Over the last month I’ve acquired 3 books that are not entirely unrelated. Not surprisingly, they all deal with topics I’ve discussed before.
In order of acquisition they are: Physics and Philosophy by Werner Heisenberg; The Book of Universes by John D. Barrow; and MATHS 1001 by Richard Elwes. Of all these, Heisenberg’s book is probably the least accessible, even though it’s written more for a lay-audience than an academic one.
Elwes’ book is subtitled Absolutely everything you need to know about mathematics in 1001 bite-sized explanations. Under the subtitle is a mini-bite-sized blurb presented as an un-credited quote: ‘More helpful than an encyclopaedia, much easier than a textbook’.
Both of these claims seem unrealistic, yet the blurb is probably closer to the end result than the subtitle. I had this book whilst I spent a recent 4 day sojourn in hospital and it ensured that I never got bored.
But Barrow’s book is the most compelling, not least because he’s not just an observer but a participant in the story. Barrow covers the entire Western history of ‘cosmology’ from Stonehenge to String Theories. This is a book that really does attempt to tell you everything you wanted to know about theories of the universe(s). And Barrow’s book is certainly worth writing a post about, because he revealed things to me that I hadn’t known or considered before.
On the back fly cover, Barrow’s credentials are impressive: ‘Professor of Mathematical Sciences and Director of the Millennium Mathematics Project at Cambridge University, Fellow of Clare Hall, Cambridge, a Fellow of the Royal Society, and current Gresham Professor of Geometry at Gresham College, London.’ As an understatement, the citation continues: ‘His principal area of scientific research is cosmology…’. It’s rare to find someone, so highly respected in an esoteric field, who can write so eloquently and incisively for a lay audience. Paul Davies comes to mind, as does Roger Penrose, both of whom get mentioned in the pages.
Not surprisingly, even though Barrow’s narrative goes from Aristotle to Ptolemy to Copernicus then Galileo, Kepler and Newton, it resides mostly in the 20th Century, specifically post Einstein’s theories of relativity. Einstein’s field equations have really dictated all theoretical explorations into cosmology from their inception to the present day, and Barrow continually reminds us of this, despite all the empirical data that has driven our best understanding of the universe to date, like Hubble’s constant and the microwave background radiation.
One of the revelations I found in this text, is that Alan Guth’s inflationary hypothesis virtually guarantees that there is a multiverse. Inflation is like a bubble and beyond the bubble, which must always lie beyond the horizon of our expanding universe, are all the anomalies and inconsistencies that we expect to find from a Big Bang universe. The hypothesis contains within it the possibility that there are numerous other inflationary bubbles, many of which could have occurred prior to ours. Barrow also points out that, if there are an infinite number of universes, than any event with probability greater than 0 could occur an infinite number of times. Only mathematicians and cosmologists truly understand just how big infinity is and what its consequences are. Elwes’ book (MATHS 1001) also brings this point home, albeit in a different way. Barrow’s point is that if there are an infinite number of universes then there are an infinite number of you(s) doing exactly what you are doing now as well as an infinite number living infinitely different lives. The fact that they will never encounter each other means that they can exist without mutual awareness except as philosophical speculations like I’m doing now.
For most people the thought of an infinite number of themselves living infinitely variable lives is enough to turn them off the infinite multiverse hypothesis. It should also make one reconsider the idea of an infinite afterlife.
The other philosophical concept that Barrow discusses at length is the anthropic principle and how it is virtually unavoidable in the face of our existence. Another of his relevations (to me) was that we don’t live in one of the most ‘probable’ universes. He demonstrates that if we were to produce a bell curve of probable universes that our particular universe exists in the ‘tail’ and not at the peak as one might expect.
As he says: “Universes that don’t produce the possibility of ‘observers’ – and they do not need to be like ourselves – don’t really count when it comes to comparing the theory with the evidence.”
He then goes on to say: “This is most sobering. We are not used to the existence of cosmologists being a significant factor in the evaluation of cosmological theories.”
There is a link between this idea and quantum mechanics, which I’ll return to later. It was explored specifically by John Wheeler and discussed at length by Paul Davies in his book, The Goldilocks Enigma. People are often dismissive about the idea of why there is something rather than nothing. Recently, Stephen Law, in a debate with Peter Atkins, said that this was the wrong question without elaborating on why it was or what the right question might be. The point is that without conscious entities there may as well be nothing, because only conscious entities, like us, give meaning to the universe at all. To dismiss the question is to say that the universe not only has no meaning but should have no meaning. It’s not surprising (to me) that the people who insist our existence has no meaning also insist that we have no free will. I challenge both premises (or conclusions, depending how they’re framed).
Slightly off track, but only slightly; Barrow immediately follows this relevation with another of equal importance. Life in a universe requires both lots of time and lots of space, so we should not be so surprised that we live in such a vast expanse of space bookended by equally vast amounts of time. It is because life requires enormous complexity that it also requires enormous time to create it.
Again, to quote Barrow: “This is why we should not be surprised to find that our universe is so old. It takes lots of time to produce the chemical building blocks needed for any type of complexity. And because the universe is expanding, if it is old, it must be big – billions of light years in extent.”
Stephen Hawking recently created a minor furor when he claimed the entire universe could have arisen from nothing. People who should know better, or should simply read more, were derisive of the statement, believing he was giving fundamentalists ready-made ammunition by kicking an own goal. Back in the 1980s, Paul Davies in his book, God and the New Physics (covers much the same material as Dawkins’ The God Delusion, only in more depth) quotes Alan Guth that “the Universe is the ultimate free lunch”. Barrow also points out that gravity in the way of potential energy (therefore negative energy) can exactly balance all the positive energy of mass and radiation (through E=mc2) so that the energy balance for the entire universe can be zero.
Heisenberg’s uncertainty principle allows that matter (therefore energy) can and is produced all the time (via ‘quantum fluctuations’) albeit for very short periods of time. The shorter the time, the higher the energy, via the relationship of Planck’s constant, h. So a quantum mechanism for producing something from nothing does exist. That it can happen on a cosmological scale is not so improbable if all the principle forces of nature: gravitation, electromagnetic, electroweak and strong nuclear; can all meet as equal magnitude in the crucible we call the Big Bang. In his discussion on ‘grand unification’ Barrow leaves gravity out of it. I’ve glossed over this for the sake of brevity, but Barrow discusses it in detail. He also discusses the asymmetry between matter and anti-matter that allows anything to exist at all. (He wrote another book on 'symmetry-breaking' with Joseph Silk called The Left Hand of Creation.)
Another revelation I found in Barrow’s book was his discussion of string theories, now collectively called M theory, and the significance of Calib-Yau spaces or manifolds, of which there are over 10500 possibilities (remember 1 billion is only 109). Significantly, all these predict that gravity can be expressed by Einstein’s field equations. So Einstein still dominates the landscape, though what he would make of this development is anyone’s guess.
This means that our quest for a ‘Theory of Everything’ has led to a multitude of universes of which ours is one in 10500. But Barrow goes further when he explains “There are an infinite number of possible universes. The number is too large to be explored systematically by any computer.”
But Barrow’s best revelation is left to the next to last page when he claims that he and Douglas Shaw have recently postulated that the cosmological constant (which ‘adds an additional equation to those first found by Einstein’) is given by the relationship (tp/tu)2 where tp is Planck’s fundamental time, 10-43 sec, and tu is the current age of the universe, 4.3x1017 sec. tp is the smallest quantity of time predicted by quantum mechanics, so is effectively the basic unit of time for the whole universe. By postulating the cosmological constant as a squared ratio dependent on the age of the universe it gives a rational reason, as opposed to a mystical one, why it is the value we observe today of 0.5x10-121. What’s more, their postulate makes a prediction that the curvature of the universe is -0.0056. Current observations give between -0.0133 and +0.0084, but more accurate maps of the microwave background radiation should ‘be able to confirm or refute this very precise prediction’.
There is an intriguing connection between the anthropic principle and quantum mechanics. The Copenhagen interpretation, led by Bohr and given support by Heisenberg, attempts to bridge the gap between the classical world and the quantum world, by stating that something becomes manifest only after we’ve made a ‘measurement’. I think Bohr took this literally and John Wheeler, who was a loyal disciple of Bohr’s, took it even further when he extrapolated it to the cosmos. Paul Davies explores John Wheeler’s thesis in The Goldilocks Enigma, whereby Wheeler proposes a reverse causal relationship, a cosmological quantum loop in effect, between our observation of the universe and its existence. Most people find this too fantastical to entertain, yet it ties quantum mechanics to the anthropic principle in a fundamental way.
Elwes’ book also discusses quantum mechanics and explicates better than most I’ve read, when he expounds that the wave function (given by Schrodinger’s equation) ‘is no longer a valid description of the state of the particle. It is difficult to avoid the conclusion that whenever someone (or perhaps something) takes a measurement, the quantum system mysteriously jumps from being smoothly spread out, to crystallizing at a specific position.’ (italics in the original)
One can’t help but compare Heisenberg’s book (Physics and Philosophy) with Schrodinger’s (What is Life?), which I reviewed in November 2009. Both men made fundamental contributions to quantum theory, for which they were both awarded Nobel prizes, yet they maintained philosophical differences over its ramifications. Schrodinger’s book is a far better read, not least because it’s more accessible. Both impress upon the reader the significance of mathematics in fathoming the universe’s secrets. Schrodinger appealed to Platonism whereas, to my surprise, Heisenberg appealed to the Pythagoreans, who influenced Plato’s Academy and its curriculum of arithmetic, geometry, astronomy and music – Pythagoras’s quadrivium. In particular, Heisenberg quotes Russell on Pythagoras: “I don’t know of any other man who has been as influential as he was in the sphere of thought.”
Quantum phenomena suggests to me that everything is connected. Why do radioactive half lives follow a totally predictable rule statistically but individually are not predictable at all? It’s like the decay exists at a holistic level rather than a unit level. Planck’s constant gives an epistemological limit to our ability to predict or know. At the other end of the scale, the universe exists for us at a time when we can make sense of it. Barrow, along with Douglas Shaw, entails Planck’s constant as a fundamental unit of time in an equation that suggests we understand it only because we are here at this specific time in its history. There is no other explanation, and maybe there is no other explanation required.
Addendum 1: Scientific American (through Paul J. Steinhardt) have a for-and-against discussion on the merits of Alan Guth's 30 year old inflationary theory, and include a reference to Roger Penrose's ideas that I discussed in a post last January.
Addendum 2: Yes, I've changed the title (Sep 2017).
Sunday 15 May 2011
Friday 6 May 2011
God with no ego
An unusual oxymoron, I know, but, like anything delivered tongue-in-cheek, it contains an element of serious conjecture. Many years ago (quarter of a century), I read a book on anthropology, which left no great impression on me except that the author said that there were 2 types of culture world wide. One cultural type had a religion based on a ‘creator’ or creation myth, and the other had a religion based on ancestor worship.
I would possibly add a third, which is religion based on the projection of the human psyche. In a historical context, religion has arisen primarily from an attempt to project our imagination beyond the grave. Fascination in the afterlife started early for humans, if ritual burials are anything to go by. By extension, the God of humans, in all the forms that we have, is largely manifest in the afterlife. The only ‘Earthly’ experiences of God or Gods occur in mythology.
Karen Armstrong, in her book, The History of God demonstrates how God has evolved over time as a reflection of the human psyche. I know that Armstrong is criticised on both sides of the religious divide, but The History of God is still one of the best books on religion I have read. It’s one of her earliest publications when she was still disillusioned by her experience as a Carmelite nun. A common theme in Armstrong’s writing is the connection between religion and myth.
