Notice I use the plural for something that represents a collection of universes. That’s because there are multiple versions of them; according to Max Tegmark there are 3 levels of multiverses.
I’m about to do something that I criticise others for doing: I’m going to challenge the collective wisdom of those who are much smarter and more knowledgeable than me. I’m not a physicist, let alone a cosmologist, and I’m not an academic in any field – I’m just a blogger. My only credentials are that I read a lot, especially about physics by authors who are eminently qualified in their fields. But even that does not give me any genuine qualification for what I’m about to say. Nevertheless, I feel compelled to point out something that few others are willing to cognise.
This occurred to me after I wrote my last post. In the 2 books I reference by Paul Davies (The Mind of God and The Goldilocks Enigma) he discusses and effectively dismisses the multiverse paradigm, yet I don’t mention it. Partly, that was because the post was getting too lengthy as it was, and, partly, because I didn’t need to discuss it to make the point I wished to make.
But the truth is that the multiverse is by far the most popular paradigm in both quantum physics and cosmology, and this is a relatively recent trend. What I find interesting is that it has become the default position, epistemologically, to explain what we don’t know at both of the extreme ends of physics: quantum mechanics and the cosmos.
Davies makes the point, in Mind of God (and he’s not the only one to do so), that for many scientists there seems to be a choice between accepting the multiverse or accepting some higher metaphysical explanation that many people call God. In other words, it’s a default position in cosmology because it avoids trying to explain why our universe is so special for life to emerge. Basically, it’s not special if there are an infinite number of them.
In quantum mechanics, the multiverse (or many words interpretation, as it’s called) has become the most favoured interpretation following the so-called Copenhagen interpretation championed by Niels Bohr. It’s based on the assumption that the wave function, which describes a quantum particle in Hilbert space doesn’t disappear when someone observes something or takes a measurement, but continues on in a parallel universe. So a bifurcation occurs for every electron and every photon every time it hits something. What’s more, Max Tegmark argues that if you have a car crash and die, in another universe you will continue to live. And likewise, if you have a near miss (as he did, apparently) in this universe, then in another parallel universe you died.
In both cases, cosmology and quantum mechanics, the multiverse has become the ‘easy’ explanation for events or phenomena that we don’t really understand. Basically, they are signposts for the boundaries or limits of scientific knowledge as it currently stands. String Theory or M Theory, is the most favoured cosmological model, but not only does it predict 10 spatial dimensions (as a minimum, I believe) it also predicts 10500 universes.
Now, I’m sure many will say that since the multiverse crops up in so many different places: caused by cosmological inflation, caused by string theory, caused by quantum mechanics; at least one of these multiverses must exist, right? Well no, they don’t have to exist – they’re just speculative, albeit consistent with everything we currently know about this universe, the one we actually live in.
Science, as best I understand it, historically, has always homed in on things. In particle physics it homed in on electrons, protons and neutrons, then neutrinos and quarks in all their varieties. In biology, we had evolution by natural selection then we discovered genes and then DNA, which underpinned it all. In mechanics, we had Galileo, Kepler and Newton, who finally gave us an equation for gravity, then Einstein gave us relativity theory that equated energy with mass in the most famous equation in the world, plus the curvature of space-time giving a completely geometric account of gravity that also provided a theoretical foundation for cosmology. Faraday, followed by Maxwell showed us that electricity and magnetism are inherently related and again Einstein took it further and gave an explanation of the photo-electric effect by proposing that light came in photons.
What I’m trying to say is that we made advances in science by either finding more specific events and therefore particles or by finding common elements that tied together apparently different phenomena. Kepler found the mathematical formulation that told us that planets travel in ellipses, Newton told us that gravity’s inverse square law made this possible and Einstein told us that it’s the curvature of space-time that explains gravity. Darwin and Wallace gave us a theory of evolution by natural selection, but Mendel gave us genes that explained how the inheritance happened and Francis and Crick and Franklin gave us the DNA helix that is the key ingredient for all of life.
My point is that the multiverse explanation for virtually everything we don’t know is going in the opposite direction. Now the explanation for something happening, whether it be a quantum event or the entire universe, is that every possible variation or physical manifestation is happening but we can only see the one we are witnessing. I don’t see this as an explanation for anything; I only see it as a manifestation of our ignorance.
Addendum: This is Max Tegmark providing a very cogent counterargument to mine. I think his argument from inflation is the most valid and his argument from QM multiple worlds, the most unlikely. Quantum computers won't prove parallel universes, because they are dependent on entanglement (as I understand it) which is not the same thing as multiple copies. Philip Ball makes this exact point in Beyond Weird, where he explains that so-called multiple particles only exist as probabilities; only one of which becomes 'real'.
Tuesday 15 September 2015
Sunday 13 September 2015
Physics, mathematics, the Universe - is Reason its raison d'être?
I’ve just read Paul Davies’ The Mind of God: Science & The Search for Ultimate Meaning, published in 1992, so a couple of decades old now. He wrote this as a follow-up to God and the New Physics, which I read some years ago. This book is more philosophical and tends to deal with cosmology and the laws of physics – it’s as much about epistemology and the history of science as about the science itself. Despite its age, it’s still very relevant, especially in regard to the relationship between science and religion and science and mathematics, both of which he discusses in some depth.
Davies is currently at The University of Arizona (along with Lawrence Krauss, who wrote A Universe from Nothing, amongst others), but at the time he wrote The Mind of God, Davies was living and working in Australia, where he wrote a number of books over a couple of decades. He was born and educated in England, so he’s lived on 3 continents.
Davies is often quoted out of context by Christian fundamentalists, giving the impression that he supports their views, but anyone who reads his books knows that’s far from the truth. When he first arrived in America, he was sometimes criticised on blogs for ‘promoting his own version of religion’, usually by people who had heard of him but never actually read him. From my experience of reading on the internet, religion is a sensitive topic in America on both sides of the religious divide, so unless your views are black or white you can be criticised by both sides. It’s worth noting that I’ve heard or read Richard Dawkins reference Davies on more than a few occasions, always with respect, even though Davies is not atheistic.
Davies declares his philosophical position very early on, which is definitely at odds with the generally held scientific point of view regarding where we stand in the scheme of things:
I belong to the group of scientists who do not subscribe to a conventional religion but nevertheless deny that the universe is a purposeless accident… I have come to the point of view that mind – i.e., conscious awareness of the world – is not a meaningless and incidental quirk of nature, but an absolute fundamental facet of reality. That is not to say that we are the purpose for which the universe exists. Far from it. I do, however, believe that we human beings are built into the scheme of things in a very basic way.
