Discussion:
The Universe Is Not A Sphere
Add Reply
LaurenceClarkCrossen
2024-11-12 21:35:12 UTC
Reply
Permalink
The Universe Is Not A Sphere

So, parallel lines on its surface do not meet.
That would not make the space within it curve even if it were.
rhertz
2024-11-12 22:24:42 UTC
Reply
Permalink
Post by LaurenceClarkCrossen
The Universe Is Not A Sphere
So, parallel lines on its surface do not meet.
That would not make the space within it curve even if it were.
The Universe has these dimensions, for a xyz Cartesian frame, centered
on Earth:

x axis: from - infinite to + infinite

y axis: from - infinite to + infinite

z axis: from - infinite to + infinite

So, it has no shape, no boundaries and is timeless, eternal.

NEVER EVER the human bacteria will know what is it. NEVER.

But some degenerate genetic garbage, in their pseudo-science, pretend to
know about it, and find publishers. As well as SATANISTS.
LaurenceClarkCrossen
2024-11-12 22:57:11 UTC
Reply
Permalink
Riemann was a brilliant geometer who made the elementary error of
reifying space by claiming parallel lines could meet. Schwarzschild and
Einstein carried through with that mistake, making people believe it was
intelligent.
Ross Finlayson
2024-11-12 23:14:31 UTC
Reply
Permalink
Post by LaurenceClarkCrossen
Riemann was a brilliant geometer who made the elementary error of
reifying space by claiming parallel lines could meet. Schwarzschild and
Einstein carried through with that mistake, making people believe it was
intelligent.
Art students know there's a point at infinity.
LaurenceClarkCrossen
2024-11-12 23:45:45 UTC
Reply
Permalink
Ross: Another pointless comment.
J. J. Lodder
2024-11-24 08:53:18 UTC
Reply
Permalink
Post by Ross Finlayson
Post by LaurenceClarkCrossen
Riemann was a brilliant geometer who made the elementary error of
reifying space by claiming parallel lines could meet. Schwarzschild and
Einstein carried through with that mistake, making people believe it was
intelligent.
Art students know there's a point at infinity.
A whole line at infinity of them, even,

Jan
Ross Finlayson
2024-11-24 18:16:40 UTC
Reply
Permalink
Post by J. J. Lodder
Post by Ross Finlayson
Post by LaurenceClarkCrossen
Riemann was a brilliant geometer who made the elementary error of
reifying space by claiming parallel lines could meet. Schwarzschild and
Einstein carried through with that mistake, making people believe it was
intelligent.
Art students know there's a point at infinity.
A whole line at infinity of them, even,
Jan
One idea about the quadrant is to shrink it to a box,
given that the ray from origin (in a Cartesian space)
in x = y is an "identity dimension" and rather "original"
itself, then that the hyperbola, xy = 1 andx = 1/y and y = 1/x,
its corner, is parameterized to go out the identity line
and result in the limit connecting (0, \infty) and (\infty, 0).


Then, it's possible to make some ways for like a Fourier-style
analysis, instead a "hyperbolic hat", from shrinking the quadrant
to a box, which now has a diagonal this identiy line, and reverse
diagonal the asymptotic hyperbola.


This way then one may imagine an entirely novel or at least
to my meager experience otherwise unknown analytic series,
like Fourier for bounded regions yet furthermore rather boxed,
and arrive at a thing.


Yes it's so that behind an point at infinity are more points
at infinity, like beyond the speed of sound is the speed of
light is, in classical theories, the speed of gravity, infinity.

You know, 0 meters per second is infinity seconds per meter, ...,
thus it takes infinitely-many higher-orders of the derivatives
of displacement to help define the under-defined changes of
whatever are dynamics in "rest" and "motion".