I’ve referred to Ludwig Feuerbach in previous posts for his famous quote: God is the outward projection of the human psyche (I think he said ‘man’s inner nature’), so I’ve taken a bit of licence; but I think that’s as good a definition of God as you’re going to get. Feuerbach also said that ‘God is in man’s image’ not the other way round. He apparently claimed he wasn’t an atheist, yet I expect most people today would call him an atheist.
For most people, who have God as part of their existential belief, it is manifest as an internal mental experience yet is ‘sensed’ as external. Neurologist, Andrew Newberg of University of Pennsylvania, has demonstrated via brain imaging experiments that people’s experience of ‘religious feelings [God] do seem to be quite literally self-less’. This is why I claim that God is purely subjective, because everyone’s idea of God is different. I’ve long argued that a person’s idea of God says more about them than it says about God.
I would make an analogy with colour, because colour only occurs in some sentient creature’s mind, even though it is experienced as being external to the observer. There is, of course, an external cause for this experience, which is light reflected off objects. People can equally argue that there is an external cause for one’s experience of God, but I would argue that that experience is unique to that person. Colour can be tested, whereas God cannot.
Contrary to what people might think, I’m not judgemental about people’s belief in God – it’s not a litmus test for anything. But if God is a reflection of an individual’s ideal then judge the person and not their God.
When I was 16, I read Albert Camus’ La Peste (The Plague) and it challenged my idea of God. At the time, I knew nothing about Camus or his philosophy, or even his history with the French resistance during WWII. I also read L’Etranger (The Outsider) and, in both books, Camus, through his protagonists, challenges the Catholic Church. In La Peste, there is a scene where the 2 lead characters take a swim at night (if my memory serves me correctly) and, during a conversation, one of them conjectures that it would possibly be better for God if we didn’t believe in God. Now, this may seem the ultimate cynicism but it actually touched a chord with me at that time and at that age. A God who didn’t want you to believe in God would be a God with no ego. That is my ideal.
I would possibly add a third, which is religion based on the projection of the human psyche. In a historical context, religion has arisen primarily from an attempt to project our imagination beyond the grave. Fascination in the afterlife started early for humans, if ritual burials are anything to go by. By extension, the God of humans, in all the forms that we have, is largely manifest in the afterlife. The only ‘Earthly’ experiences of God or Gods occur in mythology.
Karen Armstrong, in her book, The History of God demonstrates how God has evolved over time as a reflection of the human psyche. I know that Armstrong is criticised on both sides of the religious divide, but The History of God is still one of the best books on religion I have read. It’s one of her earliest publications when she was still disillusioned by her experience as a Carmelite nun. A common theme in Armstrong’s writing is the connection between religion and myth.
I’ve referred to Ludwig Feuerbach in previous posts for his famous quote: God is the outward projection of the human psyche (I think he said ‘man’s inner nature’), so I’ve taken a bit of licence; but I think that’s as good a definition of God as you’re going to get. Feuerbach also said that ‘God is in man’s image’ not the other way round. He apparently claimed he wasn’t an atheist, yet I expect most people today would call him an atheist.
For most people, who have God as part of their existential belief, it is manifest as an internal mental experience yet is ‘sensed’ as external. Neurologist, Andrew Newberg of University of Pennsylvania, has demonstrated via brain imaging experiments that people’s experience of ‘religious feelings [God] do seem to be quite literally self-less’. This is why I claim that God is purely subjective, because everyone’s idea of God is different. I’ve long argued that a person’s idea of God says more about them than it says about God.
I would make an analogy with colour, because colour only occurs in some sentient creature’s mind, even though it is experienced as being external to the observer. There is, of course, an external cause for this experience, which is light reflected off objects. People can equally argue that there is an external cause for one’s experience of God, but I would argue that that experience is unique to that person. Colour can be tested, whereas God cannot.
Contrary to what people might think, I’m not judgemental about people’s belief in God – it’s not a litmus test for anything. But if God is a reflection of an individual’s ideal then judge the person and not their God.
When I was 16, I read Albert Camus’ La Peste (The Plague) and it challenged my idea of God. At the time, I knew nothing about Camus or his philosophy, or even his history with the French resistance during WWII. I also read L’Etranger (The Outsider) and, in both books, Camus, through his protagonists, challenges the Catholic Church. In La Peste, there is a scene where the 2 lead characters take a swim at night (if my memory serves me correctly) and, during a conversation, one of them conjectures that it would possibly be better for God if we didn’t believe in God. Now, this may seem the ultimate cynicism but it actually touched a chord with me at that time and at that age. A God who didn’t want you to believe in God would be a God with no ego. That is my ideal.
Friday 22 April 2011
Sentience, free will and AI
In the 2 April 2011 edition of New Scientist, the editorial was titled Rights for robots; We will know when it’s time to recognise artificial cognition. Implicit in the header and explicit in the text is the idea that robots will one day have sentience just like us. In fact they highlighted one passage: “We should look to the way people treat machines and have faith in our ability to detect consciousness.”
I am a self-confessed heretic on this subject because I don’t believe machine intelligence will ever be sentient, and I’m happy to stick my neck out in this forum so that one day I can possibly be proven wrong. One of the points of argument that the editorial makes is that ‘there is no agreed definition of consciousness’ and ‘there’s no way to tell that you aren’t the only conscious being in a world of zombies.’ In other words, you really don’t know if the person right next to you is conscious (or in a dream) so you’ll be forced to give a cognitive robot the same benefit of the doubt. I disagree.
Around the same time as reading this, I took part in a discussion on Rust Belt Philosophy about what sentience is. Firstly, I contend that sentience and consciousness are synonymous, and I think sentience is pretty pervasive in the animal kingdom. Does that mean that something that is unconscious is not sentient? Strictly speaking, yes, because I would define sentience as the ability to feel something, either emotionally or physically. Now, we often feel something emotionally when we dream, so arguably that makes one sentient when unconscious. But I see this as the exception that makes my definition more pertinent rather than the exception that proves me wrong.
In First Aid courses you are taught to squeeze someone’s fingers to see if they are conscious. So to feel something is directly correlated with consciousness and that’s also how I would define sentience. Much of the brain’s activity is subconscious even to the extent that problem-solving is often executed subliminally. I expect everyone has had the experience of trying to solve a puzzle, then leaving it for a period of time, only to solve it ‘spontaneously’ when they next encounter it. I believe the creative process often works in exactly the same way, which is why it feels so spontaneous and why we can’t explain it even after we’ve done it. This subconscious problem-solving is a well known cognitive phenomenon, so it’s not just a ‘folk theory’.
This complex subconscious activity observed in humans, I believe is quite different from the complex instinctive behaviour that we see in animals: birds building nests, bees building hives, spiders building webs, beavers building dams. These activities seem ‘hard-wired’, to borrow from the AI lexicon as we tend to do.
A bee does a complex dance to communicate where the honey is. No one believes that the bee cognitively works this out the way we would, so I expect it’s totally subconscious. So if a bee can perform complex behaviours without consciousness does that mean it doesn’t have consciousness at all? The obvious answer is yes, but let’s look at another scenario. The bee gets caught in a spider’s web and tries desperately to escape. Now I believe that in this situation the bee feels fear and, by my definition, that makes it sentient. This is an important point because it underpins virtually every other point I intend to make. Now, I don’t really know if the bee ‘feels’ anything at all, so it’s an assumption. But my assumption is that sentience, and therefore consciousness, started with feelings and not logic.
In last week’s issue of New Scientist, 16 April 2011, the cover features the topic, Free Will: The illusion we can’t live without. The article, written by freelance writer, Dan Jones, is headed The free will delusion. In effect, science argues quite strongly that free will is an illusion, but one we are reluctant to relinquish. Jones opens with a scenario in 2500 when free will has been scientifically disproved and human behaviour is totally predictable and deterministic. Now, I don’t think there’s really anything in the universe that’s totally predictable, including the remote possibility that Earth could one day be knocked off its orbit, but that’s the subject of another post. What’s more relevant to this discussion is Jones’ opening sentence where he says: ‘…neuroscientists know precisely how the hardware of the brain runs the software of the mind and dictates behaviour.’ Now, this is purely a piece of speculative fiction, so it’s not necessarily what Jones actually believes. But it’s the implicit assumption that the brain’s processes are identical to a computer’s that I find most interesting.
The gist of the article, by the way, is that when people really believe they have no free will, they behave very unempathetically towards others, amongst other aberrational behaviours. In other words, a belief in our ability to direct our own destiny is important to our psychological health. So, if the scientists are right, it’s best not to tell anyone. It’s ironic that telling people they have no free will makes them behave as if they don’t, when allowing them to believe they have free will gives their behaviour intentionality. Apparently, free will is a ‘state-of-mind’.
On a more recent post of Rust Belt Philosophy, I was reminded that, contrary to conventional wisdom, emotions play an important role in rational behaviour. Psychologists now generally believe that, without emotions, our decision-making ability is severely impaired. And, arguably, it’s emotions that play the key role in what we call free will. Certainly, it’s our emotions that are affected if we believe we have no control over our behaviour. Intentions are driven as much by emotion as they are by logic. In fact, most of us make decisions based on gut feelings and rationalise them accordingly. I’m not suggesting that we are all victims of our emotional needs like immature children, but that the interplay between emotions and rational thought are the key to our behaviours. More importantly, it’s our ability to ‘feel’ that not only separates us from machine intelligence in a physical sense, but makes our ‘thinking’ inherently different. It’s also what makes us sentient.
Many people believe that emotion can be programmed into computers to aid them in decision-making as well. I find this an interesting idea and I’ve explored it in my own fiction. If a computer reacted with horror every time we were to switch it off would that make it sentient? Actually, I don’t think it would, but it would certainly be interesting to see how people reacted. My point is that artificially giving AI emotions won’t make them sentient.
I believe feelings came first in the evolution of sentience, not logic, and I still don’t believe that there’s anything analogous to ‘software’ in the brain, except language and that’s specific to humans. We are the only species that ‘downloads’ a language to the next generation, but that doesn’t mean our brains run on algorithms.
So evidence in the animal kingdom, not just humans, suggests that sentience, and therefore consciousness, evolved from emotions, whereas computers have evolved from pure logic. Computers are still best at what we do worst, which is manipulate huge amounts of data. Which is why the human genome project actually took less time than predicted. And we still do best at what they do worst, which is make decisions based on a host of parameters including emotional factors as well as experiential ones.
I am a self-confessed heretic on this subject because I don’t believe machine intelligence will ever be sentient, and I’m happy to stick my neck out in this forum so that one day I can possibly be proven wrong. One of the points of argument that the editorial makes is that ‘there is no agreed definition of consciousness’ and ‘there’s no way to tell that you aren’t the only conscious being in a world of zombies.’ In other words, you really don’t know if the person right next to you is conscious (or in a dream) so you’ll be forced to give a cognitive robot the same benefit of the doubt. I disagree.
Around the same time as reading this, I took part in a discussion on Rust Belt Philosophy about what sentience is. Firstly, I contend that sentience and consciousness are synonymous, and I think sentience is pretty pervasive in the animal kingdom. Does that mean that something that is unconscious is not sentient? Strictly speaking, yes, because I would define sentience as the ability to feel something, either emotionally or physically. Now, we often feel something emotionally when we dream, so arguably that makes one sentient when unconscious. But I see this as the exception that makes my definition more pertinent rather than the exception that proves me wrong.
In First Aid courses you are taught to squeeze someone’s fingers to see if they are conscious. So to feel something is directly correlated with consciousness and that’s also how I would define sentience. Much of the brain’s activity is subconscious even to the extent that problem-solving is often executed subliminally. I expect everyone has had the experience of trying to solve a puzzle, then leaving it for a period of time, only to solve it ‘spontaneously’ when they next encounter it. I believe the creative process often works in exactly the same way, which is why it feels so spontaneous and why we can’t explain it even after we’ve done it. This subconscious problem-solving is a well known cognitive phenomenon, so it’s not just a ‘folk theory’.
