I saw this Oscar-winning movie last weekend, and, tellingly, despite very recently winning the Oscar for Best Documentary, it’s only being shown in one cinema in the whole of Melbourne. And yet everyone with internet access should watch this movie, because its message affects all of us.
For those living under a rock, Edward Snowden famously revealed that the US is capturing all our on-line activities and mobile phone calls, even though, as revealed in the film, various representatives of the government had been openly denying this (even under oath) for some time. The closest we get to acknowledgement is when someone says, in a Senate Committee Hearing, in response to this very question about accessing people’s digital communications: “Not willingly.” Reading between the lines, one could conclude that it could happen ‘accidentally’, which suggests a couple of options: the information is available if they want to access it; or they might accidentally access someone’s data whilst trying to access someone else’s, whom they can legitimately target (via a court order or whatever judicial process is required). As it turns out, thanks to Snowden’s expose, we know it’s the first option.
Ethically, there are 2 distinct but related issues implicit in the same movie. Are the American Government’s activities in this regard, ethical, and is it ethical for Snowden to use his position of privileged information to break his Government’s trust (as well as the law) by revealing them to the rest of the world?
There is a third ethical issue, entwined with the previous 2: is it ethical for the American Government to pursue Snowden with the full force of its law, treating him, effectively, as a traitor and a spy (they are charging him under the espionage act)?
Let’s deal with the first ethical issue first; after all, it’s the one that triggered the other two. As pointed out in the movie, this ‘action’ on the part of the American Government is a consequence of 9/11 and the threat of terrorist attacks anywhere in the Western world. It’s also pointed out in the movie that England have even more comprehensive measures than the US, regarding tracking everyday digital information of its own citizens.
On the same day I saw this film, I heard a news bulletin that here in Australia, the Government is currently debating a bill requiring internet providers to keep all user activity (in Australia) for however many years (I don’t know if there’s a limit). Interestingly, the only proviso the Opposition suggested is that journalists be protected in order to protect their sources. This is a very important point, because it’s only journalists that can keep politicians honest, and journalists’ roles in providing a conduit for Snowden’s ‘leak’ was crucial to his expose. I’ve said before that the health of a democracy can be measured by the freedom that journalists are allowed in criticising their elected leaders. Keeping sources ‘secret’ has been critical (at least, in Australia) in allowing journalists that particular freedom.
There are similarities between this documentary and the not-so-recent movie, Kill the Messenger, because, in both cases, someone exposed the Government or the Government’s agents in activities that the public were unaware of, and, in both cases the Government, or its agencies, effectively destroyed the whistleblowers’ lives.
But this parliamentary debate taking place in Australia reveals an ethical distinction, which, in my view, is worth noting. In Australia, because it has to be passed as Parliamentary law, it cannot be done without the public’s awareness, and, I feel, this is where the American Government went wrong. I don’t have an issue with them keeping all my digital data, most of which, like this blog, is freely available to the public anyway. And I understand how such data is crucial to stopping terrorist attacks, so, as long as the data capture is not used to persecute me personally, I have no problem.
Having said that, the movie points out how data collection on a nation’s citizens is a first step in controlling or oppressing that citizenry. So, hand in hand with this action is an essential ‘trust’ that it will be used only for spoiling terrorist attacks and that the essential democratic character of the nation won’t be compromised in the process. In some ways, this is a moot point because, after watching this film, I couldn’t help but feel that this will never be reversed. We already live in a quasi-Orwellian environment where our entire lives can be tracked digitally, if someone so requires. We effectively have no secrets regarding our on-line activity (including mobile phone communications).
Towards the end of the movie, there is a news clip of President Obama saying that we needed ‘to have this debate’, implying that it could have occurred without Snowden’s revelations. However, this is contradicted by earlier video footage (alluded to above) that, even under oath, no one was going to admit to this whilst the public remained ignorant.
And this brings to the fore Snowden’s ethics. There are some similarities here between Snowden and Assange, both of whom are now living in exile, because both had sensitive material that embarrassed the American Government in particular. However, Snowden is probably more like Chelsea (Bradley) Manning, who had access to and leaked the relevant files, in that both men acted on their conscience at considerable personal cost.
But, in the case of Snowden, he demonstrates neither the naivety of Manning nor the ego of Assange. It is clear from the outset that Snowden understood fully the consequences of his actions, and is remarkably calm throughout his entire dealings with the specific journalists he colluded with in order to make public what the American Government preferred to remain covert. This is the crux of the issue for me: not that the American Government is collecting all our communications data, but that they did it behind our backs and are now enraged that some individual dared to let everyone know.
There is some irony that Snowden now lives in exile with his partner in Russia, a country not renown for honouring freedom of speech or freedom of the press. If Snowden had done to Russia, what he’s done to America, he probably would have been assassinated. As it is, in America, they will lock him up and throw away the key, just like they’ve done to Manning, assuming they ever catch him.
Saturday, 21 March 2015
Saturday, 14 March 2015
Today is π Day
I only found about this yesterday, via COSMOS online. Actually, it's Pi Day tomorrow in the US where it originated because, using American date nomenclature, March 14 (3/14) gives the first 3 digits of pi. But this year is special because the date is 3/14/15, which are the first 5 digits and it will be the only time in the whole century.
π, as everyone knows, is the ratio of the circumference of a perfect circle to its diameter, irrespective of the size of the circle. But it's a very nerdy number, because it turns up in the most unexpected places, like quantum mechanics and Euler's famous formula: eiπ + 1 = 0; earning the sobriquet, 'God's own equation'. A simple derivation can be found here.
