, and I’ve made it a lifetime passion. This blog does little more than pass on and share, and occasionally provide insights. But I also attempt to provoke thought, and if I should ever fail at that then I should call it quits.
So this post is one of those thought-provoking ones, because it challenges centuries of culturally accepted norms. I’m a single bloke who’s never married, so I’m hardly an expert on relationships, but this is a philosophical position on relationships garnered both from experience and observation.
Recently, I took part in a discussion on Eli’s blog, Rustbelt Philosophy, whereby I cited Nietzsche from Beyond Good and Evil that most people take a philosophical position on visceral grounds and then rationalise it with an argument. As I commented on Eli’s blog, I think this is especially true for religious arguments, but it has wider applications as well. The more we invest in a theory (for example) the less likely we are to reject it, even in the face of conflicting evidence.
I’m currently reading Roger Penrose’s latest book, Cycles of Time (to be the subject of a future post) and he readily acknowledges his personal prejudices in outlining his iconoclastic theory for the origins of our universe. The point I’m making, and its relevance to this post, is that I too have prejudices that shape my views on this topic.
In the last decade or 2 there has been a strong and popular resurgence in Jane Austen’s novels (through film and TV), which indicates they have strong universal themes. Jane Austen suffered from the prejudices of her day when women were not supposed to earn money, and the class structure, in which she lived, precluded intelligent women, like herself, from attaining fulfilling lives. Everything was dependent on them marrying the right bloke, or more clinically, marrying into the right family. I have to say that I’ve seen examples of that narrow-minded thinking even in my own lifetime. Austen had her novels published through a male intermediary and on her grave there is no mention that she was an author because it was considered a sleight for a woman to admit she had a profession.
But the theme of every Austen novel that I’ve seen (I haven’t read any of them) is that the woman finds the right bloke despite the obstacles that her society puts in her way. And the right bloke is the one who demonstrates that he’s a genuine friend and not someone who is playing the social game according to the rules of their society. Austen was an iconoclast in her own right, and the fact that her stories still ring true today, indicates that she was revealing a universal truth.
Somewhere in my childhood I realised that women are in fact the stronger sex, and that whilst men can’t live without women, they can live without us. But this is only one reason that I believe women should do the choosing and not the men. The mechanics of courtship also indicate that it is the woman who chooses even though the bloke thinks it’s him. I remember seeing a documentary on speed-dating once, and the facilitator made the exact same observation. Personally, I wasn’t surprised.
In many respects, I think the best analogy in the animal kingdom is with birds. The male really just wants to have sex, so what does he do? He sings or he flashes colourful plumage or he performs a dance or he builds a bower, and then the female chooses the one she thinks is best, not the other way round. Now, this is an analogy, but I think it applies to humans just as well. Whilst it is the woman who might arguably wear the plumage, she does the selecting, and it is the men who perform. We show off our wit and conversation, we drive flash cars and buy big houses and use whatever talents we may have to impress. I read somewhere recently (Scientific American Mind) that in mixed company it is the men who tell the jokes and the women who do the laughing.
So my argument is that we woo but women select. I believe this is the natural order and centuries of cultural, religious and political control have attempted to overturn it. All our institutions have been patriarchal and marriage is arguably the most patriarchal of them all.
And this is where my argument reflects the sentiment expressed by Nietzsche, because I have a rational justification to support my intuitively-premised prejudice. It is the woman who has most to lose in a relationship because she’s the one who gets pregnant. So what I’m arguing is that it should be her choice all the way down the line. It is the woman who should determine the parameters and limits of a relationship. It is she who should decide how intimate it should become and whether marriage is an option, not the bloke. I would even argue that men cope with rejection better than women. Our sex drive is like a tap, easy to turn on, not so easy to turn off, but that’s what masturbation is for.
Anyone who has read my book, Elvene, will recognise a feminist theme that pretty well reflects the philosophy I’ve outlined above. It wasn’t intentional, and it was only afterwards that I realised that I had encapsulated that theme into my writing. Considering it’s set in the future, not the past, it has little in common with Jane Austen. As one of its reviewers pointed out, the book also deals with relationship issues like respect, honesty and generosity of spirit.