This complex subconscious activity observed in humans, I believe is quite different from the complex instinctive behaviour that we see in animals: birds building nests, bees building hives, spiders building webs, beavers building dams. These activities seem ‘hard-wired’, to borrow from the AI lexicon as we tend to do.
A bee does a complex dance to communicate where the honey is. No one believes that the bee cognitively works this out the way we would, so I expect it’s totally subconscious. So if a bee can perform complex behaviours without consciousness does that mean it doesn’t have consciousness at all? The obvious answer is yes, but let’s look at another scenario. The bee gets caught in a spider’s web and tries desperately to escape. Now I believe that in this situation the bee feels fear and, by my definition, that makes it sentient. This is an important point because it underpins virtually every other point I intend to make. Now, I don’t really know if the bee ‘feels’ anything at all, so it’s an assumption. But my assumption is that sentience, and therefore consciousness, started with feelings and not logic.
In last week’s issue of New Scientist, 16 April 2011, the cover features the topic, Free Will: The illusion we can’t live without. The article, written by freelance writer, Dan Jones, is headed The free will delusion. In effect, science argues quite strongly that free will is an illusion, but one we are reluctant to relinquish. Jones opens with a scenario in 2500 when free will has been scientifically disproved and human behaviour is totally predictable and deterministic. Now, I don’t think there’s really anything in the universe that’s totally predictable, including the remote possibility that Earth could one day be knocked off its orbit, but that’s the subject of another post. What’s more relevant to this discussion is Jones’ opening sentence where he says: ‘…neuroscientists know precisely how the hardware of the brain runs the software of the mind and dictates behaviour.’ Now, this is purely a piece of speculative fiction, so it’s not necessarily what Jones actually believes. But it’s the implicit assumption that the brain’s processes are identical to a computer’s that I find most interesting.
The gist of the article, by the way, is that when people really believe they have no free will, they behave very unempathetically towards others, amongst other aberrational behaviours. In other words, a belief in our ability to direct our own destiny is important to our psychological health. So, if the scientists are right, it’s best not to tell anyone. It’s ironic that telling people they have no free will makes them behave as if they don’t, when allowing them to believe they have free will gives their behaviour intentionality. Apparently, free will is a ‘state-of-mind’.
On a more recent post of Rust Belt Philosophy, I was reminded that, contrary to conventional wisdom, emotions play an important role in rational behaviour. Psychologists now generally believe that, without emotions, our decision-making ability is severely impaired. And, arguably, it’s emotions that play the key role in what we call free will. Certainly, it’s our emotions that are affected if we believe we have no control over our behaviour. Intentions are driven as much by emotion as they are by logic. In fact, most of us make decisions based on gut feelings and rationalise them accordingly. I’m not suggesting that we are all victims of our emotional needs like immature children, but that the interplay between emotions and rational thought are the key to our behaviours. More importantly, it’s our ability to ‘feel’ that not only separates us from machine intelligence in a physical sense, but makes our ‘thinking’ inherently different. It’s also what makes us sentient.
Many people believe that emotion can be programmed into computers to aid them in decision-making as well. I find this an interesting idea and I’ve explored it in my own fiction. If a computer reacted with horror every time we were to switch it off would that make it sentient? Actually, I don’t think it would, but it would certainly be interesting to see how people reacted. My point is that artificially giving AI emotions won’t make them sentient.
I believe feelings came first in the evolution of sentience, not logic, and I still don’t believe that there’s anything analogous to ‘software’ in the brain, except language and that’s specific to humans. We are the only species that ‘downloads’ a language to the next generation, but that doesn’t mean our brains run on algorithms.
So evidence in the animal kingdom, not just humans, suggests that sentience, and therefore consciousness, evolved from emotions, whereas computers have evolved from pure logic. Computers are still best at what we do worst, which is manipulate huge amounts of data. Which is why the human genome project actually took less time than predicted. And we still do best at what they do worst, which is make decisions based on a host of parameters including emotional factors as well as experiential ones.
Sunday 3 April 2011
Why we shouldn’t take religion too seriously
This arose from an article in last week’s New Scientist titled Thou shalt believe – or not by Jonathan Lanman (26 March 2011, pp.38-9). Lanman lectures at the school of anthropology and Keble College, Oxford University. He’s giving a talk, entitled Atheism Explained, at St. Mary’s University College Twickenham, UK on 5 April (a couple of days away).
Lanman spent 2008 studying atheism in US, UK, Denmark and online. As a result of his research, Lanman made a distinction between what he calls ‘non-theism’ and ‘strong atheism’, whereby non-theists are effectively agnostic – they don’t really care – and strong atheists vigorously oppose religious belief on moral and political grounds. He found a curious correlation. In countries that are strongly and overtly religious, strong atheism is more predominate, whereas in countries like Sweden, where religion is not so strong, the converse is true. In his own words, there is a negative correlation between strong atheism and non-theism.
I live in Australia where there is a pervasive I-don’t-care attitude towards religious belief, so we are closer to the Swedish model than the American one. In fact, when I visited America a decade ago (both pre and post 911, as well as during) I would say the biggest difference between Australian and American culture is in religion. I spent a lot of time in Texas, where it was almost a culture shock. My experience with the blogosphere has only reinforced that impression.
What is obvious is that where religion takes on a political face then opposition is inevitable. In Australian politics there are all sorts of religious flavours amongst individual politicians, but they rarely become an issue. This wasn’t the case a couple of generations ago when there was a Protestant/Catholic divide through the entire country that started with education and permeated every community, including the small country town where I grew up. That all changed in the 1960s, and, with few exceptions, no one who remembers it wants to revisit it.
Now there is a greater mix of religions than ever, and the philosophy is largely live and let live. Even as a child, religion was seen as something deeply personal and intimate that wasn’t invaded or even shared, and that’s an attitude I’ve kept to this day. Religion, to me, is part of someone’s inner world, totally subjective, influenced by culture, yes, but ultimately personal and unique to the individual.
If people can’t joke about religion in the same way we joke about nationality, or if they feel the need to defend their beliefs in blood, then they are taking their religion too seriously. Even some atheists, in my view, take religion too seriously, when they fail, or refuse, to distinguish between secular adherents to a faith and fundamentalists. If we want to live together, then we can’t take religion too seriously no matter what one’s personal beliefs may be.
Lanman spent 2008 studying atheism in US, UK, Denmark and online. As a result of his research, Lanman made a distinction between what he calls ‘non-theism’ and ‘strong atheism’, whereby non-theists are effectively agnostic – they don’t really care – and strong atheists vigorously oppose religious belief on moral and political grounds. He found a curious correlation. In countries that are strongly and overtly religious, strong atheism is more predominate, whereas in countries like Sweden, where religion is not so strong, the converse is true. In his own words, there is a negative correlation between strong atheism and non-theism.
I live in Australia where there is a pervasive I-don’t-care attitude towards religious belief, so we are closer to the Swedish model than the American one. In fact, when I visited America a decade ago (both pre and post 911, as well as during) I would say the biggest difference between Australian and American culture is in religion. I spent a lot of time in Texas, where it was almost a culture shock. My experience with the blogosphere has only reinforced that impression.
What is obvious is that where religion takes on a political face then opposition is inevitable. In Australian politics there are all sorts of religious flavours amongst individual politicians, but they rarely become an issue. This wasn’t the case a couple of generations ago when there was a Protestant/Catholic divide through the entire country that started with education and permeated every community, including the small country town where I grew up. That all changed in the 1960s, and, with few exceptions, no one who remembers it wants to revisit it.
Now there is a greater mix of religions than ever, and the philosophy is largely live and let live. Even as a child, religion was seen as something deeply personal and intimate that wasn’t invaded or even shared, and that’s an attitude I’ve kept to this day. Religion, to me, is part of someone’s inner world, totally subjective, influenced by culture, yes, but ultimately personal and unique to the individual.
If people can’t joke about religion in the same way we joke about nationality, or if they feel the need to defend their beliefs in blood, then they are taking their religion too seriously. Even some atheists, in my view, take religion too seriously, when they fail, or refuse, to distinguish between secular adherents to a faith and fundamentalists. If we want to live together, then we can’t take religion too seriously no matter what one’s personal beliefs may be.
Sunday 20 March 2011
Ayaan Hirsi Ali’s story
I’ve just completed reading Aayan Hirsi Ali’s autobiography, Infidel. It’s the latest book in my book club (refer my blog roll) following on from another autobiography from another refugee, Anh Do, The Happiest Refugee. Do is a stand-up comic and television celebrity in Australia, and his brother, Khoa, is a successful filmmaker and former Young Australian of the Year. They are ‘boat people’, who are stigmatised in this country, and Khoa was actually dangled over the side of a boat by pirates when he was only 2 years old. It has to be said that our major political parties show a clear deficit in moral and political courage on the issue of ‘boat people’.
But I’ve detoured before I’ve even got started. We, in the West, live in a bubble, though, occasionally, through television, films and books, like Hirsi Ali’s, we get a glimpse into another world that the rest of us would call hell. And this hell is not transient or momentary for these people, but relentless, unforgiving and even normal for those who grow up in it. Hirsi Ali is one of the few people who has straddled these 2 worlds, and that makes her book all the more compelling. As Aminata Forna wrote in the Evening Standard: “Hirsi Ali has invited [us] to walk a mile in her shoes. Most wouldn’t last a hundred yards.”
There are many issues touched on in her story, none perhaps more pertinent than identity, but I won’t start there. I will start with the apparent historical gap between some Islamic cultures and the modern Western world – a clash of civilisations, if you like. I remember the years between my teens and mid twenties were the most transformational, conflicted and depressing in my life. Like many of my generation, it was a time when I rejected my parents’ and society’s values, not to mention the religion I had grown up with, and sought a world view that I could call my own. To some extent that’s exactly what Hirsi Ali has done, only she had to jump from a culture still imbued with 6th Century social mores into the birth of the second millennium. I can fully understand what drove her, but, looking back on my own coming-of-age experience, I doubt that I could emulate her. What she achieved is a monumental leap compared to my short jump. For me, it was generational; for her, it was trans-cultural and it spanned millennia.
Much of her book deals with the treatment of women in traditional Muslim societies, treated, in her own words, as ‘minors’ not adults. One should not forget that the emancipation of women from vassals to independent, autonomous beings with their own rights has been a very lengthy process in Western society. Most societies have been historically patriarchal in both the East and West. The perception and treatment of women as second-class citizens is not confined to Islamic societies by any means. But it does appear that many Islamic cultures have the most barbaric treatment of women (enshrined in law in many countries) and are the most tardy in giving women the social status they deserve, which is equality to men.
This attitude, supported by quotes from the Qur’an, demonstrates how dangerous and misguided it is to take one’s morals from God. Because a morality supposedly given by God, in scripture, can’t be challenged and takes no account of individual circumstances, evolution of cultural norms, progress in scientific knowledge or empathy for ‘others’. And this last criterion is possibly the most important, because it is the ability to treat people outside one’s religion as ‘others’ that permits bigotry, violence and genocide, all in the name of one’s God. This is so apparent in the violence that swept through Hirsi Ali’s home country, Somalia, and became the second most salient factor, I believe, in the rejection of her own religion.
