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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.
Suppose you could have a large cluster of small computers to compute things which are highly parallelizable. This cluster should probably be arranged in a sphere to make the computers as close together as possible. The source of computation requests would probably be placed in the centre of the sphere. So the turnaround time of the computers on the surface of the sphere is then bounded by the time needed for light to travel the radius of the sphere twice. To keep the outer computers busy, you need a longer queue of processing requests. Any pointers to papers about this?
I'd like to see an analysis for the breakeven point; for what problems would a sphere of a given radius containing computers of a given speed provide a speedup, such that any larger radius would diminish the return, despite adding to the aggregate computing power?
Reversible computers don't drain the charge to ground. One major goal is minimal power use, which means that, whenever possible, you don't discharge anything. In particular, you want to move the charge from one capacitor to another instead of to ground; which of the capacitors is determines whether the bit is a one or a zero.
Of course, there are only certain operations you can do without discharging a capacitor to ground or charging it to Vcc. And there's obviously some energy expenditure in the resistence of the wires, capacitor leakage and the effort of getting the computation to go forward.
Note that the given speed limit is on state change rate. Those states could represent much more complex operations than simple arithmetic. All in all the article is nice, but I enjoyed the one on Hans Moravec's page more, where Feynman pondered about the ultimate library. Regards, Marc
But like writing fast or dog slow programs with a given programming language, there might be very different approaches (regarding computational power) to use the physics for building fast computers.
Thus there is a physical limit, as well as a logical limit (theories of computation and complexity) to consider.
And of course it depends totally on the problem, if parallelism can be exploited.
Search for "reversible" in this article.
Your example is one, that can't take advantage of parallelism. I would rather give an divide and conquer type algorithm (like sorting) as example for recursion and parallelism.
Actually short times allow for high energy fluctuations (dt * dE >= hbar), this is the very basic reasoning for the existance of short lived (so called virtual) particles in quantumn field theory, with its complications on the number of particle being not constant in physical process and the fact that one can not observe bare bone particles.
This could mean that fast processes have to deal with disturbance from such energy fluctuations, providing physical limits as well for fast computing.
Considering the physical theory (here: non relativistic quantumn mechanics, which is still an approximation of nature) used to derive the limitations is sufficient.
You imply that I challenged this physical upper limit on state change rate in this discussion, but I did not.
My point is different. It goes down to the question about the relationship between rate of state changes on one hand, and the ability to perform a fast computation on the other hand.
The naive view is similiar to the view many cpu buyers have in regard of clocking speed. It goes along the line "The more MHz, the faster the CPU". As we know, this is not a valid measure to compare for example a Pentium IV and a PPC CPU. They are not comparable by clocking speed alone. Eg the one cpu might perform a floating point multiplication much faster than the other cpu in terms of clock cycles.
The classical theories of computation solve this problem, by mapping programs onto a very simple model of a computer, the Turing machine or register machine, or real RAM and then doing comparisions. The operations in these models are precisely defined, like incrementing a register, or decrementing a register, or testing if it is zero.
As we know there, a computation needs a certain number of basic operations as well as a certain amount of memory. Classical complexity theory tells us, how exactly memory and number of needed operations are related for these easy computation models. In fact both are subject to the "size" of the input data as well. Like I said, this only well understood for these deliberatly simple choosen computation models (Turing machines etc).
In this discussion, we were talking about limitations of computing. It makes sense to think about the most powerful computing architecture envisioned so far. And that is the model of quantumn computer at present. In this setup your computer is a quantumn mechanical system. Your input data corresponds to the initial states of the system, your computation is a measurement of the system, this meaning a physical process that kicks the system from its inital state into its final state, the final state encoding your result data.
The trick with quantumn computers is that one arranges that measurement to reduce a large number of possible solutions/states into one final state. This is decribed sometimes as doing all computations at once.
You will immediatley notice, that computation in this setup is achieved by exactly one state change, the measurement that kicks your system into final state.
Now lets translate this abstract mumbo jumbo back into real things. The first quantumn systems explored were some couple of nucleii in a big magnet, a NMR mesurement device. Initial state corresponds to some inital states of these nucleii, typically their rotational and spin degrees of freedom. Measurement means bombing these nucleii with some electromagnetic radiation and looking for the states of the nucleii after that.
