On 12/4/23 3:10 PM, Laurence Clark Crossen wrote:

The Big Bang and the Center of the Universe The velocity-distance relationship interprets the redshift-distance relationship as caused
by the Doppler shift of starlight. This relationship is the same in
every direction from Earth. This requires we are at the center of
the universe.

Nope! In a homogeneous and isotropic universe this would hold at any
location, and THERE IS NO "CENTER".

An infinite universe would have no place to expand to so such a
universe can not expand.

More nonsense. You simply do not understand differential geometry or GR.

You REALLY need to learn basic physics before attempting to write about it.

Tom Roberts

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On 12/4/23 6:30 PM, Laurence Clark Crossen wrote:

On Monday, December 4, 2023 at 3:22:39 PM UTC-8, Tom Roberts wrote:

On 12/4/23 3:10 PM, Laurence Clark Crossen wrote:

The Big Bang and the Center of the Universe The velocity-distance
relationship interprets the redshift-distance relationship as
caused by the Doppler shift of starlight. This relationship is
the same in every direction from Earth. This requires we are at
the center of the universe.

Nope! In a homogeneous and isotropic universe this would hold at
any location, and THERE IS NO "CENTER".

There is a center in a finite, homogeneous, and isotropic universe.

You have insufficient imagination. This is simply not true.

For example, the surface of the sphere S^2 is finite, homogeneous, and isotropic, yet it has no "center".

As you probably don't understand this, I mean no center
IN THE MANIFOLD ITSELF. You must consider its intrinsic
properties only, and cannot embed it in E^3, because this
is an analogy for the universe, and as you point out,
there is no "enclosing space" in which the universe could
be embedded.

An infinite universe would have no place to expand to so such a
universe can not expand.

More nonsense. You simply do not understand differential geometry
or GR.

Or mathematical infinities.

No matter what differential geometry or GR says an infinite universe
cannot expand.

Again, not true. You have insufficient imagination. The FLRW manifold
with zero spatial curvature is an example of an infinite universe that
does expand.

It is the distance between galaxies that is expanding.
IOW it is the metric that is expanding. For an infinite
universe, the manifold is an infinite topological space
and "expansion" simply does not (cannot) apply to it.

You are the one making the extraordinary claim,

My claims are not "extraordinary" at all, they are just standard
differential geometry and GR. Again, you wallow in your own ignorance.

You are like a caveman thinking that a wheel is
"extraordinary". Today, of course, it isn't.
Today we have differential geometry and GR.

You REALLY need to learn basic physics before attempting to write
about it.

Then, your usual ad hominems instead of reasoning or knowledge.

The problem is YOURS, in that you simply do not understand. I cannot
reason with your refusal to learn, and I display my knowledge in every post.

YOU, on the other hand, display your ignorance with
every post.

Tom Roberts

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On 12/5/2023 1:17 AM, Tom Roberts wrote:

On 12/4/23 6:30 PM, Laurence Clark Crossen wrote:

On Monday, December 4, 2023 at 3:22:39 PM UTC-8, Tom Roberts wrote:

On 12/4/23 3:10 PM, Laurence Clark Crossen wrote:

The Big Bang and the Center of the Universe The velocity-distance
relationship interprets the redshift-distance relationship as
caused by the Doppler shift of starlight. This relationship is
the same in every direction from Earth. This requires we are at
the center of the universe.

Nope! In a homogeneous and isotropic universe this would hold at any
location, and THERE IS NO "CENTER".

There is a center in a finite, homogeneous, and isotropic universe.

You have insufficient imagination. This is simply not true.

For example, the surface of the sphere S^2 is finite, homogeneous, and isotropic, yet it has no "center".

    As you probably don't understand this, I mean no center
    IN THE MANIFOLD ITSELF. You must consider its intrinsic
    properties only, and cannot embed it in E^3, because this
    is an analogy for the universe, and as you point out,
    there is no "enclosing space" in which the universe could
    be embedded.

To expand on this, where is the center of the SURFACE of a globe, or the
earth? In which country or ocean is it? I am explicitly not talking
about the center of the 3D earth itself, thousands of km below the
surface, but the point ON THE SURFACE which is the center OF THE
SURFACE. I repeat: Center of the 2D SURFACE, not the 3D center below it.