Pi is the best known so-called transcendental number and, of course, it has an infinite string of digits that appear to be truly random (refer COSMOS link above). COSMOS also explain that if you toss a coin 2n times, and n is large enough, then the probability of getting equal number of heads and tails is 1/√(nπ). Mathematics contains many hidden formulae like this that give unexpected relationships relevant to the real world.
Addendum: It should be pointed out that today is also Albert Einstein's birthday and this year is the centenary of his masterpiece, the General Theory of Relativity, not to be confused with the Special Theory, which he penned 10 years earlier in 1905.
π, as everyone knows, is the ratio of the circumference of a perfect circle to its diameter, irrespective of the size of the circle. But it's a very nerdy number, because it turns up in the most unexpected places, like quantum mechanics and Euler's famous formula: eiπ + 1 = 0; earning the sobriquet, 'God's own equation'. A simple derivation can be found here.
Pi is the best known so-called transcendental number and, of course, it has an infinite string of digits that appear to be truly random (refer COSMOS link above). COSMOS also explain that if you toss a coin 2n times, and n is large enough, then the probability of getting equal number of heads and tails is 1/√(nπ). Mathematics contains many hidden formulae like this that give unexpected relationships relevant to the real world.
Addendum: It should be pointed out that today is also Albert Einstein's birthday and this year is the centenary of his masterpiece, the General Theory of Relativity, not to be confused with the Special Theory, which he penned 10 years earlier in 1905.
Sunday, 1 March 2015
Chaos – nature’s preferred means of evolution and dynamics
Ian Stewart is a highly respected mathematician and populariser of mathematics. He has the rare ability to write entire books on the esoteric side of mathematics with hardly an equation in sight. The ‘new edition’ of Does God Play Dice? has the subtitle, The New Mathematics of Chaos, and that’s what the book is all about. The first edition was published in 1989, the second edition in 1997, so not that new any more. Even so, he gave me more insights and knowledge into the subject than I knew existed. I’d previously read Paul Davies’ The Cosmic Blueprint, which does a pretty good job, but Stewart’s book has more depth, more examples, more explanations and simply more information. In addition, he does this without leaving me feel stranded in the wake of his considerable intellect.
For a start, Stewart puts things into perspective, by pointing out how chaos pervades much of the natural world – more so than science tends to acknowledge. In physics and engineering classes we are taught calculus and differential equations, which, as Stewart points out, are linear, whereas most of the dynamics of the natural world are non-linear, which make them ripe for chaotic analysis. We tend to know about chaos through its application to systems like weather, fluid turbulence, population dynamics yet its origins are almost purely mathematical. Throughout the book, Stewart provides numerous examples where the mathematics of chaos has been applied to physics and biology.
Historically, he gives special attention to Poincare, whom he depicts almost as the ‘father of chaos’ (my term, not his) which seems appropriate as he keeps returning to ‘Poincare sections’ throughout the book. Poincare sections are hard to explain, but they are effectively geometrical representations of periodic phenomena that have an ‘attractor’. That’s an oversimplification, but ‘attractors’ are an important and little known aspect of chaos, as many chaotic systems display an ability to form a stable dynamical state after numerous iterations, even though, which particular state is often unpredictable. The point is that the system is ‘attracted’ to this stable state. An example, believe it or not, is the rhythmic beat of your heart. As Stewart explains, ‘the heart is a non-linear oscillator’.
Relatively early in the book, he provides an exposition on ‘dynamics in n-space’. Dimensions can be used as a mathematical concept and not just a description of space, which is how we tend to envisage it, even though it’s impossible for us to visualise space with more than 3 dimensions. He gives the example of a bicycle, something we are all familiar with, having numerous freedoms of rotation, which can be mathematically characterised as dimensions. The handle bars, each foot pedal as well as the wheels all have their own freedom of rotation, which gives us 5 at least, and this gives 10 dimensions if each degree of freedom has one variable for position and one for velocity.
He then makes the following counter-intuitive assertion:
What clinches the matter, though, is the way in which the idea of multi-dimensional spaces fit together. It’s like a 999-dimensional hand in a 999-dimensional glove.
In his own words: ‘a system with n degrees of freedom – n different variables – can be thought of as living in n-space.’ Referring back to the bicycle example, its motion can be mathematically represented as a fluid in 10 dimensional space.
Stewart then evokes a theorem, discovered in the 19th Century by Joseph Liouville, that if the system is Hamiltonian (meaning there is no friction) then the fluid is incompressible. As Stewart then points out:
…something rather deep must be going on if the geometric picture turns dynamics not just into some silly fluid in some silly space, but renders it incompressible (the 10-dimensional analogue of ‘volume’ doesn’t change as the fluid flows).
The reason I’ve taken some time to elaborate on this, is that it demonstrates the point Stewart made above – that an abstract n-dimensional space has implications in reality – his hand-in-glove analogy.
Again, to quote Stewart:
I hope this brings you down to Earth with the same bump I always experience. It isn’t an abstract game! It is real!
Incompressibility is such a natural notion, it can’t be coincidence. Unless you agree with Kurt Vonnegut in Cat’s Cradle, that the Deity made the Universe as an elaborate practical joke.
The point is that the relationships we find between mathematics and reality are much more subtle than we can imagine, the implication being that we’ve only scratched the surface.
