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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.
"When a scientist says something is possible, they're probably right;
when a scientist says something is impossible, they're probably wrong."
--Anonymous
Computers will never reach a plateau of operating capacity. Even if we were to design a computer so fast that it was limited by the speed of light, we could then design a warp core to generated a warp field around the computer and enable FTL (faster than light) processing. At least, this is how they do it on Star Trek TNG.
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.
Not exactly that kind of bottom.
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
You're thinking in the wrong discipline. Reversable computing happens already all the time.
Think of it this way - a photon hits an electron in it's ground state, raising it to a higher state. Then, it emits an identical photon and drops to it's ground state again. Effectively, You added energy to store a bit (0 -> 1) of information in an electron. Then the operation reversed, and you gained the original energy back.
The problem with reversible computing is getting the information out in a reversible way. In my example above, how do we know if the electron is a 0 or a 1? we have to extract the photon to do it, thus destroying the reversibility. Now, there are some quantum properties that can be measured without destroying the reversibility, but they are difficult to control (the system easily loses coherence).
Reversible computers don't use the same 'modern electronics' that your current computer does. but they are theoretically possible (using only a small amount of energy to observe the state). Just not yet practical. Wait around a bit.
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
The argument went like this: if a computer system can map out every possible finite state (i.e. board position in chess) of a game, then from any point in the game it can be determined what the winning moves are (if there are any, that is.) For a game like chess there are relatively few board postions possible -- thus, all board positions could be explored and the game could conceivably be "solved" at some point by a computer (of course in a brute force sense only, but solved none-the-less.) Any human player would be hopeless against such an adversary.
However, in a game such as checkers, there are many many more possible board positions (I think the estimate I recall was 10^69, could be incorrect though . . .) so that compiling a complete library of all board postions would take considerably longer than the projected life-span of the universe (as estimated by the halflife of a proton). This would be true even if you used a ridiculously large computing system -- say, .1% of the available mass in the universe. So, the argument goes, a computer will never be able to brute-force beat a human at checkers.
It was an old SciAm article that I'm thinking of . . . if I can dig up the original I'll paste it in.
irreversiable gah, spelcheck
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
Well... I meant that there is a physical limit to the thermodynamics that control computers just as there is a phyical limit to the size that you can design a transistor.
;-)
In a since, we're both right. You're right, my analogy is a poor one, but it still serves its purpose.
Thanks
One problem to note with reversible computing is that your computer has to have enough memory to store every bit of information ever entered into it. I'm pretty sure that it can compress the info, but eventually you'll have to have an energy expensive and very hot 'information dumping' process. I say it's a problem, but of course normal computing requires the same thing, and doesn't let you choose when you do it.
Actually, no. It seems that way (that's what I thought at first too). But that's the cool part about it... you simply reverse the process by reversing the direction that you increment the Program Counter. I'll give a short example in pseudo assembly:
; assume that $1 and $2 are both 0 ADDI $1 32 ADDI $2 24 ADD $1 $2 ; at this point $1 should hold 56. ; and at no point have we stored anything in memory ; ok.. now let's do these instructions in reverse. ; normally, we wouldn't manually do it this way ; because the CPU would switch it, but this works SUB $1 $2 ; ok.. $1 now contains 32 SUBI $2 24 ; now $2 contains 0 SUBI $1 32; now $1 contains 0 This is a fairly primitive example, but it proves the point. The other thing is that there cannot be a MOVE instruction. Memory can be exchanged with a register value, but not copied. So, all you have to do is run the instructions backwards... I promise!!!
botched the assembly... sorry:
; assume that $1 and $2 are both 0
ADDI $1 32
ADDI $2 24
ADD $1 $2
; at this point $1 should hold 56.
; and at no point have we stored anything in memory
; ok.. now let's do these instructions in reverse.
; normally, we wouldn't manually do it this way
; because the CPU would switch it, but this works
SUB $1 $2 ; ok.. $1 now contains 32
SUBI $2 24 ; now $2 contains 0
SUBI $1 32; now $1 contains 0
Heh.. Thanks...
/is/ with Dr. Frank. Actually, I have a meeting with him in half an hour to discuss this topic.
