Calculating A Theoretical Boundary To Computation

TMB writes "Lawrence Krauss and Glenn Starkman, astrophysicists at Case Western Reserve University (and in LK's case, author of a number of books including Physics of Star Trek), just submitted this nice little paper to Phys. Rev. Letters. It claims that in an accelerating universe, the existence of a future event horizon puts a fundamental physical limit on the total amount of calculation that can be done, even in an infinite time. This limit is much smaller than the traditional Hawking-Beckenstein entropy. Among other things, this implies that and Moore's Law must have a finite lifetime, here calculated to be 600 years, and that consciousness must be finite."

Exception

[Zweistein_42]

"consciousness must be finite"

Except, of course, for those using certain popular mind-expanding substances ;)

Seriously though - it seems we are finding a new limit every day. Wasn't it last week that they theorized limitations on data storage, as well as data transmission speed?

enough!

[Anonymous Coward]

Moore's law was never intended to be a scientific theory. It was just a useful observation. It has never had anything other than economic incentive to keep it going. Using it to discuss the calculational ability of the universe is idiotic.

Re:Exception

[kemapa]

Why not spend less time figuring out the limitations and more time working to break those limitations? Or maybe limitations need to be set in order to break them!

Re:Roger Penrose - linky link?

[Flyboy Connor]

Penrose is a mathematician who attempts to be philospohical and fails miserably, because he can't distinguish his intuition from fact. You don't need a link. Just remember that he wrote "The Emperor's New Mind", and coil away in horror.

Re:Infinite Wisdom?

[TrueJim]

Or looked at another way, proof that any "manifestation" of a supreme being in this universe must have finite wisdom, even if somehow (however nonsensical) a supreme being "outside" this universe might still have infinite wisdom. So in order to be known to mankind, you'd need to transmit a "finite" approximation of yourself -- hmmm...

Re:And in other news...

[mjh]

This article contains a very large number of assumptions, which may well prove not to be the case (constant cosmological constant, no FTL communication/travel, no access to other universes etc. etc.). Still, an interesting intellectual exercise I suppose... ;-)

That's an interesting perspective. I haven't RTFA, but aren't those assumptions fairly reasonable? Considering that we have Einstein with a proof that faster than light is impossible, it doesn't seem unreasonable to assume it.

Maybe the article is based on assumptions. But if they're all pretty reasonable assumptions, then it would seem to be a pretty good conclusion. Or am I missing something?

Moore's Law? It's not a theory, just a curve!

[heironymouscoward]

Moore's Law is not a physical theory, it is the observation of a common phenomenon, namely the curve that technology goes through as it becomes cheaper and eventually free.

All technologies seem to obey this general law. Software, chips, disk space, they all tend to zero.

Even a passenger jet costs a fraction of what it did 20 years ago.

Moore's Law turns this around to say that for the same price we can expect more and more capacity. Long before 600 years are passed, this capacity will effectively reach "infinite", being the point where no-one can use more capacity or power, no matter what the application. At which point Moore's Law will gently slow down.

Re:Sweet

[Total_Wimp]

This is great work.

If there's a limit to consiousness on the high end of an expanding universe then we should also be able to make educated guesses at the low end and then put a front time on the resulting "wave" of intelligence.

If we have a beggining of the "wave" then we should be able to make better educated guesses about the distribution of intelligence in the universe and possible level of advancement of any intelligent life we might find. We might discover, for example, that we're reletively advanced (came early in the wave) and that we're less likely to find more advanced life. On the other hand, we may find that we're late in the wave and thus likely surrounded by life much more advanced than us.

This could be a much better way of looking at extraterrestrial life than just guessing based on the number of stars.

TW

well, duh

[Too Much Noise]

(note of caution - let's see whether this gets accepted, looks more like a Science article than a Phys. Rev. Lett. one to me)

so ... duh. This is more or less a geometrical analysis (finite causal volume) + basic information theory. No questions asked about physics of inflation and how would that affect the result. So you end up with a trivial result, too - a finite volume can only hold a finite amount of information. If a lot of other assumptions hold - such as whether the available energy in this volume is really finite (how does one sustain an infinitely accelerating model this way?)

Re:assumptions

[D-Cypell]

This is a question that I tend to think about from time to time...