This is a usual topic in my podcasts,
https://www.youtube.com/@rossfinlayson .
Ross Finlayson
2024-11-24 20:28:55 UTC
Reply
Permalink
Post by Ross Finlayson
Post by J. J. Lodder
Post by Ross Finlayson
Post by LaurenceClarkCrossen
Riemann was a brilliant geometer who made the elementary error of
reifying space by claiming parallel lines could meet. Schwarzschild and
Einstein carried through with that mistake, making people believe it was
intelligent.
Art students know there's a point at infinity.
A whole line at infinity of them, even,
Jan
One idea about the quadrant is to shrink it to a box,
given that the ray from origin (in a Cartesian space)
in x = y is an "identity dimension" and rather "original"
itself, then that the hyperbola, xy = 1 andx = 1/y and y = 1/x,
its corner, is parameterized to go out the identity line
and result in the limit connecting (0, \infty) and (\infty, 0).
Then, it's possible to make some ways for like a Fourier-style
analysis, instead a "hyperbolic hat", from shrinking the quadrant
to a box, which now has a diagonal this identiy line, and reverse
diagonal the asymptotic hyperbola.
This way then one may imagine an entirely novel or at least
to my meager experience otherwise unknown analytic series,
like Fourier for bounded regions yet furthermore rather boxed,
and arrive at a thing.
Yes it's so that behind an point at infinity are more points
at infinity, like beyond the speed of sound is the speed of
light is, in classical theories, the speed of gravity, infinity.
You know, 0 meters per second is infinity seconds per meter, ...,
thus it takes infinitely-many higher-orders of the derivatives
of displacement to help define the under-defined changes of
whatever are dynamics in "rest" and "motion".
This is a usual topic in my podcasts,
Of course energy's conserved, in locales, is the idea,
and entelechy, the connection, is, conserved as a constant,
so, usual conservation laws are continuity laws too,
where of course you can find a great amount of consideration,
of the constant conservation of connectedness continuity,
where though energy's conserved: in vacuum energy, so,
the sum-of-histories sum-of-potentials is always evaluated
instantaneously at every instant, and that's conserved.

There's either conserved or created/destroyed, of course
it's to be considered that creation and conservation are
the two sorts of ideas about tendencies and propensities,
of least action and action-at-least, about dissipation
and attenuation also oscillation and restitution,
that our analytical logicist positivism is also
quite ideal and thoroughly on its own all the terms.

It's a continuum mechanics, ..., this field theory a gauge theory.
(An inertial system and a differential/integral system.)

So, the "identity dimension" is sort of like the origin
in projection, and the envelope of various integral equations
including "the linear fractional equation", Clairaut's and
d'Alembert's, then the actual definition of motion: is
that the current way today, it is under-defined, so the
current way today, it was given some further definition,
"worlds turn".

There's a hundred and more hours of lectures in my podcasts,
it's about Foundations, then though mostly it's the result
of an extended letter-writing campaign of about 10's thousands
essays, in short form.

Of course energy is in a sense always "potential", in
a sum-of-potentials theory where the potential fields
are the real fields, even the classical fields.

All one theory, ....
Thomas Heger
2024-11-26 09:27:54 UTC
Reply
Permalink
Post by Ross Finlayson
Post by J. J. Lodder
Post by Ross Finlayson
Post by LaurenceClarkCrossen
Riemann was a brilliant geometer who made the elementary error of
reifying space by claiming parallel lines could meet. Schwarzschild and
Einstein carried through with that mistake, making people believe it was
intelligent.
Art students know there's a point at infinity.
'at' and 'point' mean essentially the same thing.

But it is, of course, wrong to assign a point to infinity, because
infinity is not a point and it is impossible to be there (hence there is
no 'at').
Post by Ross Finlayson
Post by J. J. Lodder
A whole line at infinity of them, even,
Jan
One idea about the quadrant is to shrink it to a box,
It is also impossible to shrink infinity in any way, because infinity
will remain infinitely large, even after significant shrinking.
Post by Ross Finlayson
given that the ray from origin (in a Cartesian space)
in x = y is an "identity dimension" and rather "original"
itself, then that the hyperbola, xy = 1 andx = 1/y and y = 1/x,
its corner, is parameterized to go out the identity line
and result in the limit connecting (0, \infty) and (\infty, 0).
inf = 1/0

hence

inf * 0 =1

hence

0/inf = 1/inf²

;-)

but infinity is also not a number!


