A master storyteller talks about his craft

This is a brief interview with Ang Lee, where he talks about his latest movie as well as his career and his philosophy. I've been a fan of Lee ever since I saw The Wedding Banquet and have seen most of his movies, including Crouching Tiger Hidden Dragon, Sense and Sensibility and Brokeback Mountain, all of which illustrate his eclectic interests, extraordinary range and mastery of genres.

I haven't seen The Life of Pi, but I read the book by Yann Martel many years ago, after it won the Booker Prize, and was singularly impressed. Given its philosophical nature, one should not be surprised that Lee was attracted to this story, despite its obvious challenges, both technically and thematically.

This interview reveals, more than most, the relationship between the artist and his art. How his art informs him in the same way it informs his audience. All artists strive for an authenticity that effectively negates the pretentiousness and ego that is so easily obtained, especially with success. Ang Lee demonstrates this better than most.

Addendum: A very good review here.

What’s real?

Eric Scerri, who is a lecturer in chemistry and the history and philosophy of science at the University of California, Los Angeles, asks a very basic question in last week’s New Scientist (24 Nov. 2012, pp.30-1): how do we know what’s real?

In the world of physics and chemistry, scientists deal with lots of unobservables like electrons and photons (we see their effects) not to mention all the varieties of quarks that can never be seen in isolation, even in theory. Now an electron, and even a positron, will leave a track in a cloud chamber which can be photographed, but quantum phenomena are so anti-intuitive that people are sure to ask: is it real? Where ‘it’ is the Schrodinger wave function that no longer plays a role once the event in question is ‘observed’. In fact, an earlier issue of New Scientist dared to address that very question (28 Jul. 2012, pp.29-31), and it goes to the heart of the longstanding debate as to what quantum mechanics really means epistemologically. The truth is that no one really knows.

The fact is that since so much of modern science, especially the fundamentals that underpin physics and chemistry, is based on unobservables, it leads people to argue for a form of relativism whereby anything is valid. This point of view is supported by the belief that all scientific theories are temporary, given their historical perspective.

The gist of Scerri’s article is a discussion on the philosophical approach proposed by John Worrall in 1989 (Philosopher of Science at the London School of Economics) called “Structural Realism”.  To quote Scerri: ‘For Worrall, what survives when scientific theories change is not so much the content (entities) as the underlying mathematical structure (form).’

Scerri gives the example of Fresnell’s theory of light (involving an aether, 1812) being replaced by Maxwell’s electromagnetic theory.  Worrall argues that some of Fresnell’s mathematics can be found in Maxwell’s theory, therefore ‘structurally’ Fresnell’s theory is still sound even if the aether is not. The same criterion can be applied to Einstein’s theory of relativity compared to Newton’s mechanics. Newton’s inverse square law for gravity is still intact in Einstein’s theory and all of Einstein’s equations reduce to Newton’s when the speed of light becomes irrelevant.

Scerri’s own field of expertise is chemistry and he’s written books on the periodic table, so, not surprisingly, that becomes a point of discussion. Dmitri Mendelev published his paper in 1869, when the structure of atoms and all their components were unknown. Most people are unaware that it wasn’t until the 1920s when Bohr, Heisenberg, Schrodinger and Pauli were pioneering quantum mechanics that the periodic table suddenly made sense. It reflects the orbital shells that quantum theory predicts.

At my country high school, we had a farsighted science teacher (Ron Gunn) who taught us what all these quantum shells were (without telling us that it was quantum mechanics) so that we could make sense of all the properties that the periodic table predicts. As Scerri points out, the periodic table literally embodies the quantum mechanical structure of the atom. This is something that Mendelev could never have known about, in the same way that Darwin didn’t know in 1859 that DNA underpins his entire theory of evolution.

In fact, Scerri also references Darwin and DNA as another example of mathematical structure underpinning a theory and ensuring its continuity a century and a half later. To quote again:

‘But DNA only takes things so far: to go deeper we need to take a mathematical direction. DNA determines the sequence of bases, A, T, G and C. This becomes a question of mathematical combinations… played out during the human genome project.’

Of course, this does not mean that all mathematical models determine reality, as Ptolemy’s epicyclic solar system demonstrates; only the ones that survive scientific revolutions. In this context, no one knows if string theory will follow Ptolemy or Einstein.

Stephen Fry proselytises Classical Music

I don't know how anyone can't be a fan of Stephen Fry. In this debate at Cambridge University he's at the top of his form. His analogies are as outrageous as they are comical; his argument is both informative and entertaining. The world is a very lucky place and we are fortunate who live in his time.

I need to acknowledge Sally Whitwell, who embedded it on her site with an appropriate quote taken from his closing words.

Empirical data confirms climate change already happening for a century

Statistically, Australia’s temperature has risen approximately 1°C in the last 110 years and the oceans have risen 15-17 cm in the same period. Spring comes about 2 weeks earlier. If you don’t believe me then watch this special episode of Catalyst, aired last week on the ABC: scientific evidence of climate-change, not a left-wing conspiracy. And if it’s happened here then it’s happened all over the world.

Climate change is only one symptom of humanity’s unprecedented evolutionary success. The reason so many people, including numerous politicians, are in denial over this world-wide phenomenon is because it’s another consequence of infinite economic growth: the paradigm we are all addicted to, irrespective of political persuasion. Europe is currently finding out what happens when we reach the limit of consumerism and it will eventually happen everywhere sometime in the 21^st Century. At some point we can no longer rely on a burgeoning next generation to maintain a non-sustainable economic growth, yet that’s the great denial; an even greater denial than the belief that climate-change is a global, scientifically promoted conspiracy.

