I mentioned in my last post, a recent acquisition: What is Life? by Erwin Schrodinger. This is a book that I’d heard about on more than a few occasions, so expectations were high, and I can honestly say it doesn’t disappoint. It says a lot that the copy I have is the eighteenth edition published in 2008, and it was originally published in 1944.
It started off as a series of lectures for the Dublin Institute for Advanced Studies at Trinity College, Dublin in February 1943. He then added an epilogue, On Determinism and Free Will. This segues into another essay (book really) called Mind and Matter which is another set of lectures delivered at Trinity College, Cambridge in 1956. The collection is bookended by a one-page Forward written by Roger Penrose in 1991, and Autobiographical Sketches, written as a virtual appendix by Schrodinger himself in November 1960.
Erwin Schrodinger is most famously known for the set of equations that bear his name, formulated in 1925/6 and for which he was awarded a Nobel Prize in 1933. They are the fundamental equations for quantum mechanics, arguably no less important than Einstein’s equations of relativity that I discussed in my previous post.
This collection is essentially a book on philosophy, that starts off by explaining the role of statistics in physics, then the role of quantum mechanics in evolutionary biology, then a philosophical discourse on mind that leads to a discussion on religion and finally epistemology. It’s a slim volume, a little over 150 pages long (leaving aside his autobiographical sketches). Yet I would recommend that all philosophers and students of philosophy should read it. To quote Paul Davies on the back cover:
“In these little books [Schrodinger] set down … most of the great conceptual issues that confront the scientist who would attempt to unravel the mysteries of life. This combined volume should be compulsory reading for all students…”
According to Penrose’s Forward, this book influenced J.B.S. Haldane and Francis Crick. Considering that it’s over 60 years old and was written before the discovery of DNA, it gives a remarkable insight into the role of mutations in evolutionary biology. Not only that, but Schrodinger explains the role of quantum mechanics in creating mutations. But he begins by explaining how virtually all of physics is statistical, giving examples ranging from Brownian motion, to the physics of magnetism, to radioactivity. His salient point is that, in each of these cases, no one can say when an individual element (atom) might change or react, but statistically they all follow strict mathematical rules. This is a mystery that struck me when I studied physics in high school, and here is a Nobel Prize winning physicist confirming what I thought then: it’s a facet of nature that defies our intuitive logic yet it’s been proven in virtually every arena of physics. We can’t predict the outcome of an individual element but we can predict the overall outcome with preternatural accuracy. He also explains the role of scale: the magnitude of numerical atoms or molecules that make up the smallest physical entities, which is what gives statistical power to many of nature’s dynamics.
Schrodinger then addresses the fundamentals that make life unique, including the fact that every cell contains the ‘code’, effectively the ‘blueprint’ that determines every facet of an organism like us. Remember, this is decades before the structure of DNA was discovered, yet Schrodinger explains how ‘isomers’ can create a code analogous to the way Morse code can be created by just dots and dashes, and this code determines how a life form functions, appears and grows.
His book is full of these little treasures – so obvious when he points them out – yet never really contemplated by most of us. One name that keeps appearing throughout this volume is Ludwig Boltzman, whom Schrodinger considered of no less significant to our knowledge of physics than Planck or Einstein. He explains the contribution that Boltzman made to thermodynamics, and entropy in particular, including the simple mathematical equation that encapsulates it. He also explains the role this has on the ‘arrow of time’. Few people appreciate that entropy determines the direction of time in physics, not relativity nor quantum mechanics. This was first pointed out to me by Penrose, in his book The Emperor’s New Mind. But Schrodinger covers it better still (only in the second part on Mind). He explains it by evoking statistical outcomes and the very simple analogy of shuffling a pack of cards. How many times would you need to shuffle a pack to get it in the right order. In effect this is entropy, and it’s like trying to reorganise the molecules of a broken egg to return it to its unbroken state.
On the subject of life and entropy, he addresses the fact that life alone seems to defy the second law of thermodynamics (actually, it doesn’t, otherwise we wouldn’t die). Nevertheless, life has a dynamism unlike non-organic molecular structures that defies our intuition. Schrodinger introduces the term, ‘negative entropy’, to explain how organisms increase the entropy of the environment; effectively the expense they impose for keeping themselves alive, whether they be primates like us, or bees, or trees in a forest.
In his short treatise on Determinism and Free Will, which he writes as an ‘Epilogue’ to the first set of lectures, he ventures, without apology, into the metaphysical, and acknowledges an influence by Aldous Huxley, specifically his The Perennial Philosophy. Early in this essay he says: “…I wish to emphasize that in my opinion , and contrary to the opinion upheld in some quarters, quantum indeterminancy plays no biological relevant role … except perhaps by enhancing their purely accidental character in such events as meiosis, natural and X-ray-induced mutation and so on…”
I find this a strange declaration, since he had just elaborated at length on the role of quantum mechanics in mutations, which are the causal factors in evolutionary biology, with natural selection being nature’s scythe so to speak. In the previous passage to the one quoted, Schrodinger emphasises that quantum mechanics is ‘statistico-deterministic’, which means that determinism is not completely eliminated by quantum phenomena as many people seem to believe. However, mutations are purely chance and, importantly, rare events, which Schrodinger explains in detail in the body of his lectures, so biological evolution is far from deterministic at its root cause.
It’s impossible in the space I’ve allotted myself here, to do justice to Schrodinger’s book, but whilst it’s full of gems from the opening pages, it’s towards the end that it becomes truly philosophical. Schrodinger tackles the problem of mind in a way that one rarely finds. For a start, he points out that we tend to ignore ‘the elephant in the room’, though, of course, he doesn’t use that phrase, whereby it’s only through mind that the universe has any meaning at all. And that, when we examine the universe - exactly in the way he has throughout the book - we effectively pretend that mind is not part of it. I’ve attempted to address this myself in a previous post on Subjectivity: The Mind's I (June 09). Schrodinger uses the term ‘objectivation’ which he’s obviously coined himself to highlight this point. He alludes to religion (specifically the Eastern religion of the Upanishads) by postulating that there is ‘one mind’ not many, without which the universe would not exist, not because it requires a God to create it, but because, there would be no reason for it to exist without mind. I may not be doing him justice here, so I would beg you read his words yourself, but that’s how I interpret him. I can actually see his point, and I’ve made similar arguments myself: without consciousness there is no point to the universe at all. I need to point out, by the way, that Schrodinger rejected orthodox religion early in his life, and he makes almost no reference to God, except, at one point, to acknowledge: "when God is experienced.. he must be missing in the space-time picture" just like our minds are.
