Alan Turing’s 100th Birthday today

Alan Turing is not as well known as Albert Einstein, yet he arguably had a greater impact on the 20^th Century and was no less a genius. Turing was not only one of the great minds of the 20^th Century but one of the great minds in Western philosophy. In fact, in January, Nature called him “one of the top scientific minds of all time”. He literally invented the modern computer in his head in the 1930s as a thought experiment, whilst simultaneously solving one of the great mathematical problems of his age: the so-called ‘halting problem’. I’ve described this in a previous post (Jan. 2008) whilst reviewing Gregory Chaitin’s book, Thinking about Godel and Turing, but the occasion warrants some repetition.

The 2 June 2012 edition of New Scientist had a feature on Turing by John Graham-Cumming, and it covers in greater detail and erudition anything I can write here. For the public at large, Turing is probably best known for his role at Bletchley Park, in the 2^nd World War, deciphering the Enigma code used by German U-boats. Turing’s contribution remained ‘classified’ until after his death, though, according to Wikipedia, he received an OBE ‘for his work at the Foreign Office’. Turing worked with Gordon Welchman on the Bombe, a machine they designed to run ‘cribs’ to decipher the enigma code. And, with mathematician Bill Tutte, he also developed a method to decode the Tunny cipher, which was used for high-level messages in Hitler’s command.

Turing also developed a ‘portable’ code called ‘Delilah’, which was unique in that it depended on clock-arithmetic, making it very difficult to decode compared to other ciphers. According to Graham-Cumming, the details of this have only recently been declassified.

Turing also became fascinated with mathematics in nature in his childhood, like the recurrence of Fibonacci sequences in spiral patterns in daisy petals and sunflower heads. In 1952 he published a paper on “The chemical basis of morphogenesis”, whereby ‘…specific chemical reactions were responsible for the irregular spots and patches on the skin of animals like leopards or cows, and the ridges inside the roof of the mouth.’ He provided a mathematical model (a computer simulation) of 2 chemicals interacting via diffusion and reaction in a chaotic yet repetitive fashion that would result in a variegated pattern. He speculated that this could become manifest as a literal pattern on animal skins if the 2 chemicals either turned on or off specific cells. Again, according to Graham-Cumming, as recently as January this year, researchers at King’s College London demonstrated Turing’s theory ‘…that 2 chemicals control the ridge patterns inside a mouse’s mouth.’

But, in scientific and mathematical circles, Turing is best known for his ‘proof’ of the ‘halting problem’, which is actually very simple to formulate but difficult to prove. Basically, Turing conjured a thought experiment of a machine that could compute an algorithm until it either found an answer or it didn’t, which meant it could run forever (the ‘halting problem’). Turing was able to prove that one could not determine in advance whether the algorithm would stop or not. An example is Goldbach’s conjecture, which can be easily formulated by an algorithm and run on a computer. At present there is no proof of the Goldbach conjecture but it has been derived by computers up to 100 trillion or 10¹⁴. Obviously, if we knew it could stop or not we could determine if it was true or not to infinity. The same is true for Riemann’s hypothesis, probably the most famous unsolved problem in mathematics. Chaitin (mentioned above) has invented a term, Ω (Omega) to provide a probability of Turing’s algorithm stopping. To quote from a previous post:

Chaitin claims that this is his major contribution to mathematics, arising from his invention of the term ‘Ω’ (Omega), though he calls it a discovery, to designate the probability of a programme ‘halting’, otherwise known as the ‘halting probability’.

But it was in conjuring his ‘thought experiment’ that Turing mentally invented what we now call a computer. I expect computers would have been invented without Turing in the same way relativity would have been discovered without Einstein, yet that is not to diminish either man’s genius or singular contribution. Turing’s insight was to imagine a ‘tape’ of infinite length with instructions that not only performed the algorithm but performed actions on the tape itself. It’s what we recognise today as software. Turing realised that this allowed a ‘universal’ machine to exist, now called a ‘universal Turing machine’, because the tape could instruct one machine to do what all possible machines could do. All modern computers are examples of Universal Turing Machines, including the one I’m using to write and post this blog.