I consider the vast amount of storage required for the average human being to function. Try making a list of all the faces you would instantly recognise, celebrities, friends, family, work-mates etc. The storage for that alone would be immense.

Perhaps the brain is just the processor, acting on some transdimensional storage area. Its not totally crazy right?

To take this a step further, perhaps our entire consciousness is stored externally and the brain is just the connector. Trippy yes... impossible no...

On an even more off-topic note, I wonder how many people actually spot the reference to a popular cult TV show in your sig... chalk a yes up for me ;o)

Re:enough!

[janimal]

Using it to discuss the calculational ability of the universe is idiotic.

No it isn't. It gives an excellent measure of scale! The statement that Moore's law is limited by the universe to 600 years duration gives an idea of how unimaginably FREAKING FAST our technology is expanding at the moment. 600 years in the scale of all time is a really short time.

Also, it sorta shows how far we are from the limit in terms of what we are capable of at the moment.

J

Re:Infinite Wisdom?

[wa5ter]

By existing outside the universe, and acting on it, (Through Jesus), God would invalidate the conditions of this model. (That and the pillars of Salt, the 40 days and nights of rain, etc) God is adding or removing energy from the equation.

All that aside, should God be the only infinite being, it rather bodes ill for the old 'Heaven' concept.

Re:Infinite Wisdom?

[jaoswald]

I don't think your conclusion is correct; once you've supposed that there is some extension of the universe beyond the space-time assumed in this calculation, the conclusions no longer hold.

The original calculation was made using a particular geometry of space-time. Assuming a different geometry, such as a connection to such an extension, would result in a different calculation.

Furthermore, its not clear your definition of "wisdom" is congruent to the definition of "consciousness" which is postulated in the article.

Re:Therefore God doesn't exist

[Artifakt]

It would make it impossible for God to exist IF He has to fit totally inside a finite universe. Last I looked, most claims for God also include Him being outside/before the universe.

Re:Idiot

[0123456]

But Penrose clearly doesn't understand what he's talking about either...

Re:Limits to pr0n?

[phil reed]

"pr0n" is a deliberate misspelling, intended to let the message slip past dumb proxy filtering.

Re:enough!

[janimal]

You're beyond my very limited comprehension of the universe. But, yes, if matter is being created at the centre of the universe, I can see how the amount of computation and information may not have a bound upper limit.

I wish this discussion was in the scope of the computational power of my consciousness, though. I cannot begin to fathom the implications of matter being CREATED at the centre of the universe. I don't think I fully grasp my tax return filings (I'm filing in Poland this year), much less this discussion.

Re:Exception

[jaoswald]

There isn't any kind of "figuring out" to be done. If the assumptions behind the calculation are correct, you'd have to find a different universe to live in.

That said, the limitation is far beyond what human engineering could conceivably exploit. The universe is freaking huge.

There are plenty of plain old engineering problems to be solved here on earth before we get within even an unbelievably tiny fraction of the problem posed by this theoretical calculation.

Your comment is on par with worrying that there are only 3 billion men/women to satisfy one's need for sex, and therefore needing to find a way to quickly double Earth's population. There are much smaller practical limits that are imposed by other constraints which could be modified. For example, by learning to dress properly.

My personal theory:

[theLOUDroom]

1. A computer to fully simulate the actions of a given piece of mass, MUST be of equal size or larger than the mass it's trying to do a computer simulation of.
2. This computer MUST simulate the actions of this mass at the same speed or slower than the actions it's actually trying to simulate.

Wham! There's you upper bound on computing (at least for "full" simulations).... now all you need to do is figure out how much mass and time is available in the universe :)

Note: I'm not about to propose this in earnest to the scientific community. It's just a casual musing of mine. CONSTRUCTIVE criticism is welcome.

Re:Therefore God doesn't exist

[RhettLivingston]

Genesis indicates God created our Universe. A verse in Proverbs indicates that the first thing God created was "wisdom". Most interpret that to mean the laws and rules of everything in our universe from Physics to human relationships. So, he exists both outside of our universe and independently of its laws.

Re:Allow me to point out a huge assumption

[j. andrew rogers]

"This assumes that consciousness is based solely on computation. Not proven yet."

Ignoring the strong mathematical and theoretical evidence that it is based on computation, let me ask you: What do you think "computation" is?