He talks at length about 3 philosophers he considers significant: Plato, Kant and Einstein, all relating to epistemology. In regard to Plato, he gives easy-to-follow examples in both geometry and arithmetic to demonstrate “...true relations whose truth is not only unassailable, but is obviously there forever; the relations held and will hold irrespective of our inquiry into them. A mathematical truth is timeless, it does not come into being when we discover it.”
Then he proceeds to Kant, giving one of the best accounts I’ve read concerning Kant’s controversial views on space and time, which leads to the discussion on the ‘arrow of time’ (and Boltzman’s resolution that I referenced earlier). “He [Kant] would show plainly that space was necessarily infinite and believed firmly that it was in the nature of the human mind to endow it with the geometrical properties summarized by Euclid.”
This leads to Einstein who revealed that space and time are not independent as Kant thought, and is not Euclidean either. However, Schrodinger makes the following point: “Einstein has not – as you sometimes hear – given the lie to Kant’s deep thoughts on the idealization of space and time; he has, on the contrary, made a step towards its accomplishment.”
I’m not sure I agree with Schrodinger on this particular point. Space and time do exist outside the human mind – in fact, space-time is arguably the very fabric of the universe – which, on the surface, does put the lie to Kant’s interpretation as I’ve read it in his Critique of Pure Reason. Having said that, Schrodinger does argue that it is only mind that sees time as past, present and future, and that is an insight that is undeniable as it is obvious. It brings us back to the question: what meaning does the universe have without mind? Einstein showed that time is (relativistically) dependent on the observer, and to that extent, one could say relativity theory supports Kant’s contention of time being internal.
Lastly, Schrodinger touches on a point that is at once obvious, yet rarely, if ever, contemplated, which he calls: “The Mystery of the Sensual Qualities”. In particular, he discusses colour and sound, and he discusses both of them in depth, explaining that, whilst they are both frequency-dependent, the means in which we perceive them and they are propagated are entirely different. For example, colours of quite different frequencies can be mixed to produce a new colour of a frequency that is identical to a single colour of the same frequency and we can’t sense the difference. On the other hand, when sounds of different frequencies are mixed, as in music, we have no trouble in delineating them. But that’s not the main point he is making. The main point is that, whilst we can perform experiments with instruments to give ‘objective’ analysis of colours and sounds, we can’t objectively identify the sensing of them – that is entirely a ‘subjective’ affair. I’ve made this point myself in other posts. It’s why I argue that AI will never ‘sense’ colours and sounds like we do. In fact, it’s why I argue that AI will never have ‘mind’. Schrodinger argues this point better than any other author I’ve read. Of course, he makes no mention of AI, even though Turing had already set that ball rolling in Schrodinger’s own time.
In his autobiographical notes, Schrodinger explains how he learnt English (from an Aunt) even before he had learnt to write German. (He also mentions in passing that his mother’s Aunt had ‘six Angora cats’, which is the only reference to cats in the entire volume.) He was conscripted in the first World War, but spent World War 2 in Dublin; in fact, from 1939 through to 1956, for which he considered himself very fortunate. He called it “My Long Exile, but without the bitter association of the word, as it was a wonderful time.”
Schrodinger’s transcribed lectures are provocative, erudite and articulate. He makes you think deeply about topics and philosophical issues that are common place yet are fundamentally and inexplicably profound. It is one of the best philosophical books I’ve read and I’m surprised it’s not a prescribed text, though perhaps it is in some parts of the world. I know I will read it again.
Many people, in fact most, whether they be scientists, philosophers or theologians, will disagree with Schrodinger. But that’s not the point. The point is that he makes you think about issues you believe you have resolved when you almost certainly haven’t.
Sunday 15 November 2009
Sunday 8 November 2009
Einstein’s Code and Kerr’s Solution
When I started this blog, over 2 years ago now, I never anticipated picking up ‘followers’ and now I feel the need to maintain some sort of standard. For those who do follow this blog, it is obvious that I don’t comment on a regular basis (although I do on other people’s blogs) but that I only write when something especially attracts my attention. It’s becoming increasingly a blog where I want to share rare intellectual discoveries rather than express my opinions, though I do that as well.
Two recent such discoveries, are Cracking the Einstein Code by Fulvio Melia and What is Life by Erwin Schrodinger. The second book is a classic that I’ve wanted to read for a long time, while the first was an unexpected discovery. This post will focus on Melia’s book, subtitled, Relativity and the Birth of Black Hole Physics, and Schrodinger’s tome will probably be a subject for a future post.
Melia’s book is largely concerned with a little-known aspect of Einstein’s General Theory of Relativity (yes, it deserves capitals): a Kiwi called Roy Kerr, in 1963, unlocked the code inherent in Einstein’s 6 field equations that gave a description of space-time for a rotating body, which is the normal reality for massive bodies in the universe, from planets like ours to entire galaxies.
Now I need to say at the start, that whilst I write on esoteric topics, my knowledge is limited in the extreme, unlike the authors whom I read. Anyone following recent comments on this blog will notice that a generous intellect, called Timmo, has made critical comments on 2 of my former posts (Quantum Tunneling, Oct. 09 and Nature's Layers of Reality, May 09). I wish to acknowledge Timmo’s contribution and I welcome someone who really does know what they’re talking about when it comes to physics.
What I especially like about Melia’s account is that he acknowledges all the other people who contributed to the success of relativity theory (specifically, the General Theory), most of whom I’d never heard of. Like many people, I thought that Einstein’s theory had come effectively fully-fledged from his own mind. I wasn’t aware that there was a history of significant contributions from its conception right up to 1963, almost a decade after Einstein’s death.