One cannot discuss Turing without talking about the circumstances of his death, because it was a tragedy comparable to the deaths of Socrates and Lavoisier. Turing was persecuted for being a homosexual after he went to the Police to report a burglary. He was given a choice of imprisonment or ‘medical castration’ by hormone treatment, which he accepted. In 1954, at the relatively young age of 41, he committed suicide and the world lost a visionary, a genius and a truly great mind. John Graham-Cumming, the author of the 5 page feature in New Scientist, successfully campaigned for an official apology for Turing from the UK government in 2009. Given the current debate about gay marriage, it is apposite to remember the injustice that was done just over half a century ago to one of the greatest minds of all time. I’ve no doubt that there are many people who believe that Turing could have been ‘cured', such is the ignorance that still pervades many of the world’s societies, and is often promulgated by conservative religious groups, who have a peculiarly backward and anachronistic view of the world. Turing was ahead of his time in many ways, but in one way, tragically.

Addendum: For more detailed information, there is the Wiki site linked above, and Andrew Hodges dedicated Site. The Stanford Encyclopedia of Philosophy gives a good account of Turing’s seminal work in artificial intelligence. Andrew Hodges gives a good account of his untimely attitude to being openly homosexual and an insight into his modest character. There is a very strong sense of an extraordinary visionary intellect who was a victim of prejudice. 

Prometheus, the movie

Everyone is comparing Ridley Scott’s new film with his original Alien, and there are parallels, not just the fact that it’s meant to be a prequel. The crew include an android, a corporate nasty and a gutsy heroine, just like the first two movies. There are also encounters with unpleasant creatures. Alien was a seminal movie, which spawned its own sequels, albeit under different directors, yet it was more horror movie than Sci-Fi. But SF often combines genres and is invariably expected to be a thriller. Prometheus is not as graphically or viscerally scary as Alien, but it’s more a true Sci-Fi than a horror flick. In that respect I think it’s a better movie, though most reviewers I’ve read disagree with me.

Prometheus is a good title because it’s the Greek story about the Gods giving some of their abilities to humankind. Scott’s tale is a 21^st Century creation myth, whereby mankind goes in search of the ‘people’ who supposedly ‘engineered’ us. One of the characters in the film quips in response to this claim: ‘There goes 3 centuries of Darwinism.’ From a purely scientific perspective, it’s possible that DNA originally came from somewhere else, either as spores or in meteorites or an icy comet, but it would have been very simple life forms at the start of evolution not the end of it. The idea that someone engineered our DNA so it would be compatible with Earthbound DNA destroys the suspension of disbelief required for the story, so it’s best to ignore that point.

But lots of Sci-Fi stories overlook this fundamental point when aliens meet Earthlings and interbreed for example (Avatar). And I’ve done it myself (in my fiction) though only to the extent that humans could eat food found on another planet. I suspect we could only do that, in reality, if the food contained DNA with the same chirality as ours. The universal unidirectional chirality of DNA is one of the strongest evidential factors that all life on Earth had a common origin.

But I have to admit that Ridley has me intrigued and I’m looking forward to the sequel, as the final scenes effectively promise us one. One of the major differences with Alien and its spinoffs is that there is a mystery in this story and the heroine is bent on finding the answer to it. She wants to find out who made us and where they came from and why they did it. There is an obvious religious allusion here, but this is closer to the Greek gods, suggested by the title rather than the Biblical god. Having said that, our heroine wears a cross and this is emphasised. I expect Ridley wants us to make a religious connection.

Good Sci-Fi in my view should contain a bit of philosophy – make us think about stuff. In this case, stuff includes the possibility of life on other worlds and the possibility that there may exist civilizations greater than ours, to the extent that they could have created us. We find it hard to imagine that we are the end result of a process that started from stardust; that something as complex and intelligent as us could not have been created by a greater intelligence. Ridley brings that point home when the android asks someone how would they feel about meeting their maker, as he has had to. So I’m happy to see where Ridley is going with this – it’s a question that most people have asked and not been satisfied with the answer. I don’t think Ridley is going to give us a metaphysical answer. I expect he’s going to challenge what it means to be human and what responsibilities that entails in the universe’s creation. 

Philosophy in action - on gay marriage

Last night I went and saw a live stage production of 8 by Dustin Lance Black (whose screenwriting credits include Milk and J. Edgar), a one-off production at Her Majesty’s Theatre in Melbourne. It was a fund-raiser for the lobby group, Australian Marriage Equality, so tickets were not cheap yet the theatre was packed.