When I first saw Hirsi Ali interviewed on TV (7.30 Report, ABC Australia) after she left Holland for America, she made the statement that Islam could never coexist in a Western secular society, logically based on her experience in Holland. In an interview I heard on the radio last year (also in Australia, with Margaret Throsby) I felt she had softened her stance and she argued that Muslims could live in a secular society. She was careful to make a distinction between Islam as a religion and Islam as political ideology (refer my post Dec. 2010). My personal experience of Muslims is that they are as varied in their political views as any other group of people. I know of liberal Muslims possibly because I hold liberal views, so that should not be surprising. But it gives me a different view to those who think that all Muslims are fundamental Islamists, or potentially so. One of Hirsi Ali’s messages is that an over-dependence on tolerance in a secular society can cause its own backlash.
I’ve written elsewhere (The problems with fundamentalism, Jan. 2008) that the limits of tolerance is intolerance of others. In other words, I am intolerant of intolerance. When Muslims, or anyone else of political persuasion, start to preach intolerance towards any other group then the opposition towards that intolerance in a healthy secular society can be immense. Australia has experienced that on a national level about a decade ago and it was ugly. Xenophobia is very easily aroused in almost any nation it would appear. People who preach hatred and bigotry, no matter who they are or which group they represent, and no matter how cleverly they disguise their rhetoric, should all be treated the same – they should be refuted and denounced in the loudest voices at the highest levels of authority.
But, as the events in Somalia demonstrate, it’s not just religion that can inflame or justify violence. Clan differences are enough to justify the most heinous crimes. All through her story, Hirsi Ali describes how everyone could find fault with every other group they came in contact with. Muslims and Africans are not alone in this prejudicial bias – I grew up with it in a Western secular society. The more insular a society is, the more bigoted they are. This is why I agree with Hirsi Ali that children should not be segregated in their education. The more children mix with other ethnicities the less insular they become in their attitudes towards other groups.
In a post I wrote on Evil (one of my earliest posts, Oct. 2007) I expounded on the idea that most of the atrocities committed in the last century, and every century beforehand for that matter, were based on some form of tribalism or an ingroup-outgroup mentality. This tribalism could be familial, religious, political, ethnic or national, but it revolves around the idea of identity. We underestimate how powerful this is because it’s almost subconscious.
Hirsi Ali’s book is almost entirely about identity and her struggle to overcome its strangulation on her life. All the role models in her young life, both female and male, were imbued with the importance and necessity of identity with her clan and her religion. In her life, religion and culture were inseparable. Her grandmother made her learn her ancestry off by heart because it might one day save her life, and, in fact, it did when she was only 20 years old and a man held a knife to her throat. By reciting her ancestry back far enough she was able to claim she was his ‘sister’ and he let her go.
People often mistakenly believe that their conscience is God whispering in their mind’s ear, when, in fact, it’s almost entirely socially and culturally formed, especially when we are children. It’s only as adults that we begin to question the norms we are brought up with, and then only when we are exposed to other social norms. A way that societies tend to overcome this ‘questioning’ is to imbue a sense of their cultural ‘superiority’ over everyone else’s. This comes across so strongly in Hirsi Ali’s book, and I recognised it as part of my own upbringing. To me, it’s a sign of immaturity that someone can only justify their own position, morally, intellectually or socially, by ridiculing everyone else’s.
One of the strongest influences on Hirsi Ali and her sister, Haweya, were the Western novels that they were exposed to: not just literary standards but pulp fiction romances. It reinforced my view that storytelling, and art in general, is the best medium to transmit ideas. It was this exposure to novels that led them to believe that there were other cultures and other ways of living, especially for women. Stories are what-ifs – they put us in someone else’s shoes and challenge our view of the world. It’s not surprising that some of the world’s greatest writers have been persecuted for their subversiveness.
But this leads to the almost heretical notion that only a society open to new ideas can progress out of ossification. If there is one singular message from Hirsi Ali’s book it’s that fundamentalism (of any stripe) does not only have to be challenged, but overcome, if societies want to move forward and evolve for the betterment for everyone, and not just for those who want to hold the reigns of power.
The real gulf that Hirsi Ali jumped was not religious but educational. I’ve argued many times that ignorance is the greatest enemy facing the 21st Century. Religious fundamentalism is arguably the greatest obstacle to genuine knowledge and rational thinking in the world today. Somewhat surprisingly, this is just as relevant to America as it is to any Islamic nation. The major difference between Islamic fundamentalism and Christian fundamentalism is geography, not beliefs.
Hirsi Ali is foremost a feminist. She once argued that Islam and the West can’t coexist, but she has since softened that stance. Perhaps, like me, she has met Muslim feminists who have found a way to reconcile their religious beliefs with their sense of independence and self-belief. Arguably, self-belief is the most important attribute a human being can foster. The corollary to this is that any culture that erodes that self-belief is toxic to itself.
I’ve written elsewhere (care of Don Cupitt, Sep. 09) that the only religion worth having is the one that you have hammered out for yourself. You don’t have to be an atheist to agree with Hirsi Ali’s basic philosophy of female emancipation, but you may have to challenge some aspects of scripture, both Christian and Islamic, if you want to live what you believe, which is what she has done.
But I’ve detoured before I’ve even got started. We, in the West, live in a bubble, though, occasionally, through television, films and books, like Hirsi Ali’s, we get a glimpse into another world that the rest of us would call hell. And this hell is not transient or momentary for these people, but relentless, unforgiving and even normal for those who grow up in it. Hirsi Ali is one of the few people who has straddled these 2 worlds, and that makes her book all the more compelling. As Aminata Forna wrote in the Evening Standard: “Hirsi Ali has invited [us] to walk a mile in her shoes. Most wouldn’t last a hundred yards.”
There are many issues touched on in her story, none perhaps more pertinent than identity, but I won’t start there. I will start with the apparent historical gap between some Islamic cultures and the modern Western world – a clash of civilisations, if you like. I remember the years between my teens and mid twenties were the most transformational, conflicted and depressing in my life. Like many of my generation, it was a time when I rejected my parents’ and society’s values, not to mention the religion I had grown up with, and sought a world view that I could call my own. To some extent that’s exactly what Hirsi Ali has done, only she had to jump from a culture still imbued with 6th Century social mores into the birth of the second millennium. I can fully understand what drove her, but, looking back on my own coming-of-age experience, I doubt that I could emulate her. What she achieved is a monumental leap compared to my short jump. For me, it was generational; for her, it was trans-cultural and it spanned millennia.
Much of her book deals with the treatment of women in traditional Muslim societies, treated, in her own words, as ‘minors’ not adults. One should not forget that the emancipation of women from vassals to independent, autonomous beings with their own rights has been a very lengthy process in Western society. Most societies have been historically patriarchal in both the East and West. The perception and treatment of women as second-class citizens is not confined to Islamic societies by any means. But it does appear that many Islamic cultures have the most barbaric treatment of women (enshrined in law in many countries) and are the most tardy in giving women the social status they deserve, which is equality to men.
This attitude, supported by quotes from the Qur’an, demonstrates how dangerous and misguided it is to take one’s morals from God. Because a morality supposedly given by God, in scripture, can’t be challenged and takes no account of individual circumstances, evolution of cultural norms, progress in scientific knowledge or empathy for ‘others’. And this last criterion is possibly the most important, because it is the ability to treat people outside one’s religion as ‘others’ that permits bigotry, violence and genocide, all in the name of one’s God. This is so apparent in the violence that swept through Hirsi Ali’s home country, Somalia, and became the second most salient factor, I believe, in the rejection of her own religion.
When I first saw Hirsi Ali interviewed on TV (7.30 Report, ABC Australia) after she left Holland for America, she made the statement that Islam could never coexist in a Western secular society, logically based on her experience in Holland. In an interview I heard on the radio last year (also in Australia, with Margaret Throsby) I felt she had softened her stance and she argued that Muslims could live in a secular society. She was careful to make a distinction between Islam as a religion and Islam as political ideology (refer my post Dec. 2010). My personal experience of Muslims is that they are as varied in their political views as any other group of people. I know of liberal Muslims possibly because I hold liberal views, so that should not be surprising. But it gives me a different view to those who think that all Muslims are fundamental Islamists, or potentially so. One of Hirsi Ali’s messages is that an over-dependence on tolerance in a secular society can cause its own backlash.
I’ve written elsewhere (The problems with fundamentalism, Jan. 2008) that the limits of tolerance is intolerance of others. In other words, I am intolerant of intolerance. When Muslims, or anyone else of political persuasion, start to preach intolerance towards any other group then the opposition towards that intolerance in a healthy secular society can be immense. Australia has experienced that on a national level about a decade ago and it was ugly. Xenophobia is very easily aroused in almost any nation it would appear. People who preach hatred and bigotry, no matter who they are or which group they represent, and no matter how cleverly they disguise their rhetoric, should all be treated the same – they should be refuted and denounced in the loudest voices at the highest levels of authority.
But, as the events in Somalia demonstrate, it’s not just religion that can inflame or justify violence. Clan differences are enough to justify the most heinous crimes. All through her story, Hirsi Ali describes how everyone could find fault with every other group they came in contact with. Muslims and Africans are not alone in this prejudicial bias – I grew up with it in a Western secular society. The more insular a society is, the more bigoted they are. This is why I agree with Hirsi Ali that children should not be segregated in their education. The more children mix with other ethnicities the less insular they become in their attitudes towards other groups.
In a post I wrote on Evil (one of my earliest posts, Oct. 2007) I expounded on the idea that most of the atrocities committed in the last century, and every century beforehand for that matter, were based on some form of tribalism or an ingroup-outgroup mentality. This tribalism could be familial, religious, political, ethnic or national, but it revolves around the idea of identity. We underestimate how powerful this is because it’s almost subconscious.
Hirsi Ali’s book is almost entirely about identity and her struggle to overcome its strangulation on her life. All the role models in her young life, both female and male, were imbued with the importance and necessity of identity with her clan and her religion. In her life, religion and culture were inseparable. Her grandmother made her learn her ancestry off by heart because it might one day save her life, and, in fact, it did when she was only 20 years old and a man held a knife to her throat. By reciting her ancestry back far enough she was able to claim she was his ‘sister’ and he let her go.
People often mistakenly believe that their conscience is God whispering in their mind’s ear, when, in fact, it’s almost entirely socially and culturally formed, especially when we are children. It’s only as adults that we begin to question the norms we are brought up with, and then only when we are exposed to other social norms. A way that societies tend to overcome this ‘questioning’ is to imbue a sense of their cultural ‘superiority’ over everyone else’s. This comes across so strongly in Hirsi Ali’s book, and I recognised it as part of my own upbringing. To me, it’s a sign of immaturity that someone can only justify their own position, morally, intellectually or socially, by ridiculing everyone else’s.
One of the strongest influences on Hirsi Ali and her sister, Haweya, were the Western novels that they were exposed to: not just literary standards but pulp fiction romances. It reinforced my view that storytelling, and art in general, is the best medium to transmit ideas. It was this exposure to novels that led them to believe that there were other cultures and other ways of living, especially for women. Stories are what-ifs – they put us in someone else’s shoes and challenge our view of the world. It’s not surprising that some of the world’s greatest writers have been persecuted for their subversiveness.
But this leads to the almost heretical notion that only a society open to new ideas can progress out of ossification. If there is one singular message from Hirsi Ali’s book it’s that fundamentalism (of any stripe) does not only have to be challenged, but overcome, if societies want to move forward and evolve for the betterment for everyone, and not just for those who want to hold the reigns of power.
The real gulf that Hirsi Ali jumped was not religious but educational. I’ve argued many times that ignorance is the greatest enemy facing the 21st Century. Religious fundamentalism is arguably the greatest obstacle to genuine knowledge and rational thinking in the world today. Somewhat surprisingly, this is just as relevant to America as it is to any Islamic nation. The major difference between Islamic fundamentalism and Christian fundamentalism is geography, not beliefs.