Firstly, there is David Hilbert (who is extraordinarily famous in mathematics) and who had a correspondence with Einstein and helped him to develop his field equations. In fact, according to Melia, Hilbert actually published the equations on
But even Hilbert “could not overcome a serious problem – how to demonstrate that energy is conserved in Einstein’s theory.” From a conceptual point of view, this had always troubled me about relativity, and it wasn’t until I read Feynman’s account in Six Not-So-Easy Pieces, that I believe I understood it. What I didn’t know, before reading Melia’s account, is that a woman, Emmy Noether, who worked with Hilbert at Gottingen University, was the one who resolved this issue by introducing symmetries in connection with conservation laws, specifically conservation of momentum and energy. To paraphrase Melia,
Einstein’s General Theory of Relativity is premised on the ‘Principle of Equivalence’. Standing in a stationary elevator car in earth’s gravity is equivalent to being accelerated in an elevator car ‘vertically’ in gravity-free space (vertical, in this context, means being pulled from above our heads so our feet are pressed against the floor of the car). Gravity is felt as a force, by us on earth, only because we are stopped from falling. In free fall, no one feels a force being exerted on them, whether they are in a space ship orbiting the earth or jumping off a cliff. This is the key conceptual point to grasp about Einstein’s theory of gravity (which is the General Theory of Relativity). In free fall there is no force, even though this is counter-intuitive when you are earth-bound, because we rarely experience free-fall for any meaningful period of time without dying.
I don’t claim to understand Noether’s Theorem, but I understand its significance. Noether died relatively young in
Likewise, I’d never heard of Roy Kerr before reading Melia’s book, yet his contribution to relativistic physics is arguably no less significant. According to Melia, Kerr’s Theorem is the fundamental methodology used to investigate black holes (theoretically) to this day.
Kerr completed his undergraduate course at
Unaware of this (at the time), Kerr decided that pure mathematics wasn’t his forte and so went into applied mathematics instead, specifically relativistic physics. It is well known (amongst people who take an interest in physics) that Karl Schwarzschild was the first to provide a solution to Einstein’s field equations for the simplest, idealised scenario of a completely symmetrical sphere in a vacuum. He was a Professor of Potsdam University but formulated his solution whilst serving on the Russian front in WW1. He became ill soon after and died after returning home, but his name remains forever associated with black holes, which are a natural theoretical consequence of his solution.
Kerr’s solution (known as Kerr’s Theorem) was not realised until 1963 when he was at the
Spectroscopy analyses the exact wavelengths of light emitted by a distant star, and from the Doppler shift we are able to determine how fast they retreat from us and thus how far away they are. There is a direct proportional relationship between how fast stars retreat and how far away they are using Hubble’s constant, named after Edwin Hubble who first discovered this phenomenon.
The first quasar, 3C273, was discovered by Maarten Schmidt at the Palomar Observatory in California, but because they were only seen as radio sources, spectroscopic analysis was not possible until a light source could be found to be directly associated with the radio source. Hence Hazard’s brilliant idea, subsequently employed at Parkes, to pinpoint quasar 3C273. And it was Schmidt who did the spectroscopic analysis, revealing that the light was red-shifted by an enormous 16% making it much further away then anyone had imagined.
During the 1960s,
The curious aspect of Schmidt’s discovery is that, at the very first Texas Symposium on Relativistic Astrophysics in 1963, Kerr gave a 10minute lecture on his Theorem, which was virtually ignored because all the participants were far more interested in the recently discovered quasar. Yet Kerr’s Theorem gave the only relativistic solution to spinning black holes, which is exactly what quasars are.
Melia is meticulous in his coverage of all the people who contributed to our understanding of relativistic physics, both theoretically and experimentally. Not only the well known ones like Karl Schwarzschild, John Wheeler, Roger Penrose and Stephen Hawking, but unknown heroes like Noether and Kerr. He also mentions an Australian, Brandon Carter, who used Kerr’s Theorem to show that a ‘time loop’ (or 'time machine') could theoretically be generated beyond the event horizon of a rotating black hole. (But it only works in a vacuum, which makes it a catch-22 time machine.)
The significance of Kerr’s solution is that every significant physical body we know of in the universe is rotating, so Schwarzschild’s solution would almost certainly never be applicable to reality. Kerr’s solution reveals that there are, in fact, 2 event horizons for a rotating black hole. The event horizon is where the escape velocity from a black hole becomes the speed of light so nothing can escape from it. But a spinning black hole literally drags space-time around with it, which creates an inner and outer event horizon – don’t worry, I don’t understand it either. When a body crosses the first event horizon, the parameters of space and time are reversed: space becomes time-like and time becomes space-like. This is because time freezes at the event horizon for an outside observer and the external time becomes infinite from the inside. Time becomes space-like in that it becomes static and infinite, if I interpret it correctly. When an object crosses the second event horizon they reverse again so that ‘inside’ a spinning black hole, space and time become theoretically normal again. Of course, no one knows how true this really is. The other problem is that these theoretical considerations all assume a vacuum which is not the case if something is actually ‘crossing over’. To this day, there are no solutions to Einstein’s field equations for a non-vacuum – that is, for example, inside an object like the earth or the sun – only for outside in space.
That effectively is the limit of my understanding of this subject, even after reading Melia’s book. The story of Kerr himself is no less interesting. One gets the impression that, despite his obvious talents, he was not cut out for high level academia. He did not publish everything he uncovered, and he was not competitive in the sense that he sought to outdo his rivals at every opportunity, nor was he one for self-promotion. He left
Roy Kerr writes his own afterward in Fulvio Melia’s book (they are good friends), in which he talks about the difficulties in attempting to get the advanced education he badly needed in 1950s
Sunday 11 October 2009
Watching Watchmen
Yes, I know it was released over 6 months ago, but I’ve just seen it. I don’t normally review movies on this blog – in fact, I’ve only done it once before: Man on Wire (refer The philosophy of Philippe Petit, Oct. 08), and that’s a completely different kettle of cinematic and philosophical fish.
