On 11/09/2024 02:16 PM, LaurenceClarkCrossen wrote:
Mr. Hertz:
>
Thanks for the Schwarzschild article. Having read it, it is clear he did
not understand how logically fallacious the idea of curved space is.
That is not indicative of high intelligence. Space is either an
abstraction making the curving of it irrelevant to physical space or a
vacuum making it something with no substance to curve. Curved space is
not permissible to the logical and rational scientist. It's permissible
to the licentious and deceitful. There is absolutely no empirical
evidence for it. It would require that parallel lines be proven to meet.
There is no evidence for a closed universe, which is a finite universe.
They wanted it to be finite so they could apply entropy, which only
applies to closed systems. This is unwarranted. In the Schwarzschild
article you provided he argues for assuming a curvature of space so
small as to be unnoticeable in a universe of the small size he
contemplates of 10,000 ly wide. In this way he makes his curvature
irrefutable by empirical means.
>
Schwarzschild himself says, "Thus the curvature of a hyperbolic space is
so insignificant that it cannot be observed via solar system
measurements, and because hyperbolic space is infinite, like Euclidean
space, no unusual appearances will be observed on looking at fixed star
systems."
>
The article starts: "If I presume to present a few remarks that have
neither any real practical applicability nor any pertinent mathematical
meaning, my excuse is that the topic we are considering has a particular
attraction for many of you because it presents an extension of our view
of things way beyond that due to our accessible experience, and opens
the most strange prospects for later possible experiences. That it
requires a total break with the astronomers’ deeply entrenched views
cannot but seem a further advantage to anyone convinced that all
knowledge is relative."
>
Schwarzschild wrote, "One finds oneself there — if one wants to — in a
geometrical fairyland, but the best thing about these fairy stories is
that one does not know whether they will indeed turn out to be true. The
questions as to how far we have pushed back the boundaries of this
fairyland can now be asked: how small is the curvature of space? and
what is a lower bound for its radius of curvature?‡."
The, "Fourth Dimension", is considered at least two things,
and one of them is a perspective dimension of free thought,
and the other is a perspective dimension of analytical book-keeping,
then though some have it that the absurd and ludicrous/ridiculous/
incredible follow after "Ex Falso Quodlibet", which others have
as repulsive and rejected because instead there's "Ex Falso Nihilum".
So, after Newton and "System of the World", it was also used to
help abandon and reject notions like "natural order" and other
matters of repressive fate or destiny, so, that logicist positivism
became the central underpinning of 20'th century philosophy,
falling adrift from teleology and determinism into the
existentialist/nihilist neither-nor.
So anyways the "forget what you know" bit can go stuff itself,
then there are matters of how mathematics can yet fulfill,
the things the theory, with as well some renewed teleological
metaphysics (not necessarily theological, merely a minimal
teleological), the teleological and ontological, as with
regards to that the theory belongs to the philosophers,
which as thinking beings you aspire to know or be.
Then, with regard to space-time curvature, besides the
"singularity" as asymptotic the infinity, it's more
generally for singularity theory that it's multiplicity
theory. The singularities / catastrophes / perestroikas ,
are each merely branches in multiplicity theories.
So, ..., the "spiral, space-filling curve", has,
curvature: 1/R. So, being a sort of singularity
and original itself, then it is the natural curvature
of the gauge theory's "R-gauge".
Then as with regards to modern philosophy and the
associated logic, there's mostly that the deductive
inference is a fuller completion and that any
good, relevant logic is a relevance logic and modal.
So, "Foundations" needs some fixing thoroughly.