In a fashion, this is a formulation of the Strong Anthropic Principle, which most scientists, I expect, would eschew, but it’s one that I find appealing, much for the same reasons given by Davies. The Universe is such a complex phenomenon, its evolvement (thus far) culminating in the emergence of an intelligence able to fathom its own secrets at extreme scales of magnitude in both space and time. I’ve alluded to this ‘mystery’ in previous posts, so Davies’ philosophy appeals to me personally, and his book, in part, attempts to tackle this very topic.
Amongst other things, he gives a potted history of science from the ancients (especially the Greeks, but other cultures as well) and how it has largely replaced religion as the means to understand natural phenomena at all levels. This has resulted in a ‘God-of-the-Gaps’, where, epistemologically, scientific investigations and discoveries have gradually pushed God out of the picture. He also discusses the implications of a God existing outside of space and time actually creating a ‘beginning’. The idea of a God setting everything in motion (via the Big Bang) and then watching his creation evolve over billions of years like a wound up watch (Davies’ analogy) is no more appealing than the idea of a God who has to make adjustments or rewind it occasionally, to extend the metaphor.
In discussing how the scientific enterprise evolved, in particular how we search for the cause of events, reminded me of my own attraction to science from a very early age. Children are forever asking ‘why’ and ‘how’ questions – we have a natural inclination to wonder how things work – and by the time I’d reached my teens, I’d realised that science was the best means to pursue this.
Davies gives an example of Newton coming up with mathematical laws to explain gravity that not only provided a method to calculate projectiles on Earth but also the orbits of planets in the solar system. Brian Cox in a documentary on Gravity, wrote the equation down on a piece of paper, borrowing a pen from his cameraman, to demonstrate how simple it is. But Newton couldn’t explain why everything didn’t simply collapse in on itself and evoked God as the explanation for keeping the clockwork universe functioning. So Newton’s explanation of gravity, albeit a work of genius, didn’t go far enough.
Einstein then came up with his theory that gravity was a consequence of the curvature of space-time caused by mass, but, as Cox points out in his documentary, Einstein’s explanation doesn’t go far enough either, and there are still aspects of gravity we don’t understand, at the quantum level and in black holes where the laws of physics as we know them break down. As an aside, it’s the centenary year of Einstein publishing his General Theory of Relativity and I’ve just finished reading a book (The Road to Relativity by Hanoch Gutfreund and Jurgen Renn) which goes through the original manuscript page by page explaining Einstein’s creative process.
But back to Newton’s theory, I remember, in high school, trying to understand why acceleration in a gravitational field was the same irrespective of the mass of the body, and I could only resort to the mathematics to give me an answer, which didn’t seem satisfactory. I can also remember watching a light plane in flight over our house and seeing it side-slipping in the wind. In other words, the direction of the nose was slightly offset to its direction of travel to counter a side wind. I remember imagining the vectors at play and realising that I could work them out with basic trigonometry. It made me wonder for the first time, why did mathematics provide an answer and an explanation – what was the link between mathematics, a product of the mind, and a mechanical event, a consequence of the physical world?
I’ve written quite a lot on the topic of mathematics and its relationship to the laws of nature; Davies goes into this in some depth. It is worth quoting him on the subject, especially in regard to the often stated scepticism that the laws of nature only exist in our minds.
Sometimes it is argued that laws of nature, which are attempts to capture [nature’s] regularities systematically, are imposed on the world by our minds in order to make sense of it… I believe any suggestion that the laws of nature are similar projections of the human mind [to seeing animals in the constellations, for example] is absurd. The existence of regularities in nature are a mathematical objective fact… Without this assumption that the regularities are real, science is reduced to a meaningless charade.
He adds the caveat that the laws as written are ‘human inventions, but inventions designed to reflect, albeit imperfectly, actually existing properties of nature.’ Every scientist knows that our rendition of nature’s laws have inherent limitations, despite their accuracy and success, but quite often they provide new insights that we didn’t expect. Well known examples are Maxwell’s equations predicting electromagnetic waves and the constant speed of light, and Dirac’s equation predicting anti-matter. Most famously, Einstein’s special theory of relativity predicted the equivalence of energy and mass, which was demonstrated with the detonation of the atomic bomb. All these predictions were an unexpected consequence of the mathematics.
Referring back to Gutfreund’s and Renn’s book on Einstein’s search for a theory of gravity that went beyond Newton but was consistent with Newton, Einstein knew he had to find a mathematical description that not only fulfilled all his criteria regarding relativistic space-time and the equivalence of inertial and gravitational mass, but would also provide testable predictions like the bending of light near massive stellar objects (stars) and the precession of mercury’s orbit around the sun. We all know that Riemann’s non-Euclidian geometry gave him the mathematical formulation he needed and it’s been extraordinarily successful thus far, despite the limitations I mentioned earlier.
Davies covers quite a lot in his discussion on mathematics, including a very good exposition on Godel’s Incompleteness Theorem, Turing’s proof of infinite incomputable numbers, John Conway’s game of life with cellular automata and Von Neuman’s detailed investigation of self-replicating machines, which effectively foreshadowed the mechanics of biological life before DNA was discovered.
In the middle of all this, Davies makes an extraordinary claim, based on reasoning by Oxford mathematical physicist David Deutsch (the most vocal advocate for the many worlds interpretation of quantum mechanics and a leader in quantum computer development). Effectively, Deutsch argues that mathematics works in the real world (including electronic calculators and computers) not because of logic but because the physical world (via the laws of physics) is amenable to basic arithmetic: addition, subtraction etc. In other words, he’s basically saying that we only have mathematics because there are objects in our world that we can count. In effect, this is exactly what Davies says.
This is not the extraordinary claim. The extraordinary claim is that there may exist universes where mathematics, as we know it, doesn’t work, because there are no discrete objects. Davies extrapolates this to say that a problem that is incomputable with our mathematics may be computable with alternative mathematics that, I assume, is not based on counting. I have to confess I have issues with this.
To start from scratch, mathematics starts with numbers, which we all become acquainted with from an early age by counting objects. It’s a small step to get addition from counting but quite a large step to then abstract it from the real world, so the numbers only exist in our heads. Multiplication is simply adding something a number of times and subtraction is simply taking away something that was added so you get back to where you started. The same is true for division where you divide something you multiplied to go backwards in your calculation. In other words, subtraction and division are just the reverse operations for addition and multiplication respectively. Then you replace some of the numbers by letters as ‘unknowns’ and you suddenly have algebra. Now you’re doing mathematics.
The point I’d make, in reference to Davies’ claim, is that mathematics without numbers is not mathematics. And numbers may be to a different base or use different symbols, but they will all produce the same mathematics. I agree with Deutsch that mathematics is intrinsic to our world – none of us would do mathematics if it wasn’t. But I find the notion that there could hypothetically exist worlds where mathematics is not relevant or is not dependent on number, absurd, to use one of Davies’ favourite utterances.
