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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."
"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
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.
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...
I hope that after I die the one word people use to describe me is "resurrected."
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 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
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...
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
Here's Turing's counter-example to bust Penrose's theorem:
If a machine (human in this case) can simulate a single Turing machine, and a Turing machine can simulate it, then it is exactly as capable (though perhaps not as quick) as any other Turing machine.
The first part is easy to prove: Any student who has learned Automata Theory should be able to simulate a Turing machine in their head, though it will be VERY slow and tedious.
The second is harder, but there is no reason to think that a simulation of every particle that makes up a human, plus a small environment (air, ground, food, water) around her/him will successfully simulate consciousness. The fact that today's computers are not strong enough doesn't invalidate humans being bound to a Turing machine's capabilities.
Any Turing machine is computational, therefore if the applications of Turing's thesis to humans holds, humans, and every part of them, including consciousness, are computational.
As far as Heisenburg's uncertainty theorem and quantum mechanics goes, it can be inserted into the simulator using rand().
Godel's Incompleteness Theorem doesn't apply to Turing's Theorem. Godel is talking about that there exists inconsistencies in any sufficiently complex langage (ie., the statement "this statement is a lie."). It doesn't contradict Turing's Theorem, since to disprove Turing's Theorem, we'd need to find a Turing machine that is incapable of simulating another Turing machine. All Godel says is that there will be non-sensical or impossible states in any Turing machine, but the machine can still work. (the proof that they exist is that English syntax can be programmed into any Turing machine, and the "this statement is a lie." statement inputted into the machine).
And as far a philosophy goes, so what if I'm limited to 2^2^40 states. I'll never get anywhere near experiencing all of them in the life of the universe, assuming I live that long. And in the same way that computers can execute computer games with fantasy themes, a computation human has nothing interfering with dreaming, pretending, or religion (though it might point out the silliness of latter).
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