Saturation Curves

By: hobold (, February 2, 2021 5:58 am
Room: Moderated Discussions
A bit of dangerous half knowledge about saturation curves.
Followed by a very coarse long term forecast of CPU performance.

A few rules of thumb about the simplest of saturation curves:

- they describe a gradual increase from 0% to 100%, continuous
and smooth and monotonic (i.e. no waves or plateaus)

- they are symmetrical about the 50% midpoint, and have their
steepest slope there; around that inflection point the curve
appears to be linear

- when there is any appreciable amount of measurement error on
an observed growth curve, saturation can be pretty much
indistinguishable from exponential growth up to maybe the
15% mark

- to the naked eye, saturation can look like exponential up to
even the 30% mark (but curve fitting will tell you otherwise)

Starting from the assumption that Moore's Law was indeed true
during the exponential early phase of saturation, we can make
forecasts (yes, plural!) about the asymptotical saturation

- We can say that Moore's Law was true all the way to right
now. Then we'd conclude that we have roughly three
doublings left, and it will take around seven times as
much time as it took from the first electronic processor
until today.

- Or we think that the slowdown below exponential has been
quite noticeable for some time, and we are at the 30% mark
today. Then we'd have roughly two doublings left, and we'd
run into the limit correspondingly sooner.

- And finally we could observe that general purpose CPU
performance had already slowed down to linear growth. Then
we'd conclude to be near the 50% midpoint. There would be a
single doubling left. We would reach it in roughly the same
time that it took us from the first electronic processor
until today.

To conclude:
Silicon CPU's have at least one performance doubling left, and
it will take at least another 50 years of improvements to get
there. They are unlikely to have three doublings left, but if
they turn out to do, it can easily take us over 300 years to
get there.

Take that with an unhealthy dose of salt, because it is pure
numerology, without regard for the underlying physics,
economics, or politics.

This is a forecast and not a prediction. And certainly not a
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