The play is based on a real-life trial held in California in 2010, when 2 same-sex couples (Kristin Perry and Sandy Stier, and Paul Katami and Jeff Zarillo) challenged the passing of Proposition 8 as unconstitutional. Effectively, Proposition 8, under Governor Arnold Schwarzenegger, prevented gays and lesbians from getting married.  There was a strong TV campaign supporting Proposition 8, which I’ll address later, and some of these were shown to the theatre audience as background.

It was also relayed to the audience, right at the beginning, how the play came about. Requests by the plaintiff’s team to have the trial broadcast were overturned by their opponents, but transcripts can’t be denied forever and most of the play is taken directly from the transcript. The play is actually read, with almost no props, yet real actors were used to give it authenticity.

There is an on-line version on YouTube including George Clooney, Martin Sheen and Brad Pitt as part of the cast. The Australian production I saw included its own well-known actors like Rachel Griffiths, Lisa McLune, Shane Jacobson and Magda Szubanski (from Babe for international readers). It also included Kate Whitbread as one of the plaintiffs and she was instrumental in getting the production performed. Incidentally, Kate has been producer to Aussie film-maker, Sandra Sciberras (Max’s Dreaming, Caterpillar Wish and Surviving Georgia).

This is not a play that will attract opponents of gay marriage – it was clear from the audience’s reaction that most, if not all, members were advocates. Being a fund-raiser you wouldn’t expect anything else. Opponents, no doubt would call it propaganda and biased, but the ‘opponents’ in the trial come off very badly indeed. In fact, this is the salient point because it demonstrated how weak their arguments were when subjected to the rigours of courtroom dissection and cross-examination. It’s no wonder they opposed it being broadcast.

And that’s why I call it ‘philosophy in action’ because it demonstrated the difference between a glib, emotive, made-for-TV advertising programme and critical, evidence-based argument. It was obvious from the pro-proposition 8 campaign and other rhetoric we hear in the production, that it was based on fear. Fear that same-sex marriage will infect children (yes, I mean infect not affect). Their whole campaign was based around the need to protect children from the ‘evils’ of gay parents and gays generally.

It was obvious that many conservatives actually believe that lesbianism and homosexuality are contagious – not biologically contagious, but socially contagious like cigarette smoking or alcohol consumption or drug-taking. They have a genuine fear, despite all the evidence to the contrary, that more children will become gay if gay marriage is legalized because it’s a choice that they didn’t have before. In other words, gay marriage is a lifestyle choice and has nothing to do with biology. Allowing gays and lesbians to be perceived as ‘normal’ is dangerous because kids will become ‘infected’, whereas at present they are still ‘protected’. That’s their argument in a nutshell.

In a promotional review of the play in last weekend’s Age, both Kate Whitbread and Bruce Myles (director of the Aussie version) give their more parochial reasons for putting it on. Bruce said he was ‘disgusted’ by Bob Katter’s political advertisement in the recent Queensland state election, whereby Katter used lewd images of homosexual couples juxtaposed with Campbell Newman’s (Queensland’s Liberal party contender and shoe-in to win) statement that he supported gay marriage. It was an obvious ploy on Katter’s part to exploit homophobia to undermine Newman’s commanding lead in the polls.

Both Bruce and Kate expressed outrage at six Catholic bishops in Victoria sending out 80,000 letters exhorting parishioners to lobby against gay marriage. Apparently, few parishioners were as alarmed as the bishops, going by the response. In fact, both in Australia and the US, it’s conservative religious groups who are the most vocal opponents to gay marriage. Arguments based on arcane religious texts are arguably the least relevant to the debate. It’s effectively an argument to maintain a longstanding prejudice because the Bible tells us so.

Spencer McLaren, who plays the courtroom advocate defending proposition 8, said: “What it is really about is putting prejudice and fear on trial and showing the inhumanity of the discrimination that is occurring.”

For those interested, here is the online version (90 mins).

How an equation contributed to the GFC

Ian Stewart is well known to anyone interested in mathematics - alongside Marcus du Sautoy, he is one of the great popularisers of the subject. His book, 17 Equations that Changed the World, lives up to its brief. Stewart not only gives insights into the mathematics of 17 disparate topics, but explains how they’ve affected our lives in ways we don’t see. I’ve read a number of books along similar lines, all commendable, but Stewart succeeds better than most in demonstrating how so-called pure mathematics has shaped the modern world that we all take for granted. (By all, I mean anyone who can read this via a computer and the internet.)