Anyone with a cursory interest in chaos knows that there is a relationship between chaos and fractals, and that nature loves fractals. What a lot of people don’t know is that fractals have fractional dimensions (hence the name) which can be expressed logarithmically. As Stewart points out, the relationship with chaos is that the fractal dimension ‘turns out to be a key property of an attractor, governing various quantitative features of the dynamics.’
I won’t elaborate on this as there are more important points that Stewart raises. For a start, he spends considerable time and space pointing out how chaos is not synonymous with randomness or chance as many people tend to think. Chaos is often defined as deterministic but not predictable which reads like a contradiction, so many people dismiss it out-of-hand. But Stewart manages to explain this without sounding like a sophist.
It’s impossible to predict because all chaotic phenomena are sensitive to the ‘initial conditions’. Mathematically, this means that the initial conditions would have to be determined to an infinitesimal degree, meaning an infinitely long calculation. However the behaviour is deterministic in that it follows a path determined by those initial conditions which we can’t cognise. But in the short term, this allows us to make predictions which is why we have weather forecasts over a few days but not months or years and why climate-forecast modelling can easily be criticised. In defence of climate-forecast modelling, we can use long term historical data to indicate what’s already happening and project that into the future. We know that climate-related phenomena like glaciers retreating, sea temperature rise and seasonal shifts are already happening.
This short term, long term difference in predictability varies from system to system, including the solar system. We consider the solar system the most stable entity we know, because it’s existed in its current form well before life emerged and will continue for aeons to come. However, computer modelling suggests that its behaviour will become unpredictable eventually. Jacque Laskar of the Bureau des Longitudes in Paris has shown that ‘the entire solar system is chaotic’.
To quote Stewart:
Laskar discovered… for the Earth, an initial uncertainty about its position of 15m grows to only 150m after 10 million years, but over 100 million years the error grows to 150 million kilometres.
So while chaos is 'deterministic', it's computably indeterminable, which is why it's 'unpredictable'. I've written another post on that specific topic.
In the last chapter, Stewart attempts to tackle the question posed on the front cover of his book. For anyone with a rudimentary knowledge of physics, this is a reference to Einstein’s famous exhortation that he didn’t believe God plays dice, and Stewart even cites this in the context of the correspondence where Einstein wrote it down.
Einstein, of course, was referring to his discomfort with Bohr’s ‘Copenhagen interpretation’ of quantum mechanics; a discomfort he shared with Erwin Schrodinger. I’ve written about this at length elsewhere when I reviewed Louisa Gilder’s excellent book, The Age of Entanglement. Stewart takes the extraordinary position of suggesting that quantum mechanics may be explicable as a chaotic phenomenon. I say extraordinary because, in all my reading on this subject, no one has ever suggested it and most physicists/philosophers would not even consider it.
I have come across some physicist/philosophers (like David Deutsch) who have argued that the ‘many worlds’ interpretation of quantum mechanics can, in fact, explain chaos. A view which I’m personally sceptical about.
Stewart resurrects David Bohm’s ‘hidden variables’ interpretation, preferred by Einstein, but generally considered disproved by experiments confirming Bell’s Inequality Theorem. It’s impossible for me to do justice to Stewart’s argument but he does provide the first exposition of Bell’s theorem that I was able to follow. The key is that the factors in Bell’s Inequality (as it’s known) refer to correlations that can be derived experimentally. The correlations are a statistical calculation (something I’m familiar with) and the ‘inequality’ tells you whether the results are deterministic or random. In every experiment performed thus far, the theorem confirms that the results are not deterministic, therefore random.
Stewart takes the brave step of suggesting that Bell’s Inequality can be thwarted because it relies on the fact that the results are computable. Stewart claims that if they’re not computable then it can’t resolve the question. He gives the example of so-called ‘riddled basins’ where chaotic phenomena can interact with ‘holes’ that allow them to find other ‘attractors’. Again, an oversimplification on my part, but as I understand it, in these situations, which are not uncommon according to Stewart, it’s impossible to ‘compute’ which attractor a given particle would go to.
Stewart argues that if quantum mechanics was such a chaotic system then the results would be statistical as we observe. I admit I don’t understand it well enough to confer judgement and I have neither the mathematical nor physics expertise to be a critical commentator. I’ll leave that to others in the field.
I do agree with him that the wave function in Schrodinger’s equation is more than a ‘mathematical fiction’ and it was recently reported in New Scientist that a team from Sydney claim they have experimentally verified its reality. But I conjecture that ‘Hilbert space’, which is the abstract space where the wave function mathematically exists, may be what’s real and we simply interact with it, but there is no more evidence for that than there is for the ‘multiple universes’ that is currently in favour and gaining favour.
Towards the very end of the book, Stewart hypothesises on how different our view of quantum mechanics may be today if chaos theory had been discovered first, though he’s quick to point out the importance of computers in allowing chaos to be exploited. But he makes this interesting observation in relation to the question on the cover of his book:
Now, instead of Einstein protesting that God doesn’t play dice, he probably would have suggested that God does play dice. Nice, classical, deterministic dice. But – of course – chaotic dice. The mechanism of chaos provides a wonderful opportunity for God to run His universe with deterministic laws, yet simultaneously to make fundamental particles seem probabilistic.
Of course, in the real world, dice are chaotic because the outcome of a throw is subject to the sensitivity of the initial conditions, which is the throw itself. The same with a coin toss. So each throw has its own initial conditions, which creates the randomness from throw to throw that we observe.