In essence, I think the patriarchal cultural mores that we’ve had for centuries are not only past their use-by-date, but are in conflict with the natural order for human relationships. Our societies would be a lot more psychologically healthy if that was acknowledged.
So this post is one of those thought-provoking ones, because it challenges centuries of culturally accepted norms. I’m a single bloke who’s never married, so I’m hardly an expert on relationships, but this is a philosophical position on relationships garnered both from experience and observation.
Recently, I took part in a discussion on Eli’s blog, Rustbelt Philosophy, whereby I cited Nietzsche from Beyond Good and Evil that most people take a philosophical position on visceral grounds and then rationalise it with an argument. As I commented on Eli’s blog, I think this is especially true for religious arguments, but it has wider applications as well. The more we invest in a theory (for example) the less likely we are to reject it, even in the face of conflicting evidence.
I’m currently reading Roger Penrose’s latest book, Cycles of Time (to be the subject of a future post) and he readily acknowledges his personal prejudices in outlining his iconoclastic theory for the origins of our universe. The point I’m making, and its relevance to this post, is that I too have prejudices that shape my views on this topic.
In the last decade or 2 there has been a strong and popular resurgence in Jane Austen’s novels (through film and TV), which indicates they have strong universal themes. Jane Austen suffered from the prejudices of her day when women were not supposed to earn money, and the class structure, in which she lived, precluded intelligent women, like herself, from attaining fulfilling lives. Everything was dependent on them marrying the right bloke, or more clinically, marrying into the right family. I have to say that I’ve seen examples of that narrow-minded thinking even in my own lifetime. Austen had her novels published through a male intermediary and on her grave there is no mention that she was an author because it was considered a sleight for a woman to admit she had a profession.
But the theme of every Austen novel that I’ve seen (I haven’t read any of them) is that the woman finds the right bloke despite the obstacles that her society puts in her way. And the right bloke is the one who demonstrates that he’s a genuine friend and not someone who is playing the social game according to the rules of their society. Austen was an iconoclast in her own right, and the fact that her stories still ring true today, indicates that she was revealing a universal truth.
Somewhere in my childhood I realised that women are in fact the stronger sex, and that whilst men can’t live without women, they can live without us. But this is only one reason that I believe women should do the choosing and not the men. The mechanics of courtship also indicate that it is the woman who chooses even though the bloke thinks it’s him. I remember seeing a documentary on speed-dating once, and the facilitator made the exact same observation. Personally, I wasn’t surprised.
In many respects, I think the best analogy in the animal kingdom is with birds. The male really just wants to have sex, so what does he do? He sings or he flashes colourful plumage or he performs a dance or he builds a bower, and then the female chooses the one she thinks is best, not the other way round. Now, this is an analogy, but I think it applies to humans just as well. Whilst it is the woman who might arguably wear the plumage, she does the selecting, and it is the men who perform. We show off our wit and conversation, we drive flash cars and buy big houses and use whatever talents we may have to impress. I read somewhere recently (Scientific American Mind) that in mixed company it is the men who tell the jokes and the women who do the laughing.
So my argument is that we woo but women select. I believe this is the natural order and centuries of cultural, religious and political control have attempted to overturn it. All our institutions have been patriarchal and marriage is arguably the most patriarchal of them all.
And this is where my argument reflects the sentiment expressed by Nietzsche, because I have a rational justification to support my intuitively-premised prejudice. It is the woman who has most to lose in a relationship because she’s the one who gets pregnant. So what I’m arguing is that it should be her choice all the way down the line. It is the woman who should determine the parameters and limits of a relationship. It is she who should decide how intimate it should become and whether marriage is an option, not the bloke. I would even argue that men cope with rejection better than women. Our sex drive is like a tap, easy to turn on, not so easy to turn off, but that’s what masturbation is for.
Anyone who has read my book, Elvene, will recognise a feminist theme that pretty well reflects the philosophy I’ve outlined above. It wasn’t intentional, and it was only afterwards that I realised that I had encapsulated that theme into my writing. Considering it’s set in the future, not the past, it has little in common with Jane Austen. As one of its reviewers pointed out, the book also deals with relationship issues like respect, honesty and generosity of spirit.
In essence, I think the patriarchal cultural mores that we’ve had for centuries are not only past their use-by-date, but are in conflict with the natural order for human relationships. Our societies would be a lot more psychologically healthy if that was acknowledged.
