Slashdot Mirror
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."
This doesn't mention Penrose's work, which is very much like this.
"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?
- To err is human; but to really screw up, you need a computer
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.
We should now be able to compute the asymptotic limit of web-server bandwidth for slashdot-proofness per year for 600 years. I bet it's a constant price in street dollars.
I was a physics undergrad at Case, and actually had Starkman as a professor for a mathematical physics course. I have chatted with Krauss a few times since graduation on science topics involving public education. These are good guys, glad to see them headlining slashdot this morning.
"and that consciousness must be finite."
So they are saying that, using fundamental physics and mathematics, they have proof that if somebody has infinite wisdon, the universe can not be expanding?
--- Hindsight is 20/20, but walking backwards is not the answer.
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... ;-)
Galileo: "The Earth revolves around the Sun!"
Score: -1 100% Flamebait
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.
Please use the mirrors. In Australia, the closest one is here.
Can you even define consciousness?
Are we talking about the physical computational capacity of a headful of neurons, which is finite by definition unless you believe that the brain can somehow reach into unknown dimensions somewhat like early CPUs used bank shifting to increase their RAM range?
Or are we talking about the sensation we have of being alive, a sensation that is arguably simply generated by our brains as a mechanism to ensure our survival. Yes, the vaunted consciousness that reacts a full 1/4 second after the fact when we do most common actions such as crossing the road, kicking a ball, picking up a cup, or typing comments to Slashdot?
The definition of "consciousness" is seriously under debate and it's meaningless to discuss whether it's finite or infinite.
Most likely, consciousness is a sense, like sight or sound. Would you frame the discussion of your sense of smell in terms of computational power? No, me neither.
Mu.
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Strongly suggest you read Vernor Vinge's A Fire Upon The Deep - he develops a very interesting view of expansion of the universe and consciousness.
If you've not heard of Vinge before that isn't a big surprise, but he did write True Names as well - the very foundation of the cyberpunk/hacker genre. This is also a good read if you can actually locate it.
I am very easy to get along with, but I don't have time to waste being nice to people who are being stupid. -Theo
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.
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"...consciousness must be finite."
This assumes that consciousness is based solely on computation. Not proven yet.
And for that matter, even if consciousness is nothing more than computation, how can we put a limit on an activity in space-time when we don't even know how space-time functions, or even how many dimensions it has?
Weaselmancer
Weaselmancer
rediculous.
(note of caution - let's see whether this gets accepted, looks more like a Science article than a Phys. Rev. Lett. one to me)
... 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?)
so
It's like at the bar -- the later in the night you attempt to pick up chicks, the fewer of them are still available.
but so far there's nothing to suggest that consciousness is based within the brain, let alone is computational. Sure there's evidence to suggest that consciousness is based within the brain. If the brain is damaged, consciousness can be removed or reduced (level of). That alone is a strong ling that consciousness is brain based. Enough brain damage and one can die or be reduced to a vegitable, metaphorically speaking. That seems to be a distinct reduction in consciousness. Smaller brains seem to have varying but usually lesser degrees of consciousness. Dogs have some level of conscousness, but it doesn't seem to be to same degree as, say, humans or even chimps. Defining consciousness itself is difficult, though. Is consciousness merely intelligence? Intellectual capacity? Awareness of surroundings? Memory? A combination of these? Something else? Something else is a slippery slope, though, as one can define consciousness as something which is intentionally unmeasurable or unknowable.
There are some intersting ideas as to what the end of the universe could be.
There's also another theory about that if a couple particles collide with enough energy they can create a more perfect vacuum that would essentially "take over" the current universe (I suppose like an implosion). Maybe somebody knows the link for this.
I mention this as a backdrop for an interesting short story by Isaac Asimov called The Last Question. This link is a summary and contains significant spoilers, you may want to read the story first I think that it is apropos, as it deals with a powerful computer called Multivac.
This story is interesting to read, and interesting humanistic view. Good for pondering this slashdot thread/story. Good science fiction is useful.
Take the cheese to sickbay, the doctor should see it as soon as possible - B'Elanna Torres, "Learning Curve"
Not commenting on the paper itself, but it has been submitted to PRL, not accepted. It hasn't gone through that wonderful process of peer-review that is the very heart of the scientific method (that and falsifiability but thats another topic). NASA has been setting a particularily bad example here with science by "press release". PRL is not an easy journal to publish in, lets wait until other experts have a look and not cheat the scientific method like this. PRL should not be mentioned in connection with this paper until this get published - Anyone can submit a paper to PRL...
