In the latest issue of Philosophy Now (Issue 124, February / March 2018) I read a review of a book, Experiencing Time by Simon Prosser, ‘a lecturer in philosophy at St Andrews University,’ (Scotland, presumably). The reviewer was Heather Dyke, who ‘has taught philosophy at Otago, NZ and at the London School of Economics’.
I haven’t read Prosser’s book, but I was particularly taken by this quote (albeit out of context): "…if no physical system can detect the passage of time, then neither can the human mind". Basically (according to Dyke), Prosser rejects what he calls ‘A-Theory’ that past, present and future is how time manifests itself and, what’s more, is dynamic in as much as past, present and future keep changing all the time (my italics). ‘B-Theory’ simply states that events are temporally related – some events precede other events but there is ‘no objective distinction between past, present and future, and that time is not dynamic’ (Prosser’s position). I can’t do Prosser justice, but I can use my own philosophical position to critique what Dyke presented.
Prosser came up with a thought experiment, which Dyke only partly expounds upon: “a physical device that could detect whether or not time was passing, and thus tell whether or not A-Theory was true”. According to Dyke, Prosser contends that his detector, which uses ‘light... [to] illuminate when it detects the passage of time’, can’t distinguish between A-Theory and B-Theory, because ‘it will illuminate’ in both cases. This apparently leads him to the conclusion that I quoted above: if time can’t be detected by his ‘device’ then ‘neither can the human mind’.
My own position is that both A-Theory and B-Theory are correct, because B-Theory is just A-Theory without consciousness. Consciousness is the 'time-passing detector' that Prosser claims can’t exist. Consciousness is the only phenomenon that exists in a continuous present, as Erwin Schrodinger pointed out in his prescient book, What is Life?. Schrodinger doesn’t claim that this is a unique attribute of consciousness, but I do. I contend that everything else in the Universe either exists in the past or the future. Only consciousness surfs a wave of time which we experience as a constant now. That is why the concepts of past, present and future have no reference without consciousness; and, on that point, Prosser and I might even agree.
I’ve written a few posts on time, and in one I quoted William Lawrence Bragg:
Everything that has already happened is particles, everything in the future is waves. The advancing sieve of time coagulates waves into particles at the moment ‘now’.
I’m the only person I know who believes that quantum mechanics and classical physics are complementary rather than different versions of the same reality. Schrodinger’s equation is fundamentally a description of a wave function that only exists in Hilbert space, which theoretically can have up to infinite dimensions. Schrodinger’s equation has been superseded by QED (quantum electrodynamics) but the wave function and its phase change with respect to time and the Born mechanism to convert it into probabilities in the ‘real world’ (not Hilbert space) still apply. Also there is no time in Hilbert space, so ‘time’ in the famous time dependent Schrodinger equation can only exist in the classical physics world.
It is for all these reasons that I argue that they are different worlds that happen to interface at what’s called the ‘decoherence’ of the wave function, when the Schrodinger equation no longer applies. That’s right: Schrodinger’s equation only applies in Hilbert space, not the real world, even though time in the real world determines the phase of the wave function.
But I believe Lawrence Bragg (as distinct from his father, William Henry Bragg) provided a clue. Basically, it all makes sense to me if quantum mechanics is the future and classical physics is the past. The Born rule, that gives us the probability of an ‘event’ occurring in the real world (in the future), is mathematically equivalent to running Schrodinger’s equation both forward and backward in time – a point made by Schrodinger himself. Superposition makes perfect sense in Hilbert space if time doesn’t exist. Feynman’s path integral method assumes all paths are possible but most of them cancel each other out and we are left with the most probable path. He demonstrates this most efficaciously when he explains mirror reflection using quantum mechanics (as expounded in his book, QED).
For a photon of light, time is zero, and light is arguably the most commonly known quantum phenomenon that we witness all the time. We know that light has a finite velocity, otherwise, as someone pointed out (Caspar Henderson in A New Map of Wonders), everything would happen at once. A photon of light could literally see the entire life of the universe in its lifetime, which is zero from its perspective. Light is effectively in the future until it interacts with matter, as Bragg inferred.