But Watchmen is such a good movie on so many levels, and it encapsulates so much of the American psyche, especially the not-so-recent paranoia of the Cold War, as well as our universal infatuation with violence. And the cinematic references: Apocalypse Now and Dr. Strangelove being the most obvious; both relevant to the cold war era. I am an outsider, regarding
In
I think the violence in movies has had one tragic consequence in real life. In the last 5 years, in
One of the characters in the movie, The Comedian, is quite literally a psychopath, yet he is clearly tolerated by his brethren because he’s on the side of 'good'. He is an allegory for the darker side of the American psyche, in particular, what Dick Cheney referred to as the ‘dark side’ of foreign operations. There is a scene in a bar in
Back in
I’ve said in a previous post on Storytelling (Jul.09) that comic books are our equivalent to Greek mythology, and, like all mythology, allegory should be its core ingredient. In this regard, I felt Watchmen doesn’t disappoint, especially with the character, Doctor Manhattan. Named after the
One of the advantages of reviewing a film so long after its release is I don’t feel guilty about giving away the ending. Doctor Manhattan effectively becomes an allegory for God, especially when it’s his ability to destroy on a cataclysmic, even biblical, scale that finally achieves world peace. This is a particularly pessimistic view of humanity, exemplified by the Bible in my view. We are inherently self-destructive by nature and only a fear of a superhuman (therefore supernatural) force can stop us from achieving our genetically determined destiny (in biblical terms, original sin). So, in a way, it’s a cautionary tale – but the moral of the tale in my view is that paranoia is what will lead to our self-annihilation and not Divine vengeance.
There are 2 things that make Watchmen an exceptional movie. Firstly, it’s cinematic rendering is close to perfect. A combination of film noir and graphic realisation that sets the standard above anything else I’ve seen, including The Matrix and Sin City. But it’s the rendering of the characters that really sets this movie above the norm for comic book movies. The romance between Nite Owl and Silk Spectre is completely believable. Only Bryan Singer’s Superman Returns compares in the genre and Singer is a master storyteller. But all the characters, in particular, the deeply, psychically wounded Rorschach, have a psychological depth one doesn’t expect in these movies. Again, I would reference Singer’s original X-Men as one of the few comparable movies in the genre, and of course Heath Ledger’s memorable rendition of The Joker in The Dark Knight.
But it’s as allegory for the American psyche, in all its contradictions, that I feel this movie delivers. It competes with Apocalypse Now and Dr. Strangelove on that level, both of which it unashamedly honours, and that’s the highest praise I can give it.
Oh, and I almost forgot to mention the soundtrack - from Philip Glass to Leonard Cohen to Bob Dylan to Jimi Hendrix - what more could one ask for?
Sunday 4 October 2009
Quantum Tunneling
In some respects this logically follows on from a post I wrote in July this year, Quantum Mechanical Philosophy, which is one of the more esoteric essays I’ve written on this blog. Hopefully, this essay will be less so, as the source material is well written and aimed at the uninitiated.
But I need to recount the gist of that post to make the relevant connection: specifically, the enigmatic
The thought experiment was elaborated upon by Podolsky and Rosen, so it became known as the Einstein-Podolsky-Rosen or EPR experiment. It examines the purported ‘action-at-a-distance’ phenomenon predicted by quantum physics for certain traits of particles or photons, which Einstein described, quite accurately, as ‘spooky’. If you have 2 particles with a common origin (could be photons with opposite polarisation or subatomic particles like electrons with opposite ‘spins’), then separate them over any distance whatsoever, you will not know what the spin or polarity, or whatever quantum mechanical trait you are measuring, is, until you take the actual measurement. The ‘spooky’ bit is that as soon as you make the measurement the ‘twin’ particle will instantaneously become the opposite. Before the measurement or observation is made the particles are in, what’s called, a ‘superposition’ of states – it can be either one or the other.
Einstein realised that this conjecture contradicted his special theory of relativity, which states that no signal or means of communication between particles of any kind can travel faster than the speed of light, which had already been confirmed by experiment. John Bell developed a mathematical equation that analysed correlations of hypothetical results from the thought experiment that would categorically prove either Einstein or Bohr wrong.
Alain Aspect developed a real experiment to test
As I point out in that previous post, the upshot of this is that either faster-than-light actions are possible (called non-locality) or there is no objective reality. Non-locality is self-explanatory (you can’t communicate faster than the speed of light) but no objective reality means that the thing doesn’t exist until someone measures it or takes an observation. I discuss this in more detail (lots of detail) in my previous post, but that’s effectively the
My conclusion was to accept non-locality (faster-than-light connections) in order to keep objective reality, and I made specific reference to David Bohm’s unpopular interpretation, known as the ‘hidden variables theory’. Bohm believed that there was a hidden set of parameters that govern the particles which we can’t see or detect.
To quote David Deutsch (who doesn’t agree with Bohm at all): ‘A non-local hidden variable theory means, in ordinary language, a theory in which influences propagate across space and time without passing through the space in between.’
And this leads me to quantum tunneling, because that’s exactly what quantum tunneling does, only it happens over short distances, not the distances used in the EPR experiment, which could theoretically include the other side of the universe.
I’ve just read an excellent book on this subject, Zero Time Space subtitled, How Quantum Tunneling Broke the Light Speed Barrier, authored by Gunter Nimtz and Astrid Haibel. Originally published in German in 2004, it was published in English in 2008. This book could be read by people with only a rudimentary knowledge of physics, as it contains only a few simple equations, among them Planck’s equation: E = hf where E is energy, f is frequency of a ‘wave’ and h is Planck’s constant, 6.6 x 10-34 Js (Joules seconds). The authors also include Snell’s law of refraction and the universal wave equation of wavelength times frequency equals velocity (I can’t find the symbol, lambda, for wavelength, in my arsenal of fonts). One of the annoyances is that there is a type-setting error in this particular equation (in the book). If someone is going to include equations, especially for people unfamiliar with them, I wish they could at least get them checked during type-setting. The same applies to Richard Feynman’s excellent book on relativity theory, Six Not-So-Easy Pieces where I found 3 type-setting errors amongst the equations scattered throughout the book. In both cases the books are aimed at people who are not familiar with the material, which means they won’t know the errors are there.