What must be achieved by the experment is, that we must be able to map the input data of a problem onto the initial states of these nucleii. The output states must also correspond to a solution of the problem under consideration. Further the measurement process must correspond to the solution procedure of the problem.
As we have ttl logic gates for simple operations like AND OR NOT, researchers have to think of building quantumn logic gates. Thus systems that can handle input data with their initial states, where act of measurement corresponds to some useful operation on the input data, and the output states can be translated back into a nice result on the input data.
Question: What kind of operation can be encoded by such an experiment?
Actually I don't know. I believe however that it might be a very complex one. Take for example a chain. It just hangs down and by this finds an optimal solution to a variational problem. Or fire some photons from air into water, the travel in way, that corresponds again to the solution of a hairy differential equation. Or a chemical reaction with many molecules can solve some crazy combinatorical problem in a couple of microseconds.
The topic touched here, is the topic of representation. Everyone with a decent level of math knows, that there are different representations of the same problem, the one harder to solve, the other easier. In fact this on of the basic problem solving strategies in applied mathematics:
- find a representation where a problem is easy
- transform problem into that context
- solve problem in the easy representation
- transform problem (and solution) back
Examples are diagonalization of matrices or finding of the inverse of an integral operator (eg Green's functions in partial differential equations) by Fourier transformation, algebraic invertation, and Fourier back transformation.So in this regard I want to argue that we can choose different physical setups that might enable us to do a more or less complex computation in one state change.
So it is not only about quantity (number of states changes) but also about quality (what computation is performerd with this change).
You Sir, misunderstand what this kind of theoretical computer science is about.
It is using a mathematical theory: using mathematical objects like sets and mappings, a simple mathematical model is formulated. Then one tries to analyze the implications of this model by application of the laws of mathematical logic.
The mathematical model you are talking about is the register machine or Turing machine (or a model of equivalent computational strength). What you cited in upper case is a logical consequence, a theorem or lemma, thus a truth for just this model.
What makes this computer science and not plain mathematics is, that we believe that these simple models are adequate representations of what we think computers and computations are.
One of the fundamental assumptions of these models, and that is why I call them classical computational models, is that they are based on a thinking that corresponds to the common sense thinking of classical physics. Like you said, these models assume that only one fundamental operation can be performed in one time step (clock cylcle, whatever unit of time). But, as Feynman never stopped to preach, nature is not classical! It is much more strange. Experiments verify that nature has some weirdnesses only accurately described by quantumn mechanics or theory of relativity so far. These are results that are not compatible with commons sense, but are still compatible with the mathematical models of theoretical physics, thus compatible with mathematical logic. And that is where quantumn computing comes into place. What happens if one makes use of this strange effects, like two photons that seem to interact with no time delay, although they are far apart, or the phenomenom what is colled as collapse of the wave function in quantumn mechanics, to build a faster computer?
Somehow quantum computers are supposed to make this nondeterministic which means that given a single state I can be in multiple states after the next step, and somehow the right one is picked out at the end.
You surely heard of Schroedinger's cat. It is a truth from quantumn mechanics, that systems can be in an entangled/mixed state and that only the act of measurement/looking will put it into an decisive output state. The act of measurement itself is one of the conceptual weaknesses of quantumn mechanics. Most physicists just take for granted that it happens and know how to deal with it in calculations and experimental setup. The theory behind it is hardly distinguishable from philosophy. (As far as I understood, it is the problematic of observed system and observer who really can't be seperated into two entities, with two wavefunctions, but are connected, and thus would be described only be a common wavefunction. This way it is hard to get results. We would ultimately have to analyze the wavefunction of the whole universe to get results. Thanks god, this not necessary most of the time, the conceptual separation of the universe into seperate physical subsystems is often useful)
As our minds were evolved in a environment that is mostly goverend by classical physics, we have really trouble to grasp such strange truths. We know the formulas and are able to set up experiments and get results, but this no intuitive understanding. To quote Feynman again, he was sure that nobody understood quantumn mechanics.
The radical idea behind quantumn computing is to take advantage of these strange effects. (strange to us classical minds, perhaps not strange to some hypothetical life form evolved in an environment where quantumn mechanics would be dominant in every day life)
I just don't buy into taking a deterministic model of computation (which the article seems to be using) and expecting it to crank out the general travelling salesman problem in any reasonable time.