/not/ need to be saved. While it is important that state data is not destoyed, it is only necessary to guarentee reversiblity on the hardware level.
but the research I'm doing
Intermediate state data does
State data is necessary if you're performing irreversible operations.
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? :)
You hit it right on.. the overflow would be bad. Anytime there is a loss of data, reversibility won't work (unless that data is saved somewhere).
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.
The light speed limit is for light in a vacuum. Nothing moves faster than c. Plently of things move through cecium vapour faster than light.
Imagine a Beowulf cluster of those things.
It'll suck the paint off your house and give your family a permanent orange afro.
-B
keep in mind that the fundamental physics limitations are based on several physical theories - not absolute, god-given truths. we have come a long way since newton.
second, keep in mind that the current physical theories generally pose more questions than answers, e.g. we know that there are more things that we don't know than things that we know.
we must remember that our theories are useful tools for many things, but we must also remember that they are just theories. if we don't, then all we have done is replace God with Science.
my physics professor in College said to me "a good theory is one that can be proven wrong". i still don't quite understand what he meant by it, but maybe it was "i rather know something is wrong for sure than not know whether it's true or false - and theories, by their very nature, can never absolutely be proven true"
i like this idea: it's possible that Moore's Law actually is a law of nature, while quantum physics, general relativity and the speed of light are all theories that will crumble eventually.
not likely. but possible.
I was thinking about the same subject from the other direction recently. For my research I am trying to simulate the growth of silicon germanium crystals. The usual way of approaching a physics problem like this is to make simplified approximations of what actually happens. For example, hard-to-model processes like diffusion are measured by experiment or found from standard relations. But these simplifications can yield a model which is subtly wrong and fails to predict unexpected behavior.
What I really want to do is model the entire crystal growth from the most fundamental physics (quantum mechanics or something like string theory). That way the simulation is not just an approximation of reality but is indistinguishable from reality! How fast of a computer do I need for this full-detail simulation?
Well, that depends on the size of the system I'm trying to simulate. How big of a computer do I need to model a 1g chunk of matter? Logically, it seems that at least 1g of computer would be required to model 1g of arbitrary material in real time. (Otherwise, I could simply model a 1g computer with a 0.5g one, which in turn is actually simulated on a 0.25g computer and so on.) So, perfectly simulating a 10g crystal would take 10g of "ultimate laptop" processing. But if, like the article mentions, the laptop uses ordinary matter rather than plasma then the computation rate is 10^40 ops/second rather than 10^51 ops/second. This implies that my 1kg super laptop would need 31.7 years to simulate 1 second of growth for a 10g crytal! How much computation would be required to mimic The Matrix? To perfectly simulate life on Earth would require a computer at least as large as the Earth itself!
So, although 2 GHz processors sound fast and the ultimate laptop in this article seems unfathomable, we have many applications today that can take all the computation speed available. A near future application for ultracomputing is the modelling of protein folding for drug design. There, the amount of matter being simulated is small fractions of a gram and the leveraging of computer weight and time is worthwhile.
AlpineR
It is worth noting that Lloyd's thought experiments in these areas were preceded by similar speculations over 4 years ago in Anders Sandberg's paper The Physics of Information Processing Superobjects: Daily Life Among the Jupiter Brains. Lloyd has extended them a bit by bringing Black Holes into the picture.
Now, what we will be able to engineer in this century, using diamondoid molecular nanotechnology, is solar system sized nested layer Dyson shell supercomputers. This is a unique architecture that I have named a Matrioshka Brain. It will allow us to most efficiently use the entire power output of the sun and compute somewhere in the range of 10^42 to 10^52 ops per second.
Interestingly enough, Michael Franks has a paper "Reversibility in optimally scalable computer architectures" which postulates a solar system sized reversible architecture that would out-compute any non-reversible architecture. This too would be using atomic-scale engineering. Unfortunately it requires the power output of an A or B class star (~50,000 suns) and requires an amount of silicon equal to the mass of Saturn (our solar system doesn't even come close to having that unless we mine the sun for it). After we have developed machines of these architectures, our development comes to a slow halt unless our ability to do sub-atomic engineering can be developed. I'll be quite happy with what we can get out of atomic-scale engineering -- it supplies enough computronium for roughly a trillion-trillion human minds for those who choose to upload.