Earlier in the book, Davies expresses scepticism at the idea that the laws of nature could arise with the universe – that they didn’t exist beforehand. In other words, he’s effectively arguing that they are transcendent. Since the laws are firmly based in mathematics, it’s hard to argue that the laws are transcendent but the mathematics is not.
I have enormous respect for Davies, and I wonder if I’m misrepresenting him. But this is what he said, albeit out of context:
Imagine a world in which the laws of physics were very different, possibly so different that discreet objects did not exist. Some of the mathematical operations that are computable in our world would not be so in this world, and vice versa.
Speaking of mathematical transcendence, he devotes almost an entire chapter to the underlying mystery of mathematics’ role in explicating natural phenomena through physics, with particular reference to mathematical Platonists like Kurt Godel, Eugene Wigner and Roger Penrose. But it’s a quote from Richard Feynman, who was not a Platonist as far as I know, that sums up the theme.
When you discover these things, you get the feeling that they were true before you found them. So you get the idea that somehow they existed somewhere… Well, in the case of physics we have double trouble. We come across these mathematical interrelationships but they apply to the universe, so the problem of where they are is doubly confusing… Those are philosophical questions that I don’t know how to answer.
Interestingly, in his later book, The Goldilocks Enigma (2006), Davies distances himself from mathematical Platonism and seems to espouse John Wheeler’s view that both the mathematics and the laws of nature emerged ‘higgledy-piggledy’ and are not transcendent. He also tackles the inherent conflict between the Strong Anthropic Principle, which he seems to support, and a non-teleological universe, which science virtually demands, but I’ll address that later.
Back to The Mind of God, he discusses in depth one of the paradigms of our age that the Universe can be totally understood by algorithms leading to the possibility that the Universe we live in is a Matrix-like computer simulation. Again, referring to The Goldilocks Enigma, he discounts this view as a variation on Intelligent Design. Towards the end of Mind of God, he discusses metaphysical, even mystical possibilities, but not as a replacement for science.
But one interesting point he makes, that I’ve never heard of before, was proposed by James Hartle and Murray Gellmann, who claim:
…that the existence of an approximately classical world, in which well-defined material objects exist in space, and in which there is a well-defined concept of time, requires special cosmic initial conditions.
In other words, they’re saying that the Universe would be a purely quantum world with everything in superpositional states (nothing would be fixed in space and time) were it not for ‘the special quantum state in which the universe originated.’ James Hartle developed with Stephen Hawking the Hawking-Hartle model of the Universe where time evolved out of a 4th dimension in a quantum big bang. It may be that Hartle’s and Gellmann’s conjecture is dependent on the veracity of that particular model. The link between the two ideas is only alluded to by Davies.
Apropos to the book’s title, Davies spends an entire chapter on ‘God’ arguments, in particular cosmological and ontological arguments that require a level of philosophical nous that, frankly, I don’t possess. Having said that, it became obvious to me that arguments for God are more dependent on subjective ‘feelings’ than rational requirements. After lengthy discussions on ‘necessary being’ and a ‘contingent universe’, and the tension if not outright contradiction the two ideas pose, Davies pretty well sums up the situation with this:
What seems to come through such analyses loud and clear is the fundamental incompatibility of a completely timeless, unchanging, necessary God with the notion of creativity in nature, with a universe that can change and evolve and bring forth the genuinely new…
In light of this, the only ‘God’ that makes sense to me is one that evolves like ‘Its’ creation and, in effect, is a consequence of it rather than its progenitor.
One of the points that Davies makes is how the Universe is not strictly deterministic or teleological, yet it allows for self-organisation and the evolvement of complexity; in essence, a freedom of evolvement without dictating it. I would call this pseudo-teleological and is completely consistent with both quantum and chaotic events, which dominate all natural phenomena from cosmological origins to the biological evolution of life.
This brings one back to the quote from Davies at the beginning of this discussion that the universe is not a meaningless accident. Inherent in the idea of meaningfulness is the necessary emergence of consciousness and its role as the prime source of reason. If not for reason the Universe would have no cognisance of its own existence and it would be truly ‘purposeless’ in every way. It is for this reason that people believe in God, in whatever guise they find him (or her, as the case may be). Because we can find reason in living our lives and use reason to understand the Universe, the idea that the Universe itself has no reason is difficult to reconcile.
Davies is currently at The University of Arizona (along with Lawrence Krauss, who wrote A Universe from Nothing, amongst others), but at the time he wrote The Mind of God, Davies was living and working in Australia, where he wrote a number of books over a couple of decades. He was born and educated in England, so he’s lived on 3 continents.
Davies is often quoted out of context by Christian fundamentalists, giving the impression that he supports their views, but anyone who reads his books knows that’s far from the truth. When he first arrived in America, he was sometimes criticised on blogs for ‘promoting his own version of religion’, usually by people who had heard of him but never actually read him. From my experience of reading on the internet, religion is a sensitive topic in America on both sides of the religious divide, so unless your views are black or white you can be criticised by both sides. It’s worth noting that I’ve heard or read Richard Dawkins reference Davies on more than a few occasions, always with respect, even though Davies is not atheistic.
Davies declares his philosophical position very early on, which is definitely at odds with the generally held scientific point of view regarding where we stand in the scheme of things:
I belong to the group of scientists who do not subscribe to a conventional religion but nevertheless deny that the universe is a purposeless accident… I have come to the point of view that mind – i.e., conscious awareness of the world – is not a meaningless and incidental quirk of nature, but an absolute fundamental facet of reality. That is not to say that we are the purpose for which the universe exists. Far from it. I do, however, believe that we human beings are built into the scheme of things in a very basic way.
In a fashion, this is a formulation of the Strong Anthropic Principle, which most scientists, I expect, would eschew, but it’s one that I find appealing, much for the same reasons given by Davies. The Universe is such a complex phenomenon, its evolvement (thus far) culminating in the emergence of an intelligence able to fathom its own secrets at extreme scales of magnitude in both space and time. I’ve alluded to this ‘mystery’ in previous posts, so Davies’ philosophy appeals to me personally, and his book, in part, attempts to tackle this very topic.
Amongst other things, he gives a potted history of science from the ancients (especially the Greeks, but other cultures as well) and how it has largely replaced religion as the means to understand natural phenomena at all levels. This has resulted in a ‘God-of-the-Gaps’, where, epistemologically, scientific investigations and discoveries have gradually pushed God out of the picture. He also discusses the implications of a God existing outside of space and time actually creating a ‘beginning’. The idea of a God setting everything in motion (via the Big Bang) and then watching his creation evolve over billions of years like a wound up watch (Davies’ analogy) is no more appealing than the idea of a God who has to make adjustments or rewind it occasionally, to extend the metaphor.