Of course, both Stewart’s and Einstein’s reference to a Deity is tongue-in-cheek, but I’ve long thought that chaos provides the ideal mechanism for a Deity to intervene in the Universe. Having said that, I don’t believe in Divine intervention, because it assumes that God has a plan that 'He' needs to keep interfering with. I prefer to think that God is simply the laws of the Universe (a la Einstein’s God) and they will run their course.
Chaos may be 'deterministic' but you can't rerun a chaotic phenomenon and get the same result - that's how chaos was discovered. The Universe obeys 'strange attractors', which provides stability to some systems while still being ultimately unpredictable. We don't know enough to know why the Universe turned out the way it did. Every age has its own sphere of ignorance, but chaos suggests that the future cannot be ultimately known. In other words, there appears to be a limit to what it's possible to know and not just a limit dependent on our cognitive abilities.
For a start, Stewart puts things into perspective, by pointing out how chaos pervades much of the natural world – more so than science tends to acknowledge. In physics and engineering classes we are taught calculus and differential equations, which, as Stewart points out, are linear, whereas most of the dynamics of the natural world are non-linear, which make them ripe for chaotic analysis. We tend to know about chaos through its application to systems like weather, fluid turbulence, population dynamics yet its origins are almost purely mathematical. Throughout the book, Stewart provides numerous examples where the mathematics of chaos has been applied to physics and biology.
Historically, he gives special attention to Poincare, whom he depicts almost as the ‘father of chaos’ (my term, not his) which seems appropriate as he keeps returning to ‘Poincare sections’ throughout the book. Poincare sections are hard to explain, but they are effectively geometrical representations of periodic phenomena that have an ‘attractor’. That’s an oversimplification, but ‘attractors’ are an important and little known aspect of chaos, as many chaotic systems display an ability to form a stable dynamical state after numerous iterations, even though, which particular state is often unpredictable. The point is that the system is ‘attracted’ to this stable state. An example, believe it or not, is the rhythmic beat of your heart. As Stewart explains, ‘the heart is a non-linear oscillator’.
Relatively early in the book, he provides an exposition on ‘dynamics in n-space’. Dimensions can be used as a mathematical concept and not just a description of space, which is how we tend to envisage it, even though it’s impossible for us to visualise space with more than 3 dimensions. He gives the example of a bicycle, something we are all familiar with, having numerous freedoms of rotation, which can be mathematically characterised as dimensions. The handle bars, each foot pedal as well as the wheels all have their own freedom of rotation, which gives us 5 at least, and this gives 10 dimensions if each degree of freedom has one variable for position and one for velocity.
He then makes the following counter-intuitive assertion:
What clinches the matter, though, is the way in which the idea of multi-dimensional spaces fit together. It’s like a 999-dimensional hand in a 999-dimensional glove.
In his own words: ‘a system with n degrees of freedom – n different variables – can be thought of as living in n-space.’ Referring back to the bicycle example, its motion can be mathematically represented as a fluid in 10 dimensional space.
Stewart then evokes a theorem, discovered in the 19th Century by Joseph Liouville, that if the system is Hamiltonian (meaning there is no friction) then the fluid is incompressible. As Stewart then points out:
…something rather deep must be going on if the geometric picture turns dynamics not just into some silly fluid in some silly space, but renders it incompressible (the 10-dimensional analogue of ‘volume’ doesn’t change as the fluid flows).
The reason I’ve taken some time to elaborate on this, is that it demonstrates the point Stewart made above – that an abstract n-dimensional space has implications in reality – his hand-in-glove analogy.
Again, to quote Stewart:
I hope this brings you down to Earth with the same bump I always experience. It isn’t an abstract game! It is real!
Incompressibility is such a natural notion, it can’t be coincidence. Unless you agree with Kurt Vonnegut in Cat’s Cradle, that the Deity made the Universe as an elaborate practical joke.
The point is that the relationships we find between mathematics and reality are much more subtle than we can imagine, the implication being that we’ve only scratched the surface.
Anyone with a cursory interest in chaos knows that there is a relationship between chaos and fractals, and that nature loves fractals. What a lot of people don’t know is that fractals have fractional dimensions (hence the name) which can be expressed logarithmically. As Stewart points out, the relationship with chaos is that the fractal dimension ‘turns out to be a key property of an attractor, governing various quantitative features of the dynamics.’
I won’t elaborate on this as there are more important points that Stewart raises. For a start, he spends considerable time and space pointing out how chaos is not synonymous with randomness or chance as many people tend to think. Chaos is often defined as deterministic but not predictable which reads like a contradiction, so many people dismiss it out-of-hand. But Stewart manages to explain this without sounding like a sophist.
It’s impossible to predict because all chaotic phenomena are sensitive to the ‘initial conditions’. Mathematically, this means that the initial conditions would have to be determined to an infinitesimal degree, meaning an infinitely long calculation. However the behaviour is deterministic in that it follows a path determined by those initial conditions which we can’t cognise. But in the short term, this allows us to make predictions which is why we have weather forecasts over a few days but not months or years and why climate-forecast modelling can easily be criticised. In defence of climate-forecast modelling, we can use long term historical data to indicate what’s already happening and project that into the future. We know that climate-related phenomena like glaciers retreating, sea temperature rise and seasonal shifts are already happening.