You do need to save the intermediate state information. That is why Frank's design for the ultimate reversible computer is so big (see my other post on this topic). You should keep in mind that you can compute for "free" (if you do it slowly), its erasing bits that costs you money (generates entropy as heat). Logical AND operations erase information such that you cannot run the calculation backwards. You have to design the hardware such that it has no such information destroying operations.
The fact that we are accelerating towards the Vinge Singularity is ignored. Kurzweil is extensively documenting this at KurzweilAI.net (unavailable today). Various estimates place this between 2020 and 2050. Once we have autonomous self-replicating systems (nanobots), we can dismantle the planets and turn it into computronium. We will come very close to the limits of the computational capacity allowed within our solar system within this century. Even if this fast ramp is not realized, you underestimate the progress that will be made in extending the human lifespan. We have the genome now, we will rapidly decode much of it over the next decade and begin to design and implement anti-aging therapies. Unless you are over 50 years old or will reject the use of such technologies, the probability that you will make it to 200 is quite high. Sorry, you have to face the problem. :-)
The title is correct, Knowledge is unlimited, but the rest of the post is not; read the short essay Can the Universe be Known?, by Carl Sagan. (I think that's the essay name)
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!
>For all you know, there are states "below absolute zero"
Not possible by the definition
That's like saying something can go slower than 0 mph. Not possible. Since speed(not velocity) is always positive. Since temperature is just a measurement of how fast "stuff" is moving around and absolute 0 is when nothing is moving you can't get colder. Saying otherwise just shows your ignorance.
It has been statistically shown that helmets increase the risk of head injury.
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."
The physics limitations apply to massively parallel machines as well. Read the article. Multiple CPU's still work by changing state. If you've got a million CPU's, and together they weigh less than a kilogram, they all have a collective maximum number of state changes per second as computed in the article for an arbitrary device of that mass.
> 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
It's not. Remember that the 2nd law is only probablistic. There's nothing stopping entropy from decreasing in a closed system, it's just that for unbound systems of large numbers of particles a decrease in entropy is stupdendously unlikely to happen.
In any case, the underlying definition of the entropy of a system at a given energy is Boltzmann's constant k times the natural log of the number of states the system can assume at the given energy. For the dipole system, the energy of the system is proportional to the number of anti-parallel dipoles times the strength of the imposed field, i.e. E = C*Nap*M, or Nap = E/CM. So if the system has energy E, you know how many dipoles are anti-parallel, but not which ones. If there are N total dipoles and Nap of them anti-parallel then there are Nap!/Nap!(N-Nap)! ways to arrange those Nap dipoles and hence there are that many states. If you examine the behavior of that function (or its natural log), you'll see it increases from Nap=0 to Nap=N/2 and then decreases from Nap=N/2 to Nap=N. This means that the entropy increases from as total energy E goes from 0 to (N/2)(C*M) but then decreases as E goes from (N/2)(C*M) to N(C*M).
As I said, see a statistical mechanics textbook.
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.
Roads? Where we're going, we don't need "roads"!
120 characters isn't enough to explain it.
As your sig said, much better to be commented on then moderated..
First of all, I would have to agree with you that it is pretty much safe to say that we can't predict the maximum speeds, or storage compacity of anything these days. The technology involved in computing is very complex, and ever changing.
I see a few flaws in the article. Fist off, quantum computing is not convention computing, and does not rely as heavily on the binary ones and zeros typically associated with computing. In this sence quantum theory becoming a reality in it's self would prove this theory incorrect. As soon as you introduce a new "neutel" state, where a typical atom's state would be translated into more than just a 1 or 0.
In a sence the author of that essay is safe though. If Moore's law hold true, that every 18 months computers are doubling in number of transistors, and thus speed, it will take nearly 200 years to reach the physical limit on computing speed. So for 200 years the author will be correct. This makes it hard to prove him wrong in this day in age.
