Universal Limits on Computation fromShane Conder's Whateveritis of Nothing

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Universal Limits on Computation

This is an excellent article, in my opinion, about the future of computation and about the universe itelf.

The abstract is:

The physical limits to computation have been under active scrutiny over the past decade or two, as theoretical investigations of the possible impact of quantum mechanical processes on computing have begun to make contact with realizable experimental configurations. We demonstrate here that the observed acceleration of the Universe can produce a universal limit on the total amount of information that can be stored and processed in the future, putting an ultimate limit on future technology for any civilization, including a time-limit on Moore’s Law. The limits we derive are stringent, and include the possibilities that the computing performed is either distributed or local. A careful consideration of the effect of horizons on information processing is necessary for this analysis, which suggests that the total amount of information that can be processed by any observer is significantly less than the Hawking-Beckenstein entropy associated with the existence of an event horizon in an accelerating universe.

In my previous ramblings about the size and age of the universe, I had not considered the whole horizon aspect of it. Basically, in a universe that is expanding at an accelerated rate, the observable universe gets smaller. Actually, the article puts it that objects that get beyond the horizon cease to be in causal contact with the observer. That means that the state of an object beyond the causal horizon has absuletely no impact on the observer in any way. Curiously enough, it can't actually have an impact on any other observable object, either, because by the time the causal effect gets to the observable object (as of now) it will no longer be observable. (This, of course, assumes no effect can traverse the distance faster than the speed of light.

Put in another way, if you have two objects, A and B being observed and A is closer than B, then the following works. Currently, B causes A to look red. If B changes such that it now makes A look blue that change in B would still be while it was within the horizon. If B exits the horizon and goes through a change that now would make A look green, by the time that change can effect A, A will have left the horizon. Clearly, once any object leaves the horizon the observer can never learn anything new about it, even by studying changes within the horizon.

This also means that the observable universe gets smaller while the total universe expands. It's this reduction in size, and thus energy, that places a limit on overall infomration processing that can be done. The assumption is that the results of the information processing have to be obvservable. A tree that falls in a forest without being observed still fell because you can later observe that it was fallen. A tree that falls in a forest outside the horizon is irrelevant because no such forest can be observed... ever. Put another way, it didn't fall because it doesn't exist in the universe. Of course, this implies the universe as the observable stuff around the observer.

Curiously, in this accelerating, expanding universe the end of time comes when no fundementally lowest level thing has an causal effect on any other lowest level thing because the rest have gone beyond its horizon. This would be perfect entropy as there is neither observable nor mutable state.

Strangely, this would seem to imply that the accelerating, expanding universe is be driven by some force so strong that it rips everyhing apart to its lowest level fundamental building blocks that can then no longer have a cause on each other. There are many flaws here. First, this force pulling (or pushing) everything apart at an accelerated rate has to, itself, be made up of lowest level fundamental building blocks. Secondly, if there are only two fundamental building blocks and they are in causal range, they still can't act on each other. Why? Because there is nothing else available to pass between them. Also curious, this can be expanded to any number of lowest level building blocks.

And if I keep rambling I'm going to randomly reverse my ramblings. So I'll stop there. For now.

Posted by Shane on April 28, 2004 3:03 PM | Permalink

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This is an excellent article, in my opinion, about the future of computation and about the universe itelf. The abstract is:

The math in the article is fairly simple, relatively speaking, and they describe what they mean in words, too. Their conclusion that Moore's Law can only work for about 600 years, regardless of physical manifestation, is astounding. An article I read a while back stated that within 30-40 years, computing power will meet that of the computing power of the human brain. Given Moore's Law has been going for a while now, that still leaves on the order of 500 years of it for information processing to exceed that of the human brain (as it is now). That's good news, in my opinion. In my previous ramblings about the size and age of the universe, I had not considered the whole horizon aspect of it. Basically, in a universe that is expanding at an accelerated rate, the observable universe gets smaller. Actually, the article puts it that objects that get beyond the horizon cease to be in causal contact with the observer. That means that the state of an object beyond the causal horizon has absuletely no impact on the observer in any way. Curiously enough, it can't actually have an impact on any other observable object, either, because by the time the causal effect gets to the observable object (as of now) it will no longer be observable. (This, of course, assumes no effect can traverse the distance faster than the speed of light. Put in another way, if you have two objects, A and B being observed and A is closer than B, then the following works. Currently, B causes A to look red. If B changes such that it now makes A look blue that change in B would still be while it was within the horizon. If B exits the horizon and goes through a change that now would make A look green, by the time that change can effect A, A will have left the horizon. Clearly, once any object leaves the horizon the observer can never learn anything new about it, even by studying changes within the horizon. This also means that the observable universe gets smaller while the total universe expands. It's this reduction in size, and thus energy, that places a limit on overall infomration processing that can be done. The assumption is that the results of the information processing have to be obvservable. A tree that falls in a forest without being observed still fell because you can later observe that it was fallen. A tree that falls in a forest outside the horizon is irrelevant because no such forest can be observed... ever. Put another way, it didn't fall because it doesn't exist in the universe. Of course, this implies the universe as the observable stuff around the observer. Curiously, in this accelerating, expanding universe the end of time comes when no fundementally lowest level thing has an causal effect on any other lowest level thing because the rest have gone beyond its horizon. This would be perfect entropy as there is neither observable nor mutable state. Strangely, this would seem to imply that the accelerating, expanding universe is be driven by some force so strong that it rips everyhing apart to its lowest level fundamental building blocks that can then no longer have a cause on each other. There are many flaws here. First, this force pulling (or pushing) everything apart at an accelerated rate has to, itself, be made up of lowest level fundamental building blocks. Secondly, if there are only two fundamental building blocks and they are in causal range, they still can't act on each other. Why? Because there is nothing else available to pass between them. Also curious, this can be expanded to any number of lowest level building blocks. And if I keep rambling I'm going to randomly reverse my ramblings. So I'll stop there. For now.