Yay, determinism! (Silly philosophical question)

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Yay, determinism! (Silly philosophical question)

Postby Ideas sleep furiously. » Tue Aug 02, 2011 11:22 am UTC

Ok this is a silly little question about a potential paradox in a deterministic system.

I was thinking that in an entirely deterministic system, that everything could potentially be predicted, assuming one could gather all the information within that system.
So I came up with this scenario.

A scientist invents a machine that can predict the future based upon deterministic ideals, i.e. everything acts based upon past conditions. (Assume there are no flaws in the machine)
The scientist using this machine, then watches himself in the future performing an action.
Can he then subvert performing the action? Despite the fact that the machine includes the use of itself by the scientist as a part of the deterministic system?

P.S. Sorry if this is in the wrong section, it kind of involves science and philosophy, so I figured I would put it here.
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Re: Yay, determinism! (Silly philosophical question)

Postby Dopefish » Tue Aug 02, 2011 12:23 pm UTC

Relevant.

Also I'm pretty sure there's at least one free will (which this basicly amounts to asking about) thread over in SB.

Basicly, such a computer can't exist, so even if the universe was entirely deterministic, one couldn't have a computer within that universe that made all those predictions with perfect accuracy. If such a computer was magicked into existence and the universe was deterministic, then he wouldn't be able to avoid performing the relevant action(s).

There's probabilistic aspects of our universe though, so we in real life don't need to worry about such paradoxes.

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Re: Yay, determinism! (Silly philosophical question)

Postby Tass » Tue Aug 02, 2011 12:43 pm UTC

What you have here is a system that as a part of the system contains a complete representation of that system, including the representation itself, leading to an infinite regression. As such it is impossible to answer even if the world was deterministic.

We can of course put the machine outside "the universe", having its only interaction with the world be the prediction, and then give a random prediction (or none), run the simulation, see what happens, give that prediction instead, and then iterate until the predictions does not change. In that case he can not avoid the prediction happening, most likely cause he will not want to. But what if the series does not converge? What it enters a loop where predicting A causes him to do B and vice versa? This is possible because the predictive machinery is not predicting its own action here. (Or with the impossible infinite regression of a machine simulating a world with a machine simulating a world with a machine... etc. you could say that there are an infinity of worlds every other in which A is predicted and every other in which B is predicted, all of them wrong.

Maybe the machine does not actually simulate, but rather looks into the future through a wormhole. In this case the laws of physics would have to be solved (or solve themselves whatever that means) self-consitently in this space-time region containing closed time-like curves. The non-converging series is not an option here as everything happens in the same space-time, nature simply has to find a solution that does converge (one should always exist). In this case: No, he cannot avoid doing what he saw himself doing, although he will be at high risk of missinterpreting what he saw, giving a surprising truth to many ancient greek tragedies.

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Re: Yay, determinism! (Silly philosophical question)

Postby Charlie! » Tue Aug 02, 2011 12:55 pm UTC

No machine can perfectly predict the world including itself. In order to predict your responses to its output it must know its output, which it doesn't. The obvious impossible thing is to ask it to output 1 if you're about to read a 1 and 0 if you're about to read a 0, and add a NOT gate.
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Re: Yay, determinism! (Silly philosophical question)

Postby Ideas sleep furiously. » Tue Aug 02, 2011 1:00 pm UTC

Charlie! wrote:No machine can perfectly predict the world including itself. In order to predict your responses to its output it must know its output, which it doesn't. The obvious impossible thing is to ask it to output 1 if you're about to read a 1 and 0 if you're about to read a 0, and add a NOT gate.


Like Skynet, it is self aware. (Ofc it has this http://xkcd.com/534/)

It would derive it's own output using phyisical law (them all being known in the hypothetical)
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Re: Yay, determinism! (Silly philosophical question)

Postby doogly » Tue Aug 02, 2011 1:39 pm UTC

Of course it would. Do you think any other computer is using anything besides physics to run?
If a machine can simulate a universe that includes itself, then there is not just determinism, but overdeterminism. This is of course an option, I suppose. It just seems like all of the "work" in your question is done in setting up the premise. If you want me to grant that such a machine exists, I have no problem at all saying that therefor there is nothing like free will or choice in the world.
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Re: Yay, determinism! (Silly philosophical question)

Postby 314man » Tue Aug 02, 2011 3:56 pm UTC

Is it not possible for the machine to enter it's own loop that would predict the future correctly? As in the machine already has determined that the person will look at the machine and the future will happen as 'determined', even though the person is aware of what will happen. Basically, instead of being in a world where A is predicted, but because the person wants to change the future, the world is actually B, so then the machine predicts again (and infinite loop), can it not just predict a world Z, which by that prediction, we actually are in world Z.

E.g. The machine will predict that the person will kill a certain man. The person thinks it's nonsense and would never kill a man. But events happen, and despite seeing the prediction (or even because the person saw it), he ends up killing the man.

If anyone has seen Minority Report, I'm thinking along those lines.

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Re: Yay, determinism! (Silly philosophical question)

Postby Soralin » Tue Aug 02, 2011 4:15 pm UTC

Well there's the idea that the universe is computationally efficient. That you can't perfectly simulate something in the universe more simply and faster than the existence of that object itself, if that's the case. Of course, predicting imperfectly is always possible, but no contradiction there.

