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The really neat physics argument limiting Moore's law (to my eye) is the ultimate limit on the information content in a given region of space. It turns out to b

by Steuard 15y ago

The really neat physics argument limiting Moore's law (to my eye) is the ultimate limit on the information content in a given region of space. It turns out to be impossible to pack entropy (and thus information) more densely than in a black hole. Because the entropy of a black hole scales with surface area rather than volume, Moore's law runs up against the maximum number of bits containable within the solar system (or even the galaxy or the entire observable universe) surprisingly quickly. I haven't looked at the numbers lately, but I seem to recall that those absolute limits show up within a few centuries, tops.

bobbydavid 15y ago
Here's some napkin math: Moore's law says that the number of transistors on a chip doubles approximately every two years. The Core i7 Sandy Bridge has ~2.3 billion transistors [1], and measures 434 mm^2 [1]. Silicon has a density of 2.4g/cm^3 [2] or .0024g/mm^3. Silicon's atomic weight is 28 --- meaning ~610^23 atoms of Silicon weigh 28 grams --- which means a single atom weighs 4.710^-23g. Let us pretend that Si crystals are simple-cubic (they're actually diamond-cubic [3]). In that case, a 1x1x1mm cube of crystal weighs 2.410^-3g == 5.210^19 atoms. The cube root of this number, 3.710^6, is the number of atoms on a side, so the number of atoms on a mm^2 face is 1.410^13. The chip is 434 mm^2, so the face has about 6.1*10^15 atoms on it, otherwise known as 6 million billion. For roundness, say we have 2 billion transistors on the chip today. Log_2(6,000,000) == 22. If Moore's law continues until the year 2053, there would be more transistors than atoms on the surface of the chip :-) [1] http://www.tomshardware.com/reviews/core-i7-3960x-x79-sandy-bridge-e,3071.html http://www.tomshardware.com/reviews/core-i7-3960x-x79-sandy-... [2] http://en.wikipedia.org/wiki/Silicon http://en.wikipedia.org/wiki/Silicon [3] http://en.wikipedia.org/wiki/Diamond_cubic http://en.wikipedia.org/wiki/Diamond_cubic
- sammyo 15y ago
  That is for what is essentially a 2D chip surface. Certainly layering chips has not been a viable option so far but look at the various "nano" machines that have been in science news, today a micron-sized modle truck, perhaps the next/next gen chips will have fractal surfaces that extend/configure/grow dynamically.
- DennisP 15y ago
  Do away with your heat dissipation problem by going to reversible computing, and you aren't restricted to surface atoms anymore. The black hole argument goes way beyond that, though. It's the ultimate physical limit of the universe, rather than what's potentially practical or imaginable. Even a computer built of neutronium might not reach that limit.
  - IsTom 15y ago
    Long live the UL-class computations!
    - DennisP 15y ago
      I googled but didn't find anything I understood. Can you explain without giving a course in computation theory?
      - IsTom 15y ago
        You can think about decision problems (such that you answer "yes" or "no" to a question) as trying to find a path in (very specific) a graph. UL consists (in a hand-waving fashion) of problems that can be stated in such way by undirected graphs of polynomial size. Roughly it means "if I'm in state s and can go to s' I can also go back from s' to s", which is a reversible computation -- reversible processes are not required by thermodynamics to create heat.
        bobbydavid 15y ago
        In my experience, UL is "unambiguous log", decision problems that require no more than logarithmic space, and also have a single unique proof (if it exists). It seems like UL-computers would be optimized for finding the path through the maze to the cheese, but log space is a pretty severe restriction...
        IsTom 15y ago
        Undirected st-connectivity is UL complete (and by showing that it's in L it was shown that UL = L). Logarithmic space is just an arbitrary constraint. It could be polynomial or exp-space.
- Symmetry 15y ago
  Its not actually obvious that you can't have more transistors than atoms, but I'm not sure it isn't possible in theory. I can imagine electrons in different orbitals having different interactions, or having for different energy levels in an interaction to effectively double the number of transistors. There are theoretical limits to the density of useful computation, but they don't correspond neatly to atoms or such.
  - technolem 15y ago
    Well, for example say you are using light based computing and transistors. Light doesn't interfere with itself for the most part so you can reuse the same transistors to add more cores by sending more channels of light through. You just need to add a gateway/filter at the end to let them communicate. Viola 1 million channels at maximum density gives a few hundred thousand times as many transistors as atoms.
redwood 15y ago
Thanks for reminding me of the totally mind-blowing fact that information density of a black hole is proportional to its surface area instead of volume. Some have argued this makes the universe analogous to a hologram: a 3d projection out of 2d.