It is hard to common-sense recognize that while the quantumn physical processes are governd by probabilities, the laws that govern these probabilities are exact. For example a given process might have a random outcome, but still I can deduce from the laws that it must have a probability less than 1/3, and can make use of that given bound in the construction of my machine. You see, randomness does not mean, that there is no prediction possibly, also the kind of predictive strength is much less than in classical physics, it is still much beter than using a crystal ball.
Due to their propabilistic natures, quantum computers were thought to be very instable and not able to yield deterministic results.
The first crucial idea of quantumn computing was Feynman's (?) idea of recognizing classical computation/complexity theory as based on assumptions of classical physics and thus exploiting the not before used quantumn mechanical behaviour computationally, as described above.
The second crucial idea was Peter Shor's idea of using error correction strategies in the context of quantumn computing. As I understood, this was the theoretical break through. That idea provides the needed stability.
Shor by the way, was also the guy who proposed the prime factorization algorithm that was qualitativly better than anything classical computational/complexity theory said.
Actually, the preparation of the initial states is already part of the quantumm computational solution procedure.
For example the idea behind a quantum computer doing a massive parallel database query would be to have all possible search results feature in the superposition of the inital states of the system.
The query would be the measurement that picks that state as final state, that represents the match.
These problems can be mapped onto bits and these can be mapped into the qbits of a quantumn computer.
If we had to tour 2^n cities, the data set would consist of tuples (city1, .., city2^n).
We could map that onto 2^n x 2^n = 2^2n bits.
So we would need a 2^2n quantum bits in a quantumn computer, that represent the 2^(2^2n) possible outcomes.
This boils down to question if it will be possible to get such a large number of qbits in superposition. I believe nobody knows if this is physically or technically possible.
We also don't know if there is some experimental setup, whose measurement would collapse that superposition into the optimal TSP soulution.
Perhaps a whole series of more fundamental computational steps/measurements needs to be done by a quantumn computer.
Like I wrote above, I don't know what kind of basic quantumn computing operations are possible to built, but I believe that it could be more complex ones that simple increments. I am sure a look over the fence into the domain of analog computing would give some useful hints of what might be possible.
Even if you use the physical analogue of creating lengths of strings tied together at the various city nodes and pull the "cities" in question until the strings are tight and selecting the tight path, every atom moving in the process is a state change
It will possibly not such a simple mechanical setup but some much more crazy arrangement of basic quantumn computing components, that implement abstract operations. Perhaps it is not a single state change but it might turn out to need qualitativley much less than an algorithm on a classical computer.
And even if you prove that P=NP, you still need an algorithm that traverses the data, examines it, compares different links, etc, and every step in the algorithm is AT LEAST a state change
The reasoning from classical complexity theory shows that the work of digesting the input data is part of the overall work, an algorithm performs. But it is also true, that the models assume that one symbol of input data is digested at a time. Perhaps the inherent paralellism of a quantumn computer can save effort here to, by having some read-all-input-at once feature. I simply don't know.
Hm.. I should really try to get an expert to judge this discussion.
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
Equations 1 and 2, etc. do not require conversion to kinetic energy of any kind; they're just restatements of the fundamental de Broglie wavelength:
E = h-bar * nu
from high school physics. This gives the light wavelength if the object is a photon (zero rest mass), otherwise this wave effect is called the "probability wave" and is reputed to have connections to alternate universes, etc.
It doesn't matter if E is rest mass or kinetic energy; the wavelength effect is the same, and in fact originally derives from special relativity. Heisenberg's principle is essentially a statement of the resolving power of these waves, for instance in electron microscopes, or in any measuring instrument. Equations 1 and 2 say that one can't measure much more often than delta t, which is fairly straightforward since one is working with waves whose period is at least delta t.
---- "If we have to go on with these damned quantum jumps, then I'm sorry that I ever got involved" - Erwin Schrodinger
The upper bound is on the number of measurable physical states that any physical system with mass 1kg can attain in a certain time period.
The verbiage about E=mc^2 is redundant, the author is simply restating the fact that E in equations 1 and 2 is, and has always been, relativistic mass-energy, not what appears on your PG&E bill.