Einstein discovered, mathematically, as opposed to empirically, that time is fluid, which means it passes at different rates depending on the observer. It’s gravity that ultimately determines the rate of time, because a particle (any particle) in free fall follows maximum relativistic time (as expounded by Feynman in another book, Six Not-So-Easy Pieces). Any deviation from free fall means that time will slow down, and that’s Einstein’s theories of relativity (both of them) in a nutshell.
Now, you may think that if time ‘flows’ at different rates in different locations then they must all have different ‘nows’ but there is no logical reason for that. Quantum entanglement suggests that now can exist across the Universe, even though Einstein himself never accepted that possibility.
In fact, Einstein argued that the now that we all experience is totally subjective – there is no objective now. I think that the finite age of the Universe, along with quantum entanglement, suggests that he was wrong, but others will work that out in the future, one way or another.
But the now that everyone experiences is a consequence of consciousness, because only consciousness surfs on a constant now.
Addendum 1: Loop quantum gravity theorist, Carlo Rovelli, has defined ‘now’ as the 'edge of the big bang', and that is as good a definition of an 'objective now' as you will find. An objective now can be translated or frozen in time like when you take a photograph or the background cosmic radiation, which is 380,000 years after the big bang (or thereabouts). In other words, objective ‘nows’ are relational as opposed to the present which becomes the past as soon as it arrives, except to sentient creatures like us.
Addendum 2: Roger Penrose, whose comprehension and discussion of quantum mechanics makes my ruminations appear simplistic, uses a metaphor of a mermaid sitting between the sea and the land to represent the relationship between QM and classical physics. He consistently talks about QM in 3 phases: U, R and C. U is the evolution of the wave function (described by Schrodinger’s equation in Hilbert Space). R is the 'decoherence' of the wave function, usually in the form of a measurement or observation. And C is classical physics, or the real world, where the detection takes place. U, R and C represent a sequence, which is consistent with my thesis that, relationally, QM is the future and classical physics is the past.
Addendum 3: Carlo Rovelli (refer Addendum 1) has said that ‘at a fundamental level, time disappears’, which is a well known mathematical conundrum in quantum cosmology (refer Paul Davies in The Goldilocks Enigma). My point would be that if you were looking into the future, you’d expect time to disappear.
Monday, 26 February 2018
Saturday, 3 February 2018
My Heroes
Most people have heroes – usually sporting heroes, sometimes war heroes and sometimes political heroes. Well, I have heroes of science and philosophy.
Probably my earliest hero was Albert Einstein. To give a bit of backstory, in my preteens I had already taken an interest in science, but really it was zoology and animals of any description. People (relatives) used to give me books on animals all the time and I spent a lot of time drawing pictures of them as well as reading about them. But one day, and I can remember it vividly, as in where I was (not at home) and who gave it to me, I was given a book on The Atom. I was somewhere between 10 and 12, so it coincided roughly with when I started high school and it set the direction of my inquiring mind for ever.
So when I was 15 or 16, my mind was ripe when I saw a documentary on Albert Einstein on our black and white TV, probably produced by the BBC. I was smitten not only by the man’s genius but also his eccentricities and his obvious disregard for what people thought of his appearance. For example, he didn't wear socks. I also admired his courage for his pacifist stance, even though he famously wrote a letter to Roosevelt advocating the development of an atomic bomb before Germany did. His life was full of contradictions and paradoxes. He was a Jew yet agnostic, he was a pacifist yet came up with the famous equation that allows nuclear fission to occur, and his theories of relativity are paradoxes incarnate: time and space can shrink if you travel fast enough. I remember thinking all these things from watching that programme. And I can remember for the first time someone explaining that Einstein deduced that gravity wasn’t a force but a curve in spacetime. I found that so outlandish that it took many years (decades) before I properly understood it.
I’ve written elsewhere on this blog, an exposition of his general theory of relativity, which I took mostly from Richard Feynman’s excellent book, Six Not-So-Easy Pieces. Einstein got some things wrong but that does not diminish the man’s stature. Having said that, I think he had a better understanding of quantum mechanics than people give him credit for, and one should remember that he coined the term ‘photon’ to explain the photo-electric effect, which is purely a quantum phenomenon. But I think he was wrong to believe that the world is totally deterministic with no room for free will.