by Steuard 15y ago

bobbydavid 15y ago

Here's some napkin math: Moore's law says that the number of transistors on a chip doubles approximately every two years. The Core i7 Sandy Bridge has ~2.3 billion transistors [1], and measures 434 mm^2 [1]. Silicon has a density of 2.4g/cm^3 [2] or .0024g/mm^3. Silicon's atomic weight is 28 --- meaning ~610^23 atoms of Silicon weigh 28 grams --- which means a single atom weighs 4.710^-23g. Let us pretend that Si crystals are simple-cubic (they're actually diamond-cubic [3]). In that case, a 1x1x1mm cube of crystal weighs 2.410^-3g == 5.210^19 atoms. The cube root of this number, 3.710^6, is the number of atoms on a side, so the number of atoms on a mm^2 face is 1.410^13. The chip is 434 mm^2, so the face has about 6.1*10^15 atoms on it, otherwise known as 6 million billion. For roundness, say we have 2 billion transistors on the chip today. Log_2(6,000,000) == 22. If Moore's law continues until the year 2053, there would be more transistors than atoms on the surface of the chip :-) [1] http://www.tomshardware.com/reviews/core-i7-3960x-x79-sandy-bridge-e,3071.html http://www.tomshardware.com/reviews/core-i7-3960x-x79-sandy-... [2] http://en.wikipedia.org/wiki/Silicon http://en.wikipedia.org/wiki/Silicon [3] http://en.wikipedia.org/wiki/Diamond_cubic http://en.wikipedia.org/wiki/Diamond_cubic

sammyo 15y ago
That is for what is essentially a 2D chip surface. Certainly layering chips has not been a viable option so far but look at the various "nano" machines that have been in science news, today a micron-sized modle truck, perhaps the next/next gen chips will have fractal surfaces that extend/configure/grow dynamically.
DennisP 15y ago
Do away with your heat dissipation problem by going to reversible computing, and you aren't restricted to surface atoms anymore. The black hole argument goes way beyond that, though. It's the ultimate physical limit of the universe, rather than what's potentially practical or imaginable. Even a computer built of neutronium might not reach that limit.
- IsTom 15y ago
  Long live the UL-class computations!
  - DennisP 15y ago
    I googled but didn't find anything I understood. Can you explain without giving a course in computation theory?
    - IsTom 15y ago
      You can think about decision problems (such that you answer "yes" or "no" to a question) as trying to find a path in (very specific) a graph. UL consists (in a hand-waving fashion) of problems that can be stated in such way by undirected graphs of polynomial size. Roughly it means "if I'm in state s and can go to s' I can also go back from s' to s", which is a reversible computation -- reversible processes are not required by thermodynamics to create heat.
      - bobbydavid 15y ago
        In my experience, UL is "unambiguous log", decision problems that require no more than logarithmic space, and also have a single unique proof (if it exists). It seems like UL-computers would be optimized for finding the path through the maze to the cheese, but log space is a pretty severe restriction...
        IsTom 15y ago
        Undirected st-connectivity is UL complete (and by showing that it's in L it was shown that UL = L). Logarithmic space is just an arbitrary constraint. It could be polynomial or exp-space.
Symmetry 15y ago
Its not actually obvious that you can't have more transistors than atoms, but I'm not sure it isn't possible in theory. I can imagine electrons in different orbitals having different interactions, or having for different energy levels in an interaction to effectively double the number of transistors. There are theoretical limits to the density of useful computation, but they don't correspond neatly to atoms or such.
- technolem 15y ago
  Well, for example say you are using light based computing and transistors. Light doesn't interfere with itself for the most part so you can reuse the same transistors to add more cores by sending more channels of light through. You just need to add a gateway/filter at the end to let them communicate. Viola 1 million channels at maximum density gives a few hundred thousand times as many transistors as atoms.

redwood 15y ago

Thanks for reminding me of the totally mind-blowing fact that information density of a black hole is proportional to its surface area instead of volume. Some have argued this makes the universe analogous to a hologram: a 3d projection out of 2d.