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."

Comments

Roger Penrose

[andy666]

This doesn't mention Penrose's work, which is very much like this.

Re:Roger Penrose

[julesh]

I haven't seen anything by Penrose which is like this. In fact, this article states an assumption ("consciousness is fundamentally computational in nature") that directly contradicts Penrose's most well known result, a rather dubious pseudo-mathematical "proof" that consciousness _cannot_ be computational as a consequence of Godel's Incompleteness Theorem.

So, no, it isn't really like Penrose's work.

Re:Roger Penrose

[wytcld]

Penrose in recent years isn't saying "consciousness isn't a computer." Rather in collaboration with Stuart Hameroff and a number of physicists is saying that "consciousness is a quantum computer."

So for all you /.'ers whose first reaction is: "He says we're not computers. Uncool!" consider the contrary reaction: "He says we're quantum computers. Way cool!" Also note that, as all /.'ers should know, quantum computers don't have the same limitations as conventional computers on capacity, thus the well-known threat they pose to encryption, being able to break it (in theory) in trivially short time periods.

Re:enough!

[spangineer]

Exactly - Moore's law is certainly not a real scientific law. It often approximates what actually happens, but because it's based on human activity, it's not very precise. Humans are unpredictable, and thus, cannot possibly be the basis for a scientific law (as far as I know)

Law 6 a : a statement of an order or relation of phenomena that so far as is known is invariable under the given conditions b : a general relation proved or assumed to hold between mathematical or logical expressions.

arXiv reaches it's computational limit!

[mattjb0010]

Please use the mirrors. In Australia, the closest one is here.

Re:enough!

[jcoleman]

Ummm...read that again. Moore's Law is not the basis of this paper. Physicists and mathematicians using economic theories (yes, Moore's Law is economic in nature) to predict physical laws are neither published nor credentialed. The finiteness of Moore's Law is an implication of the findings of this paper.

A Fire Upon The Deep by Vernor Vinge

[puzzled]

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.

Re:enough!

[julesh]

Have you read the article? All it states is that no civilisation could possibly extend Moore's Law beyond 600 years. That's the only reference to Moore's Law in the entire article, and its a reasonable one. It puts into terms we can (just about) understand the implications of the discovery. Who knows what 1.5 * 10^220 bits of information processed is? But 600 years of development at the current rate is slightly more imaginable (although, I'll admit, only marginally so).

This paper has not been published

[jludwig]

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...

Re:Roger Penrose - linky link?

[Theatetus]

Kurt Godel DID prove that mathematics is infinite. No matter how many rules and computations, OF ANY KIND, that you write down (or program into a computer) those rules can't be complete and consistent.

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.

because you imply that a person should be able to distinguish intuition from fact. That this is a basic error has been pointed out by: Plato, Descartes, Kant, Husserl

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.