TH
...
Ross Finlayson
2024-11-27 01:18:24 UTC
Reply
Permalink
Post by Thomas Heger
Post by Ross Finlayson
Post by J. J. Lodder
Post by Ross Finlayson
Post by LaurenceClarkCrossen
Riemann was a brilliant geometer who made the elementary error of
reifying space by claiming parallel lines could meet. Schwarzschild and
Einstein carried through with that mistake, making people believe it was
intelligent.
Art students know there's a point at infinity.
'at' and 'point' mean essentially the same thing.
But it is, of course, wrong to assign a point to infinity, because
infinity is not a point and it is impossible to be there (hence there is
no 'at').
Post by Ross Finlayson
Post by J. J. Lodder
A whole line at infinity of them, even,
Jan
One idea about the quadrant is to shrink it to a box,
It is also impossible to shrink infinity in any way, because infinity
will remain infinitely large, even after significant shrinking.
Post by Ross Finlayson
given that the ray from origin (in a Cartesian space)
in x = y is an "identity dimension" and rather "original"
itself, then that the hyperbola, xy = 1 andx = 1/y and y = 1/x,
its corner, is parameterized to go out the identity line
and result in the limit connecting (0, \infty) and (\infty, 0).
inf = 1/0
hence
inf * 0 =1
hence
0/inf = 1/inf²
;-)
but infinity is also not a number!
TH
...
The "infinity, mathematical" is an interesting thing,
I enjoy studying it and have studied it since at least
thirty years, though also at least about forty-five
years ago the word "INFINITY" was in the language.

Sort of like "ALL" and other universals - INFINITY
is always in the context.

That "infinity-many iota-values either sum to or produce 1",
is the idea of standard infinitesimals that just like a
line integral and the line elements or path integral, in
a line, and path elements, makes that mathematical and
the mathematical physics particularly has infinity.

Are you familiar with "mathematical formalism the
modern mathematics way: axiomatic set theory with
descriptive set theory in model theory"?

See, here there are at least three models of continuous
domains, where the usual account of "set theory's" (really
meaning the "a standard linear curriculum" as with regards
to what "mathematical foundations", is, i.e. set theory
plus models of rationals after integers then LUB and
measure 1.0 furthermore axioms), the usual account, has
one, the Archimedean field reals, that here there are
first line reals, or infinitely-many constant iota-values
in a row, line-reals, then field-reals for example by
the standard formalism, then signal-reals, and getting
involved with real halving- and doubling- spaces that
taking individua of continua sometimes doubles and
sometimes halves, the real analytical character.

So, I must imagine that you have each these three
kinds of continuous domains in your theory, as with
regards then to various law(s), plural, of large
numbers (infinities, actually, effectively, practically,
or potentially).

Surely your mathematical physics for real analysis at some
point employs these three, not inter-changeable or
equi-interpretable, yet according to "bridges" or
"ponts" pretty much the integers or bounds, like they
are called the path integral or real numbers or
signal theory.