Regarding his famous theories of relativity: the special theory and the general theory; I would argue that you can’t have one without the other. In fact, I’ve long contended (though others may differ) that the paradoxes inherent in the special theory of relativity can only be resolved with the general theory. From my perspective, I found it necessary to come to grips with the general theory before the special theory, even though Einstein published them in the reverse order with a 10 year gap in between.
Of course, heroes have heroes of their own, and Einstein’s heroes were Newton, Maxwell and Faraday; all of whom occupied my mind in my early years learning about physics.
In that golden age of physics, as it’s often called, there were many luminaries: Niels Bohr, Max Planck, Werner Heisenberg, Erwin Schrodinger, Louis de Broglie, Wolfgang Pauli and Max Born. These are the best known involved in the emerging field of quantum mechanics, which also included Einstein. Out of these, I would give special mention to Erwin Schrodinger, not just because of his eponymous equation but because his mind ranged outside his field into biology and the Hindu text, the Vedas (of which I know nothing). In particular, he wrote a short tome called What is Life? which includes a chapter on the mind.
Schrodinger’s equation is all the more remarkable because it was suppositional. As Feynman once said: ‘It can’t be derived from anything we know.’ Yet it's been called 'the most important equation in all of mathematical physics' by John Barrow (amongst others) because it give us the energy levels of electrons in matter, which gives us all of chemistry. The wave function which lies at the heart of Schrodinger's equation and QED (Feynman’s own integral path method of QM) is an enigma in itself. It exists in Hilbert space, an abstract domain of possibly infinite dimensions and it’s disputable whether it has a physical significance or is just a convenient mathematical fiction. It effectively underpins everything we can see and touch, but not gravity apparently. Richard Elwes in his book, Maths 1001, says that ‘The Schrodinger equation is not limited to the wave functions of individual particles, but… potentially the wave function of the entire universe.’
Alan Turing is a hero of mine, whose life was cut short because he was prosecuted (and persecuted) for being homosexual, yet he was one of the greatest minds, not only of the 20th Century, but in the history of science. He’s most famously known for his pivotal role in deciphering the German enigma code during WW2. The not-so-recent movie (2014), The Imitation Game, starring Benedict Cumberbatch, was a travesty in my view, which is not a reflection on Cumberbatch but the producers and writers of the film.
Alan Turing was first a logician and he came up with the concept of the modern computer as a thought experiment to solve a mathematical conundrum, called the ‘halting problem’. Basically he proved that a machine (computer) could not solve algorithmically if a particular problem could be solved by the computer or not. To give an example: the Riemann hypothesis, which states that all complex roots (zeros) of the Zeta function are of the form ½ + ib. I’ve explained this in more detail elsewhere, but it is the most famous unsolved problem in mathematics since 1859, when Riemann proposed it as a method for determining the number of prime numbers up to any given Real number.
The point is that these zeros can be calculated on a computer, and have been in to the trillions, but of course they can’t be computed to infinity unless you have an infinite amount of time. What Turing proved generally (not just for Riemann’s hypothesis) is that you can’t determine in advance if the computer will stop or not. Obviously, if the computer stops the hypothesis is false.
So I would select these 3 as my 20th Century heroes. Now this is purely subjective and therefore I feel compelled to give reasons or criteria for my choices. A hero is someone who inspires you and to whom you may feel an affinity or someone you aspire to emulate. All these men had faults, though Turing, ironically, was possibly the least egotistical of them and the most respectful to the opposite sex. He was quite open about his homosexuality at a time when it was considered a psychiatric illness and a criminal activity. All 3 of them were geniuses beyond question, and they all impacted the 20th Century in ways that most of us are unaware of.