This is torture and a violation of human rights

About 6 months ago I talked about the need to change cultural attitudes towards girls from so-called traditional cultures – specifically, to outlaw arranged marriages without the girl’s consent.

The practice of female genital mutilation, erroneously called female circumcision by those who practice it, is arguably even more barbaric and more confronting to Western cultural norms. Even though it is illegal in Australia, many people are reluctant to report it, such is the cultural divide between those who practice it and those who find it abhorrent.

If ever there was an argument to be made against moral relativism, this would have to be one of the most compelling examples. It also highlights how morality for most people, and most societies, is not based on objective criteria, as we like to contend, but on long-accepted social norms.

To prevent this practice requires more than legal prosecution, but a cultural change of attitude. Fundamentally, it needs to be recognised for what it is – torture of a pre-adolescent or adolescent girl. As demonstrated in this video, the people who perpetrate these crimes justify their actions as fulfilling the girl’s destiny. Like most changes to social norms this will ultimately be a generational change within the communities who practice it, not just a change in the law.

The genius of differential calculus

Newton and Leibniz are both credited as independent ‘inventors’ of calculus but I would argue that it was at least as much discovery as invention, because, at its heart, differential calculus delivers the seemingly impossible.

Calculus was arguably the greatest impetus to physics in the scientific world. Newton’s employment of calculus to give mathematical definition and precision to motion was arguably as significant to the future of physics as his formulation of the General Theory of Gravity. Without calculus, we wouldn’t have Einstein’s Theory of Relativity and we wouldn’t have Schrodinger’s equation that lies at the heart of quantum mechanics. Engineers, the world over, routinely use calculus in the form of differential equations to design most of the technological tools and infrastructure we take for granted.

Differential calculus is best understood in its application to motion in physics and to tangents in Cartesian analytic geometry. In both cases, we have mathematics describing a vanishing entity, and this is what gives calculus its power, and also makes it difficult for people to grasp, conceptually.

Calculus can freeze motion, so that at any particular point in time, knowing an object’s acceleration (like a free-falling object under gravity, for example) we can determine its instantaneous velocity, and knowing its velocity we can determine its instantaneous position. It’s the word ‘instantaneous’ that gives the game away.

In reality, there is no ‘instantaneous’ moment of time. If you increase the shutter speed of a camera, you can ‘freeze’ virtually any motion, from a cricket ball in mid-flight (baseball for you American readers) to a bullet travelling faster than the speed of sound. But the point is that, no matter how fast the shutter speed, there is still a ‘duration’ that the shutter remains open. It’s only when one looks at the photographic record, that one is led to believe that the object has been captured at an instantaneous point in time.

Calculus does something very similar in that it takes a shorter and shorter sliver of time to give an instantaneous velocity or position.

I will take the example out of Keith Devlin’s excellent book, The Language of Mathematics; Making the invisible visible, of a car accelerating along a road:

x = 5t² + 3t

The above numbers are made up, but the formulation is correct for a vehicle under constant acceleration. If we want to know the velocity at a specific point in time we differentiate it with respect to time (t).

The differentiated equation becomes dx/dt, which means that we differentiate the distance (x) with respect to time (wrt t).

To get an ‘instantaneous’ velocity, we take smaller and smaller distances over smaller and smaller durations. So dx/dt is an incrementally small distance divided by an incrementally small time, so mathematically we are doing exactly the same as what the camera does.

But dx occurs between 2 positions, x₁ and x₂, where dx = x₂ – x₁

This means:  x₂ is at dt duration later than x₁.

Therefore  x₂ = 5(t + dt)² + 3(t + dt)

And x₁ = 5t² + 3t

Therefore  dx = x₂ – x₁ = 5(t + dt)² + 3(t + dt) - (5t² + 3t)

If we expand this we get:  5t² + 10tdt + 5dt² + 3t + 3dt – 5t² – 3t

{Remember: (t + dt)² = t² + 2tdt + dt²}

Therefore dx/dt = 10t dt/dt + 5dt²/dt + 3dt/dt

Therefore dx/dt = 10t + 3 + 5dt

The sleight-of-hand that allows calculus to work is that the dt term on the RHS disappears so that dx/dt gives the instantaneous velocity at any specified time t. In other words, by making the duration virtually zero, we achieve the same result as the recorded photo, even though zero duration is physically impossible.

This example can be generalised for any polynomial: to differentiate an equation of the form, 
y = ax^b

dy/dx = bax^(b-1)  which is exactly what I did above:

If y = 5x² + 3x

Then dy/dx = 10x + 3

The most common example given in text books (and even Devlin’s book) is the tangent of a curve, partly because one can demonstrate it graphically.

If I was to use an equation of the form y = ax² + bx + c, and differentiate it, the outcome would be exactly the same as above, mathematically. But, in this case, one takes a smaller and smaller x, which corresponds to a smaller and smaller y or f(x). (Note that f(x) = y, or f(x) and y are synonymous in this context). The slope of the tangent is dy/dx for smaller and smaller increments of dx. But at the point where the tangent’s slope is calculated, dx becomes infinitesimal. In other words, dx ultimately disappears, just like dt disappeared in the above worked example.

Devlin also demonstrates how integration (integral calculus), which in Cartesian analytic geometry calculates the area under a curve f(x), is the inverse function of differential calculus. In other words, for a polynomial, one just does the reverse procedure. If one differentiates an equation and then integrates it one simply gets the original equation back, and, obviously, vice versa.