On 17 Jan 2017 13:09 +0000, from tfb at tfeb.org (Tim Bradshaw):
> I think we've all lived in a wonderful time where it seemed like
> various exponential processes could continue for ever: they can't.

I'm personally inclined to agree with Tim here. That's not to say that
I don't think some of those processes could be pushed a bit farther,
but as much as we would love it in some cases, a function on the form
f(x)=Ca^{Dx} (for any values of C, D and a) describing something that
can exist in the real world simply cannot continue forever before
encountering some real-world limit.

Zoom out what appears to be an exponential curve and more often than
not, it turns out that what looked like an exponential curve was
really the first portion of a S curve or (even worse in many cases) a
portion of a parabola. Either that, or it's something like the
Tsiolkovsky rocket equation or the relativistic colinear velocity
addition formula, where the exponent is something you try very hard to
_avoid_ the effects of for one reason or another.

What could conceivably change that picture somewhat is a total
paradigm shift in computing, kind of like if large general-purpose
quantum computers turn out to be viable after all. But even in that
case I'm pretty sure that at some point we would realize that we are
on the same kind of S curve or parabola there as well, only having
delayed the inevitable or shifted the origin.

That's not to say that even steady-state computer power can't provide
huge benefits. It absolutely can. Even the computers we have and are
able to actually build today are immensely powerful both in terms of
computational capability and storage, and they are, to a large degree,
scalable with the proper software and algorithms. The kind of computer
I have _at home_ today (which wasn't even top of the line when I put
it together a few years ago) would have been considered almost
unimaginably powerful just a few decades ago.

-- 
Michael Kjörling • https://michael.kjorling.se • michael at kjorling.se
                 “People who think they know everything really annoy
                 those of us who know we don’t.” (Bjarne Stroustrup)