http://www.idsia.ch/~juergen/computeruniverse.html I just know there will be a problem here with this.Please Register or Log in to view the hidden image! But what does anyone think of the idea?
I'd call an eternal, omnipotent creator a pretty simple explanation but I'm not sure that has much scientific value. These are basically the same question, except the second (which I disagree with) is presuming a particular answer for the first. Is this a solipsistic question? For the former, simply wait until it becomes the latter. Then it becomes a simple matter of applying and adjusting, as needed, our current scientific theory. Please Register or Log in to view the hidden image!
Well, the metaphysics is encapsulated in the creator of a program that describes/explains the universe. Also in the creator of the machine it runs on, possibly a UTM or some generalised Turing machine. You disagree that we think the future is more random than the past? Doesn't that imply the existence of multiple histories, just as it imples multiple possible futures? Well, it's certainly an anthropomorphic question; it assumes you know that you're an observer and that you can't discount the existence of other (possibly an infinite number of) observers. Indeed, this is corroborated a lot by daily existence, and depends on how you define "observer". No, postdiction isn't prediction, something a good explanation can do.
I was being a little bit ornery with all of my responses, but my point here was that claiming that a program which allows "all universes to exist" is a simple one and therefore a reasonable explanation, happens to be arguably more complex yet just as descriptive and explanatory as me saying God did it... Yes, no and no. I think there is one past and one future with no wiggle room for either. The answer here is obvious...I'm the *only* observer. The world is a figment of my imagination, including you. I'm anxious to see what my subconscious mind comes up with for "your" response to this. Maybe that's the simplest explanation of all? We don't need infinite computing power because my mind only needs to create reality as my simulated body experiences it.:cheers:
Deep Thought "However, a very short program that runs for a million years before giving an answer is not very practical." I demand that something about Vroomfondel and Majikthise may or may not go here.
Yes, I demand that you are either correct or mistaken. Clearly, the Kolmogorov complexity has the same value as a heart-shaped puddle evaporating on the sidewalk.
What about the idea of a continuum of options for a measure of complexity? I can remember that Penrose says a few things about complexity (and the complex numbers) in The Road to Reality, but nothing about Majikthise, or what his history was. In other words, he indeed may or may not be in the program. Um, I'm hoping you guys are understanding Maxwell's demon (or daemon). And that it can be described algorithmically; in fact it has a connection to this Gibb's ensemble whatsaname. This fellow is the hypothetical observer of molecules of gas who can open a small trapdoor and let selected ones move into another closed volume (of, you know, space); this is like the sorting algorithm, nein?
On a more serious note, this exposes the connection between information, work, and entropy. Place free-moving pistons on each side of the volume with the trap door in the center. The demon can use work (by pushing the gas to one side using one of the pistons and closing the trap door) to reduce entropy and gain information about the molecule's whereabouts. If he already knows the whereabouts of the molecules, he can close the trap door, advance the free-moving piston, then release the molecules to produce work (increasing entropy and losing information in the process).
How does pushing the gas to one side reduce entropy? Don't you mean the demon does work on the gas ("use work" seems a bit clunky, where does the demon get it from so it can be "used")? Suppose the demon knows the relative amounts of gas in each half at all times, or all the states in between the state on the left, and on the right of the arrow in this diagram: Please Register or Log in to view the hidden image! I'm not sure how you get from that situation to "release the molecules" in your scenario. Are they released through the trapdoor, or is the piston released? The demon has to move the piston or the trapdoor, according to you, to "lose information". note: in the diagram the relative amounts of gas in each half are equal initially, but your scenario is a modification of this in which the amounts can change, by being pushed through the trapdoor by pistons (I guess people will need to use imagination here, to visualise this). You can also have an initial state on the left where one half is empty of gas, with a path still to the state on the right
In Szilard's engine, which is similar to the setup I described, he refers to a single gas molecule. Pushing the molecule to one side reduces entropy because the volume has been reduced which reduces uncertainty about the molecule's position. I say "uses work" only because I'm considering it a currency, in the same way that the demon "uses information" or "uses negentropy of the system". For more info see http://arxiv.org/abs/1009.5287 or search for Szilard's engine at http://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory
Yes, if you have information that the molecule is in one half or the other. But your Szilard engine has to do work to get the molecule into one half by pushing on one of the pistons. This actually increases the information entropy by the same amount it reduces the molecule's entropy--the demon gains information by doing work on the system. Also there's a proof by Brillouin, Gabor, et al, that observing the molecule (so that, for instance a partition or barrier can be lowered and trap the molecule in one half) means the demon has to emit at least one photon and this must have an energy greater than the energy of the molecule. You need to modify your system so the pistons can be moved without doing work on the molecule of gas. Say by using a barrier that can be lowered when the molecule is in one half or the other, then moving one of the pistons--the one with no molecule between it and the barrier. This means the "demon" (really the engine) must be able to tell where the molecule is, and so has to emit that photon. . .
Is it because the demon knows which half of the container the molecule is in, where before moving either piston the molecule can be in either half with equal probability? Perhaps just think of it as "information" and forget about information entropy. After all information is self-referencing, and IS nobs know about information and Shannon entropy, so we're all good.
Arfa brane, you're confusing me man! Information entropy decreases as the demon is able to reduce the potential location of the gas molecule. He does this by "using work" through pushing the piston. Reverse the situation, and he can "use information" about which side the molecule is in by freely-moving the frictionless trapdoor, then moving the frictionless piston, then opening the trap door to extract kT ln_2 Joules of work from the system.
Let's assume this is true. Initially the demon knows there is a molecule of gas in the container. Then after moving one of the pistons (let's also assume the free-moving pistons can be held in place somehow) the demon knows which half of the container the molecule is in. So now the demon knows less about the molecule than it did initially. (??) Where does the information come from about which piston to move?
No, he obviously knows more. Your definition of information entropy may need correcting, as it is considered a measure of uncertainty of a variable. Reduce the uncertainty of the location of the gas molecule and you have reduced the information entropy of that gas molecule.
Right. The demon's information content increases, information content = information entropy. Gas molecules have thermodynamic entropy, not information entropy. Physically, entropy is joules/Kelvin, information is dimensionless bits/message (although bits have a physical representation).
Increasing information content is equivalent to reducing uncertainty, reducing information entropy. Again, it appears your definition of information entropy needs correcting.
My definition of information is the number of bits required to send a message. The information content of a message like 0000, is less than the content of a message like 1011, for instance. The second message is less "uncertain" than the first because it has more content. It "conveys" more information than the first message. Information content = information entropy. The two entropy measures (thermodynamic and Shannon) have opposite signs. I believe this is no coincidence.
