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Subject: Re: No true relativist!
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On 11/09/2024 08:47 PM, LaurenceClarkCrossen wrote:
> Here's a good article: "Poincaré and Cosmic Space: Curved or not?" "The
> philosophical and historical dimensions of the concept of space have
> been scrutinized in a number of scholarly works, e.g., [Bonola 1955],
> [Torretti 1978], [Gray 1989], [Jammer 1993]. However, few of them pay
> much attention to how the possibility of curved space was received by
> astronomers and physicists in the pre-Einstein era, which is the subject
> of the present paper. More specifically, apart from an introductory
> section on early non-Euclidean geometry, I review the responses of the
> few astronomers, physicists and mathematicians who between 1872 and 1908
> expressed an interest in the question [see also Walter 1997]."
> https://shs.cairn.info/revue-philosophia-scientiae-2023-3-page-53?lang=fr

That's pretty good, I enjoy that. It helps reflect
that "indeterminate forms" or "infinity/infinity"
have that it's yet so usual that "1/infinity" gets zero'ed,
and for example small-angle-approximation is "true in
the limit", though not true and it's an approximation
except "in the infinite limit".

Mathematics then needs better and greater law(s) of
large numbers to explain infinite things, and,
particularly "convergence" when _it is well known_
that some infinite limits _do not meet_ some
otherwise usually inductively-founded convergence
criteria, in fast and slow convergence and also
as with regards to "asymptotic freedom", that most
excellent concept to go along with "mass/energy equivalency"
and "cosmological constant", that there are series
that belie all their finite inputs and refute mere induction,
as to why it is considerations of the entire _space_,
that may improve mathematics, and that most usual
formulations with "exactly one observer", are,
at best, partial and incomplete, and, as known
from non-linear analysis, having a wrong
negligeable/dominating ratio.

The "non-linear" and "non-standard" yet with
"real analytical character" is these days
the milieu. Consider for example "a space
of all the 0's and 1's", vis-a-vis, real numbers.

The complex numbers, are, not real numbers.
Yes I know there's much for modeling reflections
and rotations and including for the hypercomplex
as the Lie algebras are so ubiquitous, yet,
getting into Zariski and Kodaira after the
algebraic geometers after Lefschetz and Picarad
and into revived "integral analysis" besides
"differential analysis", has that the Eulerian-Gaussian
after deMoivre "complex analysis", has sort of
reached its limits, and you know, not reached its
infinite limits.