Monday, 29 February 2016

Probability: chance or God?

Lent 2016: Day 20

From the dawn of history, the question of chance, coincidence, probability - indeed fortuity - has intrigued mankind. Prof Fr Michał Heller's book, Filozofia przypadku, begins with an overview of how humans have taken the notion of probability from something intuitive to a mathematical, analytical tool, which in its latest iteration plays a crucial role in the understanding of quantum mechanics.

Modern mathematical approaches to the question of probability, says Fr Heller, began in the mid-17th Century with Pascal (of Wager fame) and Fermat (of Last Theorem fame). Before that, probability was the realm of philosophers. In his Physics II, Aristotle defined 'chance' as an occurrence that neither happens always, nor one that most frequently occurs in the same way.

Fr Heller says that today, the many generalisations of the probability theory, of which the most spectacular of which are non-commutative conditional expectations, because they have properties that are completely surprising to our habits of thinking. Ah now, I admit defeat. Why, because according to Wikipedia, a non-commutative conditional expectation is formally defined as: "a positive, linear mapping \Phi of a von Neumann algebra \mathcal{S} onto a von Neumann algebra \mathcal{R} (\mathcal{S} and \mathcal{R}may be general C*-algebras as well) is said to be a conditional expectation (of \mathcal{S} and \mathcal{R}) when\Phi(I)=I and \Phi(R_1SR_2) = R_1\Phi(S)R_2 if R_1, R_2 \in \mathcal{R} and S \in \mathcal{S}."

OK, I was lost at 'positive, linear mapping \Phi'. But no matter. The point is this: mathematicians are way ahead of the rest of us in understanding how probability works at the sub-atomic level and indeed, at the level of the cosmos. Our innate, intuitive ways of thinking make understanding the probabilistic nature of the structure of the Universe extremely difficult.

Fr Heller points out that the early philosophers, trying to work out the nature of matter and life without the tools available to modern science, were like blind people. And blind people are reputed to possess sensitivities compensating for their lack of sight. This, says Fr Heller, includes heightened theological sensitivities, which we have lost along the way. He suggests that we should attempt to combine our scientific knowledge with the traditional sense of knowing God.

In Ancient Greece, opinion was divided as to whether chance is the cause of everything, or whether, as Aristotle posited, that the opposite was true. Chance is the result of divine intervention, supernatural, inaccessible to our understanding. In either way, chance was seen as something that could not be analysed using mathematics. Meanwhile, says Fr Heller, Hippocrates had already come up with the concept of diagnosis and prognosis, and so was on the way towards the Scientific Method.

As late as the early 19th Century, determinism was in fashion. Pierre-Simon Laplace could believe that if an Intelligence (later named 'Laplace's Demon') was vast enough to know all the forces acting on all the atoms and the greatest bodies of the Universe, it could deduce where everything would be in the future - for eternity; nothing could be uncertain.

Then came the Second Law of Thermodynamics (Lord Kelvin, 1851), and entropy, later quantum mechanics and chaos theory. Today we know that even if Laplace's Intelligence was indeed vast enough to know the state of every single atom in the Universe  and every force acting upon every particle of matter at a given instant, the uncertainty inherent in matter is such that after a while, the Universe would veer away from the predicted outcome.

So where is God in all this? Where is purpose, and the teleological Universe? We shall see. (I genuinely don't know after three chapters how Fr Heller is going to resolve this! A true Lenten journey of discovery!)

This time last year? Not even four, or eight years ago. This is my very first blog post dated 29 February. Out of interest, could not the additional day caused by the leap year have been inserted at a slightly better time, such as having a 31 June every four years? As it is, at this dismal time of year, there doesn't feel much to celebrate. And yet there is! We've been given an extra day to enjoy, free. Someone who's reached the age of 84 has had an extra three weeks of life added on!

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