---- "If we have to go on with these damned quantum jumps, then I'm sorry that I ever got involved" - Erwin Schrodinger
You're misstating the definition of E in equations 1 and 2. E is not "maximum energy", it is defined as the exact mass-energy of the physical system, in this case 1kg. The speed of a computer is not limited by the energy available to it, it is limited by the mass-energy that is in it.
You might rephrase it by something like "Since E is the total mass-energy of the laptop, a simple unit conversion shows that the maximum number of operations per second
---- "If we have to go on with these damned quantum jumps, then I'm sorry that I ever got involved" - Erwin Schrodinger
bit shifting is inherently irreversible.
Well I guess that means multiplying and dividing by powers of two is out as well, since it turns out to be the same operation. But.. wait.. mult and div is really just a finite number of additions and subtractions.. *hmmm*
Does it have something to do with the way the cpu handles overflow for certain instructions? Or did I just convert an irreversiable algorithm? ..remember you heard it here first!.. or are you just talking out of your butt? :)
Thanks for the feedback.
You said:
Well, I entirely ommitted Lloyd's calculation for this (as I said in the article). It's too technical to include in an article on a tech enthusiast site like Ars. It's quite followable, mind you, but technical enough that I didn't think it belonged in the article.I invite you to read Lloyd's paper for yourself, and examine his approach. If you find fault with his math and physics, well, congrats! :) I'd suggest that you let Lloyd know about this, and certainly announce the results of your analysis here. An extra pair of eyes looking at Lloyd's fascinating ideas is good.
Cheers,
-Geon
geonSPAM@ISBADarstechnica.com
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); }
These kind of articles remind me of the futile
medieval debates on how many angels can dance
on a head of a pin. Same sub-arguments too-
whetner angels are material (atoms) or immaterial
(photons, quantum states), and so on.
You'll just need to use an encoded link to your base station. Or you could carry it in a fanny pack.
That could add new meaning to: "I'm loosing my mind!"
Caution: Now approaching the (technological) singularity.
I think we've pushed this "anyone can grow up to be president" thing too far.
That's an interesting conjecture. Any idea how you would go about proving it? Personally I don't believe it. It's like saying "there are an unlimited number of fish in the sea" or "there's an unlimited number of trees".
Well, there is a large number of fish in the sea, but we're taking them out faster than they grow back, so there won't continue to be a large number. There used to be a large number of trees. But we cut them down faster then they grew back, and now every tree is owned by some person or organization. And the number is still decreasing rapidly.
Personally, I don't think that anything in the universe is unlimited. Stupidity has been suggested, but even there I have my doubts. Still, there's probably a better argument to be made for an unlimited amount of stupidity than for an unlimited amount of unknown things to be learned. In fact, I doubt that the total number of things in the universe that can be know is as large as the powerset of the cardinality of the number of non-virtual elementary particles in the universe. And probably not even as large as the power set of the cardinality of the number of electrons in the universe. Now that's a LARGE number, but it sure isn't unlimited.
Caution: Now approaching the (technological) singularity.
I think we've pushed this "anyone can grow up to be president" thing too far.
Imagine a Beowulf cluster of those things.
It'll suck the paint off your house and give your family a permanent orange afro.
-B
Now everyone knows that the NSA is after my barbecue sauce recipe stored in a pgp encrypted file. Of COURSE they'll create a black hole computer just to get it. After all, that barbecue sauce IS kinda red!
Landon Noll, who is probably best known to slashdotters for his work on LavaRand, has done some work calculating the limits of how many bits a cryptographic key has to have to be immune to brute-force searching in this universe. As I recall, he was going to publish it in Scientific American, but I can't seem to find it.
At any rate, taking into account such issues as your computer crushing itself into a black hole if it gets too massive, IIRC, Landon concluded that a key of about 530 bits is Really Safe.
- jcr
The only title of honor that a tyrant can grant is "Enemy of the State."
> there might be very different approaches
> (regarding computational power) to use the
> physics for building fast computers
Different from what? Like I said, the discussion relied on no particular form of technology. The only assumption is that a computer system must "change state" in order to perform any computation. And a computer is basically a "finite state machine". And if you think a computer can compute something without changing state, then how will you know when it's produced the intended result?
I think you may have missed my point, though. Moore's law is sort of an "anti-limit". It's exactly unlike the physical "laws" which place limits on things because Moore's law implies that there is no limit (doubling every 1.5 years, yada yada yada).