This short term, long term difference in predictability varies from system to system, including the solar system. We consider the solar system the most stable entity we know, because it’s existed in its current form well before life emerged and will continue for aeons to come. However, computer modelling suggests that its behaviour will become unpredictable eventually. Jacque Laskar of the Bureau des Longitudes in Paris has shown that ‘the entire solar system is chaotic’.
To quote Stewart:
Laskar discovered… for the Earth, an initial uncertainty about its position of 15m grows to only 150m after 10 million years, but over 100 million years the error grows to 150 million kilometres.
So while chaos is 'deterministic', it's computably indeterminable, which is why it's 'unpredictable'. I've written another post on that specific topic.
In the last chapter, Stewart attempts to tackle the question posed on the front cover of his book. For anyone with a rudimentary knowledge of physics, this is a reference to Einstein’s famous exhortation that he didn’t believe God plays dice, and Stewart even cites this in the context of the correspondence where Einstein wrote it down.
Einstein, of course, was referring to his discomfort with Bohr’s ‘Copenhagen interpretation’ of quantum mechanics; a discomfort he shared with Erwin Schrodinger. I’ve written about this at length elsewhere when I reviewed Louisa Gilder’s excellent book, The Age of Entanglement. Stewart takes the extraordinary position of suggesting that quantum mechanics may be explicable as a chaotic phenomenon. I say extraordinary because, in all my reading on this subject, no one has ever suggested it and most physicists/philosophers would not even consider it.
I have come across some physicist/philosophers (like David Deutsch) who have argued that the ‘many worlds’ interpretation of quantum mechanics can, in fact, explain chaos. A view which I’m personally sceptical about.
Stewart resurrects David Bohm’s ‘hidden variables’ interpretation, preferred by Einstein, but generally considered disproved by experiments confirming Bell’s Inequality Theorem. It’s impossible for me to do justice to Stewart’s argument but he does provide the first exposition of Bell’s theorem that I was able to follow. The key is that the factors in Bell’s Inequality (as it’s known) refer to correlations that can be derived experimentally. The correlations are a statistical calculation (something I’m familiar with) and the ‘inequality’ tells you whether the results are deterministic or random. In every experiment performed thus far, the theorem confirms that the results are not deterministic, therefore random.
Stewart takes the brave step of suggesting that Bell’s Inequality can be thwarted because it relies on the fact that the results are computable. Stewart claims that if they’re not computable then it can’t resolve the question. He gives the example of so-called ‘riddled basins’ where chaotic phenomena can interact with ‘holes’ that allow them to find other ‘attractors’. Again, an oversimplification on my part, but as I understand it, in these situations, which are not uncommon according to Stewart, it’s impossible to ‘compute’ which attractor a given particle would go to.
Stewart argues that if quantum mechanics was such a chaotic system then the results would be statistical as we observe. I admit I don’t understand it well enough to confer judgement and I have neither the mathematical nor physics expertise to be a critical commentator. I’ll leave that to others in the field.
I do agree with him that the wave function in Schrodinger’s equation is more than a ‘mathematical fiction’ and it was recently reported in New Scientist that a team from Sydney claim they have experimentally verified its reality. But I conjecture that ‘Hilbert space’, which is the abstract space where the wave function mathematically exists, may be what’s real and we simply interact with it, but there is no more evidence for that than there is for the ‘multiple universes’ that is currently in favour and gaining favour.
Towards the very end of the book, Stewart hypothesises on how different our view of quantum mechanics may be today if chaos theory had been discovered first, though he’s quick to point out the importance of computers in allowing chaos to be exploited. But he makes this interesting observation in relation to the question on the cover of his book:
Now, instead of Einstein protesting that God doesn’t play dice, he probably would have suggested that God does play dice. Nice, classical, deterministic dice. But – of course – chaotic dice. The mechanism of chaos provides a wonderful opportunity for God to run His universe with deterministic laws, yet simultaneously to make fundamental particles seem probabilistic.
Of course, in the real world, dice are chaotic because the outcome of a throw is subject to the sensitivity of the initial conditions, which is the throw itself. The same with a coin toss. So each throw has its own initial conditions, which creates the randomness from throw to throw that we observe.
Of course, both Stewart’s and Einstein’s reference to a Deity is tongue-in-cheek, but I’ve long thought that chaos provides the ideal mechanism for a Deity to intervene in the Universe. Having said that, I don’t believe in Divine intervention, because it assumes that God has a plan that 'He' needs to keep interfering with. I prefer to think that God is simply the laws of the Universe (a la Einstein’s God) and they will run their course.
Chaos may be 'deterministic' but you can't rerun a chaotic phenomenon and get the same result - that's how chaos was discovered. The Universe obeys 'strange attractors', which provides stability to some systems while still being ultimately unpredictable. We don't know enough to know why the Universe turned out the way it did. Every age has its own sphere of ignorance, but chaos suggests that the future cannot be ultimately known. In other words, there appears to be a limit to what it's possible to know and not just a limit dependent on our cognitive abilities.
Saturday, 28 February 2015
Leonard Nimoy (aka Spock): 1931 - 2015
I first watched Star Trek when I was 16 or 17 on black and white TV. It
was innovative and evoked many of the ideals of the 1960s that people
from different races and backgrounds could form a team that would
explore the universe. Spock is one of the great Sci-Fi icons. I
particularly liked his appearance in J.J Abrams' Star Trek movie from
2009, where Spock meets a younger version of himself through a time warp,
as can only happen in Sci-Fi.