Putting that one (some may say petty) criticism aside, it’s a very good book on quantum mechanics for people who know very little about physics. It includes a short history of physics leading up to Einstein’s theories of relativity (with particular reference to the Special Theory) as well as quantum mechanics. They do this because the whole point of the book is to highlight how quantum tunneling breaks Einstein’s special theory of relativity, and therefore reinforces non-locality, as I described in my previous post. So the authors go to some pains to give the reader an overview of both Einstein’s theory and quantum mechanics, in conjunction with the historical context. It’s very well done.
Nimtz and Haibel, by the way, make no reference to
In the forward to the book, they briefly discuss the ‘myth… about the half-life of knowledge… It suggests that our knowledge is being declared invalid every five years by new knowledge.’ They then go on to dispel the most common representation of that myth: ‘
I made the same point in my essay on The Laws of Nature (March 08), explaining that Einstein’s equations reduce to
During this discussion they make another statement, relevant to the stability of scientific knowledge: ‘Mathematical proof has been regarded since Pythagoras and Plato as eternal, metaphysical truth.’ A statement I would agree with. For example, Reimann geometry hasn’t displaced Euclidean geometry, it has just extended our knowledge, both of the mathematical world and the physical world (through Einstein’s theory of General Relativity).
I’ve discussed on other posts, the relationship between mathematics and the natural world (refer The unreasonable effectiveness of mathematics, March 09), but no where is that more significant than in quantum mechanics. QED (Quantum Electrodynamics), for which Richard Feynman, Julian Schwinger and Sin-Itoro Tomonaga jointly won the Nobel Prize, is the most successful theory of all time. Without mathematics, quantum mechanics would be indecipherable, quite literally. Intriguingly, there are imaginary numbers in quantum theory that are completely relevant to quantum tunneling. Without imaginary numbers (created by the square route of -1, called i) quantum mechanics would never have been articulated as a meaningful theory at all.
As Nimtz and Haibel point out, it is the imaginary component of the equation that does the tunneling. When this was first derived, people just assumed that these imaginary components were unnecessary remnants of the mathematics, but that’s not the case. When tunneling occurs there is an interface where part of the signal is reflected and part is transmitted through ‘the tunnel’. The part that is reflected is mathematically ‘real’ and the part that is transmitted is mathematically ‘imaginary’. (I've since been informed this is not correct - refer Addendum 2 below.) A tunnel, by the way, is a barrier, where the particle or wave theoretically can’t travel, because it doesn’t have enough energy. The authors point out that it even occurs in the sun, otherwise the fusion, which gives us sunlight, would never occur. I should add that quantum tunneling is a feature of all transistor devices. In fact, it's the very feature that makes transistors work (called 'tunnel diode' by Nimtz and Haibel).
Both of the authors have performed experiments, to not only detect quantum tunneling, but to also measure the time elapsed. As predicted by Thomas Hartman in 1962, there is a time elapse at the ‘entrance’ to the tunnel, or the ‘interface’, between the medium and ‘the tunnel’, but the actual time spent in the tunnel is zero. This is called the Hartman effect. To quote the authors: ‘So the wave packet spreads in the tunnel in zero time and is everywhere from the entrance to the exit. This non-local phenomenon makes one feel eery.’ An understatement, if I’ve ever read one.
One of the authors, Gunter Nimtz, participated in an experiment that tunneled Mozart’s symphony in g-minor through a waveguide at superluminal speed: 4.7 times the speed of light. The elapsed time occurred at the entrance to the tunnel, as predicted by Hartman, not in the tunnel itself. In an exposition, that I will not try to repeat here, the authors explain how this quirk of nature (the elapsed time at the entrance to the tunnel) allows superluminal communication without impacting causality. The speed in the tunnel is infinite – as the Americans like to say: go figure. The title of the book, Zero Time Space, is therefore entirely appropriate.
They end the book with a brief description of wormholes and hypothetical warp drives, beloved of Sci-Fi writers, like me, that require exotic negative gravity amongst other improbabilities.
Of all the incredible manifestations of the universe, only consciousness is arguably more inexplicable or more mysterious (but no more weird) than quantum phenomena. If we didn’t observe it, no one would believe it. And if we didn’t have the mathematics to describe it, no one would be able to fathom it, even remotely.
Addendum 1: I came across this - it's very entertaining as well as informative.
Addendum 2: I would like to acknowledge Timmo (refer comments thread below) who has valiantly tried to correct all my mistakes. In particular, that the imaginary component of Schrodinger's equation plays no greater role in tunneling than the real component, if I understand Timmo correctly. Also he points out that tunneling and non-locality are independent phenomena, and possibly I misled people on that point.
He also corrects some faux pas I made concerning the Lorenz transformation and Godel's Incompleteness Theorem in response to comments I've made since the post was posted.
I confess I don't know as much as I appear to, and I wish I understood more than I actually do.
And I would like to thank Timmo for reminding me of how much I don't know.
Thursday 10 September 2009
Utopia or dystopia
I’ve written on this subject before (Living in the 21st Century, Sep.07; and The Problem with Democracy, Jun.08 ) but a recent conversation (with Dino at Coffee Plus) in combination with reading about ‘dystopian fiction’ as a subgenre of science-fiction, has led me to revisit it. A lengthy essay I wrote called Human Nature (back in Nov.07) may also be relevant to this topic.
I’ve been reading The Science Fiction Handbook by M. Keith Book and Anne-Marie Thomas, which is a very erudite analysis of various ‘seminal’ works of science-fiction along with their authors. In particular, their analysis of Octavia Butler’s Xenogenesis Trilogy (which I haven’t personally read) that works on the premise that humans appear genetically predisposed for self-destruction. H.G. Wells’ The Time Machine is another example, though Wells’ exploration is different: humans evolve into 2 species, the Morlocks and the Eloi, that symbiotically exist in an extreme master-slave relationship, or predator-prey relationship, to be more exact.
But
In an issue of COSMOS earlier this year, there was a feature article on the overpopulation of Earth and the consequences thereof. As I said in the introduction, I’ve raised this issue in earlier posts. The COSMOS article used an island metaphor which I thought was very apt. We are turning our planet into an island, but once we have over-resourced it we don’t have another island to go to. There are some people who believe that planetary colonialism will save us, but, if that’s the case, it means we haven’t addressed the problem, and, worse still, we aren’t seeking a solution.
