[FOM] Mathematics ***is*** formalising of our thought and intuition
Steve Stevenson
steve at cs.clemson.edu
Tue Jun 8 10:30:23 EDT 2010
Computation is now recognized as the third leg of the Scientific
Method and is virtually impossible today to carry out research
without computational means (including "experimental mathematics). A
practical manifestation of the points brought up by Keith and Paddy is
the "verification" and "validation" (V&V) issue in computational
science. In FOM context, verification focuses on whether the
mathematics captures the theory (and therefore a correct specification
for the computer model) and validation focuses on whether the model
predictions have anything to do with reality. Based on my experience
in V&V, I propose a paraphrase of Brouwer's concept: "Mathematics is
that activity that goes on at the interface of modeling and reasoning".
--
Steve
School of Computing, Clemson University
"As far as the laws of mathematics refer to reality, they are not
certain; as far as they are certain, they do not refer to
reality" (Einstein).
On 7Jun 2010, at 2:14, Keith Brian Johnson wrote:
> I entirely agree with Paddy Hackett: It is by observation,
> including experimentation, that the scientist determines which
> patterns are concretely instantiated. He then applies mathematics
> to those concretely instantiated patterns, using logic to reason
> validly (and, if his descriptions of his observations are correct,
> soundly) from premisses at least some of which are about those
> observations to conclusions. He trusts those conclusions to the
> extent that he trusts his descriptions of his observations to be
> correct and to the extent that he trusts mathematics' analyses of
> patterns in the abstract to be correct and to the extent that he
> trusts logic's formalization of legitimate thought processes to be
> correct.
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