Alfred Wallace and Charles Darwin are heroes because they challenged orthodoxy and are still under siege, one might say, by certain elements of the Christian church. It’s what’s been discovered in the 150 years since their time that both illuminates their theories and uncovers even greater mysteries, which is the nature of science that not only includes evolutionary biology but cosmology and quantum mechanics. Science is constantly creating new frontiers by overcoming existing ones. The difference with evolution is that it challenges long held religious tenets. Quantum mechanics is far more weird and counter-intuitive than evolution but no one denies it because it doesn’t challenge the premise that ‘man’ was made in God’s image.
Wallace and Darwin were very respectful of each other, but what I liked about Wallace, in particular, was that he was more of an amateur, an outsider, than Darwin was, but drew the same conclusions. Both men travelled to ‘exotic’ locations (including Australia, it has to be said) and discovered fauna and flora that led them to a theory of evolution by natural selection. We know that there is more to it than that, and it’s not totally resolved as many would have you believe, but I still call evolution a ‘fact’, based on the simple expediency that everything that’s been discovered since their time, that has proved them right, could just as readily have proved them wrong.
I would like to include this quote from Alfred Wallace, which I lifted from Tim Flannery’s book, The Weather Makers (about climate change):
It is among those nations that claim to be the most civilised, those that profess to be guided by a knowledge of laws of nature, those that most glory in the advance of science, that we find the greatest apathy, the greatest recklessness, in continually rendering impure this all-important necessity of life… (from Man’s Place in the Universe, 1903).
It makes me want to read his entire treatise.
As far as mathematicians go, I would include Euler as well as Riemann, whom I’ve already mentioned. Euler’s famous ‘identity’, which I’ve written about elsewhere, is arguably the most famous formula in mathematics and Feynman called it ‘the most remarkable formula in math’ when he discovered it for himself just a month before his 15th birthday. Yes, Feynman was a genius in his own right too. The number e, which is the base of the natural logarithm and gives the rate of compound interest if it’s done continuously, and is the most famous transcendental number after π, was named after Euler and is called Euler’s constant. Euler, by the way is pronounced ‘oiler’. Euler is acknowledged as the most prolific mathematician ever, but his eponymous equation which gives us his famous ‘identity’ is key to Schrodinger’s wave equation, so they are linked.
Riemann’s life was relatively short, but not only did he give us the Riemann Hypothesis, which seems to find its way into innumerable branches of mathematics, he also gave us non-Euclidean geometry which lies at the heart of Einstein’s general theory of relativity, so they are linked as well.
Special mentions need to go to Fermat and Gauss, who is called the greatest mathematician ever and was a mentor to Riemann. Fermat is best known for his famous ‘last theorem’ finally resolved by Andrew Wiles 357 years later. But he’s also known for his work on refraction (of light through glass and water) and his ‘least action’ principle which had a profound influence on the aforementioned Feynman. In fact, it’s Feynman’s employment of the least action principle to explain how gravity works that unlocked the secret to Einstein’s general theory of relativity (for me). Feynman also used this principle in his QED (quantum electrodynamics) and it’s called a Lagrangian, mathematically.
I could keep on going but I’m going to stop with the ancient Greeks, specifically Pythagoras, Socrates, Plato and Aristotle. These are all connected, because Socrates was a teacher to Plato and Plato was a teacher to Aristotle, whilst Plato’s famous ‘Academy’ was set up using Pythagoras’s quadrivium of arithmetic, geometry, music and astronomy. Aristotle, famously, was teacher to Alexander the Great but also influenced science and philosophy up until the renaissance.
About 3 decades ago I saw a documentary on Pythagoras and Plato which was an epiphany for me and started me on the path to becoming a self-declared mathematical Platonist, which has only strengthened with time. And this leads me in a strange time warp way to Roger Penrose, who is arguably the only living person I might declare a hero, because this is something I believe we share. Penrose is a bit of an iconoclast and I seem to like that in my philosophers. I don’t agree with everything he believes but no one does, or should, when it comes to philosophy. I don’t believe in gurus in any school or forum. Penrose is just as prominent in mathematics as he is in physics and he is a true philosopher. I would put Paul Davies in this category as well, whom I admire and write about often. But Penrose’s 3 worlds philosophy is one that I’ve adopted as my own and I must therefore give him due recognition. And from that perspective, I think Penrose would acknowledge his debt to Pythagoras and Plato.