Sunday, 2 January 2011
The Number Devil by Hans Magnus Enzensberger
It’s been a while since I’ve written anything really meaty on my blog and an entire year since I last wrote a post that reviewed a book on mathematics.
But what I really like about this particular post is that it renders the near to the global. This arose from a Christmas drink that I had with my neighbour across the road, Sarah, who lent me a book, that she never lends, on the proviso I write it up on my blog. So from my neighbour, who literally lives directly opposite me with her 2 sons, Andre and Emelio, to the blogosphere.
Over a bottle of Aussie red (Barossa Valley Shiraz 2008) – yes that’s worth mentioning because we both agreed that it was a bloody good drop (literally and figuratively) – we somehow got into a discussion on mathematics and the teaching of mathematics in particular, which led us to swapping books the next day.
On Christmas Day 2009, I published a post on The Bedside Book of Algebra (Michael Willers), which is the book I swapped with Sarah. The Number Devil; A Mathematical Adventure covers some of the same material but it’s aimed at a younger audience and it has a different approach. The whole purpose of this book it to reveal to young people that mathematics is a world worth exploring and not just a sadistic intellectual exercise designed by teachers to torment young developing minds. Sarah’s book has 2 bookmarks in it: one for her and one for her 7 year-old son; and her son’s bookmark is further advanced than hers.
It is written in novel-form and the premise of the narrative is very simple: the protagonist, Robert, is having tormenting dreams when he is visited by a devil, who calls himself the ‘Number Devil’ and begins to give him lessons in mathematics. It’s extremely clever, because it’s engaging and contains entertaining and informative illustrations, as well as providing exposition on some of the more esoteric mathematical concepts like infinity, transfinite numbers, combinations and permutations, Pascal’s triangle, Fibonacci numbers, prime numbers and Goldbach’s conjecture.
Whilst Enzensberger reveals the relationship between Pascal’s triangle and Fibonacci numbers, he doesn’t explain the relationship between Pascal’s triangle and the binomial theorem, which I learned in high school. He also explains the relationship between Pascal’s triangle and the combination algorithm, but not the way I learned it, which I think is more intuitive and useful. He uses diagonals (within Pascal’s triangle) whereas I learned it by using the rows.
The cleverness is that he provides these expositions without revealing to the reader how advanced these mathematical ‘lessons’ are. In fact, the reader is introduced to the ‘mysteries’ that have fascinated ‘ancients’ from many cultures across the world. Enzensberger’s inspired approach is to reveal the appeal of mathematics (that most mathematicians only find in adulthood) to young people before they are turned off it forever. He demonstrates that esoteric concepts can be taught without emphasising their esoterica.
Even the idea of a ‘number devil’ is inspired because mathematics is considered to be so devilish, and, in some cultures, mathematicians were considered to be devil’s apprentices (refer my recent post on Hypatia). In the second chapter (chapters are sequential nights of dreaming) Robert finds himself in a cave with the Number Devil, and the illustration is an obvious allusion to Plato’s cave, though no mention is made of this in the text.
At the end, the Number Devil takes Robert to ‘Number Heaven’ and ‘Number Hell’, though they appear to be the same place, where he meets some of the ‘masters’ like Russell, Fibonacci, Archimedes and a Chinese man whose name we don’t learn. We don’t meet Pythagoras who lives in a higher realm altogether, up in the clouds.
I’d recommend this book to any parent whose children show the slightest mathematical inclination and also adults who want an introduction to this esoteric world. As Sarah said, it’s like a mathematical version of Jostein Gaarder’s Sophie’s World, which is a high enough recommendation in itself.
Oh, I should mention that the illustrations are by Rotraut Susanne Berner; they augment the text perfectly.
But what I really like about this particular post is that it renders the near to the global. This arose from a Christmas drink that I had with my neighbour across the road, Sarah, who lent me a book, that she never lends, on the proviso I write it up on my blog. So from my neighbour, who literally lives directly opposite me with her 2 sons, Andre and Emelio, to the blogosphere.
Over a bottle of Aussie red (Barossa Valley Shiraz 2008) – yes that’s worth mentioning because we both agreed that it was a bloody good drop (literally and figuratively) – we somehow got into a discussion on mathematics and the teaching of mathematics in particular, which led us to swapping books the next day.