Yes, no?
Ross Finlayson
2024-11-27 18:07:19 UTC
Reply
Permalink
Post by Ross Finlayson
Post by Thomas Heger
Post by Ross Finlayson
Post by J. J. Lodder
Post by Ross Finlayson
Post by LaurenceClarkCrossen
Riemann was a brilliant geometer who made the elementary error of
reifying space by claiming parallel lines could meet. Schwarzschild and
Einstein carried through with that mistake, making people believe it was
intelligent.
Art students know there's a point at infinity.
'at' and 'point' mean essentially the same thing.
But it is, of course, wrong to assign a point to infinity, because
infinity is not a point and it is impossible to be there (hence there is
no 'at').
Post by Ross Finlayson
Post by J. J. Lodder
A whole line at infinity of them, even,
Jan
One idea about the quadrant is to shrink it to a box,
It is also impossible to shrink infinity in any way, because infinity
will remain infinitely large, even after significant shrinking.
Post by Ross Finlayson
given that the ray from origin (in a Cartesian space)
in x = y is an "identity dimension" and rather "original"
itself, then that the hyperbola, xy = 1 andx = 1/y and y = 1/x,
its corner, is parameterized to go out the identity line
and result in the limit connecting (0, \infty) and (\infty, 0).
inf = 1/0
hence
inf * 0 =1
hence
0/inf = 1/inf²
;-)
but infinity is also not a number!
TH
...
The "infinity, mathematical" is an interesting thing,
I enjoy studying it and have studied it since at least
thirty years, though also at least about forty-five
years ago the word "INFINITY" was in the language.
Sort of like "ALL" and other universals - INFINITY
is always in the context.
That "infinity-many iota-values either sum to or produce 1",
is the idea of standard infinitesimals that just like a
line integral and the line elements or path integral, in
a line, and path elements, makes that mathematical and
the mathematical physics particularly has infinity.
Are you familiar with "mathematical formalism the
modern mathematics way: axiomatic set theory with
descriptive set theory in model theory"?
See, here there are at least three models of continuous
domains, where the usual account of "set theory's" (really
meaning the "a standard linear curriculum" as with regards
to what "mathematical foundations", is, i.e. set theory
plus models of rationals after integers then LUB and
measure 1.0 furthermore axioms), the usual account, has
one, the Archimedean field reals, that here there are
first line reals, or infinitely-many constant iota-values
in a row, line-reals, then field-reals for example by
the standard formalism, then signal-reals, and getting
involved with real halving- and doubling- spaces that
taking individua of continua sometimes doubles and
sometimes halves, the real analytical character.
So, I must imagine that you have each these three
kinds of continuous domains in your theory, as with
regards then to various law(s), plural, of large
numbers (infinities, actually, effectively, practically,
or potentially).
Surely your mathematical physics for real analysis at some
point employs these three, not inter-changeable or
equi-interpretable, yet according to "bridges" or
"ponts" pretty much the integers or bounds, like they
are called the path integral or real numbers or
signal theory.
Yes, no?
Another one gets involved to have concentric cyclotrons,
in opposite directions, then getting into helping illustate
that electromagnetism's behavior of moving influence,
that is not observed in light yet reflects particularly
the electrical fields' contents, then with a neutral linac
adjacent and across those, makes a rather simple idea.


The advanced and retarded in the electromagnetic has a
lot to do with the "opposites" in the fluid model,
electrical current and liquid current, with regards
the "opposite" meaning "super-classical" effects like
skin effect versus core effect, then about curls and
eddies and vortices about magnetic moments and poles,
axoi and polloi, vis-a-vis the static, in electrodynamics,
and static, in hydrodynamics.

Anyways it's rather simple this configuration of experiment
a "neutral linac and charged cyclotron" that sees arrived
at achievable experiments with clearly obvious what would
be "non-null".


The Sagnac effect shows up a lot for light, Sagnac and Ehrenfest,
"space-time wheel" type bits, that anyways once a "neutral linac",
for example accelerated charged decaying particles that decay
to neutral, makes a quite simple describe experiment.