I wrote a recent post (just prior to Christmas) on Socrates, whom I called ‘the first philosopher’, which I admit is a bit of a stretch depending on many parameters, not least how one defines philosophy. But to put it in perspective, I described philosophy as ‘argument augmented by analysis’, because I like to believe that’s what I do. But if anything, I would aspire to be a modern ‘Socratic’ philosopher in that I would like to make people think outside their usual bounds, because I think that’s what Socrates did and it got him into serious trouble because he got young people, in particular, to challenge the status quo.
We live in a time when we are very divided politically and I think it’s more important than ever to learn about opposing views. As a philosopher, you can’t deconstruct your opponents’ arguments if you haven’t read them or heard them. Every weekend I buy 2 newspapers – one that ostensibly represents the political left and one that ostensibly represents the political right. Strange as it may seem, I find I read more of the right-leaning paper than its counterpart, because I want to know what people who have opposing views to mine are thinking and arguing.
At the head of my blog, right from its inception, I wrote a little aphorism which I believe sums up philosophy as it should be. I never expect to change people’s beliefs to mine but I do expect to make them think. I would like to think that’s what Socrates did.
Probably my earliest hero was Albert Einstein. To give a bit of backstory, in my preteens I had already taken an interest in science, but really it was zoology and animals of any description. People (relatives) used to give me books on animals all the time and I spent a lot of time drawing pictures of them as well as reading about them. But one day, and I can remember it vividly, as in where I was (not at home) and who gave it to me, I was given a book on The Atom. I was somewhere between 10 and 12, so it coincided roughly with when I started high school and it set the direction of my inquiring mind for ever.
So when I was 15 or 16, my mind was ripe when I saw a documentary on Albert Einstein on our black and white TV, probably produced by the BBC. I was smitten not only by the man’s genius but also his eccentricities and his obvious disregard for what people thought of his appearance. For example, he didn't wear socks. I also admired his courage for his pacifist stance, even though he famously wrote a letter to Roosevelt advocating the development of an atomic bomb before Germany did. His life was full of contradictions and paradoxes. He was a Jew yet agnostic, he was a pacifist yet came up with the famous equation that allows nuclear fission to occur, and his theories of relativity are paradoxes incarnate: time and space can shrink if you travel fast enough. I remember thinking all these things from watching that programme. And I can remember for the first time someone explaining that Einstein deduced that gravity wasn’t a force but a curve in spacetime. I found that so outlandish that it took many years (decades) before I properly understood it.
I’ve written elsewhere on this blog, an exposition of his general theory of relativity, which I took mostly from Richard Feynman’s excellent book, Six Not-So-Easy Pieces. Einstein got some things wrong but that does not diminish the man’s stature. Having said that, I think he had a better understanding of quantum mechanics than people give him credit for, and one should remember that he coined the term ‘photon’ to explain the photo-electric effect, which is purely a quantum phenomenon. But I think he was wrong to believe that the world is totally deterministic with no room for free will.
Regarding his famous theories of relativity: the special theory and the general theory; I would argue that you can’t have one without the other. In fact, I’ve long contended (though others may differ) that the paradoxes inherent in the special theory of relativity can only be resolved with the general theory. From my perspective, I found it necessary to come to grips with the general theory before the special theory, even though Einstein published them in the reverse order with a 10 year gap in between.
Of course, heroes have heroes of their own, and Einstein’s heroes were Newton, Maxwell and Faraday; all of whom occupied my mind in my early years learning about physics.
In that golden age of physics, as it’s often called, there were many luminaries: Niels Bohr, Max Planck, Werner Heisenberg, Erwin Schrodinger, Louis de Broglie, Wolfgang Pauli and Max Born. These are the best known involved in the emerging field of quantum mechanics, which also included Einstein. Out of these, I would give special mention to Erwin Schrodinger, not just because of his eponymous equation but because his mind ranged outside his field into biology and the Hindu text, the Vedas (of which I know nothing). In particular, he wrote a short tome called What is Life? which includes a chapter on the mind.