In discussing how the scientific enterprise evolved, in particular how we search for the cause of events, reminded me of my own attraction to science from a very early age. Children are forever asking ‘why’ and ‘how’ questions – we have a natural inclination to wonder how things work – and by the time I’d reached my teens, I’d realised that science was the best means to pursue this.
Davies gives an example of Newton coming up with mathematical laws to explain gravity that not only provided a method to calculate projectiles on Earth but also the orbits of planets in the solar system. Brian Cox in a documentary on Gravity, wrote the equation down on a piece of paper, borrowing a pen from his cameraman, to demonstrate how simple it is. But Newton couldn’t explain why everything didn’t simply collapse in on itself and evoked God as the explanation for keeping the clockwork universe functioning. So Newton’s explanation of gravity, albeit a work of genius, didn’t go far enough.
Einstein then came up with his theory that gravity was a consequence of the curvature of space-time caused by mass, but, as Cox points out in his documentary, Einstein’s explanation doesn’t go far enough either, and there are still aspects of gravity we don’t understand, at the quantum level and in black holes where the laws of physics as we know them break down. As an aside, it’s the centenary year of Einstein publishing his General Theory of Relativity and I’ve just finished reading a book (The Road to Relativity by Hanoch Gutfreund and Jurgen Renn) which goes through the original manuscript page by page explaining Einstein’s creative process.
But back to Newton’s theory, I remember, in high school, trying to understand why acceleration in a gravitational field was the same irrespective of the mass of the body, and I could only resort to the mathematics to give me an answer, which didn’t seem satisfactory. I can also remember watching a light plane in flight over our house and seeing it side-slipping in the wind. In other words, the direction of the nose was slightly offset to its direction of travel to counter a side wind. I remember imagining the vectors at play and realising that I could work them out with basic trigonometry. It made me wonder for the first time, why did mathematics provide an answer and an explanation – what was the link between mathematics, a product of the mind, and a mechanical event, a consequence of the physical world?
I’ve written quite a lot on the topic of mathematics and its relationship to the laws of nature; Davies goes into this in some depth. It is worth quoting him on the subject, especially in regard to the often stated scepticism that the laws of nature only exist in our minds.
Sometimes it is argued that laws of nature, which are attempts to capture [nature’s] regularities systematically, are imposed on the world by our minds in order to make sense of it… I believe any suggestion that the laws of nature are similar projections of the human mind [to seeing animals in the constellations, for example] is absurd. The existence of regularities in nature are a mathematical objective fact… Without this assumption that the regularities are real, science is reduced to a meaningless charade.
He adds the caveat that the laws as written are ‘human inventions, but inventions designed to reflect, albeit imperfectly, actually existing properties of nature.’ Every scientist knows that our rendition of nature’s laws have inherent limitations, despite their accuracy and success, but quite often they provide new insights that we didn’t expect. Well known examples are Maxwell’s equations predicting electromagnetic waves and the constant speed of light, and Dirac’s equation predicting anti-matter. Most famously, Einstein’s special theory of relativity predicted the equivalence of energy and mass, which was demonstrated with the detonation of the atomic bomb. All these predictions were an unexpected consequence of the mathematics.
Referring back to Gutfreund’s and Renn’s book on Einstein’s search for a theory of gravity that went beyond Newton but was consistent with Newton, Einstein knew he had to find a mathematical description that not only fulfilled all his criteria regarding relativistic space-time and the equivalence of inertial and gravitational mass, but would also provide testable predictions like the bending of light near massive stellar objects (stars) and the precession of mercury’s orbit around the sun. We all know that Riemann’s non-Euclidian geometry gave him the mathematical formulation he needed and it’s been extraordinarily successful thus far, despite the limitations I mentioned earlier.
Davies covers quite a lot in his discussion on mathematics, including a very good exposition on Godel’s Incompleteness Theorem, Turing’s proof of infinite incomputable numbers, John Conway’s game of life with cellular automata and Von Neuman’s detailed investigation of self-replicating machines, which effectively foreshadowed the mechanics of biological life before DNA was discovered.
In the middle of all this, Davies makes an extraordinary claim, based on reasoning by Oxford mathematical physicist David Deutsch (the most vocal advocate for the many worlds interpretation of quantum mechanics and a leader in quantum computer development). Effectively, Deutsch argues that mathematics works in the real world (including electronic calculators and computers) not because of logic but because the physical world (via the laws of physics) is amenable to basic arithmetic: addition, subtraction etc. In other words, he’s basically saying that we only have mathematics because there are objects in our world that we can count. In effect, this is exactly what Davies says.
This is not the extraordinary claim. The extraordinary claim is that there may exist universes where mathematics, as we know it, doesn’t work, because there are no discrete objects. Davies extrapolates this to say that a problem that is incomputable with our mathematics may be computable with alternative mathematics that, I assume, is not based on counting. I have to confess I have issues with this.
To start from scratch, mathematics starts with numbers, which we all become acquainted with from an early age by counting objects. It’s a small step to get addition from counting but quite a large step to then abstract it from the real world, so the numbers only exist in our heads. Multiplication is simply adding something a number of times and subtraction is simply taking away something that was added so you get back to where you started. The same is true for division where you divide something you multiplied to go backwards in your calculation. In other words, subtraction and division are just the reverse operations for addition and multiplication respectively. Then you replace some of the numbers by letters as ‘unknowns’ and you suddenly have algebra. Now you’re doing mathematics.
The point I’d make, in reference to Davies’ claim, is that mathematics without numbers is not mathematics. And numbers may be to a different base or use different symbols, but they will all produce the same mathematics. I agree with Deutsch that mathematics is intrinsic to our world – none of us would do mathematics if it wasn’t. But I find the notion that there could hypothetically exist worlds where mathematics is not relevant or is not dependent on number, absurd, to use one of Davies’ favourite utterances.
Earlier in the book, Davies expresses scepticism at the idea that the laws of nature could arise with the universe – that they didn’t exist beforehand. In other words, he’s effectively arguing that they are transcendent. Since the laws are firmly based in mathematics, it’s hard to argue that the laws are transcendent but the mathematics is not.
I have enormous respect for Davies, and I wonder if I’m misrepresenting him. But this is what he said, albeit out of context:
Imagine a world in which the laws of physics were very different, possibly so different that discreet objects did not exist. Some of the mathematical operations that are computable in our world would not be so in this world, and vice versa.
