hibbert@netcom.com writes:
> Another aspect of the bizarre here is the belief that "Sooner or later
> the phyxical system [will pass] out of the regime where the equation
> fit". Yes, it's true that it's common for "reality [to] deviate from
> the model", but the better job you've done of showing that some
> equation fits the real world, the less reason you have for believing
> you've found a phenomenon that should be expected to expire. A lot of
The universe is finite, even our physics is finite -- apart from
singularities, which indicate a failure of theory, not reality. Set
in a universe like this, an exponential function cannot hold for
meaningful amount of time before running into limitations of this
spacetime (we definitely do have a case of damaged goods here).
And the only way to test that an equation fits is find out why it
fits, or falsify it by empiricial means, i.e. by showing that the
system is moving out of the predictable context.
> people use "there's a first time for everything" as if it means
> everything will eventually happen, rather than that everything that
> actually does happen has a first occurence.
Huh?
> The moment when you've found a new consistency to the universe is not
> the time to start predicting that things will be different in the
> future. Exceptions to old consistencies might reasonably drive people
Funny, I disagree here. As soon as a theory has been established, duck
season is open. (Or maybe it's wabbit season).
> to look for explanations: either the old rule wasn't general enough or
> things have changed. But a newly noticed consistency is something to
> take advantage of, not something you should expect to be violated now
> that you've noticed it.
Ok, let's talk about Moore's law. Per se, it predicts only the amount
of devices you can put on an (affordable) die. Clearly, as structures
shrink by half, you can put four as many on the same surface. (The
same reason is making the hard drive storage grow larger in
exponential fashion). Simultaneously, the production costs of
semiconductors go up, unfortunately also in an exponential
fashion. Growing essentially defectless ton-weight monocrystals 300 mm
in diameter, monster optics for wafer steppers, even cleaner clean
rooms and even more complicated processes and testing devices
consisting of ten and hundreds millions of individual transistors
*are* costly.
Integrated circuits are a new technology, about three decades
old. Because defect density limits good die yield and you cannot
shrink structures below size where quantum effects start to dominate,
Moore as we know it should run out of steam somewhere in ~2014, or so
(I don't have the actual number at hand). Maybe one can make quantum
devices with semiconductor photolitho methods, which would push the
envelope a little, but I doubt it. (There are architectural tricks,
allowing one eventually use the entire wafer (a single wafer costs a
few hundred bucks to process) surface as a "good die", by shrinking
the system grain size and using defect-tolerant architectures, which
would do their own testing, etc. but this is outside of Moore's
scope).
At this stage, you have to abandon a given technology altogether. If a
successor technology (molecular circuitry) is not ready to take over
at this point, Moore linear plot will have to level off. So the total
time span where Moore has been applicable will be less than half of a
century.
I don't expect semiconductor photolitho devices to start failing Moore
now. I expect them to fail before 2020. So despite having a very nice
accurate law which has held for past three decades, the *more* "reason
you have for believing you've found a phenomenon that should be
expected to expire". Because, uh, it can't last forever. Sustainable
linear log plot growth is incommensurable with the physics of this
universe, as we know it. This is the envelope law, not some growth of
a given technology for 50 years, or so.
Surfaces of planets are finite, as the tolerable energy flux on their
surfaces. The number of atoms in a planet is finite. The energy output
of the sun is finite. The number of atoms in a solar system is
finite. The number of stars in a galaxy is finite. The numbers of
galaxies you can reach before the accelerating spacetime expansion
makes travel impossible is finite. The amount of matterenergy in a
given spacetime is probably finite.
So, unless we have new physics eventually bailing us out, we're stuck
in an universe full of limitations.
This archive was generated by hypermail 2b30 : Mon May 28 2001 - 09:50:15 MDT