The book includes the usual suspects like Pythagoras, Newton, Maxwell, Einstein, Schrodinger and lesser known ones like Boltzman, Shannon, the Bell curve, chaos theory and the Fourier transform. In all cases he explains how they have affected what we loosely call civilization. But it is the last chapter in the book that covers the Black-Scholes equation, which is most relevant to the present state of the world, and what Stewart aptly coins ‘the Midas formula’. This is the Nobel-prize-winning formula that effectively created the GFC (global financial crisis).

I was lucky enough to see the movie, The Inside Job, which had a limited release in this country, but ran for well over a month in one art-house cinema in Melbourne, such was its morbid appeal. It’s a depressing yet illuminating film because, not only do you get a recent history lesson, but you realise that no one has learnt anything and it will happen all over again.

Stewart is a mathematician yet he explains the machinations that created the current economic catastrophe with remarkable clarity and erudition, and provides antecedents that teach us how we never learn from history.

Some quotable quotes:

The banks behave like one of those cartoon characters who wanders off the edge of a cliff, hovers in space until he looks down, and then plunges to the ground.

How did the biggest financial train wreck in human history come about? Arguably, one contributor was a mathematical equation.

He then goes on to explain what derivatives are and how they became monopoly money in the hands of the biggest financial institutions in the world.

As Stewart expounds:

In 1998 the international financial system traded roughly $100 trillion in derivatives. By 2007 this had grown to one quadrillion US dollars… To put this figure into context, the total value of all the products made by the world’s manufacturing industries, for the last thousand years, is about 100 trillion US dollars, adjusted for inflation. That’s one tenth of one year’s derivative trading.

Curiously, it was a mathematician, Mary Poovey, professor of humanities and director of the Institute for the Production of Knowledge at New York University, who rang alarm bells in August 2002, when she gave a lecture at the International Congress of Mathematicians in Beijing, titled ‘Can numbers ensure honesty?’ The lecture was subtitled ‘Unrealistic expectations and the US accounting scandal’.  She pointed out, amongst other things, that ‘by 1995 [the] economy of virtual money had overtaken the real economy of manufacturing.’ She argued that  ‘[this] deliberately confusing virtual and real money… was leading to a culture in which the values of both goods and financial instruments were… liable to explode or collapse at the click of a mouse.’ This, of course, was the year after the collapse of Enron, the biggest bankruptcy in American history (at the time) to the tune of $11 billion to shareholders.

Stewart’s major point is that people used the Black-Scholes equation routinely, with no appreciation of its dependence on key assumptions. Change the assumptions and the consequences could be dire as we have since witnessed world-wide. Its proliferation was guaranteed by its Nobel-prize-winning status and the simple fact that everyone else was using it. What’s more, it could be converted into a computer algorithm, ensuring its ubiquity.

Economics doesn’t follow natural laws like gravity, nevertheless I expect chaos theory could provide some insights. It’s the human factor that appears to be the element that people leave out or ignore. I’m not an economist – it’s the area I least understand – yet a mathematician can explain to me what went wrong in the past decade in a way that makes sense. If I can understand it, why can’t the people who run economies and financial institutions?

Stewart’s final comment:

The financial system is too complex to be run on human hunches and vague reasoning. It desperately needs more mathematics, not less. But it also needs to learn how to use mathematics intelligently, rather than as some kind of magical talisman.

Addendum 1: Stewart also explains how mathematics gives credibility to human-generated climate-change, although that’s another issue. In particular, he claims: Global warming was predicted in the 1950s, and the predicted temperature increase is in line with what has been observed.

Addendum 2 (6 Sep 2012): I've just seen the movie, Margin Call, a well-drawn fictional account of this issue, with some big-name actors: Kevin Spacey, Jeremy Irons, Demi Moore, Paul Bettany and Simon Baker, amongst others. There is a reference to this equation early in the film in a dialogue between the Demi Moore character and Simon Baker character, though its significance is not explained nor its title given. Demi's character says: 'I told you not to use that equation...' (or words to that effect) and Simon's character says: 'Everyone else is using it...' (or words to that effect). An intriguing piece of dialogue that only 'people-in-the-know' would pick up on.

Addendum 3 (3 Nov 2012): This interview with Greg Smith (formerly with Goldman Sachs) reveals the real story behind Wall Street, its culture, its hypocrisy (how it wants zero government interference in the good times and government bale-out in the bad times) and, most importantly, how nothing has changed since the GFC.

Addendum 4 (30 Jun 2013): I changed the title from 'Mathematics and the Real World'. I think it was misleading and the new title is more relevant to the discussion.

