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The Ultimate Limits Of Computers
Qui-Gon writes: "Found an interesting article about the 'The Ultimate Limits of Computers' over at Ars Technica. This article is very heavy on the physics of computing, not for the faint-hearted." Somewhere between practical reality and sheer Gedankenexperiment, the exploration here keeps getting more relevant as shrinking die sizes and improving nanotech wear away at previously impassable barriers. The article is based on a paper discussing the absolute limits of computational power.
Who says that a complex problem needs a high number of state changes?
Each state change could be the result of a very high level operation, not something primitive like adding two numbers, but perhaps something like the outcome of the traveling salesman problem. Think of some clever physical setup here.
It will be due to the cleverness of the computer builders, to make most use out of the limitations.
Regards, Marc
First, thanks for the feedback.
Now, it is quite possible that I have made errors in my article. I've gone to some pains to avoid them, but things might have slipped through anyway. One never knows.
However, I do not think the matter you raise is an error. Allow me to try to explain.
First, you must keep in mind that the article is an exploration of theoretical limits, not practical ones. Practical considerations are well and good if you want to actually build such devices, but that isn't what I was intending to explore. What I wanted to talk about (and did talk about) are the absolute maximum speed limits for computers. These are almost guaranteed to be ridiculous and impractical, but as a limiting case, I think that they are still interesting.
The calculation is based on the idea that 1kg of matter has a certain maximum energy associated with it, and that maximum energy is given by Einstein's formula. Because it turns out that the theoretical speed limit of a 'computer' (which as the term is used in the article is simply anything that processes information, basically - particular architectures aren't considered) can be related to the time-energy uncertainty from quantum mechanics, it is then necessary to find out how much energy a given lump of matter can contain. And that's given by the whole E = mc^2 business.
Of course this limit is not practical. It's a theoretical upper bound. I haven't the faintest idea as to how you'd go about converting 1kg of matter into energy controllably (without, say, temporarily warming up the climate of the city you're working in), or how you'd control it enough to make it compute something you're interested in, and so on. The point isn't to look at the practical limits (those are better looked at from the perspective of current technology, i.e., Moore's law and whatnot, in my opinion), but rather the general theoretical limit.
Just as a note, you may want to look at Lloyd's paper, as the ideas for the calculation are his, and I'm just summarizing and reporting them. (Lloyd's paper, by the way, is very well written, and it's recommended reading for just about anyone who isn't scared away by some equations).
But if the above explanation doesn't satisfy you, please post why, and perhaps you can convince me that I (and Lloyd) are in error.
Cheers, -Geon
geonSPAM@arsISBORINGtechinca.com
I've just joined a research group at my University to study reversible computing. The professor in charge wrote his doctoral thesis on the subject at MIT.
.. XOR is always reversible, etc. So, a reversible CPU will probably have a more constrictive instruction set, but is still functional.
The concept is that a "normal" CPU erases information on every cycle (clearing registers, overwriting data, shifting data to nowhere, etc). When a CPU erases information, it's dissipated as heat. There are thermodynamic limits to this (kinda like Moore's law). So, if a computer could be designed not to erase data, you could reverse the CPU and get most of your energy back.
Now before you say "BS", think about it. In physics, if you know the initial state (starting position, velocity, acceleration) of an object in an isolated system, you can easily compute where it was at any given time earlier. This uses the same concept. For example, If you add 43 to a register, you can subtract 43 from that register and get your energy back.
Of course, certain instructions don't lend themselves to reversibility. For example, bit shifting is inherently irreversible. One option is to maintain a stack of "garbage data", but that's a poor solution. On the other hand, a number of instructions are reversible by default.
Reversibility is not anything new, but it does take a shift in thinking. Algorithms can be designed to run very efficiently on reversible computers, but it takes a bit more effort. Hopefully, we (the community of people studying reversible/adiabatic computers) will develop means of either converting irreversible algorithms or develop ways to make them less innefficient (double negative).
-Andy
"640K ought to be enough for anybody. "
- Bill Gates (1955-), in 1981
try { do() || do_not(); } catch (JediException err) { yoda(err); }
> There are thermodynamic limits to this (kinda
> like Moore's law).
I think you meant to say, "almost, but not quite, entirely UNlike Moore's Law".
No, the limitations that technology can overcome are engineering limitations. The limitations talked about in the article are basic fundamental physics limitations that don't depend on any particular form of technology. Note that nowhere is it said that the problem is the size of the tracings on the microchip, or heat dissipation, or whatever. It's all a matter of any physical system having a bounded energy having a corresponding bounded rate of state change. Saying that there will be another technological revolution that surpasses this is like saying we'll be able to cool things below absolute zero when we figure out how to build better condensing coils for our refrigerators.
From the: Damn-that's-neat-but-what's-the-point dept.
:)
Wow! That's some neat physics (only a part of which I understand). But really do you think we'll need to get anywhere near these sizes and amounts?
The time will come when the theory has advanced far enough that we'll drop the Von-Neumian-style of doing computing and go with something a bit more, shall I say, better? The human brain certainly doesn't have anything near those figures of capacity, and it's about 1-2kg, occupies about 1 L^3 of space.
And I don't know about you, but I LOVE the graphics. They are kicking some major ARSE. The refresh rate could be a bit higher, though, I still get blurry vision when stumbling home from the bar.
Blog,Twitter
hmmm
That is the equivilant of 542,580,000,000,000,000,000,000,000,000,000,000,00 0,000 1Ghz CPU's.