Is it the (0, 0) latitude/longitude in the Atlantic off the coast of
Africa? Why? The longitude line is arbitrary, but while the 0 latitude
line (the equator) has physical meaning, it is defined by a property of
the earth (its rotation), not some sort of "center" of the surface.
North or South Pole? Again, defined by the rotation but nothing special
about the surface itself. Maybe Mecca?

Think of a 4D hypersphere with a 3D "surface", which is our universe. In
the Big Bang theory the hypersurface of the hypersphere is expanding,
but like the regular sphere, there is no "center" of the hypersurface.
(even babbling Mitch seems to somewhat get this)

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On 12/5/2023 5:19 PM, Laurence Clark Crossen wrote:

On Tuesday, December 5, 2023 at 12:23:41 PM UTC-8, Volney wrote:

On 12/5/2023 1:17 AM, Tom Roberts wrote:

On 12/4/23 6:30 PM, Laurence Clark Crossen wrote:

On Monday, December 4, 2023 at 3:22:39 PM UTC-8, Tom Roberts wrote: >>>>> On 12/4/23 3:10 PM, Laurence Clark Crossen wrote:

The Big Bang and the Center of the Universe The velocity-distance
relationship interprets the redshift-distance relationship as
caused by the Doppler shift of starlight. This relationship is
the same in every direction from Earth. This requires we are at
the center of the universe.

Nope! In a homogeneous and isotropic universe this would hold at any >>>>> location, and THERE IS NO "CENTER".

There is a center in a finite, homogeneous, and isotropic universe.

You have insufficient imagination. This is simply not true.

For example, the surface of the sphere S^2 is finite, homogeneous, and
isotropic, yet it has no "center".

As you probably don't understand this, I mean no center
IN THE MANIFOLD ITSELF. You must consider its intrinsic
properties only, and cannot embed it in E^3, because this
is an analogy for the universe, and as you point out,
there is no "enclosing space" in which the universe could
be embedded.

To expand on this, where is the center of the SURFACE of a globe, or the
earth? In which country or ocean is it? I am explicitly not talking
about the center of the 3D earth itself, thousands of km below the
surface, but the point ON THE SURFACE which is the center OF THE
SURFACE. I repeat: Center of the 2D SURFACE, not the 3D center below it.

Is it the (0, 0) latitude/longitude in the Atlantic off the coast of
Africa? Why? The longitude line is arbitrary, but while the 0 latitude
line (the equator) has physical meaning, it is defined by a property of
the earth (its rotation), not some sort of "center" of the surface.
North or South Pole? Again, defined by the rotation but nothing special
about the surface itself. Maybe Mecca?

Think of a 4D hypersphere with a 3D "surface", which is our universe. In
the Big Bang theory the hypersurface of the hypersphere is expanding,
but like the regular sphere, there is no "center" of the hypersurface.
(even babbling Mitch seems to somewhat get this)

If you encase a space with a dodecahedron, you have twelve dimensions with the same amount of space and still have a center.

A dodecahedron has 3 dimensions and 12 faces, not 12 dimensions. Its
surface is 2 dimensional folded into 3 dimensional space. Where is the
center of the surface of the dodecahedron located? Justify your answer.
Again, NOT the center of the 3D object. The center of the surface.

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On 12/5/2023 4:11 PM, Laurence Clark Crossen wrote:

On Tuesday, December 5, 2023 at 12:23:41 PM UTC-8, Volney wrote:

On 12/5/2023 1:17 AM, Tom Roberts wrote:

On 12/4/23 6:30 PM, Laurence Clark Crossen wrote:

On Monday, December 4, 2023 at 3:22:39 PM UTC-8, Tom Roberts wrote: >>>>> On 12/4/23 3:10 PM, Laurence Clark Crossen wrote:

The Big Bang and the Center of the Universe The velocity-distance
relationship interprets the redshift-distance relationship as
caused by the Doppler shift of starlight. This relationship is
the same in every direction from Earth. This requires we are at
the center of the universe.

