
Laplace’s Demon - bribri
http://rjlipton.wordpress.com/2014/08/08/laplaces-demon/
======
roblev
For me the main problem with the "if the demon says TV then I listen to the
radio" paradox is that it asks the demon to predict its own computation.

Take as an example COnways game of life. It is perfectly predictable in the
future - given current state, I can easily predict the state N steps in the
future (I just run the simulation on my side computer). And clearly my side
prediction will have no impact on how the game-of-life evolves. I can even
insert my prediction into the game-of-life by changing the value of my cell
(alive=watch TV, dead=listen to radio). Even if a "perverse" in-game character
chooses to do the opposite of my prediction, it doesn't alter the fact that I
can perfectly predict future of the game universe.

But if I am asked to make that prediction _inside_ the game of life using a
program embedded in the game-of-life, then that is a lot harder. It seems very
unlikely that I could encode the state of the universe in a way that allows my
prediction program to run in any way more efficiently than just letting the
game-of-life play out. I'm pretty sure that the Halting problem could be used
to demonstrate this.

So for me it makes a big difference whether you constrain the demon to "in
universe" computation or "out of universe" computation.

~~~
espadrine
To me, there are two more issues with that demon paradox.

First, that it is assumed that its answer has a physical representation in
reality. The fact that solving a non-trivial maze from the inside is
impossible without moving through the maze doesn't mean the maze cannot be
solved without moving. It can be solved from above the maze. Similarly,
assuming quantum mechanics is accurate in that every particle has a random
nudge in its position and velocity, if we had access to the random generator,
we could create that demon; otherwise, the solution would be expressed in
terms of what that generator produces: a solution which doesn't have a
physical representation, but is merely a probability distribution.

Second, there is this assumption that its answer be crystal clear for us to
understand. Any amount of work with symbolic computation gives the intuition
that sometimes, the answer isn't atomic. In that case, the demon's answer
could be "if I say that you listen to the radio, what you will do is watch TV.
Otherwise, you will listen to the radio".

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harshreality
Isn't mention of chaos theory irrelevant? Chaos is the effect you get when you
can't measure something accurately enough, or you can't (don't have enough
computational power) to run a perfect reality simulation with those
measurements (even if they're good enough in theory to form the basis of an
accurate prediction) in reasonable time, or both.

I think the main premise rests on the same confusion about free will that
shows up in Newcomb's paradox. Either there is free will that transcends
anything's ability to predict, even in theory (perfect knowledge/measurement
and infinite computation), or there is not. If there is not, then a
demon/AI/God setting up a test/prediction based on your future decision may be
possible, but your awareness of that fact will simply be an input into your
future decision-making... an input that the demon/AI/God already accounted for
when making the prediction. Just because something is recursive does not mean
it's not deterministic. I happen to believe that Laplace's demon exists, it's
called physics, but its state is the physical world, so it predicts things
will happen at exactly the moment they happen (the prediction/computation
being entropic decay); unfortunately that doesn't seem very useful for
predictions in the practical sense.

If there is free will that transcends physics, then prediction is
fundamentally impossible by something bound to physics—so it's a thought
experiment where some things are bound to the laws of physics and others are
not. What is the purpose of conducting thought experiments about the physical
world, based on supernatural axioms? "Free will exists," the claim goes, and
yet "here's a thing that can collapse free will and issue arbitrarily accurate
predictions on human behavior." And then, "Let's see what happens when these
axioms are applied to someone in the physical world choosing whether to try to
make more money or less."

~~~
alephnil
> Isn't mention of chaos theory irrelevant?