Hirsi Ali is foremost a feminist. She once argued that Islam and the West can’t coexist, but she has since softened that stance. Perhaps, like me, she has met Muslim feminists who have found a way to reconcile their religious beliefs with their sense of independence and self-belief. Arguably, self-belief is the most important attribute a human being can foster. The corollary to this is that any culture that erodes that self-belief is toxic to itself.
I’ve written elsewhere (care of Don Cupitt, Sep. 09) that the only religion worth having is the one that you have hammered out for yourself. You don’t have to be an atheist to agree with Hirsi Ali’s basic philosophy of female emancipation, but you may have to challenge some aspects of scripture, both Christian and Islamic, if you want to live what you believe, which is what she has done.
Wednesday 2 March 2011
A discussion on Wiki-Leaks without Assange
This is, in effect, a follow-up from a previous post on Wiki-Leaks (The forgotten man, last month), though from a different point of view. It’s a truly international discussion with 3 participants from the US, one from Iceland and one from Berlin, chaired in front of a live TV audience in Australia. This discussion is more diverse than the 4 Corners programme I referenced in my earlier post, and, arguably, more balanced as well.
When Assange was first criticised for endangering lives, I admit I considered that to be irresponsible, but events have revealed, whether by good luck or good management, that those concerns have not materialised. This aspect of the debate on Wiki-Leaks is discussed at length in this programme. The other thing that is brought out in this discussion is that you really can’t preach transparency if you can’t practice it.
But I think the most significant aspect of all this is how the internet has changed the way information can be delivered. Closing down Wiki-Leaks will be like trying to put the genie back into the bottle. Whatever happens to Assange, the world’s media will never be the same again. Wiki-Leaks has changed the rules and I don’t think, short of totalitarian measures, they can be reversed.
Addendum: For the latest refer this post (16 August 2012)
When Assange was first criticised for endangering lives, I admit I considered that to be irresponsible, but events have revealed, whether by good luck or good management, that those concerns have not materialised. This aspect of the debate on Wiki-Leaks is discussed at length in this programme. The other thing that is brought out in this discussion is that you really can’t preach transparency if you can’t practice it.
But I think the most significant aspect of all this is how the internet has changed the way information can be delivered. Closing down Wiki-Leaks will be like trying to put the genie back into the bottle. Whatever happens to Assange, the world’s media will never be the same again. Wiki-Leaks has changed the rules and I don’t think, short of totalitarian measures, they can be reversed.
Addendum: For the latest refer this post (16 August 2012)
Saturday 19 February 2011
Metaphysics in mathematics revisited
I recently wrote a post on E. Brian Davies’ book, Why Beliefs Matter (Metaphysics in mathematics, science and religion). Davies is Professor of Mathematics at Kings College London, so his knowledge and erudition of the subject far outweighs mine. I feel that that imbalance was not represented in that post, so this is an attempt to redress it.
Davies’ book is structured in 5 parts: The Scientific Revolution; The Human Condition; The Nature of Mathematics; Sense and Nonsense; and Science and Religion.
Davies addresses mathematical Platonism in 2 parts: The Human Condition and The Nature of Mathematics. Due to the nature of my essay, I believe I gave him short thrift and, for the sake of fairness as well as completeness, I seek to make amends.
For a start, Davies discusses Platonism in its wider context, not just in relation to mathematics, but in its influence on Western thought, regarding religion as well as science. Many people have argued that Aquinas and Augustine were both influenced by Platonism, to the extent that Earth is an imperfect replica of Heaven where the perfect ‘forms’ of all earthly entities exist. There is a parallel view expressed in some interpretations of Taoism as well. Note that one doesn’t need a belief in ‘God’ to embrace this viewpoint, but one can see how it readily marries into such a belief.
Davies discusses at length Popper’s 3 worlds: World 1 (physical); World 2 (mental); and World 3 (cultural). Under a subsection: 2.7 Plato, Popper, Penrose; he compares Popper’s 3 worlds with Penrose’s that I expounded on in my previous post: Physical, Mental and Mathematical (Platonic). In fact, Davies concludes that they are the same. I’m sure Penrose would disagree and so do I.
There is a relationship between mathematics and the physical world that doesn’t exist with other cultural ideas. Even non-Platonists, like Paul Davies and Albert Einstein, acknowledge that the correlation between mathematical relationships and physical phenomena (like relativity and quantum mechanics for example) is a unique manifestation of human intelligence. In his book, The Mind of God (a reference to Hawking’s famous phrase) Paul Davies devotes an entire chapter to this topic, entitled The Mathematical Secret.
On the other hand, Brian Davies produces compelling arguments that mathematics is cultural rather than Platonic. He compares it to other cultural entities like language, music, art and stories, all of which are products of the human brain. In one of his terse statements in bold type he says: Mathematics is an aspect of human culture, just as are language, law, music and architecture.
But, as I’ve argued in one of my previous posts (Is mathematics evidence of a transcendental realm? Jan. 08) there is a fundamental difference. No one else could have written Hamlet other than Shakespeare and no one else could have composed Beethoven’s Ninth except Beethoven, but someone else could have discovered Schrodinger’s equations and someone else could have discovered Riemann’s geometry. These mathematical entities have an objectivity that great works of art don’t.
Likewise I think that comparisons with language are misleading. No one has mathematics as their first language, unless you want to include computers. Deaf people can have sign language as a first language, but mathematics is not a communicative language in the same way that first languages are. In fact, one might argue that mathematics is an explanatory language or an analytic language; it has no nouns or verbs, subjects and predicates. Instead it has equalities and inequalities, propositions, proofs, conjectures and deductions. Even music is more communicative than mathematics which leads to another analogy.
Is music the score on the page, the sounds that you hear or the emotion it creates in your head? Music only becomes manifest when it is played on a musical instrument, even if that musical instrument is the human voice. Likewise mathematics only becomes manifest when it is expressed by a human intelligence (and possibly a machine intelligence). But the difference is that mathematical concepts have been expressed by various cultures independently of each other. Mathematical concepts like quadratic equations, Pascal’s triangle and logarithms have been discovered (or invented) more than once.
Davies makes the point that invention is a necessary part of mathematics, and I wouldn’t disagree. But he goes further, and argues that the distinction between invention and discovery cannot be readily drawn, by comparing mathematics to material inventions. He argues that a stone axe may have been the result of an accidental discovery, and Galileo’s pendulum clock was as much a discovery as an invention. I would argue that Galileo discovered a principle of nature that he could exploit and people might say the same about mathematical discoveries, so the analogy can actually work against Davies’ own argument if one rewords it slightly.
In my previous post, I did Davies an injustice when I referred to his conclusion about mathematical Platonism being irrelevant. In section 3.2 The Irrelevance of Platonism, Davies explains how some constructivist theories (like Jordan algebras) don’t fit into Platonism by definition. I don’t know anything about Jordan algebras so I can’t comment. But the constructivist position, as best I understand it, says that the only mathematics we know is what we’ve created. A Platonist will argue that the one zillionth integer of pi exists even if no one has calculated it yet, whereas the constructivist says we’ll only know what it is when we have calculated it. Both positions are correct, but when it comes to proofs, there is merit in taking the constructivist approach, because a proof is only true when someone has taken the effort to prove it. This is why, if I haven’t misconstrued him, Davies calls himself a mathematical ‘pluralist’ because he can adjust his position from a classicalist to a formalist to a constructivist depending on the mathematics he’s examining. A classicalist would be a Platonist if I understand him correctly.
I still haven’t done Davies justice, which is why I recommend you read his book. Even though I disagree with him on certain philosophical points, his knowledge is far greater than mine, and the book, in its entirety, is a worthy contribution to philosophical discourse on mathematics, science and religion, and there aren’t a lot of books that merit that combined accolade.
Davies’ book is structured in 5 parts: The Scientific Revolution; The Human Condition; The Nature of Mathematics; Sense and Nonsense; and Science and Religion.
Davies addresses mathematical Platonism in 2 parts: The Human Condition and The Nature of Mathematics. Due to the nature of my essay, I believe I gave him short thrift and, for the sake of fairness as well as completeness, I seek to make amends.
For a start, Davies discusses Platonism in its wider context, not just in relation to mathematics, but in its influence on Western thought, regarding religion as well as science. Many people have argued that Aquinas and Augustine were both influenced by Platonism, to the extent that Earth is an imperfect replica of Heaven where the perfect ‘forms’ of all earthly entities exist. There is a parallel view expressed in some interpretations of Taoism as well. Note that one doesn’t need a belief in ‘God’ to embrace this viewpoint, but one can see how it readily marries into such a belief.
Davies discusses at length Popper’s 3 worlds: World 1 (physical); World 2 (mental); and World 3 (cultural). Under a subsection: 2.7 Plato, Popper, Penrose; he compares Popper’s 3 worlds with Penrose’s that I expounded on in my previous post: Physical, Mental and Mathematical (Platonic). In fact, Davies concludes that they are the same. I’m sure Penrose would disagree and so do I.
There is a relationship between mathematics and the physical world that doesn’t exist with other cultural ideas. Even non-Platonists, like Paul Davies and Albert Einstein, acknowledge that the correlation between mathematical relationships and physical phenomena (like relativity and quantum mechanics for example) is a unique manifestation of human intelligence. In his book, The Mind of God (a reference to Hawking’s famous phrase) Paul Davies devotes an entire chapter to this topic, entitled The Mathematical Secret.
On the other hand, Brian Davies produces compelling arguments that mathematics is cultural rather than Platonic. He compares it to other cultural entities like language, music, art and stories, all of which are products of the human brain. In one of his terse statements in bold type he says: Mathematics is an aspect of human culture, just as are language, law, music and architecture.
But, as I’ve argued in one of my previous posts (Is mathematics evidence of a transcendental realm? Jan. 08) there is a fundamental difference. No one else could have written Hamlet other than Shakespeare and no one else could have composed Beethoven’s Ninth except Beethoven, but someone else could have discovered Schrodinger’s equations and someone else could have discovered Riemann’s geometry. These mathematical entities have an objectivity that great works of art don’t.
Likewise I think that comparisons with language are misleading. No one has mathematics as their first language, unless you want to include computers. Deaf people can have sign language as a first language, but mathematics is not a communicative language in the same way that first languages are. In fact, one might argue that mathematics is an explanatory language or an analytic language; it has no nouns or verbs, subjects and predicates. Instead it has equalities and inequalities, propositions, proofs, conjectures and deductions. Even music is more communicative than mathematics which leads to another analogy.
Is music the score on the page, the sounds that you hear or the emotion it creates in your head? Music only becomes manifest when it is played on a musical instrument, even if that musical instrument is the human voice. Likewise mathematics only becomes manifest when it is expressed by a human intelligence (and possibly a machine intelligence). But the difference is that mathematical concepts have been expressed by various cultures independently of each other. Mathematical concepts like quadratic equations, Pascal’s triangle and logarithms have been discovered (or invented) more than once.
Davies makes the point that invention is a necessary part of mathematics, and I wouldn’t disagree. But he goes further, and argues that the distinction between invention and discovery cannot be readily drawn, by comparing mathematics to material inventions. He argues that a stone axe may have been the result of an accidental discovery, and Galileo’s pendulum clock was as much a discovery as an invention. I would argue that Galileo discovered a principle of nature that he could exploit and people might say the same about mathematical discoveries, so the analogy can actually work against Davies’ own argument if one rewords it slightly.