Nope! In a homogeneous and isotropic universe this would hold at any >>>>> location, and THERE IS NO "CENTER".

There is a center in a finite, homogeneous, and isotropic universe.

You have insufficient imagination. This is simply not true.

For example, the surface of the sphere S^2 is finite, homogeneous, and
isotropic, yet it has no "center".

As you probably don't understand this, I mean no center
IN THE MANIFOLD ITSELF. You must consider its intrinsic
properties only, and cannot embed it in E^3, because this
is an analogy for the universe, and as you point out,
there is no "enclosing space" in which the universe could
be embedded.

To expand on this, where is the center of the SURFACE of a globe, or the
earth? In which country or ocean is it? I am explicitly not talking
about the center of the 3D earth itself, thousands of km below the
surface, but the point ON THE SURFACE which is the center OF THE
SURFACE. I repeat: Center of the 2D SURFACE, not the 3D center below it.

Is it the (0, 0) latitude/longitude in the Atlantic off the coast of
Africa? Why? The longitude line is arbitrary, but while the 0 latitude
line (the equator) has physical meaning, it is defined by a property of
the earth (its rotation), not some sort of "center" of the surface.
North or South Pole? Again, defined by the rotation but nothing special
about the surface itself. Maybe Mecca?

Think of a 4D hypersphere with a 3D "surface", which is our universe. In
the Big Bang theory the hypersurface of the hypersphere is expanding,
but like the regular sphere, there is no "center" of the hypersurface.
(even babbling Mitch seems to somewhat get this)

You have a very 2-dimensional comprehension as does relativity and Tom Roberts the ridiculously proud fellow.

Failure to be able to answer the question noted. In which country/ocean
is the center of the surface of the earth located?

(funny how you call me "2-dimensional" when I try to discuss 4
dimensional hyperspheres!)

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On 12/5/2023 7:30 PM, Chris M. Thomasson wrote:

On 12/4/2023 11:37 PM, Maciej Wozniak wrote:

On Tuesday, 5 December 2023 at 07:17:25 UTC+1, Tom Roberts wrote:

On 12/4/23 6:30 PM, Laurence Clark Crossen wrote:

On Monday, December 4, 2023 at 3:22:39 PM UTC-8, Tom Roberts wrote: >>>>> On 12/4/23 3:10 PM, Laurence Clark Crossen wrote:

The Big Bang and the Center of the Universe The velocity-distance
relationship interprets the redshift-distance relationship as
caused by the Doppler shift of starlight. This relationship is
the same in every direction from Earth. This requires we are at
the center of the universe.

Nope! In a homogeneous and isotropic universe this would hold at
any location, and THERE IS NO "CENTER".

There is a center in a finite, homogeneous, and isotropic universe.

You have insufficient imagination. This is simply not true.

For example, the surface of the sphere S^2 is finite, homogeneous, and
isotropic, yet it has no "center".

Oh, yes, poor halfbrain, a sphere absolutely has
a center.

Indeed. Draw a sphere at 3-ary point (x, y, z) with radii of (1, 1, 1).

If x = y = z = 0, then this sphere will be the unit sphere centered at
origin with a radius of 1.

But the SURFACE of the sphere has no center! (the surface is the set of
points such that x²+y²+z²=1)

Notice the janitor deliberately omits the word "surface" when responding
to Tom.

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On Tuesday, December 5, 2023 at 9:28:36 PM UTC-8, Richard Hertz wrote:

On Tuesday, December 5, 2023 at 9:39:40 PM UTC-3, Volney wrote:

On 12/5/2023 7:30 PM, Chris M. Thomasson wrote:

<snip>

If x = y = z = 0, then this sphere will be the unit sphere centered at origin with a radius of 1.

But the SURFACE of the sphere has no center! (the surface is the set of
points such that x²+y²+z²=1)

Notice the janitor deliberately omits the word "surface" when responding to Tom.

IMBECILE!

Yes, that's what you are, Dick.

The volume (and the surface) of any sphere HAS A CENTER!

The volume does, where is the center of the surface? Justify your answer.