Who says that a complex problem needs a high number of state changes?
</em>
<p>
Well, we could argue about how complex is "complex", and how high is "high", but that's missing the point.
<p>
The outcome of a travelling salesman problem is not a state change, unless you think you can solve the problem by flipping a bit. Even if you use the physical analogue of creating lengths of strings tied together at the various city nodes and pull the "cities" in question until the strings are tight and selecting the tight path, every atom moving in the process is a state change.
<p>
And even if you prove that P=NP, you still need an algorithm that traverses the data, examines it, compares different links, etc, and every step in the algorithm is AT LEAST a state change.
> 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.
Actually, 1 L^3 = 10^-9 m^9. So tarsi must have a 9-dimensional brain, but it's a bit small. Which could explain why his brain doesn't sound like it works any better than ours, despite having so many extra dimensions to work with.
--
Win dain a lotica, en vai tu ri silota
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
Temperature is defined thermodynamically as:
1/T = dS/dE
where S=entropy and E=energy.
It is possible (and not merely theoretically) for entropy to decrease as temperature increases, in which case temperature does go negative. Weirdly, negative temperatures are considered hotter than any positive temperature. Thankfully (?) this sort of thing can only happen when you have very constrained systems -- the classic example is N magnetic dipoles constrained such that any dipole can only point parallel or anti-parallel to an applied magnetic field. If they are all parallel (lowest energy state) and you apply energy, they will begin to flip over. As they flip over, the entropy of the system rises with the increasing energy, so the system's temperature is positive. But once half the dipoles have flipped and the increasing energy drives more and more of them into the anti-parallel state, the entropy starts decreasing with increased energy, and temperature goes negative.
Don't believe me?
I'm trying to get some figures but I believe that is considerably more instructions in a single second than the aggregate computations of every microchip's lifespan that was ever built and operated.
Someone you trust is one of us.
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.
They are able to transfer information faster than the speed of light aparently.
About 300 times as fast at the moment through cecium vapour. (Aparently it has a negative refraction index...)
Also, what about non-clocked machines (massively paralel logic machines) such as the one NASA just bought.
The limits are a bit near-sighted, methinks.
D.
Does it really matter since you only need the laptop to enter and display information? As long as the device can communicate information with any larger box (or distributed groups of boxes) it can ignore all of the "limits" mentioned. Treating the ultimate laptop like an enclosed object that cannot communicate limits the power of the laptop immensely and unfairly.
No Zen is good zen
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
Every time I read an article about a limit in some area of computing (network speed, storage, CPU speed, stupidity of A. Grove), it seems as if it's the last sign that a new method/paradigm is on the horizon, with a significant breakthrough coming.
Bring it on!
Think outside the... Hey, where'd the friggin' box go?
The only reason for quantum mechanics in this article is the fact that quantum mechanics gives a lower bound for miniaturisation (i.e. you can only keep making computer parts smaller until you get problems with the Heisenberg Unertainty Principle)
The article even specifically states that it doesn't refer to a special type of architecture.
--
This signature has been deprecated
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.
1 Megahz = 10^6 operations per second 1 Gighz = 10^9 ops per second. Moore's law seems to go for speed now too. amout 10 time faster in 5 year. so we still have to go for about 200 year before we reach this speed.
I do not think i live for another 200 year. no problem there.
Damn! the sun does not go black hole for some 10^9 years. no luck here......
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
Every year we seem to think we know every thing there is to know about physics, biology and any other science. We are convinced that our current theories are laws of nature. And every year some discovery shatters that belief in a given discipline.
"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!"
The next Slashdot story will be ready soon, but subscribers can beat the rush and slashdot the links early!
All microsoft and other OS developers seem to be able to do is add lots of features that never REALLY get used and a few that do make high impact improvements. But do smart tags, the start menu, right click context menus, etc really require massive improvements in processor speed?
I can't help but think that Win2K on my Pent III 700 laptop is using the bulk of the resources just to RUN vs the load placed on it by any apps I'm using. That seems to make no sense.
So that begs the question. The whole idea of Linux from teh start was a free Unix that ran well on OLDER (cheaper - widely available) PCs. Even today that is still true. So if LInux continues to be accepted and moves into teh desktop mainstream someday - will that effect the push on PC technology?