On Christmas Day 2009, I published a post on The Bedside Book of Algebra (Michael Willers), which is the book I swapped with Sarah. The Number Devil; A Mathematical Adventure covers some of the same material but it’s aimed at a younger audience and it has a different approach. The whole purpose of this book it to reveal to young people that mathematics is a world worth exploring and not just a sadistic intellectual exercise designed by teachers to torment young developing minds. Sarah’s book has 2 bookmarks in it: one for her and one for her 7 year-old son; and her son’s bookmark is further advanced than hers.
It is written in novel-form and the premise of the narrative is very simple: the protagonist, Robert, is having tormenting dreams when he is visited by a devil, who calls himself the ‘Number Devil’ and begins to give him lessons in mathematics. It’s extremely clever, because it’s engaging and contains entertaining and informative illustrations, as well as providing exposition on some of the more esoteric mathematical concepts like infinity, transfinite numbers, combinations and permutations, Pascal’s triangle, Fibonacci numbers, prime numbers and Goldbach’s conjecture.
Whilst Enzensberger reveals the relationship between Pascal’s triangle and Fibonacci numbers, he doesn’t explain the relationship between Pascal’s triangle and the binomial theorem, which I learned in high school. He also explains the relationship between Pascal’s triangle and the combination algorithm, but not the way I learned it, which I think is more intuitive and useful. He uses diagonals (within Pascal’s triangle) whereas I learned it by using the rows.
The cleverness is that he provides these expositions without revealing to the reader how advanced these mathematical ‘lessons’ are. In fact, the reader is introduced to the ‘mysteries’ that have fascinated ‘ancients’ from many cultures across the world. Enzensberger’s inspired approach is to reveal the appeal of mathematics (that most mathematicians only find in adulthood) to young people before they are turned off it forever. He demonstrates that esoteric concepts can be taught without emphasising their esoterica.
Even the idea of a ‘number devil’ is inspired because mathematics is considered to be so devilish, and, in some cultures, mathematicians were considered to be devil’s apprentices (refer my recent post on Hypatia). In the second chapter (chapters are sequential nights of dreaming) Robert finds himself in a cave with the Number Devil, and the illustration is an obvious allusion to Plato’s cave, though no mention is made of this in the text.
At the end, the Number Devil takes Robert to ‘Number Heaven’ and ‘Number Hell’, though they appear to be the same place, where he meets some of the ‘masters’ like Russell, Fibonacci, Archimedes and a Chinese man whose name we don’t learn. We don’t meet Pythagoras who lives in a higher realm altogether, up in the clouds.
I’d recommend this book to any parent whose children show the slightest mathematical inclination and also adults who want an introduction to this esoteric world. As Sarah said, it’s like a mathematical version of Jostein Gaarder’s Sophie’s World, which is a high enough recommendation in itself.
Oh, I should mention that the illustrations are by Rotraut Susanne Berner; they augment the text perfectly.
Tuesday, 21 December 2010
Ayaan Hirsi Ali
This woman should need no introduction, she’s been in the media in most Western countries I’m sure. I thought this was a really good interview (Tue. 21 Dec. 2010) because it gives an insight into her background as well as a candid exposition of her political and philosophical views.
I haven’t read either of her biographies, but I’ve read second-hand criticism which led me to believe she was anti-Islamic. This is not entirely true, depending on how one defines Islam. To quote her own words: “I have no problem with the religious dimension of Islam.” She’s not the first Muslim I’ve come across to differentiate between religious and political Islam. Most Westerners, especially since 9/11, believe that any such distinction is artificial. I beg to differ.
She makes it very clear that she’s against the imposition of Sharia law, the subjugation of women and any form of totalitarianism premised on religious-based scripture (irrespective of the religion). In short, she’s a feminist. She decries the trivial arguments over dress when there are other issues of far greater import, like arranged marriages, so-called circumcision of women and honour killings. (For an intelligent debate on whether the burqua should be ‘outlawed’ I refer you to this.)