From a philosophical perspective, Star Trek projected a positive, utopian scenario of human nature - envisioning a future where humans would overcome their tendency towards conflict. But it also envisioned a belief, recently expounded by Brian Cox in the final episode of his series, The Human Universe, that humans have a destiny to go beyond their Earth-bound existence.
There is a scene in Abrams' movie that is reminiscent of a scene in my novel, Elvene, where Spock is holed up in an ice cave. Such coincidences in storytelling are not uncommon, like finding the thread of a tune in a piece of music transferred into another work, though, in this case, quite unintentional, as Elvene was written many years before Abrams' Star Trek.
The newslink below to CBSNews is a very touching tribute.
Leonard Nimoy's final tweet.
From a philosophical perspective, Star Trek projected a positive, utopian scenario of human nature - envisioning a future where humans would overcome their tendency towards conflict. But it also envisioned a belief, recently expounded by Brian Cox in the final episode of his series, The Human Universe, that humans have a destiny to go beyond their Earth-bound existence.
There is a scene in Abrams' movie that is reminiscent of a scene in my novel, Elvene, where Spock is holed up in an ice cave. Such coincidences in storytelling are not uncommon, like finding the thread of a tune in a piece of music transferred into another work, though, in this case, quite unintentional, as Elvene was written many years before Abrams' Star Trek.
The newslink below to CBSNews is a very touching tribute.
Leonard Nimoy's final tweet.
Sunday, 8 February 2015
Genetic engineering is not an evil conspiracy
There is a lot of hysteria about GM foods and genetic engineering in general, yet it’s a path to providing benefit to all of humankind in the same way that all the scientific endeavours of the past 2 centuries have done for anyone living in a Western society. It’s true that science and technology has also provided us with military advances that could literally destroy the planet, but the technology that drove 2 world wars in the last century also gave us accessible air travel, computers and satellite navigation and communication, albeit the last are really consequences of the Cold War.
I’ve just finished watching Brian Cox’s BBC series, The Human Universe, and, in the last programme, he extols us to value knowledge for its own sake and not just to deliver economic gains, and to raise science to an enlightenment subject in education. He doesn’t use the term ‘enlightenment’ but I do because not enough people realise how enlightening it is and has been since the time of Copernicus, Galileo and Kepler.
In a recent episode of Catalyst, they provide a mini-doco (9 mins long) on the work of Prof David Craik, which promises breakthrough developments in medicine for the whole world using genetic engineering techniques.
I’m not sure if the programme can be accessed outside Australia, but essentially Craik has worked in the area of ‘cyclotides’, which are cyclic peptides found in nature. Cyclic peptides aren’t broken down in our bodies so we can use the structure on other peptides allowing us to deliver specific ‘drugs’ to combat specific diseases. This is molecular engineering, but we can also use plants as 'factories' to create these drugs and deliver them in their seeds to third world countries (genetic engineering).
The general public is very ignorant about the role of bio-molecular science and how the world can benefit from these interventions. Instead, genetically modified crops are seen as an evil conspiracy by corporations to control the world’s food production. The truth is that humanity has been genetically modifying crops for centuries - well before Darwin’s theory of natural selection - by artificially selecting genes in both crops and domestic animals. Almost nothing we eat hasn’t been genetically modified from its natural habitat due to human intervention.
As I’ve mentioned in other posts, very few politicians are science-literate, and many see science as a servant to economic policy and nothing more. The truth is that only science can save humanity from itself. As Brian Cox reminds us (more than once) we are ‘special’ and possibly unique to the universe, in that we can appreciate the much bigger picture of the whole universe and understand our place in it. We are the only species on the planet that has the ability to transcend our origins, and, arguably, we have an obligation to pursue that, and we can only do that through science.
I’ve just finished watching Brian Cox’s BBC series, The Human Universe, and, in the last programme, he extols us to value knowledge for its own sake and not just to deliver economic gains, and to raise science to an enlightenment subject in education. He doesn’t use the term ‘enlightenment’ but I do because not enough people realise how enlightening it is and has been since the time of Copernicus, Galileo and Kepler.
In a recent episode of Catalyst, they provide a mini-doco (9 mins long) on the work of Prof David Craik, which promises breakthrough developments in medicine for the whole world using genetic engineering techniques.
I’m not sure if the programme can be accessed outside Australia, but essentially Craik has worked in the area of ‘cyclotides’, which are cyclic peptides found in nature. Cyclic peptides aren’t broken down in our bodies so we can use the structure on other peptides allowing us to deliver specific ‘drugs’ to combat specific diseases. This is molecular engineering, but we can also use plants as 'factories' to create these drugs and deliver them in their seeds to third world countries (genetic engineering).
The general public is very ignorant about the role of bio-molecular science and how the world can benefit from these interventions. Instead, genetically modified crops are seen as an evil conspiracy by corporations to control the world’s food production. The truth is that humanity has been genetically modifying crops for centuries - well before Darwin’s theory of natural selection - by artificially selecting genes in both crops and domestic animals. Almost nothing we eat hasn’t been genetically modified from its natural habitat due to human intervention.
As I’ve mentioned in other posts, very few politicians are science-literate, and many see science as a servant to economic policy and nothing more. The truth is that only science can save humanity from itself. As Brian Cox reminds us (more than once) we are ‘special’ and possibly unique to the universe, in that we can appreciate the much bigger picture of the whole universe and understand our place in it. We are the only species on the planet that has the ability to transcend our origins, and, arguably, we have an obligation to pursue that, and we can only do that through science.