Schrodinger’s equation is all the more remarkable because it was suppositional. As Feynman once said: ‘It can’t be derived from anything we know.’ Yet it's been called 'the most important equation in all of mathematical physics' by John Barrow (amongst others) because it give us the energy levels of electrons in matter, which gives us all of chemistry. The wave function which lies at the heart of Schrodinger's equation and QED (Feynman’s own integral path method of QM) is an enigma in itself. It exists in Hilbert space, an abstract domain of possibly infinite dimensions and it’s disputable whether it has a physical significance or is just a convenient mathematical fiction. It effectively underpins everything we can see and touch, but not gravity apparently. Richard Elwes in his book, Maths 1001, says that ‘The Schrodinger equation is not limited to the wave functions of individual particles, but… potentially the wave function of the entire universe.’
Alan Turing is a hero of mine, whose life was cut short because he was prosecuted (and persecuted) for being homosexual, yet he was one of the greatest minds, not only of the 20th Century, but in the history of science. He’s most famously known for his pivotal role in deciphering the German enigma code during WW2. The not-so-recent movie (2014), The Imitation Game, starring Benedict Cumberbatch, was a travesty in my view, which is not a reflection on Cumberbatch but the producers and writers of the film.
Alan Turing was first a logician and he came up with the concept of the modern computer as a thought experiment to solve a mathematical conundrum, called the ‘halting problem’. Basically he proved that a machine (computer) could not solve algorithmically if a particular problem could be solved by the computer or not. To give an example: the Riemann hypothesis, which states that all complex roots (zeros) of the Zeta function are of the form ½ + ib. I’ve explained this in more detail elsewhere, but it is the most famous unsolved problem in mathematics since 1859, when Riemann proposed it as a method for determining the number of prime numbers up to any given Real number.
The point is that these zeros can be calculated on a computer, and have been in to the trillions, but of course they can’t be computed to infinity unless you have an infinite amount of time. What Turing proved generally (not just for Riemann’s hypothesis) is that you can’t determine in advance if the computer will stop or not. Obviously, if the computer stops the hypothesis is false.
So I would select these 3 as my 20th Century heroes. Now this is purely subjective and therefore I feel compelled to give reasons or criteria for my choices. A hero is someone who inspires you and to whom you may feel an affinity or someone you aspire to emulate. All these men had faults, though Turing, ironically, was possibly the least egotistical of them and the most respectful to the opposite sex. He was quite open about his homosexuality at a time when it was considered a psychiatric illness and a criminal activity. All 3 of them were geniuses beyond question, and they all impacted the 20th Century in ways that most of us are unaware of.
Alfred Wallace and Charles Darwin are heroes because they challenged orthodoxy and are still under siege, one might say, by certain elements of the Christian church. It’s what’s been discovered in the 150 years since their time that both illuminates their theories and uncovers even greater mysteries, which is the nature of science that not only includes evolutionary biology but cosmology and quantum mechanics. Science is constantly creating new frontiers by overcoming existing ones. The difference with evolution is that it challenges long held religious tenets. Quantum mechanics is far more weird and counter-intuitive than evolution but no one denies it because it doesn’t challenge the premise that ‘man’ was made in God’s image.
Wallace and Darwin were very respectful of each other, but what I liked about Wallace, in particular, was that he was more of an amateur, an outsider, than Darwin was, but drew the same conclusions. Both men travelled to ‘exotic’ locations (including Australia, it has to be said) and discovered fauna and flora that led them to a theory of evolution by natural selection. We know that there is more to it than that, and it’s not totally resolved as many would have you believe, but I still call evolution a ‘fact’, based on the simple expediency that everything that’s been discovered since their time, that has proved them right, could just as readily have proved them wrong.
I would like to include this quote from Alfred Wallace, which I lifted from Tim Flannery’s book, The Weather Makers (about climate change):
It is among those nations that claim to be the most civilised, those that profess to be guided by a knowledge of laws of nature, those that most glory in the advance of science, that we find the greatest apathy, the greatest recklessness, in continually rendering impure this all-important necessity of life… (from Man’s Place in the Universe, 1903).