That was my first thought as well, but consider a chaotic system in a
Newtonian universe. Laplace' demon must then have the capability to simulate
the universe to be able to predict it. What chaos theory brings is that this
simulation would require infinite precision to be done without diverging from
reality at some point (and sooner rather than later as the error grows
exponentially). Then you could use Cantor's diagonalization theorem to prove
that no such simulator could exist, even for a finite system, because even a
finite system would require an infinitely large state to represent it, and no
finitely sized simulator could represent it.

~~~
harshreality
The universe represents itself. Doesn't that imply either that the universe is
capable of infinite computation within a finite (though increasing) space, or
that it doesn't require infinite state?

There's Planck length and Planck time (entropic decay resolution?) to
consider. If those are the basis for physical laws, isn't everything finite?

~~~
alephnil
The universe represents itself, but no part of the universe is able to
predicts its own future in detail, and is as such no simulation, at least not
of itself. It just exists. The reason I said "a Newtonian universe", is
precisely because quantum physics represents a discretization, which Newtonian
physics does not, and the Planck length is a part of this discretization. The
simulator would have to be bigger than the system it simulates to be able to
represent its state, but the Cantor diagonalization argument would no longer
apply.

~~~
harshreality
But we don't live in a Newtonian universe, do we?

If the universe requires infinite computation to "go", it's doing that
computation somehow, isn't it? If the universe at perceivable scale is not
capable of infinite computation, but infinite computation is required, perhaps
it's spawning infinite universes that do computations instantly with respect
to our universe's arrow of time?

I don't understand the difference in computational requirements between
predicting (in "advance") a future (entropic future) state of the universe,
and predicting it JIT.

A functioning Newtonian universe must be capable of infinite computation,
therefore Laplace's demon can exist (for that universe), even if only by being
a copy of the universe, right?

~~~
seabee
There are two outcomes of your argument:

1) a functioning Newtonian universe is impossible

2) functioning Newtonian universes are infinitely complex

The laws of physics already established 1, making 2 a moot point.

------
gosub

        consider that there are only two options: (1) watch TV or (2) listen to the radio.
    

isn't the idea that there would be only one option, the future that already
depends on the answer? the demon should know its internal state, its answer,
and the reaction to the answer. if any answer gives a logical contradiction,
it will not give it. Also: being able to see the future does not imply being
able to tell it. A kind of cassandra curse.

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TheDong
The problem with the last two proofs is that they move the question to "the
demon must be able to predict the future, then say the prediction, and then
have that prediction be true".

The demon might see that you will watch TV, but if it says that you will
listen to the radio. If it sees both of those, even if it says something that
becomes false, that doesn't mean the demon couldn't see the future or doesn't
see the future. It merely means that the demon cannot accurately manifest the
information.

Similarly, in the paradoxical question before, it makes the assumption that
demon is honest; that it answering the question incorrectly is tantamount to
it having predicted incorrectly. To me it seems clear that the constraint that
the demon must be only honest and must transfer the knowledge into the system
it is predicting the state of without changing the state is utterly silly.

------
SCHiM
Just like all such problems the 'TV and the Radio' problem shares its root
with the liars paradox. The root cause, of course, are self referention,
determinism and recursion.

The problem is the 'prediction loop', which has no clearly defined exit.
There's no path that can be followed that will terminate it:

The demon understands every part of your brain, and knows that if it says that
you're going to watch TV while you're determined to prove it wrong will make
you listen to the radio instead. So it enters the next iteration of the loop.
This cycle would continue for infinity, which is where we perceive a paradox.

There are several naive resolutions that come to my mind. Assuming that
predicting the future takes some time, even if it's only a fraction of a
second, will allow a way out. The Demon will simply enter the loop and exit it
once the evening has passed and every possibility of 'predicting it' has
vanished. Of course this could be considered cheating, it has never been
established if the Demon's computations take time or not, but asking this
question can be considered cheating as well, since it's probably impossible to
have _only_ two possible things you could be doing. Which introduces the
second solution.

The Demon is more intelligent than you are, and while you'd sworn to yourself
that there were only two possible outcomes to this evening: doing the opposite
of what the Demon predicts, the Demon sees beyond the 'two' possibilities and
correctly predicts a third possibility that you didn't envision.