Ideas sleep furiously. wrote:It would derive it's own output using phyisical law (them all being known in the hypothetical)

If it can derive its own output, using something less than the whole computer, then what is the rest of the computer for? You could toss the rest of the computer out and use just the part that produces exactly the same output instead. :)

Also, some limitations to computation: http://en.wikipedia.org/wiki/Limits_to_computation
  • The Bekenstein bound limits the amount of information that can be stored within a spherical volume to the entropy of a black hole with the same surface area.
  • The temperature of the cosmic microwave background radiation gives a practical lower limit to the energy consumed to perform computation of approximately 4kT per state change, where T is the temperature of the background (about 3 kelvins), and k is the Boltzmann constant. While a device could be cooled to operate below this temperature, the energy expended by the cooling would offset the benefit of the lower operating temperature.
  • Bremermann's limit is the maximum computational speed of a self-contained system in the material universe, and is based on mass-energy versus quantum uncertainty constraints.

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Re: Yay, determinism! (Silly philosophical question)

Postby PM 2Ring » Tue Aug 02, 2011 5:04 pm UTC

I predict that this thread will come to a halt.

:)

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Re: Yay, determinism! (Silly philosophical question)

Postby Adam Preston » Tue Aug 02, 2011 5:15 pm UTC

Unfortunately as the machine hasn't been built you did not predict that I would continue the thread. :D
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Re: Yay, determinism! (Silly philosophical question)

Postby Tass » Wed Aug 03, 2011 6:03 am UTC

Adam Preston wrote:Unfortunately as the machine hasn't been built you did not predict that I would continue the thread. :D


He didn't predict it would halt now. Just that it won't go on forever.

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Re: Yay, determinism! (Silly philosophical question)

Postby Ideas sleep furiously. » Wed Aug 03, 2011 6:48 am UTC

I think I figured out the solution.

What the scientist or machine does is irrelevant to determinism, que sera sera.
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Re: Yay, determinism! (Silly philosophical question)

Postby Ulc » Wed Aug 03, 2011 6:52 am UTC

Entirely beside the point that such a computer can't be built, there's also the "garbage in, garbage out" problem. If you start with incorrect, or just not entirely correct, starting conditions, your predicting will per definition be flawed.

So even if we somehow managed to build a computer that could perfectly predict the future, the starting information would have to be the exact position, velocity and direction of every single atom in the universe.
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Re: Yay, determinism! (Silly philosophical question)

Postby Ideas sleep furiously. » Wed Aug 03, 2011 6:57 am UTC

Ulc wrote:Entirely beside the point that such a computer can't be built, there's also the "garbage in, garbage out" problem. If you start with incorrect, or just not entirely correct, starting conditions, your predicting will per definition be flawed.

So even if we somehow managed to build a computer that could perfectly predict the future, the starting information would have to be the exact position, velocity and direction of every single atom in the universe.


I figured that, but for this example lets just say this universe consists of a scientist in a white walled room full of air.

Besides, if one could perfectly simulate the Big Bang, that would be all you would need. Right?
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Re: Yay, determinism! (Silly philosophical question)

Postby Tass » Wed Aug 03, 2011 8:23 am UTC

Ideas sleep furiously. wrote:I figured that, but for this example lets just say this universe consists of a scientist in a white walled room full of air.


But then the machine is not a part of its simulation and we are back to this:

Tass wrote:We can of course put the machine outside "the universe", having its only interaction with the world be the prediction, and then give a random prediction (or none), run the simulation, see what happens, give that prediction instead, and then iterate until the predictions does not change. In that case he can not avoid the prediction happening, most likely cause he will not want to. But what if the series does not converge? What it enters a loop where predicting A causes him to do B and vice versa? This is possible because the predictive machinery is not predicting its own action here.

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Re: Yay, determinism! (Silly philosophical question)

Postby PM 2Ring » Wed Aug 03, 2011 2:43 pm UTC

Tass wrote:
Adam Preston wrote:Unfortunately as the machine hasn't been built you did not predict that I would continue the thread. :D

He didn't predict it would halt now. Just that it won't go on forever.

What he said. The 2Ring halting oracle doesn't have to specify when a process will terminate, just whether or not it will terminate in a finite number of steps. :)

I suppose that this thread could do with a link to Laplace's demon.
Wikipedia wrote:We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.
—Pierre Simon Laplace, A Philosophical Essay on Probabilities

[...]

Due to its assumption of determinism, Laplace's thought experiment is inherently incompatible with quantum mechanical theories, where chance is an essential part of the world's unfolding. The Heisenberg Uncertainty Principle, for example, states that exact measurements of positions and momentum may not be defined (and observed) together with more than a given precision.

[...]

In 2008, David Wolpert used Cantor diagonalization to disprove Laplace's demon. He did this by assuming that the demon is a computational device and showing that no two such devices can completely predict each other. If the demon were not contained within and computed by the universe, any accurate simulation of the universe would be indistinguishable from the universe to an internal observer, and the argument remains distinct from what is observable.

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Re: Yay, determinism! (Silly philosophical question)

Postby Yakk » Wed Aug 03, 2011 3:07 pm UTC

There are deterministic universes where it is not possible to predict the future (in the general case) within the universe in question.

As an example, the universe of Turing Machines. A given starting state evolves deterministically by relatively simple rules. At the same time, properties of such machines cannot (in general) be computed by such machines.

We can build a model of your system as an augmented Turing Machine that is able to allocate "new tapes" and write to them, then start augmented Turing Machines on such tapes (with the same powers). Such sub-machines wouldn't be able to read back from the parent machine, but the parent machine would be allowed to read the tape of the sub-machines.

We then posit the existence of an augmented Turing Machine that, given a starting state, predicts what the result would be after n steps, and does so in k << n steps. It shouldn't be all that hard to demonstrate that such a machine could not exist. In essence, in this deterministic model, it can be proven that no machine that "predicts the future" can exist in the general case.

Now, if we strip out some of the above restrictions, I'm thinking that the proof gets harder. Basically, if we allow sub-machines to interact with their parent-machines, the relatively simple proof for the above won't work. In essence, this means that if we allow the machine that predicts the future to manipulate the universe to force that future to occur, then everything works.
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