The sphere is centered at 0,0,0. The collection of x,y,z points that verify (x-0)²+(y-0)²+(z-0)²=1 define a surface equidistant to 0,0,0.

Had it been centered at x₁,y₁,z₁, the collection of x,y,z points that verify (x-x₁)²+(y-y₁)²+(z-z₁)²=1 define a surface equidistant to x₁,y₁,z₁,
anywhere in a 3D space, providing that its radius is 1. Also, its volume is centered in x₁,y₁,z₁.

Again, I'm not talking about the center of the volume, but the center of
the surface.

Where is the center OF THE SURFACE of the unit sphere?

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On 12/8/23 1:31 AM, Paul Alsing wrote:

[about the "center" of the SURFACE of a sphere] Why, it is both
everywhere and nowhere at the same time!

No. It is simply that the SURFACE of a sphere has no center WITHIN THE
MANIFOLD (i.e. any putative "center" must lie on the surface).

It would depend on where you started peeling

Nobody said anything about "peeling". Don't do that, because it cannot
be done -- the topology of S^2 is incompatible with the topology of R^2
(the plane). Likewise, any metric on S^2 is incompatible with any metric
on R^2.

The surface of a sphere simply has no center INTRINSICALLY. I explicitly
said one must NOT embed the surface into a higher-dimension space.
Similarly, the manifold used to mode the universe we inhabit cannot be
embedded in any higher-dimension space.

Most posters in this thread insist on embedding the surface of the
sphere S^2 in a 3-D euclidean space, and point to its center in the
space. They seem to have insufficient powers of abstraction to avoid
doing that and to just consider the surface ON ITS OWN.

Tom Roberts

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On 12/8/2023 12:04 PM, Richard Hertz wrote:

On Friday, December 8, 2023 at 3:35:45 AM UTC-3, Volney wrote:

<snip>

Again, I'm not talking about the center of the volume, but the center of the surface.

Where is the center OF THE SURFACE of the unit sphere?

IMBECILE!

Yes, that's still what you are.

In a Euclidean 3D space, draw two normal lines to two arbitrary contact points of the corresponding tangential planes in the sphere surface.

Where the two 3D normal lines intersect, is THE CENTER OF THE SPHERE!

And yet again, you answered the wrong question. Just as I expected.

I did NOT ask where the center of the 3D sphere is. I asked where on the surface, the center OF THE SURFACE is.

The surface of the unit sphere is the set of points, real x, y, z, which satisfies the equation x²+y²+z²=1. The center of the sphere itself is
the set of points x²+y²+z²=0, having a single solution, 0,0,0.
Obviously, there is no solution where x²+y²+z²=1 and x²+y²+z²=0 are both satisfied. I repeat: Where is the center of the set of points x²+y²+z²=1?

Fucking retarded!

That describes you perfectly as well, Dick.

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On 12/8/2023 10:27 AM, Laurence Clark Crossen wrote:

Relativity is ignorance.

War is peace.
Freedom is slavery.
Ignorance is strength

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On 12/8/2023 1:55 PM, Laurence Clark Crossen wrote:

On Friday, December 8, 2023 at 10:12:35 AM UTC-8, Volney wrote:

On 12/8/2023 10:27 AM, Laurence Clark Crossen wrote:

Relativity is ignorance.

War is peace.
Freedom is slavery.
Ignorance is strength

Speaking for yourself?

Just completing your thought.

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On 12/8/2023 4:49 PM, Laurence Clark Crossen wrote:

On Thursday, December 7, 2023 at 11:31:22 PM UTC-8, Paul Alsing wrote:

In a subset of your question, you might ask where is the geographical center of the continental USA, which does not include Alaska or Hawaiii or any of the territories, and the straightforward answer is "in Kansas" (look it up)... but for the entire

globe it all depends on the boundaries of the "peel"...

I already replied to this above:
A steel man of this defense of the Big Bang without using a fourth dimension: A spherical-shaped universe with a void in the center would still have a difference in red-shift in different directions at different points on the surface.

And the point is, the universe isn't spherical in the big bang model. A
4d hypersphere's 3d "surface" isn't a sphere just like the 2d surface of
a 3d sphere isn't a circle.