Speaking of mathematical transcendence, he devotes almost an entire chapter to the underlying mystery of mathematics’ role in explicating natural phenomena through physics, with particular reference to mathematical Platonists like Kurt Godel, Eugene Wigner and Roger Penrose. But it’s a quote from Richard Feynman, who was not a Platonist as far as I know, that sums up the theme.
When you discover these things, you get the feeling that they were true before you found them. So you get the idea that somehow they existed somewhere… Well, in the case of physics we have double trouble. We come across these mathematical interrelationships but they apply to the universe, so the problem of where they are is doubly confusing… Those are philosophical questions that I don’t know how to answer.
Interestingly, in his later book, The Goldilocks Enigma (2006), Davies distances himself from mathematical Platonism and seems to espouse John Wheeler’s view that both the mathematics and the laws of nature emerged ‘higgledy-piggledy’ and are not transcendent. He also tackles the inherent conflict between the Strong Anthropic Principle, which he seems to support, and a non-teleological universe, which science virtually demands, but I’ll address that later.
Back to The Mind of God, he discusses in depth one of the paradigms of our age that the Universe can be totally understood by algorithms leading to the possibility that the Universe we live in is a Matrix-like computer simulation. Again, referring to The Goldilocks Enigma, he discounts this view as a variation on Intelligent Design. Towards the end of Mind of God, he discusses metaphysical, even mystical possibilities, but not as a replacement for science.
But one interesting point he makes, that I’ve never heard of before, was proposed by James Hartle and Murray Gellmann, who claim:
…that the existence of an approximately classical world, in which well-defined material objects exist in space, and in which there is a well-defined concept of time, requires special cosmic initial conditions.
In other words, they’re saying that the Universe would be a purely quantum world with everything in superpositional states (nothing would be fixed in space and time) were it not for ‘the special quantum state in which the universe originated.’ James Hartle developed with Stephen Hawking the Hawking-Hartle model of the Universe where time evolved out of a 4th dimension in a quantum big bang. It may be that Hartle’s and Gellmann’s conjecture is dependent on the veracity of that particular model. The link between the two ideas is only alluded to by Davies.
Apropos to the book’s title, Davies spends an entire chapter on ‘God’ arguments, in particular cosmological and ontological arguments that require a level of philosophical nous that, frankly, I don’t possess. Having said that, it became obvious to me that arguments for God are more dependent on subjective ‘feelings’ than rational requirements. After lengthy discussions on ‘necessary being’ and a ‘contingent universe’, and the tension if not outright contradiction the two ideas pose, Davies pretty well sums up the situation with this:
What seems to come through such analyses loud and clear is the fundamental incompatibility of a completely timeless, unchanging, necessary God with the notion of creativity in nature, with a universe that can change and evolve and bring forth the genuinely new…
In light of this, the only ‘God’ that makes sense to me is one that evolves like ‘Its’ creation and, in effect, is a consequence of it rather than its progenitor.
One of the points that Davies makes is how the Universe is not strictly deterministic or teleological, yet it allows for self-organisation and the evolvement of complexity; in essence, a freedom of evolvement without dictating it. I would call this pseudo-teleological and is completely consistent with both quantum and chaotic events, which dominate all natural phenomena from cosmological origins to the biological evolution of life.
This brings one back to the quote from Davies at the beginning of this discussion that the universe is not a meaningless accident. Inherent in the idea of meaningfulness is the necessary emergence of consciousness and its role as the prime source of reason. If not for reason the Universe would have no cognisance of its own existence and it would be truly ‘purposeless’ in every way. It is for this reason that people believe in God, in whatever guise they find him (or her, as the case may be). Because we can find reason in living our lives and use reason to understand the Universe, the idea that the Universe itself has no reason is difficult to reconcile.
Thursday 3 September 2015
Ruminations on The Sparrow (SF novel by Mary Doria Russell, 1996)
Russell is a paleoanthropologist and so is one of the characters in her book (Anne) whom one thinks may represent the author’s world view, especially concerning religion and God. Anne is basically a good natured and tolerant sceptic.
Whether Anne is representative of the author’s point of view or not, I found Russell’s ideas of God, as expressed explicitly by the main character, Emilio Sandoz, a Jesuit (but also implicitly by others) to be old-fashioned, even anachronistic. The idea of God as a father figure and we being ‘His’ children is one I rejected in my teens, especially after reading Camus’ The Plague (La Peste). So, in some ways, I think Russell is applying the same literary devices as Camus (pointless and undeserved human suffering) to challenge this particular version of God that many of us grew up with.
At one point the character, Anne, asks Emilio if it’s alright for her to ‘hate God’. Towards the end of the novel, another Jesuit priest proposes the idea (not original, I suspect) that God had to make room for the existence of the Universe by removing Himself, which is really a Deistic version of God that one sometimes finds appealing to scientists, because such a God would be non-interventionist. If one takes this to its logical conclusion, there is no reason for this God to have empathy or be the anthropomorphic version we are familiar with from the Bible.
The interesting point is that people sometimes ‘find God’ in the midst of their own suffering. I think of Viktor Frankl (an Auschwitz survivor) who wrote Man’s Search for Meaning and The Unconscious God, who argued that a person can find meaning through adversity. But this supports my own view that God is something that people find within themselves and is not dependent on making God responsible for whatever happens in the world.
As Russell’s novel makes clear, if one makes God responsible for everything that happens, then He’s responsible for the suffering as well as the triumphs of the human spirit. At the start of the story’s journey, the protagonists believe that everything they’re doing is part of God’s plan – it’s meant to be – but at the end, this premise is effectively negated.
One of the attractions of Sci-Fi for me, even when I was quite young, is that it allows what-if scenarios, alternative societies. I would suggest that Frank Herbert and Ursula Le Guin were particularly adept at rendering alternative social structures. Russell’s alien society is particularly well thought through and makes one consider how it may have evolved on Earth had other hominids (like Neanderthals) survived into an agricultural world. As it is, we were (and still are) very good at exploiting economically weaker sectors of our societies, at all levels, from global to local.
There is no clear resolution, at least for me, to the ‘God question’, which is a central theme of her book. One can end up ‘hating’ God, if one follows the logical conclusion from the book’s premise to its confounding end, but I believe that the characters in the story are simply following an antiquated version of God.
P.S. I should point out that this book won the 1998 Arthur C. Clarke Award.
Whether Anne is representative of the author’s point of view or not, I found Russell’s ideas of God, as expressed explicitly by the main character, Emilio Sandoz, a Jesuit (but also implicitly by others) to be old-fashioned, even anachronistic. The idea of God as a father figure and we being ‘His’ children is one I rejected in my teens, especially after reading Camus’ The Plague (La Peste). So, in some ways, I think Russell is applying the same literary devices as Camus (pointless and undeserved human suffering) to challenge this particular version of God that many of us grew up with.