Their are limits to everything the human mind thinks up. Why? Because we are finate, and are unable to think of anything being infinate. But it is possible that the universe is infinate is it not? In an infinate universe in theory it would be possible to make somthing of infinate porportions. Yet, we can't even imagine such a device. Why? Because our minds don't think like that. Our minds are finite, and our science is derived in a finate matter.
After bringing up the question of the universe being finite, or infinate naturally religion gets brought into the equation. That's right, religion meets computing, head on. Their are religions that believe the world and time to be infinate. Alawy's was, and alway's will be. That is the fundamentals of Christianity. Then their are the others, the big bang people. The author of that article is more than likely a proponent of the big bang theory, and a finite universe with a finite ammount of time.
My personal favorite part of the article was the part which discussed the fact that the theory of relitivity and the theory of relativity can not co exist. And that their has to be a superior relationship between the 2 that has not been theorized yet. What this is saying to me is that with the nature of Quantum mechanics, their are multiple parallel "instances" or "worlds" that exist at the same moment. The theory of Relitivity exists in both "worlds" that is what the basic physics in each is based on, but that the other "worlds" exist in the state described in Quamtum physics. Thus, the missing link is the theory used to bridge the gap from one "world" to the next.
Having said that, it would in theory be possible to create this super computer that is infinately small in size, and located in another "world". Thus, it would be possible for somone to have their own "blackhole computer" with the mass of zero, located in a parrallel world, being controlled from this reality. Such a task would require the ability to retrieve information from this parrallel world. Which is the missing part of our equation. We have the theory for how matter reacts in the other world, and for how it reacts in this world. Now we just have ot be able to extract the information from that parrallel world. That my friend is Quantum Computing.
"I couldn't give him (Bill Gates) advice in business and he couldn't give me advice in technology." Linus Torvalds
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.
As for physical theories, physicists don't claim to know everything, or that all that they think they know is so; but they do claim that physical theories do explain empirical data well. The physics presented is pretty solid, and it would take a very unlikely revolution in our understanding of matter and energy to alter the conclusions presented.
IP is just rude.
Is there any torture so subl
"There are no absolutes - as Dr. Pritchett has proved irrefutably." Jim Taggart, in "Atlas Shrugged".
Ok, that has GOT to be one of the most consciously misleading quotes I've ever seen! In the book Atlas Shrugged, Jim Taggart is an utterly contemptible person. If you want to know what the point of Atlas Shrugged is, you've got to *invert* his statements.
Bjarke Roune
1) Checkers uses fewer pieces, with only two possible types (regular or king).
2) Checkers uses only half the number of board spaces as chess.
3) Although it's true that your pawns aren't going to end up in the first row, moves and positions are pretty much unlimited in chess. Note: A lot of these positions are not practical if someone is playing to win, but they are still theoretically possible.
Conclusion) Deep Blue played chess, but it would have creamed Kasparov at checkers.
If I'm wrong, let me know. It won't be the first time.
--
dman123 forever!
--
dman123 forever!
Filtering out the -1s and 0s since 1999.
Well, yes, but...relativity knocked the socks out from under Newton's notions of absolute time and place, but people still use Newtonian mechanics to design car engines. Having to be consistent with what we already know means that even if the theoretical underpinnings change, the results will look like refinement, not revolution. (There's a fine Asimov essay on this, titled something like "The Rightness of Wrong.")
wouldn't the amount of evergy available be based on the voltage supplied to the computer and the resistance of its circuits? so wouldn't the relevant equation be V=IR, not E=MC2? don't think using electricity here, we're talking about particle physics and quantum computers. so forget all your cables and contacts and resistors.He's talking about states of nuclei (being the spin of the nucleus for example)If you convert all the mass to energy (pure energy, that is) then you've got the maximum energy. you can't have a higher energy, cause you don't got any mass to convert any more.
it seems to me that a lot of people who understand alot of one (or more) of the nature sciences forget that it's all just observation and interpretation. And I guess it's not those people that find out about completely new things that break all the other previouslyassumed 'laws'. If there wouldn't be anysceptics, we wouldn't have come this farand I guess if there aren't more scepticsto come, we wouldn't even advance in science.
the problem is that the nuclei of the computer can't take any more energy when they are, in fact, already pure energy. (e=mc)
they are, in fact, already pure energy. (e=mc) at which point i'd ask: is a computer without any mass really a computer ?
wouldn't the ultimate computer be able to harness all of the energy in the universe? yes, it would. but we've limited it to a 1 kg computer with 1L.
