In discussions about free will, consciousness or interpretations of quantum mechanics people talk a great deal about whether the world is deterministic, random or something else. Well I don’t know what the ‘something else’ bit could be but I’m also starting to wonder whether the idea of randomness makes any sense.
The general idea of the distinction between a deterministic and a random universe seems to be that, in the former, events are somehow ‘fixed’ before they occur, whereas in the latter they are not – there are multiple different possible events. That sounds clear enough if you don’t think too hard about it, but if we do then we come up against the question of what do we mean by fixed? Fixed how, and by whom?
The apparent answer is that they are fixed by the ‘laws of nature’. But what are the laws of nature? Isn’t this some fairly heavy duty reifying to posit that there exist some actual laws, perhaps dwelling in some Platonic kingdom of Forms or written on magical stone tablets? Sure we have useful laws like Schrodinger’s and Einstein’s equations, but all we know for sure is that these are ideas we use to make sense of what we see and make predictions about the future. Whether they have some mysterious metaphysical existence independent of human minds is an entirely separate matter. It seems quite unlikely to me, given that every century or so we have to tweak the laws we use when further experiments and theorising show they are not completely accurate.
A Platonist might argue that there really are laws of nature out there, which determine how the universe behaves. OK if that’s the case then what about the law that is simply a description of where every single particle in the universe will be at every instant in the history of time? This is essentially a very, very long shopping list, but it also happens to perfectly describe the behaviour of the universe. Let’s call it the M-law, as it is the ‘mother of all laws’. Is that a law of nature? If it is then the universe cannot be random because everything that ever happens is described by the M-law.
So what are our choices about universe types? If we deny that laws of nature have any existence independent of human brains then everything in the universe is random because there is nothing that fixes it. If we assert the separate existence of laws of nature then nothing is random because it is all predicted by the M-law. Or, we could try and be picky and assert the existence of laws but only count them if they meet certain criteria. But what would such criteria be?
One option is to say that a law only counts if it can be known prior to the event we want to use it to predict. That would certainly disqualify the M-law. The trouble is, it would also disqualify everything else, because we cannot prove any of the laws. All we can do is build up supportive evidence for them, and there is never enough to be certain.
Sure, says the law-enthusiast, you can’t ever be completely certain, but in practice, if we are 99% certain of something, we would consider that good enough. Alright then. That does seem a bit arbitrary, but let’s go with it and see where it leads. What can we say about the motions of the planets prior to the discoveries of Kepler, Galileo and Newton? Back then we knew nothing of the ‘laws’ we now use to describe those motions, so under this criterion those laws didn’t apply, which apparently makes the motions of planets in 1347 CE random. Is that what we want?
‘Ah yes’ replies the enthusiast, ‘but you are limiting yourself to what we managed to work out based on our imperfect interpretation of the available information and our limited ability to make observations. The validity of a law should be based on all the information that was available up to that time, to an omniscient – but not future-seeing – observer, who was able to develop the best possible theories with the available information.’
Well I have to say this is getting even weirder and more implausible! We now have an ideal scientist-observer that is our yardstick for what constitutes a law of nature. If we go with that, and accept some arbitrary threshold of confidence – say 99% – on the validity of a law (leaving aside the very difficult question of how we would try to implement that threshold and whether it would be possible to validly calculate probabilities against it) then maybe we have arrived at a definition that could be pressed into use for laws of nature while excluding the M-law.
But – haven’t we ended up with a definition of randomness that is entirely epistemological? We have effectively defined a random event as one for which our ideal observer could not have 99% confidence beforehand of what the outcome would be. And the trouble with that is that we can no longer make the distinction that metaphysicists like to make between epistemological uncertainty over deterministic but chaotic events such as a coin toss, and ‘genuine’ randomness such as the decay of a radioactive isotope. With our new definition both of these types of uncertainty are ‘merely’ epistemological, and there is no such thing as metaphysical or ontological randomness. If we take this path we have to conclude that all randomness is epistemological, and there is not distinction from ‘metaphysical randomness’.
One last point to wrap up with. I went searching for a mathematical definition of randomness and came up with a complete blank. There are definitions of random variable, random (stochastic) process, probability space and various other related objects. But none of them have anything in them that captures the idea of ‘metaphysical undeterminedness’ that lurks under the popular conception of randomness. In fact, rather oddly, of the various interpretations of quantum physics, the only one that has close parallels to any of those mathematical objects in the field of probability theory is the ‘many worlds interpretation’, which looks very like the peculiar object that is a ‘stochastic process in continuous time’. That is ironic, as the many-worlds interpretation is regarded as a ‘deterministic’ interpretation, standing in contrast to the most popular ‘Copenhagen interpretation’ which is regarded as indeterministic, ie random.
Andrew Kirk Bondi Junction July 2012