It makes me want to read his entire treatise.
As far as mathematicians go, I would include Euler as well as Riemann, whom I’ve already mentioned. Euler’s famous ‘identity’, which I’ve written about elsewhere, is arguably the most famous formula in mathematics and Feynman called it ‘the most remarkable formula in math’ when he discovered it for himself just a month before his 15th birthday. Yes, Feynman was a genius in his own right too. The number e, which is the base of the natural logarithm and gives the rate of compound interest if it’s done continuously, and is the most famous transcendental number after π, was named after Euler and is called Euler’s constant. Euler, by the way is pronounced ‘oiler’. Euler is acknowledged as the most prolific mathematician ever, but his eponymous equation which gives us his famous ‘identity’ is key to Schrodinger’s wave equation, so they are linked.
Riemann’s life was relatively short, but not only did he give us the Riemann Hypothesis, which seems to find its way into innumerable branches of mathematics, he also gave us non-Euclidean geometry which lies at the heart of Einstein’s general theory of relativity, so they are linked as well.
Special mentions need to go to Fermat and Gauss, who is called the greatest mathematician ever and was a mentor to Riemann. Fermat is best known for his famous ‘last theorem’ finally resolved by Andrew Wiles 357 years later. But he’s also known for his work on refraction (of light through glass and water) and his ‘least action’ principle which had a profound influence on the aforementioned Feynman. In fact, it’s Feynman’s employment of the least action principle to explain how gravity works that unlocked the secret to Einstein’s general theory of relativity (for me). Feynman also used this principle in his QED (quantum electrodynamics) and it’s called a Lagrangian, mathematically.
I could keep on going but I’m going to stop with the ancient Greeks, specifically Pythagoras, Socrates, Plato and Aristotle. These are all connected, because Socrates was a teacher to Plato and Plato was a teacher to Aristotle, whilst Plato’s famous ‘Academy’ was set up using Pythagoras’s quadrivium of arithmetic, geometry, music and astronomy. Aristotle, famously, was teacher to Alexander the Great but also influenced science and philosophy up until the renaissance.
About 3 decades ago I saw a documentary on Pythagoras and Plato which was an epiphany for me and started me on the path to becoming a self-declared mathematical Platonist, which has only strengthened with time. And this leads me in a strange time warp way to Roger Penrose, who is arguably the only living person I might declare a hero, because this is something I believe we share. Penrose is a bit of an iconoclast and I seem to like that in my philosophers. I don’t agree with everything he believes but no one does, or should, when it comes to philosophy. I don’t believe in gurus in any school or forum. Penrose is just as prominent in mathematics as he is in physics and he is a true philosopher. I would put Paul Davies in this category as well, whom I admire and write about often. But Penrose’s 3 worlds philosophy is one that I’ve adopted as my own and I must therefore give him due recognition. And from that perspective, I think Penrose would acknowledge his debt to Pythagoras and Plato.
I wrote a recent post (just prior to Christmas) on Socrates, whom I called ‘the first philosopher’, which I admit is a bit of a stretch depending on many parameters, not least how one defines philosophy. But to put it in perspective, I described philosophy as ‘argument augmented by analysis’, because I like to believe that’s what I do. But if anything, I would aspire to be a modern ‘Socratic’ philosopher in that I would like to make people think outside their usual bounds, because I think that’s what Socrates did and it got him into serious trouble because he got young people, in particular, to challenge the status quo.
We live in a time when we are very divided politically and I think it’s more important than ever to learn about opposing views. As a philosopher, you can’t deconstruct your opponents’ arguments if you haven’t read them or heard them. Every weekend I buy 2 newspapers – one that ostensibly represents the political left and one that ostensibly represents the political right. Strange as it may seem, I find I read more of the right-leaning paper than its counterpart, because I want to know what people who have opposing views to mine are thinking and arguing.
At the head of my blog, right from its inception, I wrote a little aphorism which I believe sums up philosophy as it should be. I never expect to change people’s beliefs to mine but I do expect to make them think. I would like to think that’s what Socrates did.
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