What I found remarkable, and almost unimaginable, was how violent her childhood and upbringing were. There was violence in the school, violence in the home, violence in politics. As she points out it was so pervasive that a peaceful environment was considered unthinkable. One of the most poignant stories she tells was when she went to Holland to seek asylum, and on going to a Police Station to register, the policeman asked her if she would like a cup of coffee or tea. This was a revelation to her: that a man in uniform should offer a woman, a stranger and a foreigner, a cup of coffee or tea was simply mind-blowing.
It is beyond most of us to imagine a childhood where violence is the principal form of interrogation and negotiation between people in all walks of life: home, education and work; yet that was her life. That she can now talk of falling in love and of writing a letter to her unborn child for a hopeful future is close to miraculous.
What resonated with me was her argument that it doesn’t take 600 years to reconcile Islam with the modern secular world, but only 4 generations. I have Muslim friends, both in America and in Australia, and they belie the belief, held by many in Western societies, that Muslims can’t assimilate and yet keep their cultural and spiritual beliefs. They demonstrate to me that Ayaan Hirsi Ali is correct in her fundamental assumptions and philosophical approach.
I haven’t read either of her biographies, but I’ve read second-hand criticism which led me to believe she was anti-Islamic. This is not entirely true, depending on how one defines Islam. To quote her own words: “I have no problem with the religious dimension of Islam.” She’s not the first Muslim I’ve come across to differentiate between religious and political Islam. Most Westerners, especially since 9/11, believe that any such distinction is artificial. I beg to differ.
She makes it very clear that she’s against the imposition of Sharia law, the subjugation of women and any form of totalitarianism premised on religious-based scripture (irrespective of the religion). In short, she’s a feminist. She decries the trivial arguments over dress when there are other issues of far greater import, like arranged marriages, so-called circumcision of women and honour killings. (For an intelligent debate on whether the burqua should be ‘outlawed’ I refer you to this.)
What I found remarkable, and almost unimaginable, was how violent her childhood and upbringing were. There was violence in the school, violence in the home, violence in politics. As she points out it was so pervasive that a peaceful environment was considered unthinkable. One of the most poignant stories she tells was when she went to Holland to seek asylum, and on going to a Police Station to register, the policeman asked her if she would like a cup of coffee or tea. This was a revelation to her: that a man in uniform should offer a woman, a stranger and a foreigner, a cup of coffee or tea was simply mind-blowing.
It is beyond most of us to imagine a childhood where violence is the principal form of interrogation and negotiation between people in all walks of life: home, education and work; yet that was her life. That she can now talk of falling in love and of writing a letter to her unborn child for a hopeful future is close to miraculous.
What resonated with me was her argument that it doesn’t take 600 years to reconcile Islam with the modern secular world, but only 4 generations. I have Muslim friends, both in America and in Australia, and they belie the belief, held by many in Western societies, that Muslims can’t assimilate and yet keep their cultural and spiritual beliefs. They demonstrate to me that Ayaan Hirsi Ali is correct in her fundamental assumptions and philosophical approach.
Saturday, 11 December 2010
On-line interview for Elvene
This is a blatant promotion. Obviously the interview is totally contrived by the publisher, and if you press TOP at the end of my piece, you will get an overview of the current state of play in Oz publishing and distribution, from the perspective of one of the (minor) players.
Having said that, the questions were not vetted by me and the answers are all my own.
The term 'jack-of-all-trades' is a complete misnomer. Anyone who actually knows me, knows that I'm totally useless at all trades involving genuine dexterous skill. The rest is mostly true, though I've only written one screenplay and one novel that I'm willing to own up to.
The interview contains some of my philosophy on writing in 'nutshell' form, with the added relevance of referencing something that I've written.
Having said that, the questions were not vetted by me and the answers are all my own.
The term 'jack-of-all-trades' is a complete misnomer. Anyone who actually knows me, knows that I'm totally useless at all trades involving genuine dexterous skill. The rest is mostly true, though I've only written one screenplay and one novel that I'm willing to own up to.
The interview contains some of my philosophy on writing in 'nutshell' form, with the added relevance of referencing something that I've written.
Friday, 3 December 2010
Hypatia
Last week I saw a movie by Alejandro Amenabar called Agora, which is effectively the story of Hypatia and her death at the hands of Christian zealots in Alexandria towards the end of the Roman Empire in AD 414. So the film is based on a real event and a real person, though it is a fictional account.