In my previous post, I did Davies an injustice when I referred to his conclusion about mathematical Platonism being irrelevant. In section 3.2 The Irrelevance of Platonism, Davies explains how some constructivist theories (like Jordan algebras) don’t fit into Platonism by definition. I don’t know anything about Jordan algebras so I can’t comment. But the constructivist position, as best I understand it, says that the only mathematics we know is what we’ve created. A Platonist will argue that the one zillionth integer of pi exists even if no one has calculated it yet, whereas the constructivist says we’ll only know what it is when we have calculated it. Both positions are correct, but when it comes to proofs, there is merit in taking the constructivist approach, because a proof is only true when someone has taken the effort to prove it. This is why, if I haven’t misconstrued him, Davies calls himself a mathematical ‘pluralist’ because he can adjust his position from a classicalist to a formalist to a constructivist depending on the mathematics he’s examining. A classicalist would be a Platonist if I understand him correctly.
I still haven’t done Davies justice, which is why I recommend you read his book. Even though I disagree with him on certain philosophical points, his knowledge is far greater than mine, and the book, in its entirety, is a worthy contribution to philosophical discourse on mathematics, science and religion, and there aren’t a lot of books that merit that combined accolade.
The forgotten man
This is excellent journalism, whatever your view is on the story. It makes me angry, because the person being punished is allegedly the person who brought us the famous video footage showing ‘collateral damage’ in Iraq, which Assange called ‘collateral murder’. Is he any different to the guy who attempted to stop the tanks going to Tiananmen Square? In both cases they have effectively disappeared and become enemies of the state in their own countries.
As the title of the programme says, Private Bradley Manning has become ‘the forgotten man’, as all news coverage focuses on the indictment of Julian Assange for an alleged double rape in Sweden.
I won’t make any character or personality judgements concerning Assange because they are irrelevant to the issue. Assange may be narcissistic and he may be a delusional crusader, but it doesn’t change the case against him or the arguments concerning his journalistic rights to make public, information that may embarrass heads of government. Because, as far as I can tell, that’s exactly what he’s done.
When this first came to a head, i.e. information was leaked, our (Australian) government toed the American party line and told us that what Assange had done was dangerous, jeopardised national security and put lives at risk in the field of combat. But, after examining the evidence, the Attorney General’s Department issued a statement saying Assange had done nothing illegal under Australian law.
It should be stated that, in Australia, Assange has a lot of support, especially from journalists. All journalists know that if they had obtained the same information they would have done the same thing. Whistleblowers are always persecuted by the body that they’ve betrayed, because you can’t whistleblow without betraying the hand that feeds you. Democracies like to think that they are fairer than other countries but if you whistleblow on your government, then, even in a democracy, you won’t escape the full force of the law they can bring to bear upon you. This is true of Australia just as it is of America.
It is evident from the 4 Corners programme (refer link) that they are attempting to break Manning through torture (solitary confinement 23 hrs a day is torture) so that he will turn evidence against Assange for espionage.
Assange’s barrister, Geoffrey Robertson QC, argues that Assange won’t get a fair trial in Sweden and it will be a closed court. Assange believes that the case in Sweden is really a ploy to get him to America so they can put him on trial for espionage. Robertson (another ex-pat Aussie) is a well known human rights lawyer and famously took on Salman Rushdie’s case when he was issued a death sentence fatwah by Iran’s Ayatollah Khomeini in 1989.
What’s most alarming in the entire programme, is footage from FOX News showing right wing political commentators recommending, on American national television, that Assange should be ‘taken out’ by CIA operatives.
The solution to unwanted news in America is apparently to shoot the messenger, literally.
As the title of the programme says, Private Bradley Manning has become ‘the forgotten man’, as all news coverage focuses on the indictment of Julian Assange for an alleged double rape in Sweden.
I won’t make any character or personality judgements concerning Assange because they are irrelevant to the issue. Assange may be narcissistic and he may be a delusional crusader, but it doesn’t change the case against him or the arguments concerning his journalistic rights to make public, information that may embarrass heads of government. Because, as far as I can tell, that’s exactly what he’s done.
When this first came to a head, i.e. information was leaked, our (Australian) government toed the American party line and told us that what Assange had done was dangerous, jeopardised national security and put lives at risk in the field of combat. But, after examining the evidence, the Attorney General’s Department issued a statement saying Assange had done nothing illegal under Australian law.
It should be stated that, in Australia, Assange has a lot of support, especially from journalists. All journalists know that if they had obtained the same information they would have done the same thing. Whistleblowers are always persecuted by the body that they’ve betrayed, because you can’t whistleblow without betraying the hand that feeds you. Democracies like to think that they are fairer than other countries but if you whistleblow on your government, then, even in a democracy, you won’t escape the full force of the law they can bring to bear upon you. This is true of Australia just as it is of America.
It is evident from the 4 Corners programme (refer link) that they are attempting to break Manning through torture (solitary confinement 23 hrs a day is torture) so that he will turn evidence against Assange for espionage.
Assange’s barrister, Geoffrey Robertson QC, argues that Assange won’t get a fair trial in Sweden and it will be a closed court. Assange believes that the case in Sweden is really a ploy to get him to America so they can put him on trial for espionage. Robertson (another ex-pat Aussie) is a well known human rights lawyer and famously took on Salman Rushdie’s case when he was issued a death sentence fatwah by Iran’s Ayatollah Khomeini in 1989.
What’s most alarming in the entire programme, is footage from FOX News showing right wing political commentators recommending, on American national television, that Assange should be ‘taken out’ by CIA operatives.
The solution to unwanted news in America is apparently to shoot the messenger, literally.
Sunday 6 February 2011
Metaphysics in mathematics, science and religion
Why Beliefs Matter; Reflections on the Nature of Science, by E. Brian Davies, is one of the best books I’ve read on science, philosophy and religion, and I’ve read lots of books in all those fields. Davies is Professor of Mathematics at King’s College London and a fellow of the Royal Society. He gives one of the best arguments I’ve encountered against mathematical Platonism, which is high praise indeed from a self-confessed mathematical Platonist like myself.
There is much in this book to be commended, not least his conscientiousness in separating philosophy from science and of pointing out that ‘beliefs’ like the anthropic principle are, in fact, metaphysical considerations rather than truly scientific (it can’t be tested). He outlines the significant difference between the philosophical and scientific ramifications of quantum mechanics, which I’ve expressed myself in a post on Science, Philosophy, Religion (November 2009).
More than anything else, he reinforces the intellectual reality that philosophy often deals with questions for which there may well be no definite answers. And whilst science can provide answers in the form of empirical evidence as well as mathematically based laws to explicate them, the bigger questions, concerning our existence, the origin of the universe and a potential higher purpose, remain elusive.
The scope of Davies' book includes the history of science, the mind-body problem, induction, determinism, artificial intelligence and the modern day ‘warfare’ between science and religion, especially in America (this is not an exhaustive list). I’ll only cover 2 apparently unrelated topics: mathematical Platonism and religion and science.
Davies has no particular barrow to push, and is candid in his disagreement with his fellows on all topics, expressing bewilderment, bordering on amusement, at the hostility one often encounters concerning questions for which there are no definitive answers. One such topic is the philosophy of mathematics and its various ‘schools of thought’ that borders on religious zeal. He calls himself a mathematical ‘pluralist’ because he can see merit in alternative views. As far as mathematical Platonism goes, he expresses appreciation of its appeal to both mathematicians and physicists without necessarily agreeing with them. In his conclusion he calls it ‘irrelevant’, but only because it doesn’t really provide any theoretical benefit. In other words, being a Platonist won’t give you an advantage in understanding mathematics – it’s purely a philosophical position, with no real practical ramifications in executing formulae or even searching for new ones.
He points out that mathematical Platonism has quasi-religious overtones, which I don’t shy away from. I’ve written at least 3 posts previously on this topic, so I won’t labour the point here. It’s a very good example of a philosophical position based more on a ‘feeling’ or ‘sense’ of abstract reality, which its proponents (like myself) then support with rational argument. One of Davies’ strongest arguments is that we are the only species (that we know of) in the entire universe who can not only appreciate mathematics but make it manifest. Without an intelligence like ours, it remains completely hidden which makes its apparent essentiality questionable.
I have 2 not-unrelated responses to this argument. Firstly, all the laws of the universe, that we have discovered, from quantum mechanics to relativity to thermodynamics to the DNA code, would remain complete secrets in the exact same way, yet the universe, that we observe and exist within, is completely dependent on all these things. Secondly, mathematics is the only way we can quantify and interpret these very same laws, which leads me to contend that the mathematics is just as essential as the laws themselves. DNA is a 4 letter code, by the way, that is completely analogous to computer code, so life entails mathematics at a fundamental level.
The alternative view to this is that mathematics is an intellectual construct, purely of human origin, that has allowed us to unravel some of nature’s deepest mysteries. Roger Penrose, whose Platonist philosophy is discussed in some detail by Davies, manages to incorporate both views in a non-contradictory though paradoxical manner, which is what sold me on mathematical Platonism eventually (see below). In other words, I am a convert who came to this position via Pythagoras. In my early years of studying science, I saw mathematics as a tool that physics had seconded, but even then I struggled to reconcile natural laws with their apparent and deeply enigmatic mathematical precision (more on this below).
Davies postulates a hypothetical that there may be a species somewhere in the universe who can fathom nature’s secrets heuristically without mathematics. I can remember, when I was much younger, contemplating the same scenario and even entertained writing a sci-fi story that incorporated such a species. However, I gave up on the enterprise, when I realised that, philosophically, my world-view had changed. Physics, especially quantum mechanics, is so fundamentally dependent on mathematics for its interpretation, that any other methodology appears impossible, which is not to say that it is. Whilst quantum mechanics remains a conundrum in terms of envisaging the ultimate reality of the universe (or universes), it remains, mathematically, a completely consistent and eminently reliable metatheory.
Of course Davies’ discussion on this topic is much more comprehensive than what I’ve presented. I’ve just re-read my post on Schrodinger’s book, What is Life? and his quote concerning mathematics, “…whose truth is not only unassailable, but is obviously there forever; the relations held and will hold irrespective of our inquiry into them. A mathematical truth is timeless, it does not come into being when we discover it.” Davies also quotes Einstein, who wasn’t a Platonist: “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality.” This neatly encapsulates the paradoxical nature of mathematics that I described above.
Davies disputes the ‘independence’ claim because geometry and arithmetic didn’t evolve independently of the physical world that we’ve investigated since we first learnt to count. He also argues that not all ‘objects of reality’ can be defined or described mathematically, but he’s talking about ‘...the contents of our conversations and the products of our culture, in which mathematics is completely useless.’ No one would argue with that, but it’s obvious that Einstein’s ‘objects of reality’ are physical objects rather than cultural artefacts and mental constructs specific to the human race.
I disagree with Davies on his first point too, because mathematical investigations, at least since Newton, have evolved independently of the physical world only to be married back into it when our science has caught up with our mathematics. The most famous examples would include Riemann’s geometry being married to Einstein’s general theory of relativity and complex algebra being essential to Schrodinger’s equations for quantum mechanics. It’s as if mathematical discoveries precede physical discoveries, and, in fact, necessarily so.
There is a sense that mathematics entails a world (at least in the abstract realm) greater than our world, with multiple dimensions that can extend to infinity, of which string theory represents a potential multitude. In other words, there is more mathematics than we need to describe our physical theories, which is why Max Tegmark argues that all mathematically possible universes could exist in a multiverse. If one takes this at face value, then the mathematical world extends beyond the physical world (as Penrose points out) in the same way that the physical world extends beyond our mental world. Hence the paradox that the mind is an effective subset of the physical world, and even if the physical world is not a subset of the mathematical world (as per Tegmark), it appears, at least, to follow mathematical rules, yet mathematics is a product of the human mind. Penrose represents this relationship between the physical, mental and mathematical (Platonic) worlds as a closed circuit, one being a subset of the one before, just as I’ve described them above. Davies also addresses this aspect of Penrose’s philosophical discourse in his book, but I’ll leave that for the reader to pursue if they’re interested.
