4 ms·

Theoretical physicist explains why Moore's Law will collapse

21 points by ukdm 14y ago

tomrod 14y ago
Ah reality. You're why we can't keep nice growth patterns.
Steuard 14y 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 14y 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 14y 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 14y 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 14y ago
      Long live the UL-class computations!
      - DennisP 14y ago
        I googled but didn't find anything I understood. Can you explain without giving a course in computation theory?
        IsTom 14y 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 14y 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...
- redwood 14y 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.
DennisP 14y ago
We're nearing the limits for silicon, but we're nowhere near the limits of physics. We'll likely lose the nice smooth curve, but the long-term trend started with mechanical adding machines, and it'll probably continue well past silicon. Within the next decade, memristors will give us a big jump for certain kinds of problems. Down the road, reversible computing would be another huge leap, essentially eliminating the heat problem.
pilom 14y ago
I'm really not impressed with this guy's description. His understanding of a 3d transistor is flawed. Currently 3d transistors are just one layer of the transistor which has a rectangular cross section to reduce leakage. Future 3d processors will have transistors layered on top of other transistors. Granted heat dissipation becomes a harder problem for those processors but "a hard problem" is much easier to overcome than the theoretical laws of physics at 5nm. Also, I don't like how his go to solution for after silicon is molecular computing. He said himself that silicon breaks down when we are around 5 atoms across. How big are the molecules which we can use as switches? Much more than 5 atoms across. Molecular computing will not get a transistor density any greater than silicon will.
yoklov 14y ago
I just want to say one word to you. Just one word. Are you listening? Quantum. (edit: not that I have a clue what I'm talking about)
maeon3 14y ago
Moore's law is not a law. It's an observation, it's as much a law as my observation that the amount of rain increases in podunk at a rate of 10% per day. There may be some phenomenon where it's true for a little while, but calling it a law just makes me cringe. The law is a self fulfilling prophecy because chip makers make it as a target which is neither too ambitous nor too cautious. It should be called moore's phenomenon.
hapless 14y ago
Moore's law is a relationship between transistor count and cost. The physical limits of the universe govern transistor density. Cost may continue to drop in the face of increasing tranistor count for some years: dies will have to get bigger, but yields on big dies have a lot of improvement left. We may see chips get cheaper and cheaper even if the feature size never drops.
drcube 14y ago
Personally, I'm looking forward to cheaper and cheaper computing, rather than more and more powerful. Raspberry Pi is just the beginning. Wait until Sandy Bridges are as cheap and plentiful as 555 timers. I'd also like to see some sort of worldwide standardization on a single CPU architecture. Innovation will continue long after Moore's law.

21 points by ukdm 14y ago

Ah reality. You're why we can't keep nice growth patterns.

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 14y 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 14y 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 14y 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 14y ago
    Long live the UL-class computations!
    - DennisP 14y ago
      I googled but didn't find anything I understood. Can you explain without giving a course in computation theory?
      - IsTom 14y 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 14y 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...
redwood 14y 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.

DennisP 14y ago

We're nearing the limits for silicon, but we're nowhere near the limits of physics. We'll likely lose the nice smooth curve, but the long-term trend started with mechanical adding machines, and it'll probably continue well past silicon. Within the next decade, memristors will give us a big jump for certain kinds of problems. Down the road, reversible computing would be another huge leap, essentially eliminating the heat problem.

pilom 14y ago

I'm really not impressed with this guy's description. His understanding of a 3d transistor is flawed. Currently 3d transistors are just one layer of the transistor which has a rectangular cross section to reduce leakage. Future 3d processors will have transistors layered on top of other transistors. Granted heat dissipation becomes a harder problem for those processors but "a hard problem" is much easier to overcome than the theoretical laws of physics at 5nm. Also, I don't like how his go to solution for after silicon is molecular computing. He said himself that silicon breaks down when we are around 5 atoms across. How big are the molecules which we can use as switches? Much more than 5 atoms across. Molecular computing will not get a transistor density any greater than silicon will.

yoklov 14y ago

I just want to say one word to you. Just one word. Are you listening? Quantum. (edit: not that I have a clue what I'm talking about)

maeon3 14y ago

Moore's law is not a law. It's an observation, it's as much a law as my observation that the amount of rain increases in podunk at a rate of 10% per day. There may be some phenomenon where it's true for a little while, but calling it a law just makes me cringe. The law is a self fulfilling prophecy because chip makers make it as a target which is neither too ambitous nor too cautious. It should be called moore's phenomenon.

hapless 14y ago

Moore's law is a relationship between transistor count and cost. The physical limits of the universe govern transistor density. Cost may continue to drop in the face of increasing tranistor count for some years: dies will have to get bigger, but yields on big dies have a lot of improvement left. We may see chips get cheaper and cheaper even if the feature size never drops.

drcube 14y ago

Personally, I'm looking forward to cheaper and cheaper computing, rather than more and more powerful. Raspberry Pi is just the beginning. Wait until Sandy Bridges are as cheap and plentiful as 555 timers. I'd also like to see some sort of worldwide standardization on a single CPU architecture. Innovation will continue long after Moore's law.