Tuesday, 12 February 2013

On Richard Prosser

NZ First MP Richard Prosser has rightly come in for international condemnation for his Investigate Magazine column in which he suggested young Muslims shouldn't be allowed to travel on Western airlines because "most terrorists are Muslims".  It doesn't matter how he hedged this statement and his subsequent mealy-mouthed apology has not repaired the damage to New Zealand's reputation as a tolerant and inclusive society.

I became a NZ citizen three months ago.  During my application for this privilege I was often asked why I wanted to be a citizen rather than just a permanent resident.  My answer was always the same: I love the tolerant spirit of New Zealand, its relative absence of a class system, and its secular system of government.  That Richard Prosser should make such dishonest remarks, and still more that he serves as an MP, makes me extremely distressed for our international image.

Dishonest remarks?  Absolutely.  What's a terrorist?  Surely someone who terrorises innocent people whether the terrorist is a member of a guerilla group, an outright criminal, or a member of some country's official armed forces.  How about the terror inflicted by US drones in Pakistan and Afghanistan, or the brutality of the Israeli government to the Palestinians, or the genocide of the pygmies in the Congo Civil War; these are just a few examples.  Terror acts committed by Muslims are in a minority.

Even if Richard Prosser made a full and contrite apology which showed a genuine acceptance that he got things badly wrong he has nevertheless shown such poor judgement that he should be sacked immediately.  But to compound the aftermath his party leader Winston Peters has said there was an "element of truth" to Mr Prosser's comments and says he does not believe Prosser should apologise.

What a disgusting pair they are.

Sunday, 10 February 2013

On mathematical Platonism and faith

Mathematical Platonism is, roughly described, the belief that the entities considered in mathematics (numbers, functions, algebraic systems, etc) have a reality beyond their existence as neuronal configurations in our brains.  Non-mathematicians are often disposed to reject the belief ("Where do these entities exist?" seems to be a rather compelling objection) but many practising mathematicians are Platonists, and many more (maybe a majority, but I don't have any statistics to support this) behave as though they are Platonists.

Another way of expressing the belief is to say that mathematics is "discovered" rather than "invented".  In his short essay Barry Mazur calls this "The Question" that all mathematicians come to at some point in their metaphysical speculations.

Why does Platonism have such a strong foothold among mathematicians?  I am fascinated by this question because when I was a young pure mathematical researcher I would often maintain that the entities I thought about had an independent existence (and this was when I was only dimly aware of Platonism at all).  I had, for example, an absolute conviction that when humankind came across star-faring species they would have a mathematics in which simple groups (a particular interest of mine at the time) would play the same fundamental role that they play in terrestrial mathematics.  Why did I hold this view so strongly?  In this post I want to speculate about this psychological predisposition rather than whether it is defensible.

I suggest that Platonism has such a powerful grip on the mathematical mind because mathematical discourse is packed with the language of discovery rather than the language of invention.  This language biases us to subconsciously accept that we are finding out about things that already exist.  This tradition is very deeply rooted in our mathematical discourse and certainly appears in Euclid ("The sum of the three interior angles of a triangle equals two right angles": no doubt here that a triangle exists somewhere outside our minds).  In our modern mathematics how often do we say "There exists..."? - we even have a mathematical symbol for this phrase.  Mathematics is written in a certain style and this style abounds with phrases that suggest discovery of already existing objects.  For example here is paper published today that I selected at random: here is its abstract.
For every infinite sequence of simple groups of Lie type of growing rank we exhibit connected Cayley graphs of degree at most 10 such that the isoperimetric number of these graphs converges to 0. This proves that these graphs do not form a family of expanders.
I suggest that mathematicians cannot read that abstract without having their Platonic tendencies confirmed.  This and the entire manner in which mathematics is written explains why Platonism is the default subconscious belief of so many working mathematicians.

What this tells us is that a Platonist ought to consider his/her position in the light of these strong linguistic pressures that produce cognitive bias.  Maybe they can mount a metaphysical defence (and I confess to a wistful hope that they can).  But if they cannot it is only honest to admit that they are holding similar opinions to a committed theist.  And that brings me to the final point I wish to make.

A few studies have shown that, among scientists, mathematicians tend to hold a theistic stance more so than others.  A few years ago the US National Academy of Sciences conducted a survey about god beliefs among their members.  Apparently 14.6% of mathematicians believe in god whereas the figure for biologists is 5.5%.  I am sure we should be cautious about such figures but other surveys have also shown that mathematicians tend to belief in god in higher proportions than other scientists.

Is it not plausible that someone who has committed unthinkingly to a position of faith in the real existence of mathematical entities will be more prone to commit to a faith in the real existence of supernatural beings?

Friday, 1 February 2013

The poverty of faith

I live in Otago in the South Island of New Zealand.  We have a reasonably good local newspaper, The Otago Daily Times, that informs us of local, national and world issues in decreasing levels of detail.  On 1 February it published an opinion piece from a local resident called Ivan Grindlay entitled
No room for fantasy if you understand dynamics of God's plan.  Mr Grindlay is an elder at the Caversham Community Church. His article was a summary of a bizarre theology that told of God's intention for humanity, its perversion by the "defection" of Adam, and an ultimate resolution as the Second Coming brings the nation of Israel back into the Christian fold.  It wasn't clear whether this was Mr Grindlay's personal theology or that of the Caversham Community Church. At any rate this world-view cuts off its adherents from the understanding that we now have about the natural world.  The explanation of our world and the huge cosmos in which it is situated is grander by far than the explanations in Mr Grindlay's theology. Many readers must have smiled rather sadly that such arbitrary fantasies still hold the minds of some people in thrall.

Perhaps among the smilers will be found some members of mainstream religious beliefs. Good Christian folk who regularly attend their church, recite the Lord's Prayer and the Apostle's Creed, engaged in good works to support their own community and possibly communities overseas. Ladies and Gentlemen of these benign religious persuasions you are complicit in Mr Grindlay's ignorance.  Your own supernatural beliefs are the ambient culture that nurtures Mr Grindlay's less mainstream opinons. While you, through a mental contortion in which you cherry-pick those pieces of scripture that are convenient to believe, have access to the understanding of our wonderful universe (biology and the unity of all life because of the DNA molecule, physics and the mathematical explanation of nature's laws, astronomy and the workings of a cosmos now unimaginably larger than ever envisioned in religious tracts) you are doing more credulous folk a grave disservice. Shame on you.

Mr Grindlay has chosen a certain portion of scripture on which to found his world-view. Anglican Christians choose another portion while Roman-Catholics choose yet another (and even this ignores the schisms within these broad churches). Still another portion is seized on by Sunni Moslems, and again another by Shi'a Moslems. And then there are Jews, Hindus and many other groups each elevating certain historical writings to the status of divine revelation.

I called Mr Grindlay's fantasy an arbitrary one in my first paragraph. Indeed it is arbitrary. But so are the fantasies of every other religion. What distinguishes them from the Mr Grindlay fantasy is that they have more adherents and with numbers come respectability. But all of them to one degree or another prevent their followers from truly appreciating the world we live in - the only one we will ever have.