The last solution attacks the notion of free will, if the Demon can exactly
predict the future than this implies that the universe is deterministic. So
instead of having only two options, or a third invisible option, there is only
one real option and the demon cannot be wrong or it cannot be right.

All of these 'solutions' either introduce a new or alter a previous assumption
and are thus not really solutions to the question asked, as it stands I think
the question is unanswerable and introducing new concepts and ideas is
inevitable.

~~~
tuxcanfly
>So instead of having only two options, or a third invisible option, there is
only one real option and the demon cannot be wrong or it cannot be right.

This third neither right nor wrong option reminds me of 'Mu' found in eastern
philosophy and highlighted in Hofstadter's GEB and it forms another crucial
part of self-reference and recursion as mentioned earlier in your comment.

------
tehwalrus
The best demon would simply answer "you intend to do the opposite of whatever
I tell you." \- this would most accurately define the future state of the
universe.

Alternatively, the demon could say one thing, and send a delayed timestamped
message with the opposite.

~~~
russellsprouts
This. Constraining the demon to two responses can't work. The demon needs to
be able to give an answer with at least as much information as the entire
universe's state -- not yes or no answers. The issue with the person only
exists because the person's actions cannot be represented with a single bit of
information. But the person cannot hope to outsmart the demon if it's response
has more bits of information than the person can possibly respond with.

~~~
tehwalrus
I think the best summary is:

The disproof assumes free will, but Laplace's universe assumes free will is an
illusion. Devise an experiment to work out which is right -- a Laplace demon,
if such a thing can exist, is probably a good experiment to test this.

------
ewood
Certainly it seems impossible to construct a device that could capture the
state of a system of which it was a part, to me that's the paradox of the
watching TV/listening to the radio prediction - it transfers information from
the model into the system it models.

However perhaps a device which could capture the state of a defined system,
model it and monitor its boundary as a means of prediction would be possible?
The question is could it be possible to capture the state of a system at a
single instant and without altering the system?

------
d--b
These disproofs are completely missing the point. Laplace says: the laws of
nature are deterministic. The answers are: there is free will in the human
mind. It's no proof, these are just contradicting metaphysical statements. A
disproof that may make more sense though is to say that: in order to be able
to write the equations and know the state of the entire universe, the universe
itself cannot be infinite. Let's assume the total information of the universe
at time t could be represented by a N bits. Then in order to exist and to
calculate things, the demon needs to materially represent these N bits by at
least N elementary particules. But this means that the state of these
particles also needs to exist in the universe, and so the universe plus its
representation would be represented with at least 2N bits, which is bigger
than the size of the universe. So the demon cannot exist. In fact this is just
saying the only device capable of predicting the future is the universe
itself, and its prediction is the realization of the present itself.

------
perturbation
An interesting take on the above:

[http://dresdencodak.com/2009/02/16/exorcising-laplaces-
demon...](http://dresdencodak.com/2009/02/16/exorcising-laplaces-demon/)

------
foxhill
my attempt at a short proof about laplace's demon (they may not necessarily be
correct, however..);

laplace's demon is part of the universe.

to simulate the universe, laplace's demon must simulate itself.

assuming P!=NP, this self simulation cannot be more efficient than the "lower
level" simulation.

so either the "self-simulation" hole will become increasingly deeper (to
infinity), or the resources required to do the simulation at each level will
exponentiate away.

proof 2;

the smallest space at which a single bit of information is storable is O(a
subatomic particle). but that subatomic particle is defined by more than one
bit of information.

therefore to have knowledge of the entire state of the universe at some time
requires more matter than exists in the observable universe.

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bribri
[http://www.hawking.org.uk/does-god-play-
dice.html](http://www.hawking.org.uk/does-god-play-dice.html)

Physics oriented explanation

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eli_gottlieb
The Demon for the "radio/TV" problem just has to predict whichever option is
more likely to be a self-fulfilling prophecy.