In a section called The Human Condition, Davies introduces the subject of ‘induction’ by referring to Aristotle’s ‘four types’ of causes that he recorded and discussed in the 4th Century BC. He did this in reference to a clay pot. The ‘material cause’ is the materials that the pot is made from which is the clay. The ‘formal cause’ is its shape or form which is a pot or vase. The ‘efficient cause’ is the process involving the Potter who made it. And the ‘final cause’ is the whole reason it was made which is to store something.
I have to admit I’d never come across this before, despite having read and studied Aristotle at Uni, and Davies makes particular reference to the 4th ‘final cause’ which has disappeared in the philosophy of science, and is arguably the principal source of friction that lies between science and religion. Davies rightly points out that since Descartes, and even more so after Darwin, final cause has no place in science. This is a particular issue of contention I've had with many fundamentalists, like William Lane Craig (refer The God Hypothesis, December 2008). Even if there is a final cause for the universe, science can't tell us anything about it – it’s purely a metaphysical question.
Aristotle’s final cause refers to a human artefact, and it’s not difficult to see how God became an anthropomorphic equivalent who created the universe, life and us, which means we are the final cause. I really don’t have a problem with this, purely from a philosophical viewpoint, because it makes God dependent on us rather than the other way round. If we are the final cause then, without us, there is no reason for God to exist. Few people appreciate the reverse logic that this argument entails: it doesn’t make sense for God to exist without a purpose, and the only purpose we can come up with is us.
In a recent post (Cycles of Time, last month) I gave considerable space to the exposition of entropy, aka the 2nd law of thermodynamics. A corollary to the 2nd law is that the universe is not teleological and by inclusion neither is evolution. I would suggest that this, and not the Book of Genesis, is the main philosophical difference between science and religion. Religion infers that the universe has a purpose and science infers that it doesn’t.
Davies expounds at length on the indeterminism inherent in chaos theory as well as quantum mechanics. Another Davies (Paul Davies), when he still resided in Australia, wrote an excellent book on chaos theory called The Cosmic Blueprint. The significance of chaos theory, and its particular relationship with entropy, is that very small changes can lead to huge differential consequences. In a not-so-recent issue of New Scientist (16 October 2010) their feature article described how chaos theory appears to rule evolution. In particular, evolution is fractal in the same way that branching blood vessels are in the human body. Fractal relationships appear everywhere in nature; the best example being a coastline (Davies’ example in Cosmic Blueprint). The Mandelbrot set is fractal and so are Pollock’s paintings (like Blue Poles hanging in the Sydney Art Gallery). Fractals demonstrate the same relationship at all scales, which means, in evolutionary terms, that speciation branches appear in similar ratios at all levels. The article explains how, over 65 million years, major climatic events, major tectonic events and major evolutionary events all follow the same ‘chaotic’ patterns, though ‘...connections between them are hard to discern.’
Brian Davies, like Schrodinger (What is Life?), explains how radioactivity is statistically highly predictable whilst individualistically it is impossible to predict. In fact, Schrodinger begins his book with an exposition on how almost everything in physics is statistically determined: from magnetism to the photo-electric effect to the behaviour of gases and fluids. It’s only at a macro scale that physics appears predictable. The point is that between chaos theory, the 2nd law of thermodynamics and quantum phenomena, the universe is a lottery. As Stephen Jay Gould famously said, if you were to rerun the universe you’d get a completely different result. This flies in the face of all religious philosophy.
The last 60 pages of Davies’ 240 page book (so 25%) is devoted to a section titled, Science and Religion. He starts off with a philosophical aphorism: “We must learn to live with the fact that some disagreements cannot be resolved.” Throughout his book he places terse statements in bold type like the following:
Christian theologians ignore the fundamentalist challenge at their own peril. It is the greatest threat to rational thought and toleration at the present time.
To outsiders like myself, America appears to be one of the most polarised societies in the Western world: politically, intellectually and religiously. The all-consuming debate between evolutionary science and fundamentalist religion really doesn’t exist anywhere else in the world, certainly not to the same degree of hostility and, dare-I-say-it, desperation. It’s only taken on a global perspective because American culture is so pervasive, especially on the internet.
Davies points out that humanist philosophy goes back even further than Christianity, citing Socrates, Aristotle, Plato and even Confucius. Confucius is the earliest known philosopher (500 BC) to evoke a fundamentally empathetic approach to ethics: ‘Don’t do to others what you wouldn’t want done to yourself.’ He acknowledged the importance of trust between rulers and their subjects, arguing that trust was the last commodity a ruler could afford to lose. (Someone should point this out to Egypt’s Mubarak.) Davies argues that Mill's utilitarian philosophy has probably been the biggest influence on Western democracy, because it’s inherent in civil rights and feminist movements witnessed in the last half of the last century. Even though no one invoked Mill as the model to follow; utilitarianism is concerned with the greatest benefit to the greatest number.
At the end of his book, Davies discusses the religious views of famous scientific figures, both historical and contemporary. He is not afraid to criticise Dawkins’ The God Delusion, even though he obviously is not completely at odds with Dawkins’ philosophy. Dawkins polarises people almost like no one I know, yet he’s neither a villain nor a hero. He has a demeanour not unlike an Australian politician: provocative, rhetorically aggressive, disputatious, uncompromising and unapologetic. On the blogosphere, if you criticise Dawkins, as I have done a few times, you suddenly become a Christian apologist to his supporters. It’s a sign of insecurity that people can’t deal with criticism without adopting an extreme position. Davies, like myself, takes Dawkins to task for treating all religions and all religious followers the same. It doesn’t help his cause to alienate people who would otherwise support him. ‘The worst feature of Dawkins’ book is its failure to get to grips with the variety of religious belief. Dawkins’ real enemy is fundamentalism, but he attacks religion indiscriminately.’ I agree completely.
Davies ends with a poem by William Cecil Dampier, from which I’ll quote the last verse:
And Nature smiles – still unconfessed
The secret thought she thinks –
Inscrutable she guards unguessed
The Riddle of the Sphinx
Davies follows with these words:
The riddle of our place in the universe may never be solved, and I am content that this should be so. The struggle to divine the meaning of life is a part of being human.
Science can’t solve this riddle either; in fact it tells us that our existence is a completely arbitrary phenomenon built upon an accumulation of arbitrary phenomena. The end result (so far) is mind and mind seeks its own purpose because that’s its nature.
Addendum 1: I need to point out, in all fairness to Davies, that his discourse on mathematics is far more erudite than mine, which is not apparent from my presentation above. I attempted to address this in a later post, Metaphysics in mathematics revisited.
Addendum 2: In March 2012, I give a more definitive response to the question of teleology after re-reading Paul Davies' Cosmic Blueprint and blogging about it.
There is much in this book to be commended, not least his conscientiousness in separating philosophy from science and of pointing out that ‘beliefs’ like the anthropic principle are, in fact, metaphysical considerations rather than truly scientific (it can’t be tested). He outlines the significant difference between the philosophical and scientific ramifications of quantum mechanics, which I’ve expressed myself in a post on Science, Philosophy, Religion (November 2009).
More than anything else, he reinforces the intellectual reality that philosophy often deals with questions for which there may well be no definite answers. And whilst science can provide answers in the form of empirical evidence as well as mathematically based laws to explicate them, the bigger questions, concerning our existence, the origin of the universe and a potential higher purpose, remain elusive.
The scope of Davies' book includes the history of science, the mind-body problem, induction, determinism, artificial intelligence and the modern day ‘warfare’ between science and religion, especially in America (this is not an exhaustive list). I’ll only cover 2 apparently unrelated topics: mathematical Platonism and religion and science.
Davies has no particular barrow to push, and is candid in his disagreement with his fellows on all topics, expressing bewilderment, bordering on amusement, at the hostility one often encounters concerning questions for which there are no definitive answers. One such topic is the philosophy of mathematics and its various ‘schools of thought’ that borders on religious zeal. He calls himself a mathematical ‘pluralist’ because he can see merit in alternative views. As far as mathematical Platonism goes, he expresses appreciation of its appeal to both mathematicians and physicists without necessarily agreeing with them. In his conclusion he calls it ‘irrelevant’, but only because it doesn’t really provide any theoretical benefit. In other words, being a Platonist won’t give you an advantage in understanding mathematics – it’s purely a philosophical position, with no real practical ramifications in executing formulae or even searching for new ones.
He points out that mathematical Platonism has quasi-religious overtones, which I don’t shy away from. I’ve written at least 3 posts previously on this topic, so I won’t labour the point here. It’s a very good example of a philosophical position based more on a ‘feeling’ or ‘sense’ of abstract reality, which its proponents (like myself) then support with rational argument. One of Davies’ strongest arguments is that we are the only species (that we know of) in the entire universe who can not only appreciate mathematics but make it manifest. Without an intelligence like ours, it remains completely hidden which makes its apparent essentiality questionable.
I have 2 not-unrelated responses to this argument. Firstly, all the laws of the universe, that we have discovered, from quantum mechanics to relativity to thermodynamics to the DNA code, would remain complete secrets in the exact same way, yet the universe, that we observe and exist within, is completely dependent on all these things. Secondly, mathematics is the only way we can quantify and interpret these very same laws, which leads me to contend that the mathematics is just as essential as the laws themselves. DNA is a 4 letter code, by the way, that is completely analogous to computer code, so life entails mathematics at a fundamental level.
The alternative view to this is that mathematics is an intellectual construct, purely of human origin, that has allowed us to unravel some of nature’s deepest mysteries. Roger Penrose, whose Platonist philosophy is discussed in some detail by Davies, manages to incorporate both views in a non-contradictory though paradoxical manner, which is what sold me on mathematical Platonism eventually (see below). In other words, I am a convert who came to this position via Pythagoras. In my early years of studying science, I saw mathematics as a tool that physics had seconded, but even then I struggled to reconcile natural laws with their apparent and deeply enigmatic mathematical precision (more on this below).
Davies postulates a hypothetical that there may be a species somewhere in the universe who can fathom nature’s secrets heuristically without mathematics. I can remember, when I was much younger, contemplating the same scenario and even entertained writing a sci-fi story that incorporated such a species. However, I gave up on the enterprise, when I realised that, philosophically, my world-view had changed. Physics, especially quantum mechanics, is so fundamentally dependent on mathematics for its interpretation, that any other methodology appears impossible, which is not to say that it is. Whilst quantum mechanics remains a conundrum in terms of envisaging the ultimate reality of the universe (or universes), it remains, mathematically, a completely consistent and eminently reliable metatheory.
Of course Davies’ discussion on this topic is much more comprehensive than what I’ve presented. I’ve just re-read my post on Schrodinger’s book, What is Life? and his quote concerning mathematics, “…whose truth is not only unassailable, but is obviously there forever; the relations held and will hold irrespective of our inquiry into them. A mathematical truth is timeless, it does not come into being when we discover it.” Davies also quotes Einstein, who wasn’t a Platonist: “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality.” This neatly encapsulates the paradoxical nature of mathematics that I described above.
Davies disputes the ‘independence’ claim because geometry and arithmetic didn’t evolve independently of the physical world that we’ve investigated since we first learnt to count. He also argues that not all ‘objects of reality’ can be defined or described mathematically, but he’s talking about ‘...the contents of our conversations and the products of our culture, in which mathematics is completely useless.’ No one would argue with that, but it’s obvious that Einstein’s ‘objects of reality’ are physical objects rather than cultural artefacts and mental constructs specific to the human race.
I disagree with Davies on his first point too, because mathematical investigations, at least since Newton, have evolved independently of the physical world only to be married back into it when our science has caught up with our mathematics. The most famous examples would include Riemann’s geometry being married to Einstein’s general theory of relativity and complex algebra being essential to Schrodinger’s equations for quantum mechanics. It’s as if mathematical discoveries precede physical discoveries, and, in fact, necessarily so.