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.
Who is John Cabal?
But Penrose clearly doesn't understand what he's talking about either...
If there's only a finite amount of computation available, surely it's irresponsible to run things like SETI and the distributed.net cracking contests?! You're using up all of the sums, dammit!
Ydco co
"I guess the main argumentation of Roger Penrose is that Godel Incompleteness Theorem can not be understood by a computer,"
Penrose is just a carbon chauvinist with a chip on his shoulder. I've never seen him once offer actual proof of any such conjecture, only carbonist assertions that he can magically understand something that silicon-based life cannot: our future silicon overlords have a special place in virtual Hell reserved for his uploaded consciousness.
Penrose probably doesn't even understand what Godel's Incompleteness Theorem means. Hell, the fact that most people credit Godel with proving the incompleteness of formal axiomatic mathematics is proof that most people don't know math. Skolem's paradox can be seen as the first incompleteness proof and it predates Godel's proof.
:) No inconsistency here. No incompleteness here. All math is computable!
Skolem's paradox basically boils down to the fact that within axiomatic set theory you can prove the existence of uncountable sets, but if a model exists for the theory then it is countable. Hence according to the axiomatic system, there exist uncountably many sets, but the system can really only manifest countably many sets. This is similar to how Godel showed that formal arithmetic cannot manifest proofs for every proposition the formal axiomatic system claims exist.
While Skolem's paradox is held amongst by many mathematicians as the first incompleteness proof, in my opinion, this proves something much more significant... it proves that axiomatic set theory is semantically inconsistent.
Set theory has been problematic from the start, and even after axiomatizing it in order to avoid simple inconsistency... set theory is still plagued with inconsistency of a different form: the formalisms don't hold any meaning - they are semantically inconsistent. What the formalisms say contradicts what the formalisms mean.
The problem is that lots of people don't understand math, and even many of those that do understand it, love it so much that they are unwilling to give up the flawed parts.
For me, mathemathics is constructive recursive mathematics
Heh, heh. I guess that would be the "Schrodinger's Messiah" thought experiment.
They claim that every computation step requires at minimum energy of ln 2 k_B T (k_B is Boltzmann's constant, T is the temperature of the system). This is only true for irreversible operations such as setting or erasing a bit.
But computation doesn't have to be irreversible. There are various proposals on how to build reversible computers that don't consume this minimum energy per operation. More information about reversible computing can be found in this introduction.
OS Reviews: Free and Open Source Software
So, how many bits do I need for a symmetric cipher key in order to push a brute force search past the computational limit of the universe?
Ummm.... no. Godel proved that the axiomatic system of Russel's PM allows the construction statements which can neccessarily neither be proven true nor proven false. There are other axiomatic systems that can be complete and consistent; IIRC it was in fact Godel who proved that the first-order propositional calculus is complete and fully consistent. Godel's fork only attaches to systems that allow the construction of statements about statements; many propositional systems (like the first-order propositional calculus) do not.
Oy.... where to start? Kant's Critique of Pure Reason is nothing but 600 pages describing how people distinguish intuition from fact (though admittedly Kant was using "intuition" in a sense that we don't normally use it today). Descartes wrote his Meditations as an attempt to remove "intuition" (again, closer to Kant's sense of the word than ours, but still) from philosophy. Plato, of course, says nothing about the subject directly but narrates several dialectical processes about the subject.
All's true that is mistrusted
Er, no. At least, not within the known bounds of quantum mechanics. Your mileage may vary.
What we perceive as a continuously variable analog world just happens to have a *lot* of very closely-spaced discrete states. Each time you add volume, matter, or energy to a system you increase the number of available states by a large, but still finite, amount.
A wave could have a frequency of 1Hz, 1.1Hz, 1.00057Hz, 1.2399327772883786682676376627676367267Hz, etc. If "computation" is defined as "the act or process of evaluating with numerical or mathematical methods" then there is no physical limit to computation when using analog data storage...
Here we run into quantum mechanics once again. To take the measurement of the frequency of a wave, for instance--how do you resolve a difference down at the one part in a quintillion level? Essentially you run afoul of uncertainty principles. To reduce the uncertainty in your measurement of frequency to a low enough level to resolve such small differences, you have to pay a price in measurement time. Actually, you have the same problem when you write your data in the first place. See also my remarks about number of accessible states--storing an analog wave with a finite precision will require a certain amount of matter and energy, neither of which is available in infinite amounts*.
*probably...
~Idarubicin
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.
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.
Les Miserables Volume 1 now up with my reading of