There have been a number of mass-extinctions in Earth’s history, not just the dinosaurs, but at no other time has the rate of global species extinction been as high as it is now, and the cause is obvious: it is us. This is just one symptom, like climate change, that we are simply too successful (as a species) for our own good. If a species at the top of the food chain eats all the food then it ensures its own extinction. In effect, that’s what we are doing despite all of our harvesting techniques. We cannot live on this planet with only a handful of species to sustain us – it doesn’t work like that. Biodiversity means a healthy planet, and it’s no exaggeration to say that we are behaving like a disease.
In the last century, we have demonstrated, beyond dispute, that capitalism is the most successful economical model ever devised. But it, too, is too successful for its own good. In the recent economic crisis we have seen how the smallest dent in ‘growth’ is considered devastating. Unfortunately, economic growth means growth of everything, including: products, housing, infrastructure and, of course, people. You don’t have to have a PhD to see where this will eventually lead us, yet everyone appears to be in denial.
The ideal economic climate, as the recent ‘downturn’ revealed, is to maximise employment to maximise spending to maximise consumerism to maximise production to maximise employment, in an ever increasing cycle with no limit except the Earth’s capacity to sustain it. And it’s the last bit that everyone conveniently ignores.
As my friend Dino pointed out, in the ideal economy everyone should be in debt, which is what makes it so susceptible to bust-boom cycles, that we take for granted as being part of our modern environment. There is another side to this as well: I’m talking from my privileged position of being a member of a Western democratic society. We still live in a feudal society where the privileged few live at the expense of the massive poor, only the feudalism occurs on a global scale not a national one, so we don’t notice it so much. But just look at
But even in our special, privileged society so many people are not satisfied; in fact, they actually hate their jobs, yet will be demonstrably upset if their job is taken away from them. Our world, in short, is full of contradictions, yet no one seems to notice, or, if they do, they pretend they don’t exist.
I strongly believe that the 21st Century is going to be crunch time, whether we want to face it or not, but it’s hard to imagine anything is going to change until nature forces us to. The result, I fear, will be wars on a scale we’ve never before witnessed, which leads one to consider
In an early post on this blog, I wrote an essay on Evil (Oct.07), whereby I proposed a thesis that evil is a logical consequence of our evolutionary heritage to be territorial, which is not unique to the human species. Predators are territorial for the very reason I gave above: they need to control their resources, and they do so by rejecting intruders. This is true of lions, magpies, apes and humans, along with innumerable other species. So humans are xenophobic by nature, as history demonstrates, but there is a counter-culture to this. Humans are also highly empathetic, as are other species as well, which creates a natural antithesis to xenophobia and has allowed us to develop multi-culturally in many parts of the globe. But it’s the constraint on resources that can turn tolerance into intolerance more quickly than you can say refugees.
In my essay on Human Nature, I make the point that there are 3 human traits that have shaped our modern world. The first is our need for social contact, without which, we wouldn’t even have language; fundamental to our ability to think. But this also leads to the tribalism and its inherent problems that I alluded to in the previous paragraph. The second trait is the natural search for leadership in any group endeavour. Our hierarchical nature, that
I don’t have any easy answers to this, but I see some contradictions that may eventually resolve themselves when we are forced to face them. There is no utopia, I only see evolution, but it may well be Kuhnian rather than Darwinian. To obtain a sustainable future without losing our ability for creativity and material progress will require a change to the paradigm of infinite growth, and that means population growth must become stabilised. In many Western cultures this has already happened with the changing role of women, and this should not be reversed. Feminism, in its own way, may well save the planet, but it won’t be enough. The economic paradigm needs to change so that recycling replaces raw materials, with incentives to have long-lasting products in lieu of short-life ones that currently drive the capitalist machine. Sustainability will be forced upon us, and it’s technologically achievable, but politically difficult. Corporations have demonstrated by their activities in third world countries that they are simply amoral without regulations to enforce environmental and health compliances. A more global society is slowly changing this ethic but by how much and how soon is not easy to judge.
Economic growth needs to be decoupled from population growth but there is no sign this is achievable and no one is attempting to provide a model that may facilitate it. I feel this is the biggest dilemma that we face as a global community. Technology will slowly erode the most mind-numbing and health-debilitating occupations, so humans can do what they do best, which is to think creatively, solve problems both individually and collaboratively, and facilitate with others. And machines will do the things that they are good at: crunch astronomical numbers, do repetitive tasks at high speed and precision, and work tirelessly with no sleep and without complaint at jobs we disdain. This is the future that I try to project into my science-fiction where the word economy doesn’t even exist – but that’s a real utopia.
Addendum: The COSMOS article that I linked is actually from 2005 (Issue 3) but it's possibly even more relevant. Please read it.
Tuesday 1 September 2009
The Existential God
I was introduced to Don Cupitt on Stephen Law’s blog, about a year ago, or even earlier, when he provided a link to a radio interview with Cupitt on a BBC philosophy programme. Cupitt is a theologian, and he was being quizzed on his particularly unorthodox view of God, which, from memory, was more humanist than sacred.
More recently, I acquired his book, Above Us Only Sky, followed by a Chinese hieroglyph, which I assume means ‘sky’. Inside, the book is subtitled, The Religion of Ordinary Life, which pretty well sums up Cupitt’s entire philosophy. The book’s title is obviously a direct reference to the line in John Lennon’s song, Imagine, which also includes the line, ‘And no religion too’, and, despite being a theologian, that line could equally apply to Cupitt’s book. Right at the start of his book, he provides 27 points in, what one might call, a manifesto for living. Point 22 is headed:
“Even the Supreme Good must be left behind at once.
I, all my expressions, and even the Summum Bonumm, the Supreme Good itself, are all of them transient. Eternal happiness may be great enough to make one feel that one’s whole life has been worthwhile, but it is utterly transient. Let it go!”