Think about, if it cannot be proven wrong, it has no preditive power. Otherwise its predictions could be checked for correctness.
cf.the fallacy of untestability on everything2.com
-
This post was compiled with `% gec -O`. email me if you need the sources
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
According to this article, the total mass of the universe is 1.6*10^60 kg. As I recall, this was a number which Stephen Hawking also reached. Thus:
(1.6*10^60) * (5.4258 * 10^50) = 8.68128 * 10^110 is the actual limit of computers
Any karma trolls who make "Beowulf Cluster" comments will be shot.
Well, I do agree that the limits of present computer will be reached. However, it only means that the number of cycles of a computer is limited. We could have computers that process more complicated process per cycle. I remember reading somewhere that there are "biological" computers that can solve complicated maths problems with just one processing cycle. This is very possible. An example is the human brain. It can process certain information effortlessly that normal computers could not process. Maybe after the limits of current computers is reached, more research will be devoted into biological computers to solve specialised problems. They might not be able to solved problems that current computer solves effortlessly, but they have might have a niche is solving problems that current or even future computer cannot solve.
What got my attention was the formula being used in a different context than it was intended. If you consider that matter is energy, then 1kg could be that much energy, but for the matter to be that energy while still being matter, and to use it, seems a bit unlikely. I may be wrong, but this seems like the wrong way to find the amount of energy that the matter can contain and use. Also, when applying this equation to the splitting of atoms, you generally lose a small part of the atoms. I'm assuming these calculations tell you how much energy you would get from the matter if it were completely converted to energy, but how does the conversion of a small portion of the atom into energy tell us the total energy of the atom? Of course, this is very difficult to understand and argue about when we don't even know the exact way that matter is converted to energy - but we do know that this conversion probably involves the disappearance of subatomic particles AND the probably release of forces binding the nucleus together. So if you lose a few protons and neutrons in the nucleus, and the energy that held them in is also released, does this mean that you'll get the same energy from losing enough electrons to have the same energy as you go from the protons and neutrons?
What really seems wrong is to base the amount of energy that a mass can theoratically use on the amount of energy that we would get from losing that mass in fission. I'll have to read Lloyd's paper, but this seems wrong.
And now for some crazy theories that would require a lot more effort than i'm willing to put in right now to convert to usable arguments and fact: what if matter was simply a "higher energy state" than pure energy? A good analogy would be electrons: matter is matter because it is kept at a distance from the "nucleus" of energy that it is attracted towards by some force. When electrons fall to a lower orbit, they release energy. In a similar way, matter returning to the form of energy could release energy. The best proof of this would be anti-matter: the two pieces of matter are pulled away from energy in opposite directions, and when they come together the forces holding them up are cancelled out, causing them to fall back towards the center. I don't know how, but if this was the case, it would probably apply to this discussion in some way. I should think about this again when I wake up.
They that quote Benjamin Franklin on liberty and safety deserve neither.
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.
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. :)
That's motion blur. It's a feature.
When a preacher says he'll move a mountain, no one believes him. When a scientist says so, noone doubts him.
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?
agreed
From 1874:
"When I began my physical studies [in Munich in 1874] and sought advice
from my venerable teacher Philipp von Jolly... he portrayed to me physics
as a highly developed, almost fully matured science... Possibly in one or
another nook there would perhaps be a dust particle or a small bubble to
be examined and classified, but the system as a whole stood there fairly
secured, and theoretical physics approached visibly that degree of
perfection which, for example, geometry has had already for centuries."
- from a 1924 lecture by Max Planck (Sci. Am, Feb 1996 p.10)
From 1888:
"We are probably nearing the limit of all we can know about astronomy."