Saturday, 10 January 2015
That Mystery of Mysteries
I read an interesting article in the latest issue of Philsophy Now (Issue 105, Nov/Dec 2014) by Toni Vogel Cary titled, That Mystery of Mysteries, about the 2 centuries old debate regarding the theory of evolution and God-manipulated speciation. Toni Vogel Carey is introduced as ‘a philosophy professor in a former life, has written for twenty years… and serves on the US advisory board of Philosophy Now.’
She presents some interesting statistics that suggest ignorance in science this century is increasing rather than decreasing. For example: ‘In Great Britain, few besides evangelicals paid attention to creationism before 2002. But by 2006, a BBC poll showed that 4 out of 10 in the UK thought religious alternatives to Darwin’s theory should be taught as science in schools.’
She then gives equally scary anecdotes for the former Eastern European block countries, where, for example: ‘In 2006, Poland’s minister for education repudiated the theory of evolution, and his deputy dismissed it as “a lie”.’
She gives other examples, from various countries and educational institutions that should ring alarm bells for anyone interested in providing scientific tuition to future generations. Towards the end of her lengthy discussion that goes back to Herschel, Lyell and Darwin (of course), she cites a recent publication by Thomas Nagel, titled Mind & Cosmos (2012) (which I haven’t read, it must be stated) where ‘Nagel argues for “natural teleology”, a view of nature as forward-looking and purposeful, yet secular rather than deistic or theistic.’ And herein lies the rub: it is very difficult for us to believe that something like us (humans) could not be the consequence of some ‘cosmic plan’ (That Mystery of Mysteries), the why and wherefore we have speculated about ever since we gained the ability to think and imagine in a way that no other species can even cognise.
At the risk of going off on a complete tangent, I wish to reference an excellent BBC doco I saw recently called Apeman – Spaceman, the first of a 5 part series, Human Universe, presented by that cross between David Attenborough and a failed rock star, Brian Cox. Cox starts his programme, in a very Attenborough-like moment, attempting to cosy up to some baboons who live in the highlands of Ethiopia. Though not our closest relative and not even true baboons, Cox explains that, amongst the higher primates, they have the most complex social behaviours, second only to humans, and can even string together a series of vocalisations, thus combining sounds that have different meanings individually.
The point of this explication is to demonstrate the humungous gap that exists between humans and all other species on the planet, cognitively. One really cannot overstate this point, as many people prefer to believe that there is nothing ‘special’ about humans at all. But as Cox states explicitly, we are ‘unique’, certainly on planet Earth and possibly in the entire universe. We are unique because we are the only species that can speculate about, let alone comprehend, our place in the much larger scheme of things. It is from this unique cognitive vantage point that both religion and science arose.
If there is any one thing that defines humanity as a species it is surely curiosity. It is curiosity that has led us into space (the focus of Cox’s first episode) but also led us on an intellectual trail uncovering such wonders as mathematical calculus, nuclear physics, the human genome and every scientific discovery since we first grasped the art of writing down our thoughts so future generations could build an unassailable cumulative knowledge that has given us computers, air travel, smart phones and all the mod-cons we take for granted in Western societies the world over.
And this exceptional evolutionary ‘success’ also creates a paradox in popular Western thinking as Carey’s discussion exposes. Whilst we all accept the benefits that science has provided for us, without even thinking about them most of the time, many of us can’t accept that science has also provided an explanation for how Earthly species have developed, changed, evolved, gained ascendency and become extinct.
I believe there are 2 reasons for this. Firstly, scientific knowledge is always contingent on future discoveries. This means we never know everything, and, what’s more, we never will. There are limits to what we can know as I’ve discussed in another post. So how do I know that evolution is true? Because the biological knowledge that underpins the human genome project (DNA) also underpins the theory of evolution, completely unknown and unforeseen in Darwin’s time. This is a well documented and carefully studied case where future discoveries enhanced a contentious scientific theory beyond its originators’ (Darwin’s and Wallace’s) wildest imaginings.
But there is still a lot we don’t know about evolution: for example, how did DNA evolve and how did it originate? Did it come from outer space? In response, creationist and ID advocates can provide glib answers that, if taken seriously, close off any further avenues of investigation; effectively stemming the very curiosity that has given us what we have learned to date.
The second reason is that our intuition and common sense can let us down when it comes to scientific knowledge. There are 2 well-known examples: Einstein’s theories of relativity and quantum mechanics. Relativity theory tells us that clocks run slower when they travel faster (relative to another clock) and clocks run faster in lower gravity (like on satellites as opposed to ground level, Earth). Intuition and common sense tell us that this can’t be true, yet the GPS in your mobile phone or in the Sat-Nav of your car depend on relativity for their accuracy.
Quantum mechanics tells us that a particle can exist in superposition with itself: an electron can go through 2 slits at once and interfere with itself on the other side, though if we try and determine which slit it goes through then it will only go through one of them. Yet quantum mechanics is not only the most empirically successful theory in the entire history of science, it underpins every electronic device you use, from TVs to computers to washing machines.
As I’ve stated many times on this blog in a variety of contexts, the biggest mystery of the universe is that it created the means to understand itself, through us. As I’ve also stated, more recently, the biggest difference between religion and science is that religion maintains the universe is teleological and science tells us that it’s not. So how do I reconcile this? Basically, I argue that ‘purpose’ has evolved, meaning there was no pre-ordained plan. It’s like God really did cast a set of dice and allowed the universe to find its own purpose. Einstein famously said, "God does not play with dice", but chaos and quantum theory suggest otherwise.