His book, as the above quote exemplifies, is even more humanist than his interview, and, in fact, I would call it existentialist, hence the title of this post. I have also called myself existentialist on more than one occasion, but then so is Viktor Frankl in my view, who is not entirely an atheist either. Existentialism is not synonymous with atheism, by the way, but most theists think it is. By existentialist, I mean that we are responsible for our own destiny, which makes God less significant in the overall scheme of things. In other words, a belief in God is less relevant when one considers that moral choices, and any other choice for that matter, are completely dependent on the individual. I take the extreme view and suggest that we are responsible for God rather than God is responsible for us, but that’s so heretical I’ll desist from pursuing it for the sake of continuity.
But Cupitt’s book was a genuine surprise, because, despite its glib title, it’s actually a very meaty book on philosophy. For a start, Cupitt puts emphasis on language as the prism, or even filter, through which we analyse and conceptualise the world. To quote his point 6:
“Life is a continuous streaming process of symbolic expression and exchange.
The motion of language logically precedes the appearing of a formed and ‘definite’ world. It is in this sense that it was once said that ‘In the beginning was the Word’.”
I don’t entirely agree with him, concerning his implication that language determines our reality, but I need to digress a bit before I can address that specifically.
A central tenet of his thesis is that our Platonic heritage of a ‘perfect’ world is an illusion that we are only just starting to shed. Life is exactly what we get and that’s all it is. His philosophy is that once we realise this ‘truth’, we can live the ‘religion of ordinary life’ as his title suggests, and his manifesto specifies. In fact, he argues that this is what we already do in a secular humanist society, but we just don’t articulate it as such. Curiously, I made a similar point in a post I wrote on this blog almost 2 years ago, titled, Existentialism: the unconscious philosophy (Oct.07). Basically, I contended that, following the global Western cultural revolution of the 1960s, we adopted an existentialist philosophy without specifying it as such, or even realising it. We effectively said that we are responsible for our actions and their consequences and God has very little to do with it. I believe Cupitt is making a similar point: we achieved a revelation that humanity’s future is in our hands, and, unless we accept that responsibility, we will fail it.
But it’s in his discussion on rejecting Plato and the illusion that we inherited from him, that he returns to the significance of language:
“You can have more-or-less anything, provided only that you understand and accept that you can have it only language-wrapped – that is, mediated by language’s secondary, symbolic and always-ambiguous quality.” (Emphasis in the original.)
In highlighting this point, I’ve skipped a lot of his text, including an entire chapter on ‘Truth’ and a discussion on Descartes, and, in particular, Kant’s Critique of Pure Reason, where Kant famously contends that we will never understand the ‘thing-in-itself’, which is a direct reference to Plato’s ‘Forms’.
Like many dissertations on epistemology, Cupitt glosses over the significance of mathematics, which is arguably the most stubborn relic of Plato’s philosophy, and one that effectively side-steps Cupitt’s ‘language-wrapped’ dependence that I quoted above. I’m not a physicist but physics has interested me my whole life, and I’ve long believed that, as a discipline, it provides us with the best means of interpreting the universe and revealing its mysteries. In fact, without physics, our knowledge of the universe would still be stuck in the dark ages. But Cupitt alludes to a deep scepticism when he describes it thus:
“The physicist sets out his definitions of matter, space and time, then his laws of motion, and then his formulae for making calculations. But when he has developed his system of mathematical physics – a system of ideas – how is he to prove that there is a Real World out there of which the system is true and to which it applies? …whence do all its ideas get their ‘objective reality’?”
In other words, Cupitt is sceptical that a ‘system of ideas’, even one imbedded in mathematics, can provide an ‘objective reality’. But there are 2 points that Cupitt fails to address in his dissertation on ‘truth’ and ‘language’. Firstly, mathematics is not a language in the normal sense, although many people refer to it as if it is. Mathematical symbols are a language of sorts, but the concepts they represent, and, in particular, the relationships that mathematics describes are the closest we will get to ‘“God-given” truth’ to quote Roger Penrose (The Emperor’s New Mind). In other words, they have a universal quality unlike any other epistemic system that we know of, that arguably contain truths independent of the human mind. Now, I know many philosophers dispute this, but mathematical ‘truths’ (wherever they come from) are arguably the only abstract truths we can rely on, and do rely on all the time, in every technological marvel we exploit.
So mathematics provides us with ‘truths’ as well as a window into the ‘reality’ of the universe that we would never otherwise possess. It is on this point that I believe Cupitt and I epistemologically differ.
But it’s not epistemology per se that Cupitt is challenging when he explicates: ideas are ‘language-wrapped’; he has a deeper, theological motive. He points out how absurd it is to think that God provided us with scriptures using a language humans invented. Especially since God should be outside language in the same way ‘He’s’ supposedly outside the very universe in which we exist. What’s more, Cupitt challenges the very notion that our experience of ‘God’ by praying can be validated without language. I believe Cupitt makes a very good point here: if our ideas are language-wrapped then so is our idea of God.
In an earlier post (May 09) I referenced an essay by Raymond Smullyan called Is God a Taoist? In my post, I made a connection between Smullyan’s idea of God or Tao as ‘the scheme of things’ and the mathematical laws at different levels of scale that the universe appears to obey. This particular concept of an impersonal, non-language-wrapped God in combination with a Platonic mathematical realm is entirely compatible with Cupitt’s stated philosophy, though I doubt he would accept it. Cupitt provides an allegorical tale of a large group of Buddhist monks, one of whom gets up to speak about the Tao (Cupitt uses the term, ‘Supreme Good’), saying that: ‘No words can speak of it… It is beyond speech, it is even beyond all thought.’ When he sits down, another monk stands to address the same crowd: ‘Did the last speaker say anything?’
In a recent post on Storytelling (July 09), I made the point that without language we would think in the language of dreams, which is imagery and emotion. In fact, I argued that the language of dreams is the language of storytelling, only we are unaware of it. The story is ‘language-wrapped’ but the emotional content of the story is not, and neither is the imagery it conjures in our minds. Without these 2 components, the story is lifeless, just words on paper – it fails to engage the mind as story.