At one point the character, Anne, asks Emilio if it’s alright for her to ‘hate God’. Towards the end of the novel, another Jesuit priest proposes the idea (not original, I suspect) that God had to make room for the existence of the Universe by removing Himself, which is really a Deistic version of God that one sometimes finds appealing to scientists, because such a God would be non-interventionist. If one takes this to its logical conclusion, there is no reason for this God to have empathy or be the anthropomorphic version we are familiar with from the Bible.
The interesting point is that people sometimes ‘find God’ in the midst of their own suffering. I think of Viktor Frankl (an Auschwitz survivor) who wrote Man’s Search for Meaning and The Unconscious God, who argued that a person can find meaning through adversity. But this supports my own view that God is something that people find within themselves and is not dependent on making God responsible for whatever happens in the world.
As Russell’s novel makes clear, if one makes God responsible for everything that happens, then He’s responsible for the suffering as well as the triumphs of the human spirit. At the start of the story’s journey, the protagonists believe that everything they’re doing is part of God’s plan – it’s meant to be – but at the end, this premise is effectively negated.
One of the attractions of Sci-Fi for me, even when I was quite young, is that it allows what-if scenarios, alternative societies. I would suggest that Frank Herbert and Ursula Le Guin were particularly adept at rendering alternative social structures. Russell’s alien society is particularly well thought through and makes one consider how it may have evolved on Earth had other hominids (like Neanderthals) survived into an agricultural world. As it is, we were (and still are) very good at exploiting economically weaker sectors of our societies, at all levels, from global to local.
There is no clear resolution, at least for me, to the ‘God question’, which is a central theme of her book. One can end up ‘hating’ God, if one follows the logical conclusion from the book’s premise to its confounding end, but I believe that the characters in the story are simply following an antiquated version of God.
P.S. I should point out that this book won the 1998 Arthur C. Clarke Award.
Wednesday 2 September 2015
Oliver Sacks (9 July 1933 - 30 August 2015)
Oliver Sacks died last Sunday, but I only learned about it today. He is best known for his book, The Man Who Mistook His Wife for a Hat and the movie Awakenings, based on another book, where he is played by the late Robin Williams with Robert de Niro playing one of his patients whom he brought out of a catatonic state, even if only temporarily.
I've heard and watched interviews with Oliver Sacks when he visited Australia, which I believe he did a number of times. I wasn't aware that he was born in England (educated at Oxford) because his career as a neurologist really started in New York where he moved in 1965 and he was living in Manhattan when he died. I was also unaware that he was gay, which just goes to show that it was a non-issue for him.
Sacks was unusual for someone in his profession in that he really cared very deeply about the people whom he studied and showed a remarkable empathy for people that most of us would dismiss as unintelligible if not unintelligent. He was a remarkably good writer, and prolific, and like many scientists who can engage the public through their literary achievements, he was often criticised and devalued by some of his colleagues.
I confess that I've only read the one tome by Sacks (The Man Who Mistook His Wife for a Hat), a book of case studies showing the imperfections of the human mind, but in a way that made the reader aware of its intrinsic resilience and evoking dignity, not pity, for his subjects. So even before I heard or saw him speak, I was a fan. He combined a deep humility with a stimulating intelligence - a very rare individual indeed.
This is a well researched and very fitting obituary in The New York Times.
I will take the liberty of borrowing this quote, which is so apposite:
“And now, weak, short of breath, my once-firm muscles melted away by cancer, I find my thoughts, increasingly, not on the supernatural or spiritual, but on what is meant by living a good and worthwhile life — achieving a sense of peace within oneself. I find my thoughts drifting to the Sabbath, the day of rest, the seventh day of the week, and perhaps the seventh day of one’s life as well, when one can feel that one’s work is done, and one may, in good conscience, rest.”
I've heard and watched interviews with Oliver Sacks when he visited Australia, which I believe he did a number of times. I wasn't aware that he was born in England (educated at Oxford) because his career as a neurologist really started in New York where he moved in 1965 and he was living in Manhattan when he died. I was also unaware that he was gay, which just goes to show that it was a non-issue for him.
Sacks was unusual for someone in his profession in that he really cared very deeply about the people whom he studied and showed a remarkable empathy for people that most of us would dismiss as unintelligible if not unintelligent. He was a remarkably good writer, and prolific, and like many scientists who can engage the public through their literary achievements, he was often criticised and devalued by some of his colleagues.
I confess that I've only read the one tome by Sacks (The Man Who Mistook His Wife for a Hat), a book of case studies showing the imperfections of the human mind, but in a way that made the reader aware of its intrinsic resilience and evoking dignity, not pity, for his subjects. So even before I heard or saw him speak, I was a fan. He combined a deep humility with a stimulating intelligence - a very rare individual indeed.
This is a well researched and very fitting obituary in The New York Times.
I will take the liberty of borrowing this quote, which is so apposite:
“And now, weak, short of breath, my once-firm muscles melted away by cancer, I find my thoughts, increasingly, not on the supernatural or spiritual, but on what is meant by living a good and worthwhile life — achieving a sense of peace within oneself. I find my thoughts drifting to the Sabbath, the day of rest, the seventh day of the week, and perhaps the seventh day of one’s life as well, when one can feel that one’s work is done, and one may, in good conscience, rest.”
Tuesday 25 August 2015
Far from Men (Loin des Hommes)
This is a movie starring Viggo Mortensen, set in Algiers in 1954 and based on a short story by Albert Camus. Watching it, I was conscious of Camus’ philosophy all through it, and was not that surprised when I saw an online interview with Mortensen, who maintained that both he and the director (David Oelhoffen) drew heavily on Camus’ beliefs and principles when formulating the character of Daru.
As a friend of mine (who had already seen it) told me: it has similarities with another French movie (Of Gods and Men) both in terms of themes and geography. I reviewed Of Gods and Men (Des homes et des dieux) in June 2011. Both films involve men caught up in war against their wills and determined not to take sides, even when literally caught in the middle.
Camus had experience both in Algiers and in the French resistance during WWII, so he’s well equipped to tackle the subject matter. Viggo Mortensen’s character, Daru, teaches French to Arab children in a very remote location. Later in the movie we learn he’s lost his wife (not told how) and that he was an officer in the army during WWII (we assume, as the movie’s ‘now’ is the 1950s).
In the opening scenes, Daru is given custody of an Arab, Mohammed, who killed his cousin apparently, and whom he’s very reluctant to take charge of for reasons of humanity as much as inconvenience to his vocation as teacher.
