Determinism and Laplace’s demon

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.

 

5 thoughts on “Determinism and Laplace’s demon

  1. Jürgen Lawrenz’s is wrong, but he is right when he says the machine would have to exist outside the realm of the reality it was examining, if it were to analyse the data correctly. It cannot assess itself because it cannot pause itself; it cannot analyse its own molecules. Therefore, it either exists within our reality and cannot perform the analysis, or it exists outside of our reality and we cannot ask it anything.

    For us to interact with this device it would either have to be drawn into our reality, or we would have to exit ours. Were the machine to enter our reality, another machine would have to perform the analysis of the new reality which now included the initial machine, and if we were to leave our universe we’d remove our molecules from the examined reality. The initial machine could never have known that this would happen since its molecules weren’t present within the reality at the time of its assessment and ours were. Either way, it didn’t have the correct data. Therefore, it would be unable to provide an accurate answer.

    Put simply, it’s a paradox that tells us it’s the analytical machine that cannot possibly exist, not the concept of Determinism.

    Here’s my detailed response to Mr. Lawrenz, if he would like to know where he stumbled:

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

    That’s simply not true. You’ve applied faulty logic here. It’s the machine that’s impossible, as I hope I’ve proved above, yet you’ve granted it life and then used it to provide evidence for your argument.

    “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.”

    In this particular case the computer is inadequate and the timescales too short to perform the analysis. That doesn’t disprove Determinism. You’ve fallen foul of the Strawman fallacy. If Laplace’s claim was that a computer could predict a future event within the lifespan of a human being, you’d be right to say he’s wrong. But he didn’t.

    “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.”

    Like me, you’re of the belief that the human mind is ill equipped to model all the data and fully know the universe within which it resides. This doesn’t disprove Determinism, it simply demonstrates the enormity of the data one would need to process in order to fully map the entire timeline of the universe.

    I’d also note that when Laplace used the word atom, which has come to have new meaning to us, he was using the only vocabulary available to him to suggest any and all particles present in the universe.

    If an atom were to de-construct into another particle, the force that caused that would be understood by the ‘Demon’, and therefore the trajectory, velocity and outcome of any collision would also be known.

    “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’.”

    This, again, does not disprove Determinism, you’ve simply described the paradox facing an entity that tried to assess its own universe. If it could stand outside of the examined reality though, the paradox goes away and the second law of thermodynamics is upheld, since the entity is outwith the system.

    It appears you’ve failed to appreciate that it’s entirely possible that Determinism could exist and be unknowable. It’s a logical fallacy to insist that because we cannot know how the universe will play out that it isn’t already determined to play out in a precise manner. The truth of Determinism isn’t dependent on us being able to map it.

    “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!”

    Again, see my response above. You’ve proved the implausibility of measuring the outcomes from within by an entity (that the human mind can conceive), but you haven’t proved that the outcomes aren’t measurable from without, and you most certainly haven’t proved that the concept itself is impossible.

    In short, you’ve failed to even challenge the concept of Determinism, never mind disprove it. You’ve applied argumentum ad lapidem and then elevated yourself above all those who have applied sound logic to appreciate its feasibility, even if we question its plausibility.

    That’s a fine display of hubris, sir. I congratulate you.

  2. In my opinion your post and your perspective is totally wrong. The machine can predict the future at any given time and also gives you an answer. If you ask it ” will i go for a beer this evening?” and the reply is “yes” you can just stay at home all the evening, contradicting the machine. BUT, after interfering with the machine your answer changed and instead of going for the beer you stayed in.It’s not about the answer, it’s about the data.If it knows that you will stay in, it also knows that you want to contradict it so it will reply “yes” so you will finally stay in.The machine always knows what is about to come, all the data is inside.The misunderstanding here is that this machine is not a normal one, you cant make it or ask it questions. It is outside of our view and you can’t interfere with it.The answers can be whatever depending on the person asking but the data are only one-way.You cant export them.

    Thank you

    1. Such a machine would not answer a mere yes or no. The answer itself would affect the outcome, so the answer would more likely be, “you will get a beer if I suggest that you wont”. More precisely, it may even give you the entire likely argument and its outcome. If it has thoroughly scanned all the atoms of your mind, then it knows exactly how you will respond to every question. It could write down the conversation as it occured at exactly the same time, just like when you say the same thing as someone else at the same time, and some people will say “jinx”!

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