
Theoretical physicist explains why Moore's Law will collapse - ukdm
http://www.geek.com/articles/chips/theoretical-physicist-explains-why-moores-law-will-collapse-20120430/
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Steuard
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.

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bobbydavid
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 ~6 _10^23 atoms
of Silicon weigh 28 grams --- which means a single atom weighs 4.7_ 10^-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 2.4 _10^-3g == 5.2_
10^19 atoms. The cube root of this number, 3.7 _10^6, is the number of atoms
on a side, so the number of atoms on a mm^2 face is 1.4_ 10^13.

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-...](http://www.tomshardware.com/reviews/core-i7-3960x-x79-sandy-
bridge-e,3071.html)

[2] <http://en.wikipedia.org/wiki/Silicon>

[3] <http://en.wikipedia.org/wiki/Diamond_cubic>

~~~
DennisP
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.

~~~
bobbydavid
Could you explain a bit more about the black hole argument?

~~~
Steuard
Here's some napkin math on the black hole argument. Information is essentially
equivalent to entropy: the entropy S = k * log M, where k is Boltzmann's
constant and log M is the number of bits encoding the information. Now, it
turns out to be _fundamentally_ impossible to store more entropy in any region
of space than would be contained in a black hole of the same size: S_max = (k
A c^3)/(4 G hbar), where A is the "surface area" of the region, c is the speed
of light, G is Newton's gravitational constant, and hbar is Planck's constant.
That means the maximum number of bits of information in a region of space is
(A c^3)/(4 G hbar), or about A * (10^69 1/m^2). Our solar system is maybe 1
light year in size: about 10^16 m, so its "surface area" is 4pi r^2 ~ 10^33
m^2. That means that the solar system can hold at most 10^102 bits of
information.

If Moore's law says that computer memory doubles in capacity every 2 years,
then they'll go up by a factor of 1000 about every 20 years. We currently have
computers that hold about 10^12 bits of information, so just 90*20 = 1800
years would get up to that absolute limit, regardless of what technology we
used, unless our single computer was bigger than a light year in radius.

~~~
Steuard
Whoops! I had a feeling I was being careless at the end there. It should have
been 30x20 years rather than 90x20, so just 600 years until Moore's law is
absolutely finished regardless of technology. (That shouldn't feel all that
much closer, but it does.)

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pilom
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.

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DennisP
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.

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hapless
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.

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

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drcube
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.

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maeon3
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.

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yoklov
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)