Watching this movie I was reminded of a dream I had many decades ago where I was caught between 2 gangs in a pub (can only happen in a dream) and told I had to take sides. I surprised myself by refusing, even though it made an enemy of me to both sides, but, of course, I woke up before I had to deal with the consequences. That dream has stayed with me ever since, because it’s a metaphor for many situations we find ourselves in where we are asked to choose sides. In this film, this situation recurs repeatedly for its protagonist and we appreciate that this is Camus’ idealism tested in the crucible of battle where life and death, loyalty and execution are only separated by the thinnest of margins.
I haven’t read Camus’ original story, but I know enough about him to know that this character represents an ideal that he would have aspired to, as do most of us, but for which we are rarely tested and even fewer of us would pass.
Its relevance to the modern world is how easily it is to demonise Arabs and followers of Islam, in an Us and Them world. It’s worth watching this interview with Mortensen (though skip the first 4 minutes, which should have been cut) because he explains better than me how his world view is not so dissimilar to the character's, Daru, whom he plays.
As a friend of mine (who had already seen it) told me: it has similarities with another French movie (Of Gods and Men) both in terms of themes and geography. I reviewed Of Gods and Men (Des homes et des dieux) in June 2011. Both films involve men caught up in war against their wills and determined not to take sides, even when literally caught in the middle.
Camus had experience both in Algiers and in the French resistance during WWII, so he’s well equipped to tackle the subject matter. Viggo Mortensen’s character, Daru, teaches French to Arab children in a very remote location. Later in the movie we learn he’s lost his wife (not told how) and that he was an officer in the army during WWII (we assume, as the movie’s ‘now’ is the 1950s).
In the opening scenes, Daru is given custody of an Arab, Mohammed, who killed his cousin apparently, and whom he’s very reluctant to take charge of for reasons of humanity as much as inconvenience to his vocation as teacher.
Watching this movie I was reminded of a dream I had many decades ago where I was caught between 2 gangs in a pub (can only happen in a dream) and told I had to take sides. I surprised myself by refusing, even though it made an enemy of me to both sides, but, of course, I woke up before I had to deal with the consequences. That dream has stayed with me ever since, because it’s a metaphor for many situations we find ourselves in where we are asked to choose sides. In this film, this situation recurs repeatedly for its protagonist and we appreciate that this is Camus’ idealism tested in the crucible of battle where life and death, loyalty and execution are only separated by the thinnest of margins.
I haven’t read Camus’ original story, but I know enough about him to know that this character represents an ideal that he would have aspired to, as do most of us, but for which we are rarely tested and even fewer of us would pass.
Its relevance to the modern world is how easily it is to demonise Arabs and followers of Islam, in an Us and Them world. It’s worth watching this interview with Mortensen (though skip the first 4 minutes, which should have been cut) because he explains better than me how his world view is not so dissimilar to the character's, Daru, whom he plays.
Friday 26 June 2015
Some ruminations on a debate about the existence of God
I came across this debate on YouTube between Sye Ten Bruggencate and Matt Dillahunty (31 May 2014): “Is it Reasonable to Believe that God Exists?” I’ve come across Sye before and even argued with him on Stephen Law’s blog (or attempted to) a few years back; probably more than a few years, actually. He’s a self-described presuppositionist and a member of the Associate Reformed Presbyterian Church, who lives in Ontario, while Matt is a former Christian and now hosts a cable TV show, The Atheist Experience, based in Austin, Texas.
The debate is close to 2 hrs, including questions from the audience, which is followed by the participants’ ‘summing up’. I watched the entire debate partly because I was curious how Matt would handle Sye, who’s debating style is to make unsupported assertions then try and put the burden of proof, or disproof, onto his opponent. To give an example from my own experience: he once asked me to provide evidence that God had not made himself manifest to humankind (I’m paraphrasing from memory). I said I can’t provide evidence of something that didn’t happen, not happening. And his response was that it was my assertion therefore I had to prove it.
I was impressed by Matt’s temperament as well as his arguments, where he was very careful and precise whilst not being difficult to follow, even though he spoke quickly to ensure he stayed within the time limits imposed. Both of them were well prepared and had obviously researched each other’s positions. Sye cleverly used video excerpts of Matt to not only pre-empt Matt’s arguments but to support his own counter-arguments. Matt used humour in combination with rigid logic and precise language.
Sye’s argument was simplistic in the extreme: “It’s reasonable to believe that which is true; it’s true that God exists; therefore it’s reasonable to believe that God exists.” In his summing up Matt called it ‘kindergarten theology’ and ‘kindergarten philosophy’.
One of Sye’s key points of argument (which I’ve seen him use before) is to claim that his opponent can only argue from his (Sye’s) world view, and his world view is provided by God. He argues that any other world view is ‘absurd’, and in Matt’s case, Matt could, by his own admission, be a ‘brain in a vat’. However, Matt clarifies this by saying that he doesn’t believe he’s a brain in a vat, but it’s a well known philosophical conundrum that this can’t be proven. I first came across this in Stephen Law’s Philosopher’s Gym about 12 years ago, before I discovered him on his blog. In the debate, this logically led to a discussion on solipsism, which, Matt argued, can’t be proved to be false.
I’ve discussed this before, and, whilst all of us believe that everyone else we meet is not a figment of our imagination, there is one situation, which we have all experienced, where this is actually true. Neither Sye nor Matt mentioned this but that situation is a dream. A dream is solipsistic. So how do we know that we’re not in a dream. Because we have shared memories when we’re not in a dream. If I have a dream that includes someone I know, then when I next meet them in real life, they have no memory of that interaction, only I do. So unless one’s entire life is a dream then solipsism is a non sequitur if we have shared experiences that we can both remember.
One of the things that came out of this debate for me, and which Matt touched on briefly, is that if you have no common ground to begin with then you really can’t debate a subject. Specifically, Matt pointed out that he and Sye had different definitions of truth, which logically means that they would never be able to agree on whether something was true or not. I realised that it would be pointless for me to engage in an argument with someone whose entire world view is premised on fiction: a book of mythological stories. Sye argues that everyone knows that God exists, including babies (when Matt specifically asked him). No one can argue with that and Sye knows it, which is why he claims he’s unbeatable when it comes to arguments about the existence of God.
Matt argues that knowledge is a subset of beliefs, which I hadn’t considered before, and truth is based on evidence. Sye responded that evidence is something you take into a court and you become the judge but you can’t judge God. But if you don’t believe in God then that argument is irrelevant and without a God who actually intervenes in the assessment, one must use one’s own intellect to judge the evidence, which is what we all do all the time otherwise we wouldn’t be able to live.