... That would falsify, or not, space-contraction-linear,
and, space-contraction-rotation, each.
Ross Finlayson
2024-11-28 18:52:04 UTC
Reply
Permalink
Post by Ross Finlayson
Post by Ross Finlayson
Post by Thomas Heger
Post by Ross Finlayson
Post by J. J. Lodder
Post by Ross Finlayson
Post by LaurenceClarkCrossen
Riemann was a brilliant geometer who made the elementary error of
reifying space by claiming parallel lines could meet. Schwarzschild and
Einstein carried through with that mistake, making people believe it was
intelligent.
Art students know there's a point at infinity.
'at' and 'point' mean essentially the same thing.
But it is, of course, wrong to assign a point to infinity, because
infinity is not a point and it is impossible to be there (hence there is
no 'at').
Post by Ross Finlayson
Post by J. J. Lodder
A whole line at infinity of them, even,
Jan
One idea about the quadrant is to shrink it to a box,
It is also impossible to shrink infinity in any way, because infinity
will remain infinitely large, even after significant shrinking.
Post by Ross Finlayson
given that the ray from origin (in a Cartesian space)
in x = y is an "identity dimension" and rather "original"
itself, then that the hyperbola, xy = 1 andx = 1/y and y = 1/x,
its corner, is parameterized to go out the identity line
and result in the limit connecting (0, \infty) and (\infty, 0).
inf = 1/0
hence
inf * 0 =1
hence
0/inf = 1/inf²
;-)
but infinity is also not a number!
TH
...
The "infinity, mathematical" is an interesting thing,
I enjoy studying it and have studied it since at least
thirty years, though also at least about forty-five
years ago the word "INFINITY" was in the language.
Sort of like "ALL" and other universals - INFINITY
is always in the context.
That "infinity-many iota-values either sum to or produce 1",
is the idea of standard infinitesimals that just like a
line integral and the line elements or path integral, in
a line, and path elements, makes that mathematical and
the mathematical physics particularly has infinity.
Are you familiar with "mathematical formalism the
modern mathematics way: axiomatic set theory with
descriptive set theory in model theory"?
See, here there are at least three models of continuous
domains, where the usual account of "set theory's" (really
meaning the "a standard linear curriculum" as with regards
to what "mathematical foundations", is, i.e. set theory
plus models of rationals after integers then LUB and
measure 1.0 furthermore axioms), the usual account, has
one, the Archimedean field reals, that here there are
first line reals, or infinitely-many constant iota-values
in a row, line-reals, then field-reals for example by
the standard formalism, then signal-reals, and getting
involved with real halving- and doubling- spaces that
taking individua of continua sometimes doubles and
sometimes halves, the real analytical character.
So, I must imagine that you have each these three
kinds of continuous domains in your theory, as with
regards then to various law(s), plural, of large
numbers (infinities, actually, effectively, practically,
or potentially).
Surely your mathematical physics for real analysis at some
point employs these three, not inter-changeable or
equi-interpretable, yet according to "bridges" or
"ponts" pretty much the integers or bounds, like they
are called the path integral or real numbers or
signal theory.
Yes, no?
Another one gets involved to have concentric cyclotrons,
in opposite directions, then getting into helping illustate
that electromagnetism's behavior of moving influence,
that is not observed in light yet reflects particularly
the electrical fields' contents, then with a neutral linac
adjacent and across those, makes a rather simple idea.
The advanced and retarded in the electromagnetic has a
lot to do with the "opposites" in the fluid model,
electrical current and liquid current, with regards
the "opposite" meaning "super-classical" effects like
skin effect versus core effect, then about curls and
eddies and vortices about magnetic moments and poles,
axoi and polloi, vis-a-vis the static, in electrodynamics,
and static, in hydrodynamics.
Anyways it's rather simple this configuration of experiment
a "neutral linac and charged cyclotron" that sees arrived
at achievable experiments with clearly obvious what would
be "non-null".
The Sagnac effect shows up a lot for light, Sagnac and Ehrenfest,
"space-time wheel" type bits, that anyways once a "neutral linac",
for example accelerated charged decaying particles that decay
to neutral, makes a quite simple describe experiment.
... That would falsify, or not, space-contraction-linear,
and, space-contraction-rotation, each.
Of course equipping mathematics with more and better and
true and real mathematics of infinities and infinitesimals
may automatically then make for equipping the physical models
with more real true things about continuity and infinity
in nature.

So, mathematics has a great linear curriculum, yet at the
same time the mathematics of infinity and continuity has
multiple perspectives, as it were, to fulfill, that there
are multiple mathematical models of a continuous domain,
and multiple law(s) of large numbers, and these things that
make for what "is" the continuous mani-fold, in what "is"
an un-bounded or in-finite universe.

Thusly, any theory of everything must need resolve all
the logical paradoxes first, then make the _replete_
of the mathematical "complete", for it to be that
otherwise it's easy to derive contradictions arising
from things like the line integral and motion itself,
in the physical model the physical interpretation.

So, physics for a long time made its great efforts in
finding methods, mathematical, that yet keep infinity
"out", yet, being that it's yet always a thing, that
a measured approach to continuum mechanics being "in",
these days involves continuum mechanics, quasi-invariant
measure theory, law(s), plural, of large numbers, law(s),
plural, of convergence what make emergence, model(s), plural,
of continuous domains and spaces of 0's and 1's:
that each logic, mathematics, physics, science,
have that "mathematics _owes_ physics more and better",
about, more and better.

Continuity and infinity, ..., mathematically.

Then here for example that's "nutrino, muon, hadron physics
to make more super-symmetric continuity after electron physics",
and, "motion: change and infinitely-many higher orders of acceleration".

It's a continuum mechanics, ....