It is fairly apparent that you are using a definition of "computation" that is sufficiently narrow as to be essentially invalid for theoretical or mathematical purposes. I don't think that word means what you think it means.

Re:Finite Consciousness doesn't follow

[Patrik_AKA_RedX]

It is considered highly dubious that all aspects of consciousness are implied or explainable within current physics.

Only by religious fanatics. Science will eventualy provide a full explaination of consciousness, one without the need of fairytails about gods and mystical foobar. But our religious friends will probably not like it. Takes them of the I-am-Gods-best-friend-and-therefor-better-than-the -rest-of-the-animal-kingdom - pedestal down to the more humble I-am-just-a-thinking-animal - soapbox. No heaven or hell to go to after you die. So you'll be behaving yourself because you're civilized and not just to get the price at the end of the ride.

Re:Finite Consciousness doesn't follow

[Entropius]

There is no need for consciousness to arise from or be associated with anything non-physical, either. No assumption that the mind is something apart from matter has led to a contradiction. As in many things scientific, we just do not know which way it goes.

However, since the assumption that the mind is physical has not led to contradictions, and since humans understand physics better than theology (or whatever), scientists tend to stick with the atoms-are-all-you-get approach.

Nobody's arguing that materialism is definitely the case. But it's not been shown to *not* work, and it's certainly simpler than the alternative... ... and has more experimental evidence. Remember psycho bell tower sniper dude? He had a tumor on his amygdala.

Re:Exception

[Tedium Unleased]

Yeah, but if you don't start making useless claims about doubling times and whatnot, you don't get your name immortalized in the useless 'laws' that might get named after you.

Moore's Law... it's barely Moore's Observation.

Re:Roger Penrose

[anantherous coward]

Interesting argument, but if you are using it to disprove Penrose, then it fails because it is circular. When you say, "there is no reason to think that a simulation of every particle that makes up a human . . . successfully simulate consciousness," you are assuming what you have set out to prove.

Re:Shadows of the Mind

[Flyboy Connor]

This is completely off-topic so I'll keep it short.

I haven't read SotM, so I can't comment on that. My biggest problem with Penrose is that I personally am convinced that strong AI can be achieved, while Penrose believes that it is impossible. That does not mean that the book can't be good, but Penrose doesn't do a good job matching his arguments with those of his opponents.

He has a tendency to repeat arguments that strong AI supporters give, but in a way that they can be misunderstood, and then he misunderstands them and basically says they are stupid. Already in chapter one of ENM he starts ridiculing strong-AI supporters, without giving arguments. Later those arguments follow, but they are seriously flawed.

For example, while discussing Searle's Chinese Room experiment, he suggests that strong-AI supporters believe that "understanding Chinese" is in the book, and argues that it is stupid that a book can "understand" anything. But Turing's view (which is repeated by many others) is that the understanding is not in the book, but in the book + the human that reads the book. There is an emergent understanding of Chinese that comes from a book that describes how Chinese can be perfectly translated, and a human who strictly follows the rules that are written down in the book. This argument is mentioned by Penrose somewhere, but he just puts it aside as a very weak argument, that does not need refuting.

Writing like this annoys me immensly, and I suspect most my colleague AI researchers.

Incidentally, I think Penrose' work in mathematics is absolutely brilliant.

Re:Shadows of the Mind

[STrinity]

My problem with Penrose is this -- there's no reason to believe that human consciousness is anything more than the result of purely mechanical processes in the brain. If so, then we should theoretically be able to reproduce a human mind on a sufficiently fast computer. Whether that's practically possible is another matter.

Penrose, however, simply denies that consciousness can be electronically replicated even in theory. When asked why, he waves his hands and shouts "Quantum physics!" Now while it's certainly possible that quantum phenomenon play some role in consciousness that can't be replicated by a computer, there's no real evidence for the position and Penrose is just arguing it a priori. It's sort of the metaphysical equivalent of Creationism.

Re:Infinite Wisdom?

[Dog135]

The second law of thermodynamics apply to this universe. Not necesarily heaven.

Think of it this way: You write a program using a genetic algorithm to solve a problem. The rules used to generate the algorithm would later be ignored, and the final algorithm would be used without any change or degregation.