So Sye’s basis for truth is God, which is revealed in scripture, and my basis for objective truth is mathematics, so we couldn’t be further apart. Sye would argue that I need his world view to believe that, because mathematics wouldn’t exist without God. However, I would argue that mathematics trumps God because even God can’t change a prime number to a non-prime number or vice versa or change the value of Pi or make 2 + 2 = 5. If Sye was to respond that God is mathematics then I might agree with him, but that has nothing to do with scripture.
Addendum: I've given this some more thought, plus I've watched the entire debate again. I believe I can challenge Sye's world view. Notice I say 'challenge' because that's the best one can do; I don't believe I can get him to change his world view any more than I believe he could get me to change mine.
Just to clarify my own position, I'm not anti-theist per se (as I've explained elsewhere); I believe God is something that people find within themselves, but that's another argument for another time.
My challenge is to do with my last paragraph of my original post, because I believe that mathematics gives us the only transcendental truths we know, whilst acknowledging that not everyone agrees with that position. By transcendental, I mean that mathematical truths exist independently of the human mind and even the universe. As someone once joked: If tomorrow the universe ceased to exist, the only part of science one could continue to do would be mathematics (that’s me paraphrasing John Barrow quoting Dave Rusin). I've discussed this position elsewhere.
My challenge to Sye is that mathematics even transcends God, for the reasons I pointed out in that closing paragraph. God can't change mathematics any more than we can: he can't make 2 + 2 = 5, amongst even more esoteric mathematical concepts like changing primes. If God can't change them, then logically they are independent of God. So I have a means of finding 'truths' that transcend God, therefore I don't need God in order for them to be true. What's more, mathematics provides 'truths' that anyone with the requisite intellectual ability can discover, without reference to any religious scripture or any divine revelation.
The debate is close to 2 hrs, including questions from the audience, which is followed by the participants’ ‘summing up’. I watched the entire debate partly because I was curious how Matt would handle Sye, who’s debating style is to make unsupported assertions then try and put the burden of proof, or disproof, onto his opponent. To give an example from my own experience: he once asked me to provide evidence that God had not made himself manifest to humankind (I’m paraphrasing from memory). I said I can’t provide evidence of something that didn’t happen, not happening. And his response was that it was my assertion therefore I had to prove it.
I was impressed by Matt’s temperament as well as his arguments, where he was very careful and precise whilst not being difficult to follow, even though he spoke quickly to ensure he stayed within the time limits imposed. Both of them were well prepared and had obviously researched each other’s positions. Sye cleverly used video excerpts of Matt to not only pre-empt Matt’s arguments but to support his own counter-arguments. Matt used humour in combination with rigid logic and precise language.
Sye’s argument was simplistic in the extreme: “It’s reasonable to believe that which is true; it’s true that God exists; therefore it’s reasonable to believe that God exists.” In his summing up Matt called it ‘kindergarten theology’ and ‘kindergarten philosophy’.
One of Sye’s key points of argument (which I’ve seen him use before) is to claim that his opponent can only argue from his (Sye’s) world view, and his world view is provided by God. He argues that any other world view is ‘absurd’, and in Matt’s case, Matt could, by his own admission, be a ‘brain in a vat’. However, Matt clarifies this by saying that he doesn’t believe he’s a brain in a vat, but it’s a well known philosophical conundrum that this can’t be proven. I first came across this in Stephen Law’s Philosopher’s Gym about 12 years ago, before I discovered him on his blog. In the debate, this logically led to a discussion on solipsism, which, Matt argued, can’t be proved to be false.
I’ve discussed this before, and, whilst all of us believe that everyone else we meet is not a figment of our imagination, there is one situation, which we have all experienced, where this is actually true. Neither Sye nor Matt mentioned this but that situation is a dream. A dream is solipsistic. So how do we know that we’re not in a dream. Because we have shared memories when we’re not in a dream. If I have a dream that includes someone I know, then when I next meet them in real life, they have no memory of that interaction, only I do. So unless one’s entire life is a dream then solipsism is a non sequitur if we have shared experiences that we can both remember.
One of the things that came out of this debate for me, and which Matt touched on briefly, is that if you have no common ground to begin with then you really can’t debate a subject. Specifically, Matt pointed out that he and Sye had different definitions of truth, which logically means that they would never be able to agree on whether something was true or not. I realised that it would be pointless for me to engage in an argument with someone whose entire world view is premised on fiction: a book of mythological stories. Sye argues that everyone knows that God exists, including babies (when Matt specifically asked him). No one can argue with that and Sye knows it, which is why he claims he’s unbeatable when it comes to arguments about the existence of God.
Matt argues that knowledge is a subset of beliefs, which I hadn’t considered before, and truth is based on evidence. Sye responded that evidence is something you take into a court and you become the judge but you can’t judge God. But if you don’t believe in God then that argument is irrelevant and without a God who actually intervenes in the assessment, one must use one’s own intellect to judge the evidence, which is what we all do all the time otherwise we wouldn’t be able to live.
So Sye’s basis for truth is God, which is revealed in scripture, and my basis for objective truth is mathematics, so we couldn’t be further apart. Sye would argue that I need his world view to believe that, because mathematics wouldn’t exist without God. However, I would argue that mathematics trumps God because even God can’t change a prime number to a non-prime number or vice versa or change the value of Pi or make 2 + 2 = 5. If Sye was to respond that God is mathematics then I might agree with him, but that has nothing to do with scripture.
Addendum: I've given this some more thought, plus I've watched the entire debate again. I believe I can challenge Sye's world view. Notice I say 'challenge' because that's the best one can do; I don't believe I can get him to change his world view any more than I believe he could get me to change mine.
Just to clarify my own position, I'm not anti-theist per se (as I've explained elsewhere); I believe God is something that people find within themselves, but that's another argument for another time.
My challenge is to do with my last paragraph of my original post, because I believe that mathematics gives us the only transcendental truths we know, whilst acknowledging that not everyone agrees with that position. By transcendental, I mean that mathematical truths exist independently of the human mind and even the universe. As someone once joked: If tomorrow the universe ceased to exist, the only part of science one could continue to do would be mathematics (that’s me paraphrasing John Barrow quoting Dave Rusin). I've discussed this position elsewhere.
My challenge to Sye is that mathematics even transcends God, for the reasons I pointed out in that closing paragraph. God can't change mathematics any more than we can: he can't make 2 + 2 = 5, amongst even more esoteric mathematical concepts like changing primes. If God can't change them, then logically they are independent of God. So I have a means of finding 'truths' that transcend God, therefore I don't need God in order for them to be true. What's more, mathematics provides 'truths' that anyone with the requisite intellectual ability can discover, without reference to any religious scripture or any divine revelation.
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