Saturday, July 12, 2014

China, freewill, and the AB6030 Universe

Back from a fascinating week in Beijing. Most of the meetings were un-bloggable but there was a video-interview for Harvard Business Review China about my presenting my article to Premier Li Keqiang when I met him in London.

It was a joy to be at the South Cathedral in Beijing on Sunday and sing in the English Choir. I was welcomed like a long-lost brother by the conductor - a very talented young man who has just graduated and hopes to continue his studies in Germany.  As always the service was a living illustration of "the communion of saints" - the international (and inter-temporal) family of all believers. There must have been 20-30 different nationalities in the congregation - though unusually that morning I was the only Westerner in the English Choir.

After a lecture at a university we were taken to dinner at a restaurant which was a former prince's residence, with the staff all dressed in imperial costumes. An unusual experience and a first for me in 15 trips.  It was also an interesting experience to find Angela Merkel staying in our hotel. I saw her twice but not to speak to. The first time I was carrying things in both hands, so I bowed - she looked and nodded.

An e-correspondent and I are engaged in an energetic e-debate about freewill. He thinks that it is logically impossible for a universe created ex nihilo to have libertarian freewill . Of course if that were so I'd be tempted to say "so much the worse for creation ex nihilo" because it seems to me that without genuine freewill we can't have genuine love - let alone sin, personal responsibility, repentance etc..  However it's clear at least to me that he's begging the question (in the correct sense of that term, not the deplorable modern barbarism of using "begs the question" to mean "raises the question").

The issue is clarified by considering a "toy" discrete time universe in which there is just one object which can be in 2 states (A and B) and where uncorrelated the transition probabilities are p and q. It starts in state A at t=0 and then either changes state or doesn't at each subsequent time period. The question is whether such a universe could exist with p and q not equal to 0 or 1 - say 60% and 30% which I call the AB6030 universe.

My correspondent doesn't think AB6030 is a universe at all, but a partial and incomplete theory of a universe. I'm driven to be more specific on what I'd consider to be a "universe". So I suggest that

a Discrete Time Finite Regular Universe U = (X,R,S,T) is a finite set X of objects, a discrete ordered set T of times, a finite set S of states and a set R of rules such that if the current state vector V of U at time t is V(t) then you can in principle calculate Pr[V(t+1)| V(t)] (with the obvious abuses of notation). And that U is Deterministic iff Pr[V(t+1)|V(t)] is always either 0 or 1. 

Eventually he says that by "universe" he means "the entire history of the universe" which seems to me to make it very clear that he's begging the question. Though there is of course a venerable (and I believe misguided) tradition in Christian philosophy to say that just because God knows with certainty what we are going to do we still have freewill. As Chaucer said:
In scoles there is altercacioún
In this matier, gret disputacioún,
And hath ben of an hundred thousend men.
But yit I can not sift it to the bran,
As can the holy doctor Augustýn,
Or Boece, or the bisshop Bradwardyn,
Whether that Goddis worthy foreknowing
Constraineth me needly to do a thing,
(By need I mene simple necessitee);
Or else if ful free choice be graunted me
To do that same thing, or to do it not,
Though God foreknew it, ere that it was wrought;
Or if his knowing never constreineth me,
Save by condicional necessitee.

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