- Simon Newcomb, astronomer
From 1894:
"The more important fundamental laws and facts of physical science have
all been discovered, and these are now so firmly established that the
possibility of their ever being supplanted in consequence of new
discoveries is exceedingly remote.... Our future discoveries must be
looked for in the sixth place of decimals." Albert. A. Michelson,
speech at the dedication of Ryerson Physics Lab, U. of Chicago 1894
(Especially interesting since Einstein used Michelson's experiments with light
as the basis for special relativity.)
From 1900:
"There is nothing new to be discovered in physics now. All that remains
is more and more precise measurement" - Lord Kelvin
From a bit earlier:
"So many centuries after the Creation, it is unlikely that anyone could
find hitherto unknown lands of any value."
- Spanish Royal Commission, rejecting Christopher Columbus' proposal
to sail west.
If Newton was to do a calculation of the amount of energy in 1 kg, he would use m*g*h.
If Einstein did the calculation he would use m*c*c. What a difference.
This article is from the "Wanker Desk" at Ars Technica:
http://new.arstechnica.com/wankerdesk/
Ummm, WANKER DESK??? Does anybody know why it's called that? Do they just not know what wanker means?
...
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
Let's state things in another way: such a computer is nothing more than a physical system which (entire) evolution is used and monitored to accomplish a certain task...
Generally heavy computation is used to predict outcomes, to analyse data, normally related to physical systems, and any system is physicall.
Now, consider this: if you can built a system to such a precision you don't need to simulate anyting, anymore. Just built the damn thing fullscale, and if it doesn't work restart from zero.
What I'm saying is that a small model of a plane, for example, is a physical computer, built to model the plane.
The best simulation of a system is the system itself, if you can built arbitrary systems with little effort. And the technology to built this kind of machines requires us also to be able to built almost arbitrary systems, so in the end it will be useless to make use of it to built computers, I think.
You cannot proceed from the informal to formal by formal means
Theories are theories and our best theories are Our Best Theories. Don't blame science for shattering yesterdays Best Theories and don't misattribute the popular misconception of Truth vs. Theory to the few that actually understand what Truth and Theory are.
(and in reference to the subject line, See: Godel's Incompleteness Theorem
(2,3-Benzopyrrole)
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.
This was meant to be funny, who modded it insightful....?
Is also very incaccurate since i mix up speed and size.
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......
"powerset of the cardinality of the number of..." What does that mean? I have read that the number of electrons in the universe is estimated to be 10^80 or so, and that if the universe were to be stuffed full of electrons like neutrons in a neutron star, the number would be 10^50,000.
Numbers 31:17,18 Now kill all the boys. And kill every woman who has slept with a man,but save for yourselves every virg
You are assuming that we know all the laws of physics. Now, we certainly do know the laws of physics in a more enduring way than we know how to engineer microchips, but to say that we know all the laws of physics is silly. It amuses me how physicists have claimed to be "almost there" forever.
For all you know, there are states "below absolute zero" that we just haven't created so that they could be measured or conceptualized yet. So yes, you're right, it is like saying that - and there's nothing wrong with such a statement at all.
I believe it was Einstein who said that "science" is nothing more than the rationalization of technology.
Bob
Someone mod this comment up, I find this observation to be more fundamental than some BS about an absolute limit to computer speed.
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
If you do the math, based on our current understanding of the laws of physics, the fastest computer could attain speeds exceeding 10 to the 70th power! This is mind boggling, as this computer could simulate the entier history of earth, including all human life and civilization. That means (think 'The Matrix') that our entire reality right now could be one of these simulations!!
www.enthea.org
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.
1 L^3?!
:)
What are dimensions 4, 5, and 6 that your brain occupies?
Tim
The ultimate limit to computing power has long ago been determined to be related to the ammount of Vogon ships passing through the area building hyperspace bypasses.
Sig (appended to the end of comments I post, 54 chars)
... but once you load a MS OS on there, it'll perform as slow as a 486. The upshot is that the theoretical ultimate laptop will then cease to exist, taking the dreaded OS away ... but leaving MS wondering what legal action to take when the license exists while the OS doesn't.
m.mmm..myyy
If it were "Moore's Theory of Computational Progress" and some sort of cause were assigned to why microprocessing power must double every eighteen months, it would be like a law of physics. But without a cause, it remains just an observation of what has happened so far, not what must happen. A nuclear war, or a worldwide strike (or alien abduction) of microprocessor engineers would interrupt the steady progress of Moore's Law.