Everyone knows there is no center to the surface of a sphere.

Finally! An answer from you! It's even correct!
Now take that concept to 3 dimensions.

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On 12/8/2023 2:31 AM, Paul Alsing wrote:

On Thursday, December 7, 2023 at 10:35:45 PM UTC-8, Volney wrote:

On Tuesday, December 5, 2023 at 9:28:36 PM UTC-8, Richard Hertz wrote:

On Tuesday, December 5, 2023 at 9:39:40 PM UTC-3, Volney wrote:

On 12/5/2023 7:30 PM, Chris M. Thomasson wrote:

<snip>

If x = y = z = 0, then this sphere will be the unit sphere centered at origin with a radius of 1.

But the SURFACE of the sphere has no center! (the surface is the set of >>>> points such that x²+y²+z²=1)

Notice the janitor deliberately omits the word "surface" when responding to Tom.

IMBECILE!

Yes, that's what you are, Dick.

The volume (and the surface) of any sphere HAS A CENTER!

The volume does, where is the center of the surface? Justify your answer. >>>

The sphere is centered at 0,0,0. The collection of x,y,z points that verify (x-0)²+(y-0)²+(z-0)²=1 define a surface equidistant to 0,0,0.

Had it been centered at x₁,y₁,z₁, the collection of x,y,z points that verify (x-x₁)²+(y-y₁)²+(z-z₁)²=1 define a surface equidistant to x₁,y₁,z₁,
anywhere in a 3D space, providing that its radius is 1. Also, its volume is centered in x₁,y₁,z₁.

Again, I'm not talking about the center of the volume, but the center of
the surface.

Where is the center OF THE SURFACE of the unit sphere?

Why, it is both everywhere and nowhere at the same time! It would depend on where you started peeling the surface away from the globe in order to lay it flat on a plane. Since the are infinite ways to peel a globe there are infinite centers of the

surface.

Well, those are centers of the projection of the spherical surface, and
the centers depend on how you initially slice it. The projections are
all distortions of the surface as well. For example the Mercator map
projection has a definite center (0,0 lat-lon) but that depends on a
choice of slicing the surface from pole to pole at 180 degrees. Mercator
is distorted, particularly close to the poles.

This is undoubtedly beyond the comprehension of Dick and Larry, neither of whom has ever read a relativity textbook...

yes, they don't understand the question (likely deliberately)

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On 12/8/2023 4:56 PM, Laurence Clark Crossen wrote:

On Friday, December 8, 2023 at 12:31:28 PM UTC-8, Chris M. Thomasson wrote:

On 12/7/2023 10:32 PM, Volney wrote:

On Tuesday, December 5, 2023 at 9:28:36 PM UTC-8, Richard Hertz wrote: >>>> On Tuesday, December 5, 2023 at 9:39:40 PM UTC-3, Volney wrote:

On 12/5/2023 7:30 PM, Chris M. Thomasson wrote:

<snip>

If x = y = z = 0, then this sphere will be the unit sphere centered >>>>>> at origin with a radius of 1.

But the SURFACE of the sphere has no center! (the surface is the set of >>>>> points such that x²+y²+z²=1)

Notice the janitor deliberately omits the word "surface" when
responding to Tom.

IMBECILE!

Yes, that's what you are, Dick.

The volume (and the surface) of any sphere HAS A CENTER!

The volume does, where is the center of the surface? Justify your answer. >>>> [...]

Everywhere and nowhere? ;^) Let me throw out a point wrt unit sphere
centered at (0, 0, 0):

(1, 0, 0) this is on the surface, however is it the center? What about
point (-1, 0, 0)? lol.

:^)

Poor Chris thinks anyone in the world doesn't know the surface of a sphere has no center. Dumb relativist!

It sure took you a long time to realize this. Maybe you didn't know the
surface of a sphere has no center until you just recently figured it out?

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Den 08.12.2023 18:04, skrev Richard Hertz:

On Friday, December 8, 2023 at 3:35:45 AM UTC-3, Volney wrote:

<snip>

Again, I'm not talking about the center of the volume, but the center of the surface.