There is a sense that mathematics entails a world (at least in the abstract realm) greater than our world, with multiple dimensions that can extend to infinity, of which string theory represents a potential multitude. In other words, there is more mathematics than we need to describe our physical theories, which is why Max Tegmark argues that all mathematically possible universes could exist in a multiverse. If one takes this at face value, then the mathematical world extends beyond the physical world (as Penrose points out) in the same way that the physical world extends beyond our mental world. Hence the paradox that the mind is an effective subset of the physical world, and even if the physical world is not a subset of the mathematical world (as per Tegmark), it appears, at least, to follow mathematical rules, yet mathematics is a product of the human mind. Penrose represents this relationship between the physical, mental and mathematical (Platonic) worlds as a closed circuit, one being a subset of the one before, just as I’ve described them above. Davies also addresses this aspect of Penrose’s philosophical discourse in his book, but I’ll leave that for the reader to pursue if they’re interested.
In a section called The Human Condition, Davies introduces the subject of ‘induction’ by referring to Aristotle’s ‘four types’ of causes that he recorded and discussed in the 4th Century BC. He did this in reference to a clay pot. The ‘material cause’ is the materials that the pot is made from which is the clay. The ‘formal cause’ is its shape or form which is a pot or vase. The ‘efficient cause’ is the process involving the Potter who made it. And the ‘final cause’ is the whole reason it was made which is to store something.
I have to admit I’d never come across this before, despite having read and studied Aristotle at Uni, and Davies makes particular reference to the 4th ‘final cause’ which has disappeared in the philosophy of science, and is arguably the principal source of friction that lies between science and religion. Davies rightly points out that since Descartes, and even more so after Darwin, final cause has no place in science. This is a particular issue of contention I've had with many fundamentalists, like William Lane Craig (refer The God Hypothesis, December 2008). Even if there is a final cause for the universe, science can't tell us anything about it – it’s purely a metaphysical question.
Aristotle’s final cause refers to a human artefact, and it’s not difficult to see how God became an anthropomorphic equivalent who created the universe, life and us, which means we are the final cause. I really don’t have a problem with this, purely from a philosophical viewpoint, because it makes God dependent on us rather than the other way round. If we are the final cause then, without us, there is no reason for God to exist. Few people appreciate the reverse logic that this argument entails: it doesn’t make sense for God to exist without a purpose, and the only purpose we can come up with is us.
In a recent post (Cycles of Time, last month) I gave considerable space to the exposition of entropy, aka the 2nd law of thermodynamics. A corollary to the 2nd law is that the universe is not teleological and by inclusion neither is evolution. I would suggest that this, and not the Book of Genesis, is the main philosophical difference between science and religion. Religion infers that the universe has a purpose and science infers that it doesn’t.
Davies expounds at length on the indeterminism inherent in chaos theory as well as quantum mechanics. Another Davies (Paul Davies), when he still resided in Australia, wrote an excellent book on chaos theory called The Cosmic Blueprint. The significance of chaos theory, and its particular relationship with entropy, is that very small changes can lead to huge differential consequences. In a not-so-recent issue of New Scientist (16 October 2010) their feature article described how chaos theory appears to rule evolution. In particular, evolution is fractal in the same way that branching blood vessels are in the human body. Fractal relationships appear everywhere in nature; the best example being a coastline (Davies’ example in Cosmic Blueprint). The Mandelbrot set is fractal and so are Pollock’s paintings (like Blue Poles hanging in the Sydney Art Gallery). Fractals demonstrate the same relationship at all scales, which means, in evolutionary terms, that speciation branches appear in similar ratios at all levels. The article explains how, over 65 million years, major climatic events, major tectonic events and major evolutionary events all follow the same ‘chaotic’ patterns, though ‘...connections between them are hard to discern.’
Brian Davies, like Schrodinger (What is Life?), explains how radioactivity is statistically highly predictable whilst individualistically it is impossible to predict. In fact, Schrodinger begins his book with an exposition on how almost everything in physics is statistically determined: from magnetism to the photo-electric effect to the behaviour of gases and fluids. It’s only at a macro scale that physics appears predictable. The point is that between chaos theory, the 2nd law of thermodynamics and quantum phenomena, the universe is a lottery. As Stephen Jay Gould famously said, if you were to rerun the universe you’d get a completely different result. This flies in the face of all religious philosophy.
The last 60 pages of Davies’ 240 page book (so 25%) is devoted to a section titled, Science and Religion. He starts off with a philosophical aphorism: “We must learn to live with the fact that some disagreements cannot be resolved.” Throughout his book he places terse statements in bold type like the following:
Christian theologians ignore the fundamentalist challenge at their own peril. It is the greatest threat to rational thought and toleration at the present time.
To outsiders like myself, America appears to be one of the most polarised societies in the Western world: politically, intellectually and religiously. The all-consuming debate between evolutionary science and fundamentalist religion really doesn’t exist anywhere else in the world, certainly not to the same degree of hostility and, dare-I-say-it, desperation. It’s only taken on a global perspective because American culture is so pervasive, especially on the internet.
Davies points out that humanist philosophy goes back even further than Christianity, citing Socrates, Aristotle, Plato and even Confucius. Confucius is the earliest known philosopher (500 BC) to evoke a fundamentally empathetic approach to ethics: ‘Don’t do to others what you wouldn’t want done to yourself.’ He acknowledged the importance of trust between rulers and their subjects, arguing that trust was the last commodity a ruler could afford to lose. (Someone should point this out to Egypt’s Mubarak.) Davies argues that Mill's utilitarian philosophy has probably been the biggest influence on Western democracy, because it’s inherent in civil rights and feminist movements witnessed in the last half of the last century. Even though no one invoked Mill as the model to follow; utilitarianism is concerned with the greatest benefit to the greatest number.
At the end of his book, Davies discusses the religious views of famous scientific figures, both historical and contemporary. He is not afraid to criticise Dawkins’ The God Delusion, even though he obviously is not completely at odds with Dawkins’ philosophy. Dawkins polarises people almost like no one I know, yet he’s neither a villain nor a hero. He has a demeanour not unlike an Australian politician: provocative, rhetorically aggressive, disputatious, uncompromising and unapologetic. On the blogosphere, if you criticise Dawkins, as I have done a few times, you suddenly become a Christian apologist to his supporters. It’s a sign of insecurity that people can’t deal with criticism without adopting an extreme position. Davies, like myself, takes Dawkins to task for treating all religions and all religious followers the same. It doesn’t help his cause to alienate people who would otherwise support him. ‘The worst feature of Dawkins’ book is its failure to get to grips with the variety of religious belief. Dawkins’ real enemy is fundamentalism, but he attacks religion indiscriminately.’ I agree completely.
Davies ends with a poem by William Cecil Dampier, from which I’ll quote the last verse:
And Nature smiles – still unconfessed
The secret thought she thinks –
Inscrutable she guards unguessed
The Riddle of the Sphinx
Davies follows with these words:
The riddle of our place in the universe may never be solved, and I am content that this should be so. The struggle to divine the meaning of life is a part of being human.
Science can’t solve this riddle either; in fact it tells us that our existence is a completely arbitrary phenomenon built upon an accumulation of arbitrary phenomena. The end result (so far) is mind and mind seeks its own purpose because that’s its nature.
Addendum 1: I need to point out, in all fairness to Davies, that his discourse on mathematics is far more erudite than mine, which is not apparent from my presentation above. I attempted to address this in a later post, Metaphysics in mathematics revisited.
Addendum 2: In March 2012, I give a more definitive response to the question of teleology after re-reading Paul Davies' Cosmic Blueprint and blogging about it.
Saturday 29 January 2011
Be afraid, be very afraid
This video was attached to the following email:
Drone Controllers
For non-pilots, these controllers are in Nevada and are each flying a drone thousands of miles away in the combat zone in Iraq and Afghanistan.
Their left hand is on the throttle controlling the drone's engine.
Note all the buttons which perform various tasks without removing the hand from the throttle.
The right hand is flying the plane.
Welcome to the new world order. This is modern warfare.
Today's headline: 'Missiles fired from Nevada controlled drone aircraft kill Taliban leader'
Watch how it's done. Turn the speakers on & watch in full screen.
ALSO NOTICE THE COMFORT FROM WHICH THE "FLYERS" OPERATE.
I don’t know if this is a simulation or the real thing, but I commented on the deployment of military drones in a post I wrote last November, titled: We have to win the war against stupidity first.
If it’s the real thing then it makes me and anyone else who watches it something of a voyeur. I refuse to watch videoed assassinations because it feeds their purpose, but is this any different?
There are a lot of pertinent issues here, not least the implication that this is how wars will be fought in the future, but let’s start with the most obvious one: how is this perceived by non-Western eyes?
Let’s reverse the scenario: how would people in the West respond if this technology was adopted by Iran or North Korea or even Russia or China? At present I believe that only America and Israel actually deploy it. Is this a case of might is right? Those with the best military technology are axiomatically those with the moral prerogative to use it. Because that’s how it appears.
We routinely accuse suicide bombing as an act of cowardice, but is this perceived as any less cowardly by those who are on the receiving end?
Someone once pointed out, in reference to the deployment of U-boats by the Germans in WWI (but it actually applies to all military conflicts), if one’s opponent has a technological advantage then one’s only chance of success is to break the rules – in other words, play dirty. This is why suicide bombing is the weapon of choice by people who believe they are being invaded by a technologically superior force, especially when the superiority is indisputably dominant.
And there are other issues: the scenario is reminiscent of Milgram’s experiment, which demonstrated how easy it is to inflict mortal injuries on a complete stranger who is sight unseen. The couple in the video are so relaxed and detached from the life-and-death consequences of their actions that it makes me wonder if it’s not just a training session.
In the 1960s I can still remember reading a MAD magazine that satirically showed 2 chess opponents facing each other off with ballistic missile launchers instead of chess pieces and consequently destroying each other, the chess board and the room in which they were playing. It was a commentary on the cold war mentality of the time and the threat of intercontinental ballistic missiles, which could render the planet virtually uninhabitable without any army taking the field.
We no longer see that as a threat, but the idea of waging war without committing ground troops (which is theoretically the same scenario we have in the video) has strong political appeal despite the obvious moral issues that it raises.
There are 2 fundamental issues, one of which was addressed in my post last November. Firstly, the entire operation is dependent on ‘intelligence’ that the ‘target’ is the enemy. In Vietnam, the CIA used ‘assassination squads’ made up of local tribesmen to target specific enemies. Barry Petersen, an Australian seconded to the CIA in that conflict, fell out with his superiors when he refused to use Montagnard tribesmen, loyal to him, as assassination squads, despite their commendable military record (Frank Walker, The Tiger Man of Vietnam). His reasoning was that they would be used to settle personal vendettas, creating distrust and secondary enmity that would not help win the war. In a tribal environment, like Afghanistan and Iraq, this type of abuse of ‘intelligence’ can also occur.
But it’s the psychological component of this type of warfare that makes it most unpalatable, at least, to me. Unfortunately, intervention by Western military units have shown extraordinary lack of cultural sensitivity in the countries they become involved in. This was true in Vietnam, in Iraq, and, I suspect, Afghanistan. Sometimes military leaders on the ground recognise this when their political leaders don’t. America, in particular, doesn’t have a good record in this area.
If one insists on waging a war without face to face involvement then the consequences will be dire for everyone concerned. The psychological impact on the civilians of a country being attacked by robotic planes can not be overstated. It will foster hate, resentment and a stubborn will to reek vengeance. All you have to do is put yourself in their shoes.
Sunday 16 January 2011
Cycles of Time – a new theory of cosmology
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.
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.
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 slight 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 slight 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.
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