You Think Your Current Laptop Runs Hot?

solferino writes: "Assume engineering genius continues to allow Moore's law to hold. What are the absolute computing limits of a 1kg laptop computer as defined by the physical laws of the universe? A New Scientist article has some interesting answers."

well

i don't really see any relevance to the article, i mean, it isn't feasible to use a laptop that generates that much heat, and on top of that, why would you want to compress its dimensions until it is a black hole?? i doubt we will ever need (and i may be sorry for writing this later on) a laptop with that much power. it seems that the writer had a lot of free time on their hands, and just played around with some numbers.

Back of the envelope nanocomputer numbers.

While waiting for the article to load, I did back-of-the-envelope calculations for the performance of the best possible 1 kg computer with atom-sized features.

In case anyone else is as bored as I was, here are the calculations and the numbers:

- Assume, arbitrarily, that your device is made of carbon and has one computing element (gate or memory element) per 10 atoms, average. This gives a total of about (1000 / (12 * 10)) * 6e23 = 5e24 computing elements.

- Assume that we're going for floating-point performance, and are using most of our elements for multiplication units. Assume we're cheating and using single-precision ints (32 bits). If we're allowed to pipeline arbitrarily deeply (we're runnign a toy benchmark program), then it would take somewhere in the realm of 4000 computing elements to build an IEEE-compliant floating point multiplier. This gives us 5e24/4000 = 1.25e21 multiplication units operating in parallel.

- Assume that we're signalling using light and that the light has to travel 1 nm per clock (we're very good at routing traces). This gives a clock frequency of 3e8/1e-9 = 3e17 Hz.

- This gives us a total of 1.25e21 x 3e17 = 3.75e38 FLOPS. Less than the best, but still not too shabby.

For kicks, let's compute the power requirements of this device.

- Assume that on every clock, half of the computation units change state (we're managing to use all of the computation units all of the time, with random data). This gives 5e24 / 2 = 2.5e24 transitions per clock.

- This gives 2.5e24 * 3e17 = 7.5e41 transitions per second.

- Assume that each transiton costs about 5 eV in total (split this however you like). This gives 5 eV * 1.6e-19 J/eV = 8e-19 Joules per transition.

- This gives us a power dissipation of 6e23 watts. A bit power-hungry.

For kicks, let's compute the surface temperature of this computer assuming radiative cooling:

- Assume that our computer is a 10-cm cube, with a density comparable to that of water (this is strangely-structured carbon). This gives us a surface area of 6e-2 square metres.

- Radiative energy emission from the object will therefore be equal to 6e-2 * 5.67e-8 * T^4 = 3.46e-9 * T^4 watts, where T is the object's surface temperature.

- For a power dissipation of 6e23 watts, the object's surface temperture would be (6e23 / 3.46e-9) ^ (1/4) = 1.15e8 degrees Kelvin. A bit warm.

Summary of data for the best possible nanotech computer:

• 
  
• 5e24 computing elements.
  
• 3.75e38 FLOPS (single-precision multiplies).
  
• 3e17 Hz.
  
• 6e23 watts.
  
• Surface temperature of 1.15e8 degrees Kelvin.
  

Looks like we'd have to underclock this baby.

Derivation of computing power for a comparably-sized quantum computer is left as an exercise for the reader.

In practice, we'd probably wind up building our nanocomputers as thin films with a lot less computing power but far lower power dissipation. Possibly as nano-grains, also, depending on application.

lunch box/laptop

Personally, I think apple's new notebook should be a combination lunch box / notebook. Run it really hot, keep you coffee warm.

Re:What would Dirac say?

In fact, it could be that the reason that earth occasionally swaps poles, is that the planets are really bits used in computing some cosmic calculation. Maybe the cosmos is already prototype of one of these devices.

If this is true and the universe is just a huge computer used in a huge calculation (who's answer is obviously 42) than just think of the uptime! Script kiddiez and administrators across the world will no longer be shoving record uptime's in each others face when god comes down and utters:

12:59AM, up 10 billion years+, 6,067 million users, load average: 2.23, 1.23, 1.20

Geoff

interesting article, frivolous physics

The physical computations in the article seem a little on the soft side. However it does make an interesting observation that we are still very very far from the physical limits of computational power.

On the other hand it is not clear whether such perceived limits exist in any meaningful sense and are not just reflections of our ignorance.

I recall reading about IBM building a superfast computer to model the process of protein folding (if I remember correctly). Each such computation would take months on that (still nonexistant) enormously fast computer. However thousands of such events occur every second in any living organism...

Re:lunch box/laptop

For the last time, Apple is *NOT* abandoning the PowerPC for Intel hardware.

God's Quake Server

Maybe, just maybe, God was really just trying to create a decent Quake Server and created the universe instead.

Re:be careful...

Mysteriously though, blue light would still be able to escape from the Microsoft blackhole...

Re:God's Quake Server

And then the Devil got greedy and tried to overclock it.

What would Dirac say?

Because a computer can't contain negative energies, the spread in energy of a bit cannot be greater than its total energy. In 1998, Norman Margolus and Lev Levitin of MIT calculated that the minimum time for a bit to flip is Planck's constant divided by four times the energy.

But according to Einstein's real equation, e^2=m^2c^4 + pc^2, from which we take the square root and arrive at the equation e=mc^2 (p=0). I believe Dirac was the first to toy with the notion of negative energy (or at least question it), since the square root of a number has two answers (positive and negative).

This is good news, since it will enable Microsoft to continue to build operating systems that ccasionally crash. Granted, they will have to reprogram the error routines to include Dark Matter Underflow and Not enough matter to complete operation, but this should be trivial.

In fact, it could be that the reason that earth occasionally swaps poles [msn.com], is that the planets are really bits used in computing some cosmic calculation. Maybe the cosmos is already prototype of one of these devices.


Welcome to the desert of the real.
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It's a real bitch...

...typing on a laptop that's become a singularity. The keys are *so* close together!


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