One day I feel I'm ahead of the wheel / the next it's rolling over me / I can get back on / I can get back on
They're perfectly accurate. Just not as accurate, or as encompassing, as Einsteinian physics. It's a matter of what tool you want to use. A nail can be pounded into concrete with the head of another nail, if you have the time and patience. Or you can use a hammer. Or you can use your forehead. But you will probably get the best results with the hammer.
One day I feel I'm ahead of the wheel / the next it's rolling over me / I can get back on / I can get back on
I think this article only applies to Digital Processing. If future engineers can more effectively harness Analog Computation, then the upper limits of computational power increase substantially.
Who says the future will be digital? We sure as hell ain't digital processors....
That's great - We've defined the upper limits of digital processing and storage, but what about analog??
"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!
- have you seen my new quantum uber-laptop?
- no I cannot see it.
- of course. otherwise I won't have it.
---
- Where is my quantum computing?
- It's here. It isn't. It's here. It isn't. It's here. It isn't. It's here. It isn't.
-- There are two kind of sysadmins: Paranoids and Losers. (adapted from D. Bach)
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.... :)
Top Most Bizarre/Disturbing Error Messages
You quantum compute a physics equation. In all universes, the equation is computed.
You peek in on another quantum computer's answer.
The other universe has a different gravitational constant or perhaps gravity that is tripolar. Their equation is correct for their universe, you just got data bogus for your universe.
You run a quantum calculation on a large database of finacial data. The other universe has clients not existing in this universe. You peek at their results (ran of course days in advance of yours by quantum luck), the data you get is not the data you need.
You want a prime number with 10^5000 digits. You want to tap the quantum distributed power of all other possible quantum computers, you want these computers to divide all real numbers below 10^5000 digits to see if there are factors. There are 300 factors. You receive one number back that is the binary add (dropping everything above the 10^5000 digit mark) of those 300 factors. Did the quantum trick work? Perhaps for one or two special cases, not for the general stuff.
"Face it, a nation that maintains a 72% approval rating on George W. Bush is a nation with a very loose grip on reality.
--Blair
You're right, you got fourth post. Congrats.
Using this prominent position to comment on Timothy's deutshmerism: you are more likely to say Gedankenspiel than Gedankenexperiment. Well, at least in german, that is, though I have to admit the latter looks way cooler. Might be just me, but G.e. translates into experiments on thought rather than in.
A World in a Grain of Sand / Heaven in a Wild Flower,
Infinity in the Palm of your Hand / And Eternity in an Hour.
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.
Well, an atom of uranium weights as 235-238 atoms of hydrogen, that is 10^2 times more. It means that 10^25 nuclei of hydrogen have the same mass than 10^23 nuclei of uranium. This is approximately the same.
It's correct to speak of current and resistance, but the article is trying to find a theoretical limit, and (in a theoretical lab) one could build a superconductive computer (R more or less zero) and power it with millions of A's. It's safer to say that something cannot contain more energy than its rest mass (by definition!).
Anyhow, I hope that they will NOT install Win3K on a PC that can convert mass/energy. Just one BSOD and... whooosh! you're history (and your town too).
That's still bad theory. Good theory would have taken the mass of the inside of the battery case and converted that total enery. The original comment is right. You cannot "theoreticly" consume the processor when calculating the limit of power available to the processor!
Contrary to popular belief, coding is not all free blow-jobs and beer. Those things cost MONEY!
I read a much better summary of this topic, reviewing the same paper, on the NYTimes. Alas, it is now in the paid archives, so if anyone is interested in paying the $2.50 for the article, here it is: http://search.nytimes.com/plweb-cgi/fastweb?view=s ite&TemplateName=hitlist_MPoff.tmpl&dbname=unify&s orting=BYRELEVANCE&numresults=10&operator=AND&simp lesearch.x=10&simplesearch.y=10&query1=thedbs%3Dpa st365days%26section%3DALL%26fields%3DALL%26thequer y%3Dultimate%2520laptop&query8=from%20the%20past%2 0year&query7=ultimate%20laptop&query=(ultimate%20l aptop)%20AND%20(20000623=pdate)&query_rule=($query )
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.
