How many angels can dance on the head of a pin? Tricky. Was it inevitable that I should write this and that, now, you should be reading it? Even trickier.
The angels-pin question was originally posed as a joke. It lampooned the arcane and futile speculations of medieval theologians. They pondered the nature of the world on the basis of faith and, in our terms, profound ignorance. We have hard science. We have moved beyond such nonsense. Or have we?
Gerard ’t Hooft of Utrecht University is one of the world’s great physicists. In 1999, along with Martin Veltman, he won the Nobel prize “for elucidating the quantum structure of electroweak interactions in physics”. But, like all physicists, he has a problem, a problem so huge that, daily, it threatens to undermine the entire fabric of his discipline.
The problem is complex — some say it is beyond solution by the human mind — but it can be simply stated. Relativity and quantum theory are the two great triumphs of modern physics. The first explains the behaviour of very big things like planets, the second the behaviour of very small things like subatomic particles. They both lie, currently, beyond refutation. Planets do behave as relativity predicts and subatomic particles obey quantum theory — if they didn’t I couldn’t now be writing this on a computer and you would not be able to watch the World Cup on television.
The problem is that they contradict each other. Relativity is a “classical theory”, it can be demonstrated to act through known processes of cause and effect. Quantum theory is not. Subatomic particles behave like schizophrenics on acid. They seem to be telling us that the world is indeterminate, unpredictable and completely lacking in anything resembling our common-sense understanding of cause and effect.
Einstein hated this, arguing that “God does not play dice”. There must be something we didn’t know, some “hidden variables” that lay behind quantum phenomena that would, one day, return the quantum world safely to the bosom of classical physics. To which the quantum theorists’ response is: God does not play dice but only because he runs the casino. The indeterminacy of quantum phenomena is real and final, it is just the way the universe is made. Enter ’t Hooft.
He has just published a paper arguing that, in effect, Einstein was right. There are recognisable systems of cause and effect underlying quantum interactions. There is a hidden reality which consists of “states” that do behave deterministically. We don’t see them because they are so small and because their actions are very brief. What we see is only an outcome that appears to have no cause.
Meanwhile, over at Princeton University, two of the world’s great mathematicians, John Conway and Simon Kochen, have produced another paper — The Free Will Theorem — arguing exactly the opposite: that the world is indeed finally and absolutely indeterminate.
Exact details of these arguments are too specialised for me and, probably, for you. But the title of the Conway-Kochen paper points to what is really at stake here. Classical physics describes a universe which is predetermined by its initial conditions. If every event is absolutely determined by its preceding causes then everything that happens — including me writing this and you reading it — is inevitable and our free will is no more than a useful illusion. The future has already happened. But quantum theory casts a shaft of light into our prison cell. If the universe is actually indeterminate, then we are free.
In fact, this argument is pretty dodgy. Quantum events are, in a statistical sense, highly determinate. We may not know when one particle will do something but, over a time, we know a certain number of them will. Furthermore, if everything is utterly indeterminate then so is your will. You may freely choose to move your arm, but then find yourself lashing out with your leg. Even Conway and Kochen acknowledge that their theorem may not solve this particular problem. They ask: does free will exist? “We don’t know, but will prove in this paper that if indeed there exist any experimenters with a modicum of free will, then elementary particles must have their own share of this valuable commodity.”
If we are free, then so is everything else. In America the mathematicians believe that freedom is, indeed, the condition of the universe. In Holland the physicist believes the opposite.
Does it matter? In one sense, not in the slightest. Even if we are locked in the prison of classicism, we shall always behave as if we had free will since it is almost impossible to imagine any other way of behaving. I am not just sitting here waiting for my fingers to type, I seem — at least to myself — to be choosing to type these particular words.
But, in another sense, it matters a great deal. If I am persuaded of the absolute determinacy of the world, then I could decide to start behaving very oddly indeed. I could simply take the view that I was destined to murder by the initial conditions of the universe. Any concept of my guilt in the matter would be meaningless. Absolute determinacy is potentially one of the most dangerous ideas imaginable, threatening to subvert all our ideas of personal responsibility.
These ideas were toyed with in Luke Rhinehart’s novel The Dice Man, written in the 1970s but still on bookshelves everywhere and still the bible of a minor but global cult of the Dicelife. The hero absolves himself of all responsibility by living his life according to dice throws. But this is imperfect as he chooses the decisions he puts to the dice and which outcomes correspond to which numbers. Nevertheless, the idea that the intrusion of chance into the world offers a liberation from ordinary life is potent to contemporary imaginations formed in the shadow cast by 20th-century physics.
But such an extrapolation of a concept in physics into daily life is a strange thing to do and may, indeed, be not only dangerous but also illogical. Human consciousness is a very weird thing and Michael Lockwood, a philosopher, has pointed out that “the language of physics simply has no room in it for consciousness as it stands”. There is an issue sometimes called “what-it’s-likeness” or “qualia”. We experience ourselves and the world in a way that seems to be absolutely inaccessible to current scientific thought. I may be determined by quantum fluctuations but it doesn’t feel like it and this feeling is as real as anything else the physicists talk about. Lockwood doesn’t think we can leap straight to an anti-materialist account of consciousness — involving, perhaps, spirit or soul — from here, but we can conclude that our current science is radically incomplete.
“I think that the moral of all that is, yes, conscious states are material states,” he has said. “They are identical with neurophysiological states, but what the existence of consciousness shows is that there’s more to matter than meets the physicist’s eye. That there’s something inadequate about the physical description. Not inadequate simply because it leaves consciousness out, but that the existence of consciousness shows that, in a certain sense, it’s systematically incomplete.”
Arguments about free will based on contemporary physics may, therefore, be strictly meaningless, as meaningless, in fact, as trying to count angels on a pin head. Personally, I would add that they may be meaningless because the indeterminacy-determinacy argument can never be resolved as, I suspect, it is more about language than science.
None of which means that these debates don’t matter. They are what theology has become in our world and they tell us what we have become which is, perhaps, what we have always been — system makers who feel condemned to be, somehow, outside their own systems, unbearably caged yet intolerably free. If ’t Hooft is right, he will have transformed physics. The human world, however, will remain as stubbornly intractable as ever. The uncountable angels will, of course, dance on regardless.