I think we're covered for awhile.
Someone you trust is one of us.
In his article he claims that "The maximum energy an ultimate laptop [1kg] can contain is given by Einstein's famous formula relating mass and energy: E = mc2. Plugging in the laptop's mass, the speed of light, and combining the result with Eq. 2 tells us that the maximum number of operations per second a 1 kg lump of matter can be made to perform is 5.4258e50."
i'm assuming this is at 9e16J per second, which means to make his "ultimate laptop", he would have to split the atoms of 1kg of any material per second... which means he would need to carry a large nuclear power plant around with him (even then, I don't think they go through 1kg/s).
What he fails to understand is that Einstein's formula is an equivalence, not a potential. Maybe that is the maximum energy a mass can have, but to get at that energy (in J/s) you would have to split enough atoms that that mass was lost (your 'laptop' would get 1kg lighter every second). Unfortunately, his whole article is based on this principle, so you can't use anything he says unless you plan to sustain a nuclear reaction which loses 1kg/s in fission to power this "ultimate laptop".
He correctly used the values in the formula, but he didn't apply it correctly. Maybe he should have done a bit more research.
They that quote Benjamin Franklin on liberty and safety deserve neither.
If this picture is correct, then black holes could in principle be 'programmed': one forms a black hole whose initial conditions encode the information to be processed, lets that information be processed by the planckian dynamics at the hole's horizon, and extracts the answer to the computation by examining the correlations in the Hawking radiation emitted when the hole evaporates.
Wow! Imagine if we could make a computer as large as Earth... I believe a computer that big could calculate the answer to the question of the meaning of life, the universe, and everything!
And don't even get me started on what we could do with a Beowulf cluster of those things...
NO CARRIER
He had a great graph of the last 30+ years of GB/square inch, which seemed to coincide with Moore's Law (which, just like this article, addressed processing issues, I know. Bare with me here.). There were red lines drawn every ten years or so representing what scientists had believed to be the superparamagnetic barrier - the point at which it would be physically impossible to cram any more data onto a disk.
The guy had a great line every time one of these came up. "In 19XX Dr. XYZ at ABC University discovered the superparamagnetic barrier.... We broke it X years later." (X was usually a single digit.
My point is that it will be interesting to watch if these "scientific" finding will not require revision. True, this one may be based on sound scientific principles, but so were all those who attempted to predict the superparamagnetic barrier.
I'd rather have someone respond than be modded up.
I find it interesting that, for the most part, Moore's law has been an accurate indicator of future computing speed, and the accompying engineering and theoretical knowledge needed to reach that speed. It is amazing to think that, if the law hold up, in 200 years we would have the physics and engineering needed to build such a computer, and perhaps the knowledge to know what steps to take to make an even faster computer!
The logical solution seems to be to tap into parallel universes (quantum calculations done in a massive parallel fashion?). It also seems that intense sheilding of some sort would be needed, both to keep quantum influences out, and to keep the user from being incinerated. Unless you didn't care, because your computer was outputing to some insignificant parallel universe. Even line-of-sight lasers would be too slow of a bandwidth, since the output would be 3-D light.
Just think, about 300 years from the first radio signals to black-hole computers - no wonder Seti@Home is failing - all the aliens are playing CounterStrike on their black-hole systems! Who would have guessed that the dark matter was simply off-site storage for 5-D pron?!?
The author indicates that computing is limited by quantum mechanics and that we have quite a while (many, many years) until we reach that limit. Well, I suspect that many, many years in the future, researchers will have found yet another way to perform 'computer processing', faster and more efficient than quantum processing.
Nosce te Ipsum
"What was that?"
"Ah, just another script kiddie trying to DOS the database."
"I don't understand. He just upped and exploded."
"Yeah, his quantum computer heated up to the temperature of a supernova and then collapsed in on itself like a black hole. Happens all the time."
"Really?"
"You should see it when they try to encode movies with DivX!"
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You're still talking about practical concerns here? This calculations is simply an upper bound upon the amount of processing that can be done with 1kg occupying 1liter of volume. Nothing more. It's purely about information processing, not even about "computers" per se.
Besides, even if it was concerned with how this might be acheived, how the hell is he going to work all that stuff out? Obviously, such technology would be way beyond what we have today, so there's no way for him to use realistic figures. So trying to add practical details is a waste of time, kind of like trying to calculate how fast we'll be able to travel in the future. We know the theoretical limit (the speed of light), but we can't say what technology will be available in the future and so cannot make any useful predictions.
Every year we seem to think we know every thing there is to know about physics, biology and any other science.
You don't know many scientists do you? :)
If your assertion is true, then why would they bother doing it? If there was nothing left to know, then there would be no point in being a scientist, and no new research projects coming up.
We are convinced that our current theories are laws of nature.
The term "law of nature" is pretty loaded, and I doubt it would apply in many cases. And even then, such laws aren't universal. Consider Newton's "laws". Although they're called such, they're only applicable in certain domains (speeds much less than that of light, relatively low masses) and are only approximations to relativity. Similarly, our current physical theories (general relativity and quantum field theory) are only approximations to some higher theory which contains both. No scientist is convinced what we have now is the final "law of nature".
And every year some discovery shatters that belief in a given discipline.
I'll admit there have been, and probably always will be, some pretty amazing new discoveries that do come as a big suprise, but shattering belief? I think not. If anything, they often serve to spur on research into the various fields.
Whilst scientists can easily be as guilty of hubris as anyone else, you're portraying them in a far worse light than is deserved IMHO.