Amenabar also made the excellent film, The Sea Inside, starring Javier Bardem, which was also based on a real person’s life. In this case, a fictionalised account of a quadriplegic’s battle with the Church and government in Spain to take his own life through euthanasia.
I first came across Hypatia in Clifford A. Pickover’s encyclopedic tome, The Math Book, subtitled, From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics. He allots one double page (a page of brief exposition juxtaposed with a graphic or a photo) to each milestone he’s selected. He presents Hypatia as the first historically recognised woman mathematician. In fact she was a philosopher and teacher at the famous Library of Alexandria, even though she was a Greek, and like her father, practiced philosophy, science, mathematics and astronomy in the tradition of Plato and Aristotle. By accounts, she was attractive, but never married, and, according to Pickover, once said she was ‘wedded to the truth’. The film gives a plausible account of her celibacy, when her father explains to a suitor that, in order to marry, she would have to give up her pursuit of knowledge and that would be like a slow death for her.
The film stars Rachel Weisz in the role of Hypatia and it’s a convincing portrayal of an independent, highly intelligent woman, respected by men of political power and persuasion. The complex political scene is also well depicted with the rise of Christianity creating an escalating conflict with Jews that the waning Roman military government seems incapable of controlling.
It’s a time when the Christians are beginning to exert their newly-found political power, and their Biblical-derived authority justifies their intention to convert everyone to their cause or destroy those who oppose them. There is a scene where they drive all the Jews out of Alexandria, which they justify by citing Biblical text. The film, of course, resonates with 20th Century examples of ‘ethnic cleansing’ and the role of religious fundamentalism in justifying human atrocities. Hypatia’s own slave (a fictionalised character, no doubt) is persuaded to join the Christians where he can turn his built-up resentment into justified slaughter.
Hypatia would have been influenced by Pythagoras’s quadrivium, upon which Plato’s Academy was based: arithmetic, geometry, astronomy and music. In the movie she is depicted as a ‘truth-seeker’, who questions Ptolemy’s version of the solar system and performs an experiment to prove to herself, if no one else, that the Earth could move without us being aware of its motion. I suspect this is poetic licence on the part of Amenabar, along with the inference that she may have foreseen that the Earth’s orbit is elliptical rather than circular. What matters, though, is that she took her philosophy very seriously, and she appreciated the role of mathematics in discerning truth in the natural world. There is a scene where she rejects Christianity on the basis that she can’t accept knowledge without questioning it. It would have gone against her very being.
There is also a scene in which the Church’s hierarchy reads the well-known text from Timothy: “I suffer not a woman to teach or to control a man”, which is directed at the Roman Prefect, who holds Hypatia in high regard. The priest claims this is the word of God, when, in fact, it’s the word of Paul. Paul, arguably, influenced the direction of Christianity even more than Jesus. After all, Jesus never wrote anything down, yet Paul’s ‘letters’ are predominant in the New Testament.
Hypatia’s death, in the film, is sanitised, but history records it as brutal in the extreme. One account is that she was dragged through the streets behind a chariot and the other is that she had her flesh scraped from her by shards of pottery or sharp shells. History also records that the Bishop, Cyril, held responsible for her death, was canonised as a saint. The film gives a credible political reason for her death: that she had too much influence over the Prefect, and while they couldn’t touch him in such a malicious way, they could her.
But I can’t help but wonder at the extent of their hatred, to so mutilate her body and exact such a brutal end to an educated woman. I can only conclude that she represented such a threat to their power for two reasons: one, she was a woman who refused to acknowledge their superiority both in terms of gender and in terms of religious authority; and two, she represented a search for knowledge beyond the scriptures that could ultimately challenge their authority. I think it was this last reason that motivated their hatred so strongly. As a philosopher, whose role it was to seek knowledge and question dogma, she represented a real threat, especially when she taught ‘disciples’, some of whom became political leaders. A woman who thinks was the most dangerous enemy they knew.
Addendum: I've since read a book called Hypatia of Alexandria by Michael Deakin, Honorary Research Fellow at the School of Mathematical Sciences of Monash University (Melbourne, Australia). In the appendix, Deakin includes letters written to Hypatia by another Bishop, Synesius of Cyrene, who clearly respected, even adored her, as a former student.
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