I have a big problem with the first two paragraphs. In the first paragraph Geon states:
"It pays to keep in mind, however, that this isn't really a law, but only an observation, and does not reflect any underlying natural truths. "
In the second paraghraph he states:
"What we know is that any future technologies must obey and be constrained by the laws of physics."
I'd just like to say that I don't know that tomorrow's computing will be constrained by today's physics. This guy attacks Moore's law as being merely an observation, well what the hell is physics? It's a bunch of theories that try to explain observations! If no one ever observed anything, then there wouldn't be any physics. The moore (pardon the pun) observations we make, ideally, the closer to "the underlying truth" we get. Who knows maybe Moore's law points to an underlying truth in the drive of humankind that will actually constrain physics and change forever the way we progress and develope as a society. I'm not trying to troll here, I just didn't like the way he trash talked one observation while relying on the "inherent truths" of another. Who made him god?
V=IR has little to do with energy.
While your comment misses the point of the article entirely, I think what you mean to say is something like:
"Wouldn't the amount of energy availbalbe be based on the amp-hour rating and voltage of the battery? So wouldn't the relevant equation be E=Vnom * capacity, where Vnom is the nominal voltage of the battery, and capacity is the capacity in amp hours?"
regards,
MM
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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.
quote: "One kilogram of ordinary matter contains approximately 1025 nuclei" maybe i'm wrong but wouldn't the mass of a given number of nuclei be a function of what type of nuclei they are? for instance a uranium nucleus would be much heavier than a hydrogen nucleus.
The approximation is the 25 in the exponent. 25 plus-or-minus one gives you a factor of 100 range; normal matter is just a little more than that (1-244 for Pu244, the heaviest nucleus naturally occurring on earth).
Religion is the opiate of the masses. The wealthy smoke the real stuff.
UW-Madison is actually working on something similar. Sure, it's no black hole laptop, but it is quantum computing. Remember... It's not paranoia if they're really after you.
IWARS.
People, in general, disappoint me. Politicians even more so.
Imagine a Beowulf cluster of those!!! .. Wait there you go! I solved the problem! When one Quantum computer is no longer enough, we link them up into clusters!! Whoopee!
* goes running to the patent office *
- Tempestdata
Actually, in normal matter he estimates about 10^40 operations per second. Right now we're at approximately 10^9 (1 GHz), so that gives us a factor of 10^31 to increase. That's about 2^103, which Moore's law (x2 = 18 mo) equates to about 155 years.
I don't know about you, but I'm planning on still being alive at that time! I don't like the idea that I'm not going to be able to upgrade my neural implants any further when I'm 182.
quote: "One kilogram of ordinary matter contains approximately 1025 nuclei" maybe i'm wrong but wouldn't the mass of a given number of nuclei be a function of what type of nuclei they are? for instance a uranium nucleus would be much heavier than a hydrogen nucleus. so what extactly is "ordinary matter"? quote: "The maximum energy an ultimate laptop can contain is given by Einstein's famous formula relating mass and energy: E = m c2." wouldn't the amount of evergy available be based on the voltage supplied to the computer and the resistance of its circuits? so wouldn't the relevant equation be V=IR, not E=MC2?
Go ahead and waste your life with your inhibitions, just don't ruin other people's lives with your intolerances.
Hey, pick up this months issue of SciAm. It has a cool article on the physical limits of supercomputers. A good read.
I belong to the ______ generation.
Well, to nitpick, when you refer to the maximum number of "operations" in this sense, I think it means a 0-1 transition rather than a multiply. =)
So in the worst case where every "transistor" on your chip changes state, you'd have to divide that by a few more million/billion/whatever
I think the article mentioned something about 10^35 operations on each of 10^16 bits. So maybe it meant the CPU state is defined by 10^16 internal bits (or transistor states) and you could run that at 10^35 Hz.
I realize those numbers might be wrong... I'm just using them off the top of my head. I read it before lunch.