This is so COOL

This is a brilliant piece of simple, yet profound, scientific understanding, that anyone with a high school education should be able to follow. I can't imbed it so I provide this link.

John D. Barrow, in his book, The Constants of Nature provides a very neat graphic (p. 222 of 2003 Vintage paperback edition) that demonstrates why 3 dimensions of space and 1 of time provide the most 'livable' universe (my term, not his). Barrow has written extensively on the 'Anthropic Principle' in all its manifestations, and I keep promising myself that I'll write a post on it one day.

Why the argument for the existence of God (as an independent entity) is a non sequitur

This has been a point of discussion on Stephen Law’s blog recently, following Law’s debate with William Lane Craig last year. My contention is that people argue as if God is something objective, when, clearly it isn’t: God is totally subjective.

God is a feeling, not an entity or a being. God is something that people find within themselves, which is neither good nor bad; it’s completely dependent on the individual. Religiosity is a totally subjective phenomenon, but it has cultural references, which determine to a lesser or greater extent what one ‘believes’. Arguing over the objective validity of such subjective perspectives is epistemologically a non sequitur.

Craig’s argument takes two predominant strands. One is that atheists can’t explain the where-with-all from whence the universe arose and theists can. It’s like playing a trump card: what’s your explanation? Nil. Well, here’s mine, God: game over. If Craig wants to argue for an abstract, Platonic, non-personal God that represents the laws of the universe prior to its physical existence, then he may have an argument. But to equate a Platonic set of mathematical laws with the Biblical God is a stretch, to say the least, especially since the Bible has nothing to say on the matter.

The other strand to his argument is the Holy Spirit that apparently is available to us all. As I said earlier, God is a feeling that some people experience, but I think it’s more a projection based on one’s core beliefs. I don’t dismiss this out of hand, partly because it’s so common, and partly because I see it as a personal aspiration. It represents the ideal that an individual aspires to, and that can be good or bad, depending on the individual, as I said above, but it’s also entirely subjective.

Craig loves the so-called ‘cosmological’ argument based on ‘first cause’, but it should be pointed out that there are numerous speculative scientific theories about the origin of the universe (refer John D. Barrow’s The Book of Universes, which I discussed May 2011). Also Paul Davies’ The Goldilocks Enigma gives a synopsis on all the current ‘flavours’ of the universe, from the ridiculous to the more scientifically acceptable. Wherever science meets philosophy or where there are scientific ‘gaps’ in our knowledge, especially concerning cosmology or life, evangelists like Craig try to get a foothold, reinterpreting an ancient text of mythologies to explain what science can’t.

In other posts on his blog, Stephen Law discusses the issue, ‘Why is there something instead of nothing?’ Quite frankly, I don’t think this question can ever be answered. Science has no problem with the universe coming from nothing – Alan Guth, who gave us inflationary theory also claimed that ‘the universe is the ultimate free lunch’ (Davies, God and the New Physics, 1983). The laws of quantum mechanics appear to be the substrate for the entire universe, and it’s feasible that a purely quantum mechanical universe existed prior to ours and possibly without time. In fact, this is the Hartle-Hawking model of the universe (one of many) where the time dimension was once a fourth dimension of space. Highly speculative, but not impossible based on what we currently know.

But when philosophers and scientists suggest that the ‘why something’ question is an epistemological dead end, evangelists like Craig see this is as a capitulation to their theistic point of view. I’ve said in a previous post (on Chaos theory, Mar. 2012) that the universe has purpose but is not teleological, which is not the oxymoron it appears to be when one appreciates that ‘chaos’, which drives the universe’s creations, including life, is deterministic but not predictable. In other words, the universe’s purpose is not predetermined but has evolved.

Some people, many in fact, see the universe’s purposefulness as evidence that there is something behind it all. This probably lies at the heart of the religious-science debate, but, as I expounded in a post on metaphysics (Feb. 2011): between chaos theory, the second law of thermodynamics and quantum mechanics, a teleological universe is difficult to defend. I tend to agree with Stephen Jay Gould that if the universe was re-run it would be completely different.

Addendum 1: Just one small point that I’ve raised before: without consciousness, there might as well be nothing. It’s only consciousness that allows meaning to even arise. This has been addressed in a later post.

Addendum 2: I've added a caveat to the title, which is explained in the opening of the post. If humans are the only link between the Universe and a 'creator' God (as all monotheistic religions believe) then God has no purpose without humanity.