Its striking that for less than an Apple I in 1977, I built a 1GHz Athlon server with the latest gadgets (SCSI RAID, LCD monitored drive sleds, PC133 SDRAM, etc) A PC with this much power is staggering - even compared to boxen from a year or two ago. But do I really NEED that much power? Not really, CPU wise, but it didn't make sense ot save $20 and get 200 less MHz when AMD, at the time was selling the 1GHZ athlon as the SLOWEST CPU.
We all know that no matter what Intel & AMD come up with, Micro$oft can overload it with a bloated OS upgrade that gains you squat. But in teh world or real OSes that treat system resources as something to be used scarcely, when will enough PC power be engouh for the bulk of the users (corporate flunkies, personal PCs, and small businesses?) When will we see a split in what is used for servers vs what is used in desktop PCs? Today, the latest CPUs are showing up in desktops almost at the same time they go into servers (Xeon excluded, but even there its getting more blurry)
Just like always it'll be amazing to see where we are 5 years from now, but I just can't imagine I'll be using a 3GHz desktop PC running RedHat 12.x that probably cost me $1000 :) It boggles the mind much more than the limits physics places on signal transmission on teh dies.... :)
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--Blair
The idea of black hole computing is obviously heavy, but the requirements on a heat sink capable of handling the matter-energy conversion of one kg are staggering.
Overklocking might of course not be strictly necessary, considering the effects of general relativity.
Staggering might be descriptive of the investment costs for setting up a new singularity for each calculation, given the obvius difficulty of interactivity once a Schwartschild-barrier is in place.
One must though admire the article authors, not only on their interesting essay, but also on behalf of the courage involved in imagining the prescence of a dissapearing black hole in ones lap.
His "calculation" is nothing more than a change of state in a quantum system. In real life, any calculation is likely to involve something more complex than this - the time taken for a single change of state is the theoretical minimum time for a single operation.
No matter how the machine works, it must involve state changes in order to have calculation of any kind. Barring completely new physics involving something other than normal matter, his calculation is correct.
He's talking about the theoretical maximum limit of processing power, not what is actually acheivable. Even in the article he says that there are good reasons for using less than this, and practical concerns like architecture don't come into it at all.
It's not bad science at all, it's theoretical science.
Physics, however, is man made. In your own counter argument you said Moore's observation applies to technology and knowledge, two inherent ingredients to physics.
To use a phrase: bollocks. Physics is inherent to the Universe, and is independent of what we know about the Universe and how we are able to manipulate it. Obviously, our knowledge of physics changes, but the underlying principles remain the same.
As our technology and knowledge grows so does our ability to penetrate to the "underlying truths of nature". Hence why we no longer believe newtonian physics to be accurate.
But they are still accurate, we just now know they are only accurate within a certain domain (speed much less than the speed of light, low masses). What the author is talking about is how the fundamental physical laws of this Universe constrain processing power. Quantum mechanics (the basis of this article) is undoubtedly not the whole picture (which is why superstrings are the focus of such intense research), but in their domain it is correct, and so are the observations made in this article.
To exceed the limitations described here we will have to do our processing in some other domain - perhaps if we recreate conditions at the very start of the Universe when it was still 10/11-dimensional then we can harness additional computing power, but that wasn't what the article was talking about.
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.
I had a real problem with the science behind the article. It states:
The maximum energy an ultimate laptop can contain is given by Einstein's famous formula relating mass and energy: E = m c2. 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 5.4258 * 10 50. This means that the speed of a computer is ultimately limited by the energy that is available to it.
What he's actually saying is that you are converting the mass of the computer to energy in order to power it. So what part do you convert first? The screen? The RAM? The case? Not to mention that you have to have some way to funnel the energy into the computer without loss - it reminds me of the "massless ropes" and "frictionless pulleys" of a first-semester physics class.
Sorry folks, this article is misleading. We're going to be stuck with batteries for some time to come.
His comments about the computer operating in black hole was interesting. Similar to the minds in the Iain M Banks Culture series of books which are basically supercomputers with the outer shell in real space and the "cpu" in hyperspace......
Its also worth noting that our two main theories, Relativity and Quantum Mechanics don't work together in that they cannot both be correct, Since a new theory to bring them together is being looked for I personally don't believe quantum computers are the limit.