Then, with regards to singularity theory, one should
keep in mind that singularities, are just branches,
in multiplicity theories.


Of course it sort of requires a theory of truth and all, ....

It's a continuum mechanics.
J. J. Lodder
2024-11-29 17:41:20 UTC
Reply
Permalink
Post by LaurenceClarkCrossen
Riemann was a brilliant geometer who made the elementary error of
reifying space by claiming parallel lines could meet. Schwarzschild and
Einstein carried through with that mistake, making people believe it was
intelligent.
Dear Genius,
Could you please prove his hypothesis for us,
when you are finished putting him down?

Jan
Ross Finlayson
2024-11-29 18:48:46 UTC
Reply
Permalink
Post by J. J. Lodder
Post by LaurenceClarkCrossen
Riemann was a brilliant geometer who made the elementary error of
reifying space by claiming parallel lines could meet. Schwarzschild and
Einstein carried through with that mistake, making people believe it was
intelligent.
Dear Genius,
Could you please prove his hypothesis for us,
when you are finished putting him down?
Jan
You mean torsion and vortices in free rotation the
un-linear, making for space contraction?


If you take a look at a circle, and a diameter,
then draw inner circles, their diameters the
two radii that is the outer diameter, so that
the sum of the diameters is the same, and then,
the sum of perimeters is the same, because circles
make that for diameter d is perimeter pi d.

So, repeating this ad infinitum, makes smaller
and smaller circles bisecting each diameter,
whose sum diameter is a constant and sum perimeter
is a constant.

Then, all the down, a flat line, the, "perimeter",
or length, is not the same, it's d/2, say.

So, it's like a "pi ratio space", or, say,
"2pi ratio space", that in the infinite limit,
is different what it is according to induction.
In this way it's like Vitali's doubling measure
and Vitali and Hausdorff's equi-decomposability
of a ball to two equal balls, "doubling space",
about "doubling measure", this "pi ratio space",
"pi ratio measures". I think that's cooler than
Banach-Tarski as it's geometrical, about geometry,
that Vitali and Hausdorff were pretty great geometers.


So, now when you look at the gravitational field equations,
and Riemann's Riemann metric contribution, you'll notice
that it's sort of about a linear metric, that though
over and over again and all the down is sub-divided,
to what's a metric in the "merely linear", this,
"un-linear".


Anyways though the usual "Riemannian geometry" is
matters of perspective and projection is all.

I.e. it's Euclidean, the conformal mapping.

One can readily see it's a mathematical device
a conceit, a concession, "Riemannian geometry",
about conformal mapping with free rotation.


So, what Einstein arrived at, is mass-energy equivalency
the kinetic, that's only ever kinematic and rotational,
that it's always, "un-linear", that these days is
often called, "non-linear".

Or, that was the last derivation Einstein authored
into "Out of My Later Years", a culmination of
his thinking.

In my podcasts today is a "Logos 2000: geometry logically",
helping arrive at axiomless natural geometry.