I’m not surprised that many cultures include dreaming as part of their religion – the American Indians are possibly the best known. Australian Aborigines use the term ‘Dream-time’ (at least, that’s its English translation) as the reference to their religion, full of mythical creatures and mythical tales. In recent posts on Larry Niven’s blog, there have been a couple of references to the comparison between religion and music that people often make. Many people have made the observation that music transcends language, and to some extent that is true. The only reason, we can say that, is because music moves us emotionally, and whilst language can describe those emotions it can’t convey them, whereas music can. So I would argue that religious experience is not language-wrapped in the same way that musical experience is not language-wrapped. Again, Cupitt would beg to differ. In fact, he would dispute the religious experience and call it illusion, and he is not alone. Most philosophers would agree with him completely.
Cupitt devotes an entire chapter to the subject, ‘Religion’, where he describes it as a ‘standard’ (as in a flag) to which people rally and identify, and, to which he rightly acknowledges, represents a view of God that is no longer tenable or of value. This is the religion that divides people and incorporates an infinite being who stands outside the world and judges us all. On this point, Cupitt and I are in agreement: it’s an entirely outdated, even dangerous, concept.
“…those who split the world between good and evil in effect split their own psyches too, and the puritans, the wowsers, the morality-campaigners, the condemners and the persecutors end up as unhappy people, Bible-bashers who are themselves without religion.”
This is the origin of the neurosis that made people of my generation revolt. Cupitt also makes reference to the 1960s when he describes the change in the zeitgeist that is effectively the theme of his book. Neurosis is like hypnotism – your brain tells you to do one thing but you do something else over which you feel you have no control. If you put your mind in a strait-jacket then it will revolt in a way that will shock you. Religion can do exactly that. To quote Cupitt again:
“In one form or another around the world, organized religion still manages to keep a large percentage of humanity locked in the most wretched mental poverty and backwardness.”
Cupitt goes on to express his individualistic philosophy that he calls ‘solar living’ (as in solo or solitary) but I would call existentialism, or a variant thereof. The fundamentals of his religious philosophy is to replace ‘God’ with ‘Life’, and rather than have a relationship between an earthly existence and an immortal one, to have a relationship between the individual’s life and the continuing stream of life that involves the rest of humanity.
My own approach is to refer to the internal and external world, which is the cornerstone of my entire world philosophy, but is effectively the same concept that Cupitt expresses here, albeit using different language. (Later in the book, Cupitt rejects the inner life concept altogether.) However, unlike Cupitt, I would contend that religion is part of one’s inner world rather than the external world. This makes religion completely subjective, and, in many respects, in conflict with organised or institutionalised religion. I’ve made this point before on previous posts, and Cupitt makes a similar point, arguably the most important in the book for me:
“The only ideas, thoughts, convictions that stay with you and give you real support are ones you have formulated yourself and tested out in your own life… In effect, the only religion that can save you is one you have made up for yourself and tested out for yourself: in short, a heresy.”
Cupitt always brings the discussion back to language, and this is the source of my personal dissent with his philosophy. He makes the apparently self-evident point: ‘…there is no meaning, no truth, no reality, and no knowledge without language.’ Which is true for us humans, cognitively, but the unstated corollary is that because none of these things can exist without language, they can’t exist without humanity either. This is the crux of his entire epistemological thesis.
Language is the most obvious bridge between our internal and external world, and almost nothing can be conveyed without language, but lots of things can be felt and experienced without the intervention of language. But Cupitt would argue that any experience is meaningless, quite literally, if it can’t be expressed in language. In other words, because it comes ‘language-wrapped’, that’s what makes it real. One needs to be careful here to distinguish epistemology from ontology, and I think the 2 are being confounded.
I think religion, as it is experienced by the individual, actually has little to do with language and more to do with emotion, just like music or even storytelling. As I described above, a story is written in words, but if it doesn’t transcend the words then it’s not a story. On the other hand, Cupitt argues, categorically, that there is nothing meaningful ‘outside language’.
Religion, and therefore God, is a psychological phenomenon, just like colour. Now, everyone thinks this is a misguided analogy, but colour does not exist out there in the external world, it only exists in your mind. What exists in the external world are light waves reflected off objects. You could probably build a robot that could delineate different wavelengths of light and associate a range of wavelengths with a label, like red for instance. But the robot wouldn’t actually see the colour red like you and I do. Some monkeys can’t see colours that we can see, because they only have bichromatic vision not trichromatic, but, if we genetically engineer them, they can. Yes, that’s a fact, not internet bullshit – it’s been done.
Anyway God is an experience that some people have that ‘feels’ like something outside themselves even though it only occurs in their minds. Many people never have this experience, so they don’t believe in God. The problem with this is that some of the people who think they have this experience believe that makes them superior to those who don’t, and likewise some of the people who don’t, believe they must be axiomatically superior to those who claim they do, because they’re obviously nuts.
Cupitt doesn’t address this, but I do because it’s what creates the whole divide that is actually so unimportant. I contend it’s like heterosexuals believing that everyone should be heterosexual, because it’s unimaginable to be anything else, and homosexuals arguing that everyone should be homosexual, even though they never do. But, in the same way that I think people who are heterosexual should behave as heterosexuals and people who are homosexual should behave as homosexuals, I believe that people who have an experience that they call God should be theists, and those who don’t should be atheists.
At the end of the day, I think God is a projection. I believe that the God someone believes in says more about them than it says about God (I’ve made this point before). That way people get the God they deserve. I call it the existential God.
I’ve now gone completely away from Cupitt’s book, but don’t be put off, it’s a very good book. And it’s very good philosophy because it provokes critical thinking. Another person would write something completely different to what I have written because they would focus on something else. This is a book to which, I admit, I have not done justice. It is worth acquiring just to read the essay he wrote for a symposium on Judaic Christian dialogue – not what people expected, I’m sure.
Cupitt ultimately argues for a universal morality that ignores identity of any kind, just like Lennon’s song. Accordingly, I’ll give Cupitt the last word(s):
“Our moral posture and practice must never be associated with a claim to be… an adherent of some particular ethnic or religious group, because all those who retreat into ‘identity’ have given up universal morality and have embraced some form of partisan fundamentalism – which means paranoia and hatred of humanity.”
“…any philosopher who is serious about religion should avoid all contact with ‘organized religion’. …Which is why, on the day this book is published, I shall finally and sadly terminate my own lifelong connection with organized religion.”
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