From: James Rogers (firstname.lastname@example.org)
Date: Wed Nov 26 2003 - 16:38:27 MST
On Wed, 2003-11-26 at 11:42, Eugen Leitl wrote:
> My point precisely. Our high-level architecture has a huge
> perception/performance deficit as far as parallelism is concerned.
> We can't do it, because we just can't. Can alternative entities (AIs, aliens)
> debug 10^6 concurrent threads in the same manner as we can 2-3?
> Is this at all possible, or is all massive parallelism unattainable
> but by algorithms driven stochastically from the roots up? I wish we knew.
The amount of parallelism we can manage depends greatly on the nature of
the parallelism. Our hardware doesn't do it because our algorithm
models have limited use for it. Again, most of our parallelism is the
low ROI kind, which gives limited economic incentive to bother with it.
> The Turing machine is a nice hardware for a sequential-mind gedanken
> theorists, but as blueprint for a physical computer it sucks mossy
> rocks. People still don't realize that in this universe a sequential
> machine simply can't do most task by virtue of the universe being over,
> not to mention current realtime requirements, which are on ms..us scale.
A point that is worth making (again), is that much of our mathematics
surrounding computational theory is premised, at one or more levels, on
the UTM model. There is nothing intrinsically wrong with this, except
that as a model, UTMs are only useful in mathematics. Many computational
theorems that are inclusive of "universal" (i.e. infinite) machines look
different in important ways when constrained to the purely finite state
case from the ground up. A lot of computational theory is fairly loose
and undefinitive precisely because it has to include the edge case of
infinite machines, something which does not exist for real engineering
I first noticed the importance of this a several years ago when I
inadvertently derived a useful theorem that didn't match an existing
equivalent theorem in a "biblical" math text. The version I generated
was much more useful -- it made some additional assertions that the
"standard" version did not -- so I attempted to rectify it and see why
mine was different. It turned out that the sole difference was that my
math was explicitly constrained to purely finite cases. Not "universal"
in the mathematical sense, but universal for real-world purposes and
more useful as well.
Since then, I have become very cognizant that a great many of the things
most people believe (culturally, socially, politically, scientifically)
are based on invalid assumptions (implicit infinities, mathematical edge
cases, etc) for application in the real world. Noticing the
pervasiveness of these kinds of fallacies and unnoticed limitations even
among the "enlightened" thinkers has significantly altered my views on
many things over last few years. I've had to re-reason many things.
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