https://www.youtube.com/@rossfinlayson

The usual Newtonian laws of mechanics are a bit
under-defined, so there's room under them to
add definition to mechanics, the kinetic/kinematic.
Ross Finlayson
2024-11-29 19:43:11 UTC
Reply
Permalink
Post by Ross Finlayson
Post by J. J. Lodder
Post by LaurenceClarkCrossen
Riemann was a brilliant geometer who made the elementary error of
reifying space by claiming parallel lines could meet. Schwarzschild and
Einstein carried through with that mistake, making people believe it was
intelligent.
Dear Genius,
Could you please prove his hypothesis for us,
when you are finished putting him down?
Jan
You mean torsion and vortices in free rotation the
un-linear, making for space contraction?
If you take a look at a circle, and a diameter,
then draw inner circles, their diameters the
two radii that is the outer diameter, so that
the sum of the diameters is the same, and then,
the sum of perimeters is the same, because circles
make that for diameter d is perimeter pi d.
So, repeating this ad infinitum, makes smaller
and smaller circles bisecting each diameter,
whose sum diameter is a constant and sum perimeter
is a constant.
Then, all the down, a flat line, the, "perimeter",
or length, is not the same, it's d/2, say.
So, it's like a "pi ratio space", or, say,
"2pi ratio space", that in the infinite limit,
is different what it is according to induction.
In this way it's like Vitali's doubling measure
and Vitali and Hausdorff's equi-decomposability
of a ball to two equal balls, "doubling space",
about "doubling measure", this "pi ratio space",
"pi ratio measures". I think that's cooler than
Banach-Tarski as it's geometrical, about geometry,
that Vitali and Hausdorff were pretty great geometers.
So, now when you look at the gravitational field equations,
and Riemann's Riemann metric contribution, you'll notice
that it's sort of about a linear metric, that though
over and over again and all the down is sub-divided,
to what's a metric in the "merely linear", this,
"un-linear".
Anyways though the usual "Riemannian geometry" is
matters of perspective and projection is all.
I.e. it's Euclidean, the conformal mapping.
One can readily see it's a mathematical device
a conceit, a concession, "Riemannian geometry",
about conformal mapping with free rotation.
So, what Einstein arrived at, is mass-energy equivalency
the kinetic, that's only ever kinematic and rotational,
that it's always, "un-linear", that these days is
often called, "non-linear".
Or, that was the last derivation Einstein authored
into "Out of My Later Years", a culmination of
his thinking.
In my podcasts today is a "Logos 2000: geometry logically",
helping arrive at axiomless natural geometry.
The usual Newtonian laws of mechanics are a bit
under-defined, so there's room under them to
add definition to mechanics, the kinetic/kinematic.
The "doubling spaces" and "doubling measures" a few
years ago were the result of plain thinking about
objects of geometry, today references to them abound
in tons of recent papers in the lit-rature, one imagines
they're quite all over the place and often _thoroughly_
contrived, vis-a-vis, arriving at them, from principles.

I.e. it takes a rather thorough account of mathematics,
vis-a-vis bolting-on a fixer the stack, the stack, the
stack, the stack, the stack of derivations.

Heh "measure problem", yeah right they got "measure problems".

LaurenceClarkCrossen
2024-11-12 23:12:08 UTC
Reply
Permalink
Mr. Hertz: "While many astronomers believed the material universe to be
roughly identical to the Milky Way, Arrhenius based his cosmology on
what would later be called the perfect cosmological principle, the
postulate that the largescale appearance of the universe is the same at
any location and at any time. Arrhenius, who took Euclidean space to be
self-evident, concluded that the law of entropy growth did not apply on
a cosmic scale. By invoking radiation pressure and various energy
transfer processes between stars and nebulae he suggested that the
universe would never run down in the thermodynamic sense [Kragh 2013].
However, according to Poincaré’s detailed analysis in Hypothèses
cosmogoniques [Poincaré 1911, 239–256], [Rhee 2018, 391–405], what he
called “Arrhenius’ demon” might only retard the universal heat death,
perhaps for an exceedingly long time, but it could never escape it.7
Schwarzschild [1913] agreed with Poincaré that Arrhenius’ demon would
not work as promised and after the criticism of the two distinguished
scientists, Arrhenius’ cosmological hypothesis was essentially abandoned
by astronomers and physicists."
-"Poincaré and Cosmic Space: Curved or not?"

