Andrew asked:

I have a question about determinism. Laplace imagined that an intelligence with perfect knowledge of the state of the universe and the laws that govern it at one point in time would be able to know the past and future with absolution. It would be able to see the one way in which the predetermined future would unfold.

What if a computer existed which could do just this, and it foresaw a disaster which could be averted if someone knew about it in advance? If the computer predicts the disaster, then people will know about it and be able to stop it from happening. The computer’s prediction will be made false. If the computer predicts no disaster, then the disaster will happen because no one will know to stop it. The prediction will be false again. This seems to undermine the idea that such an ‘intelligence’ would be able to make absolute predictions. Is there a way out?

Answer by Jürgen Lawrenz

You seem not to have noticed that you answered your own question. Laplace’s determinism is impossible, therefore it is false.

This is the short, dogmatic answer. For a long answer, you would have to read a stack of books. But the shortened version of any such a book would merely come to the same conclusion, namely that the impossibility rests on the need to collect and evaluate information which, in this case, cannot be compressed into a shorter time than the events being predicted. So by the time that your computer has arrived at its prediction, it would already have occurred.

A fairly readily comprehensible model may help you here. Laplace’s proposition effectively amounts to making a graph of the lifeline of the universe from a single atom. On the assumption (a big assumption!) that atoms are immortal, you can then trace its career from beginning to end, including its interaction with all other atoms of the universe. Now Laplace surmised it is not necessary to include the full lifeline in this graph, because it is a mechanical picture of interaction, and one push-and-shove is much the same as every other. The universe in this picture therefore resembles a big machine where from the moment that you have determined one complete work cycle in which the atom is involved, the ripple effect through the entire ensemble will spread itself out in a deterministic and determinable process. Accordingly the comprehensive knowledge of one complete work cycle confers on the knower the exact processes through all future work cycles.

Of course, this theory was framed before the second law of thermodynamics was discovered. Therefore it is altogether innocent of the principle of entropy. The second law, i.e. the need to collect information, spells out that the amount of work done by this ‘intelligence’ cannot escape being part of the entropical relation. But the ‘intelligence’ cannot assess its own part in this, because it cannot (so to speak) stand outside of itself to measure its own entropy-producing work without falling into infinite regress. And so there is an end to ‘total knowledge’.

Although it is not exactly the same, the hope expressed by Laplace is similar to asking this intelligence to write down every possible number. You might wish to check the Web for the meaning of the ‘Dedekind Cut’. Once you understand what this involves, you’ll never fall for intellectual trap of total determinism again!


Answer by Geoffrey Klempner

Jürgen has talked about one notion of determinism, which relates to the theoretical possibility of prediction. However, arguably, there is another, more metaphysical sense in which we can express the (unprovable) hypothesis that the universe is, in fact deterministic. On the assumption of the truth of determinism, there is no nomologically possible world qualitatively identical with the actual world at the moment of the Big Bang, but which differs from the actual world at subsequent times. On the assumption of the falsity of determinism, there is at least one such possible world.

Why does this matter? Let’s say I’m deciding whether or not to answer Andrew’s question about Laplace. If determinism is true, then given the fact of the Big Bang (concerning whose precise details which we can only speculate), and the laws of nature (whatever these may precisely be), then there is only one logically possible world: the world where I write my answer (as I am doing now). If determinism is false, then given all these things, there are possible worlds where I go for a beer instead — as I was tempted to do, but resisted the temptation.