Addendum: This is a related post that I wrote a few years back, where, in the final paragraph, I come to a similar conclusion.
She presents some interesting statistics that suggest ignorance in science this century is increasing rather than decreasing. For example: ‘In Great Britain, few besides evangelicals paid attention to creationism before 2002. But by 2006, a BBC poll showed that 4 out of 10 in the UK thought religious alternatives to Darwin’s theory should be taught as science in schools.’
She then gives equally scary anecdotes for the former Eastern European block countries, where, for example: ‘In 2006, Poland’s minister for education repudiated the theory of evolution, and his deputy dismissed it as “a lie”.’
She gives other examples, from various countries and educational institutions that should ring alarm bells for anyone interested in providing scientific tuition to future generations. Towards the end of her lengthy discussion that goes back to Herschel, Lyell and Darwin (of course), she cites a recent publication by Thomas Nagel, titled Mind & Cosmos (2012) (which I haven’t read, it must be stated) where ‘Nagel argues for “natural teleology”, a view of nature as forward-looking and purposeful, yet secular rather than deistic or theistic.’ And herein lies the rub: it is very difficult for us to believe that something like us (humans) could not be the consequence of some ‘cosmic plan’ (That Mystery of Mysteries), the why and wherefore we have speculated about ever since we gained the ability to think and imagine in a way that no other species can even cognise.
At the risk of going off on a complete tangent, I wish to reference an excellent BBC doco I saw recently called Apeman – Spaceman, the first of a 5 part series, Human Universe, presented by that cross between David Attenborough and a failed rock star, Brian Cox. Cox starts his programme, in a very Attenborough-like moment, attempting to cosy up to some baboons who live in the highlands of Ethiopia. Though not our closest relative and not even true baboons, Cox explains that, amongst the higher primates, they have the most complex social behaviours, second only to humans, and can even string together a series of vocalisations, thus combining sounds that have different meanings individually.
The point of this explication is to demonstrate the humungous gap that exists between humans and all other species on the planet, cognitively. One really cannot overstate this point, as many people prefer to believe that there is nothing ‘special’ about humans at all. But as Cox states explicitly, we are ‘unique’, certainly on planet Earth and possibly in the entire universe. We are unique because we are the only species that can speculate about, let alone comprehend, our place in the much larger scheme of things. It is from this unique cognitive vantage point that both religion and science arose.
If there is any one thing that defines humanity as a species it is surely curiosity. It is curiosity that has led us into space (the focus of Cox’s first episode) but also led us on an intellectual trail uncovering such wonders as mathematical calculus, nuclear physics, the human genome and every scientific discovery since we first grasped the art of writing down our thoughts so future generations could build an unassailable cumulative knowledge that has given us computers, air travel, smart phones and all the mod-cons we take for granted in Western societies the world over.
And this exceptional evolutionary ‘success’ also creates a paradox in popular Western thinking as Carey’s discussion exposes. Whilst we all accept the benefits that science has provided for us, without even thinking about them most of the time, many of us can’t accept that science has also provided an explanation for how Earthly species have developed, changed, evolved, gained ascendency and become extinct.
I believe there are 2 reasons for this. Firstly, scientific knowledge is always contingent on future discoveries. This means we never know everything, and, what’s more, we never will. There are limits to what we can know as I’ve discussed in another post. So how do I know that evolution is true? Because the biological knowledge that underpins the human genome project (DNA) also underpins the theory of evolution, completely unknown and unforeseen in Darwin’s time. This is a well documented and carefully studied case where future discoveries enhanced a contentious scientific theory beyond its originators’ (Darwin’s and Wallace’s) wildest imaginings.
But there is still a lot we don’t know about evolution: for example, how did DNA evolve and how did it originate? Did it come from outer space? In response, creationist and ID advocates can provide glib answers that, if taken seriously, close off any further avenues of investigation; effectively stemming the very curiosity that has given us what we have learned to date.
The second reason is that our intuition and common sense can let us down when it comes to scientific knowledge. There are 2 well-known examples: Einstein’s theories of relativity and quantum mechanics. Relativity theory tells us that clocks run slower when they travel faster (relative to another clock) and clocks run faster in lower gravity (like on satellites as opposed to ground level, Earth). Intuition and common sense tell us that this can’t be true, yet the GPS in your mobile phone or in the Sat-Nav of your car depend on relativity for their accuracy.
Quantum mechanics tells us that a particle can exist in superposition with itself: an electron can go through 2 slits at once and interfere with itself on the other side, though if we try and determine which slit it goes through then it will only go through one of them. Yet quantum mechanics is not only the most empirically successful theory in the entire history of science, it underpins every electronic device you use, from TVs to computers to washing machines.
As I’ve stated many times on this blog in a variety of contexts, the biggest mystery of the universe is that it created the means to understand itself, through us. As I’ve also stated, more recently, the biggest difference between religion and science is that religion maintains the universe is teleological and science tells us that it’s not. So how do I reconcile this? Basically, I argue that ‘purpose’ has evolved, meaning there was no pre-ordained plan. It’s like God really did cast a set of dice and allowed the universe to find its own purpose. Einstein famously said, "God does not play with dice", but chaos and quantum theory suggest otherwise.
Addendum: This is a related post that I wrote a few years back, where, in the final paragraph, I come to a similar conclusion.
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