This is an example of giving too much ground to one's opponent and of
the consensus making a stupid mistake. Arrhenius did not need a
mechanism to prevent entropy because entropy does not apply to an open
system such as an infinite universe. That is why they wanted to presume
a finite universe.
Mikko
2024-11-13 10:19:27 UTC
Reply
Permalink
Post by LaurenceClarkCrossen
The Universe Is Not A Sphere
So it seems. However, the part of the Universe we can see looks,
except for minor irregularities, very similar to a small part of
a large sphere. But so does a small part of an Euclidean space.
Post by LaurenceClarkCrossen
So, parallel lines on its surface do not meet.
The path of a photon is a special kind of straight line. Light from
certain quasars (e.g. SBS 0957+561) come to us over two paths so that
the same qasars can be seen in two directions. This shows that two
stright lines can cross twice. Somewhere between the two crossings
they look parallel.
--
Mikko
Maciej Wozniak
2024-11-13 15:29:52 UTC
Reply
Permalink
Post by Mikko
Post by LaurenceClarkCrossen
The Universe Is Not A Sphere
So it seems. However, the part of the Universe we can see looks,
except for minor irregularities, very similar to a small part of
a large sphere. But so does a small part of an Euclidean space.
Post by LaurenceClarkCrossen
So, parallel lines on its surface do not meet.
The path of a photon is a special kind of straight line. Light from
certain quasars (e.g. SBS 0957+561) come to us over two paths so that
the same qasars can be seen in two directions. This shows that two
stright lines can cross twice.
Poincare has been explaining how absurd
such "logic" is - even before it happened.
And, of course, even relativistic idiots
are not stupid enough to stick to it for
real. In most cases of their moronic mumble
photon's paths are bent.
LaurenceClarkCrossen
2024-11-13 21:08:34 UTC
Reply
Permalink
Mikko: Straight lines can cross but not parallel lines. Lensing involves
curving of the path of light according to science. If relativity tells
you otherwise, you have been deceived.
Mikko
2024-11-14 09:42:14 UTC
Reply
Permalink
Post by LaurenceClarkCrossen
Mikko: Straight lines can cross but not parallel lines. Lensing involves
curving of the path of light according to science. If relativity tells
you otherwise, you have been deceived.
In every situation were it has been examined light in vacuum travels
along a straght line in space time. The spatial projection of that
line can be curved.
--
Mikko
Maciej Wozniak
2024-11-14 14:16:23 UTC
Reply
Permalink
Post by Mikko
In every situation were it has been examined light in vacuum travels
along a straght line in space time.
Even the idiots from your bunch of idiots,
however, are not stupid enough to stick to
that absurd for real
https://en.wikipedia.org/wiki/Gravitational_lens
and the light is bent for them.

Poincare has been explaining that such stance is
better than non-euclidean idiocies and while
you're denying that for religious reasons you're
still applying it for practical reasons.
LaurenceClarkCrossen
2024-11-14 04:24:52 UTC
Reply
Permalink
Mikko: "Is Spacetime Really a Four-Dimensional Continuum?"
Stephen J. Crothers
"Time is measured in time units T, such as seconds, hours, or years.
Distance between two places is measured in length units L, such as
metres, yards, or miles. Consequently t cannot be added to any x, y, z,
because t has time units T whereas x, y and z have length units L.
Similarly t2 cannot be added to or subtracted from x2, y2, or z2, or
vice-versa....... The act of treating ct as an independent coordinate or
independent 'dimension' does not make it either.
Since ct is not an independent coordinate, spacetime is not a
four-dimensional continuum...... Spacetime is a fallacy [1, Appendix G].
The Theory of Relativity
employs Riemannian Geometry. In Riemannian Geometry, “Any n independent
variables xi, where i takes values 1 to n, may be thought of as the
coördinates of an n-dimensional space Vn in the sense that each set of
values of the variables defines a point of Vn.” Eisenhart [2]
The term ct is no more an independent coordinate than is xy/z, or x2/y,
or (x2 + y2 + z2)/x, all of which have the units of length L."
LaurenceClarkCrossen
2024-11-14 04:43:10 UTC
Reply
Permalink
Mikko: "Minkowski-Einstein spacetime: insight from the Pythagorean
theorem" Crothers= "ABSTRACT
The Pythagorean Theorem, combined with the analytic geometry of a right
circular cone, has been used by H. Minkowski and subsequent
investigators to establish the 4-dimensional spacetime continuum
associated with A. Einstein’s Special Theory of Relativity. Although the
mathematics appears sound, the incorporation of a hyper-cone
into the analytic geometry of a right triangle in Euclidean 3-space is
in conflict with the rules of pure mathematics. A metric space of n
dimensions is necessarily defined in terms of n independent coordinates,
one for each dimension. Any coordinate that is a combination of the
others for a given space is not independent so cannot be an
independent dimension. Minkowski-Einstein spacetime contains a
dimensional coordinate, via the speed of light, that is not independent.
Consequently, Minkowski-Einstein spacetime does not exist."
Bertietaylor
2024-11-24 09:00:35 UTC
Reply
Permalink
What is infinite can have no shape. Beyond shape is the infinite.
Loading...