Where is the center OF THE SURFACE of the unit sphere?

IMBECILE!

In a Euclidean 3D space, draw two normal lines to two arbitrary contact points of the corresponding tangential planes in the sphere surface.

Where the two 3D normal lines intersect, is THE CENTER OF THE SPHERE!

Fucking retarded!

Do you mean that the person who thinks the center OF THE SURFACE
of the unit sphere is the same as THE CENTER OF THE SPHERE,
is an "IMBECILE" and a "Fucking retarded!" ?

Or are you the "IMBECILE" and "Fucking retarded!" who thinks
that the center OF THE SURFACE of the unit sphere is the same
as THE CENTER OF THE SPHERE?

It must be the former, because you are not an "IMBECILE"
and a "Fucking retarded!"

Or are you?

--
Paul

https://paulba.no/

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On 12/8/2023 4:56 PM, Laurence Clark Crossen wrote:

On Friday, December 8, 2023 at 1:07:00 PM UTC-8, Volney wrote:

On 12/8/2023 1:55 PM, Laurence Clark Crossen wrote:

On Friday, December 8, 2023 at 10:12:35 AM UTC-8, Volney wrote:

On 12/8/2023 10:27 AM, Laurence Clark Crossen wrote:

Relativity is ignorance.

War is peace.
Freedom is slavery.
Ignorance is strength

Speaking for yourself?

Just completing your thought.

Speak for yourself ass!

You must admit that it makes perfect sense. You write an illogical, contradictory statement and I match it with equally illogical,
contradictory statements which are famous.

--- SoupGate-Win32 v1.05
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On 12/8/2023 10:43 PM, Laurence Clark Crossen wrote:

On Friday, December 8, 2023 at 7:29:30 PM UTC-8, Chris M. Thomasson wrote:

On 12/8/2023 1:53 PM, Laurence Clark Crossen wrote:

Unfortunately for you, any spherical universe would necessarily have a center, and you haven't been able to explain why it wouldn't. You are the dumbest fool.

A sphere would have a single origin point, and a radius. This point is
contained in all the points in a 3d volume, and is unique for said
sphere. Surface points in this volume wrt said sphere are different than
the single origin point. There is no center on the surface.

Even if we are on the surface of a spherical universe,

Except the universe is not spherical. It is the 3D hypersurface of a hypersphere. Just like the surface of a sphere is not a circle.

--- SoupGate-Win32 v1.05
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On 12/8/2023 11:05 PM, Chris M. Thomasson wrote:

On 12/8/2023 7:43 PM, Laurence Clark Crossen wrote:

On Friday, December 8, 2023 at 7:29:30 PM UTC-8, Chris M. Thomasson
wrote:

On 12/8/2023 1:53 PM, Laurence Clark Crossen wrote:

On Friday, December 8, 2023 at 8:40:27 AM UTC-8, Tom Roberts wrote: >>>>> On 12/8/23 1:31 AM, Paul Alsing wrote:

[about the "center" of the SURFACE of a sphere] Why, it is both
everywhere and nowhere at the same time!

No. It is simply that the SURFACE of a sphere has no center WITHIN THE >>>>> MANIFOLD (i.e. any putative "center" must lie on the surface).

It would depend on where you started peeling

Nobody said anything about "peeling". Don't do that, because it cannot >>>>> be done -- the topology of S^2 is incompatible with the topology of
R^2
(the plane). Likewise, any metric on S^2 is incompatible with any
metric
on R^2.

The surface of a sphere simply has no center INTRINSICALLY. I
explicitly
said one must NOT embed the surface into a higher-dimension space.
Similarly, the manifold used to mode the universe we inhabit cannot be >>>>> embedded in any higher-dimension space.

Most posters in this thread insist on embedding the surface of the
sphere S^2 in a 3-D euclidean space, and point to its center in the
space. They seem to have insufficient powers of abstraction to avoid >>>>> doing that and to just consider the surface ON ITS OWN.

Tom Roberts

Unfortunately for you, any spherical universe would necessarily have
a center, and you haven't been able to explain why it wouldn't. You
are the dumbest fool.

