Re: Is Intel exceptionally unsuccessful as an architecture designer?

On Wed, 2 Oct 2024 7:20:47 +0000, David Brown wrote:

On 01/10/2024 23:09, MitchAlsup1 wrote:

On Tue, 1 Oct 2024 19:07:18 +0000, Niklas Holsti wrote:
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On 2024-10-01 21:20, MitchAlsup1 wrote:

On Tue, 1 Oct 2024 15:51:36 +0000, Thomas Koenig wrote:
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Mathematics is not a sciene under this definition, by the way.

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Indeed, Units of forward progress in Math are done with formal
proofs.

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Yes, in the end, but it is interesting that a lot of the progress in
mathematics happens thruogh the invention or intuition of /conjectures/,
which may eventually be proven correct and true, or incorrect and
needing modification.

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Mathematical conjectures have a spectrum of "solidity" often more
solid in one branch of math than in another.
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I am not entirely sure what you mean by that.
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A conjecture is a hypothesis that you have reasonable justification for
believing is true, but which is not proven to be true (then it becomes a
theorem).  Some conjectures have been confirmed empirically to a large
degree (such as the Riemann hypothesis) which is not proof, but can be
seen as strengthening the conjecture.  Others, such as the continuum
hypothesis, not only have no empirical evidence but have been proven to
be independent of our usual ZF set theory axioms - no evidence either
way can be found.

Other conjectures had a century or more between being conjectured with
several "things they got right" before finally drifting towards a proof
or drifting towards disproof. The width of the drift is exactly the
spectrum I stated.

There are also some mathematicians who have a philosophy of viewing some
kinds of proofs as "better" than others.  Some dislike "proof by
computer", and don't consider the four-colour theorem to be a proven
theorem yet.

Over time proofs drift towards being an axiom (at least in their little
branch of math--which might not be axiomatic in other branches). others
start out proven and drift to the point there are only proven in one
or several branches of math.

            Others are "constructivists" - they are not happy with
merely a proof that some solution must exist, they only consider the
hypothesis properly proven when they have a construction for a solution.
  In that sense, a given conjecture may have more "solidity" in one
/school/ of mathematics than in another.

that is what I am talking about--it is all a big multidimensional
spectrum of {proof or conjecture}

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But I don't quite see how a single conjecture could have more "solidity"
in one /branch/ of mathematics than another.  An example or two might
help.

A conjecture/proof in ring-sum math may not work at all in
Real-Numbers. They are different branches in the space of Math.
Some proofs only work in Cartesian Multi-D spaces and fail in
manifold spaces.

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An open (neither proved nor disproved) conjecture often collects lots of
"observed evidence", either by suggesting some interesting corollaries
or analogies that are then proved independently, or by surviving
energetic efforts to find counterexamples to the conjecture. In this
sense an open conjecture resembles a theory in physics.

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The solution to Fermat's last theorem used a large series of
then conjectures in order to demonstrate that the solution
was correct.
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Yes - and then those supporting conjectures were proven and morphed into
theorems, with the knock-on effect of making everything higher up a
proven theorem.
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This is very common in mathematics - you develop conditional proofs
building on assuming a conjecture is true, and then you (or someone
else) goes back and proves that conjecture later, or perhaps finds
another path around that part.  For many theorems in mathematics, the
complete proof is a /very/ long and winding path.

The long and winding road .. .