A sphere would have a single origin point, and a radius. This point is
contained in all the points in a 3d volume, and is unique for said
sphere. Surface points in this volume wrt said sphere are different than >>> the single origin point. There is no center on the surface.

Even if we are on the surface of a spherical universe, there should be
a difference in a redshift in different directions, and there is not,
so we must be at the center, not the surface. Of course, there is no
center to the surface of a sphere, and there is no fourth spatial
dimension.

The fun part is that any observer on the surface of a sphere might think
its at the center. Or, well, think about the great attractor, in space...

Exactly. No matter where you are on the surface of a sphere, it LOOKS
like you are at the center.

Same with the 3D universe. No matter where you are, it LOOKS like you're
at the center.

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On 12/8/2023 11:08 PM, Chris M. Thomasson wrote:

On 12/8/2023 3:33 PM, Volney wrote:

On 12/8/2023 4:49 PM, Laurence Clark Crossen wrote:

On Thursday, December 7, 2023 at 11:31:22 PM UTC-8, Paul Alsing wrote:

In a subset of your question, you might ask where is the
geographical center of the continental USA, which does not include
Alaska or Hawaiii or any of the territories, and the straightforward
answer is "in Kansas" (look it up)... but for the entire globe it
all depends on the boundaries of the "peel"...

I already replied to this above:
A steel man of this defense of the Big Bang without using a fourth
dimension:
A spherical-shaped universe with a void in the center would still
have a difference in red-shift in different directions at different
points on the surface.

And the point is, the universe isn't spherical in the big bang model.
A 4d hypersphere's 3d "surface" isn't a sphere just like the 2d
surface of a 3d sphere isn't a circle.

Everyone knows there is no center to the surface of a sphere.

Finally! An answer from you! It's even correct!
Now take that concept to 3 dimensions.

In 2d I wonder if the "center" of the surface of a unit circle can be
the point at {cos(0), sin(0)}? ;^)

The "surface" of a circle is its circumference. The circumference of a
circle has no center, either.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/9/2023 2:17 PM, Laurence Clark Crossen wrote:

On Friday, December 8, 2023 at 8:05:59 PM UTC-8, Chris M. Thomasson wrote:

On 12/8/2023 7:43 PM, Laurence Clark Crossen wrote:

On Friday, December 8, 2023 at 7:29:30 PM UTC-8, Chris M. Thomasson wrote:

On 12/8/2023 1:53 PM, Laurence Clark Crossen wrote:

On Friday, December 8, 2023 at 8:40:27 AM UTC-8, Tom Roberts wrote: >>>>>> On 12/8/23 1:31 AM, Paul Alsing wrote:

[about the "center" of the SURFACE of a sphere] Why, it is both
everywhere and nowhere at the same time!

No. It is simply that the SURFACE of a sphere has no center WITHIN THE >>>>>> MANIFOLD (i.e. any putative "center" must lie on the surface).

It would depend on where you started peeling

Nobody said anything about "peeling". Don't do that, because it cannot >>>>>> be done -- the topology of S^2 is incompatible with the topology of R^2 >>>>>> (the plane). Likewise, any metric on S^2 is incompatible with any metric >>>>>> on R^2.

The surface of a sphere simply has no center INTRINSICALLY. I explicitly >>>>>> said one must NOT embed the surface into a higher-dimension space. >>>>>> Similarly, the manifold used to mode the universe we inhabit cannot be >>>>>> embedded in any higher-dimension space.

Most posters in this thread insist on embedding the surface of the >>>>>> sphere S^2 in a 3-D euclidean space, and point to its center in the >>>>>> space. They seem to have insufficient powers of abstraction to avoid >>>>>> doing that and to just consider the surface ON ITS OWN.

Tom Roberts

Unfortunately for you, any spherical universe would necessarily have a center, and you haven't been able to explain why it wouldn't. You are the dumbest fool.

A sphere would have a single origin point, and a radius. This point is >>>> contained in all the points in a 3d volume, and is unique for said
sphere. Surface points in this volume wrt said sphere are different than >>>> the single origin point. There is no center on the surface.

Even if we are on the surface of a spherical universe, there should be a difference in a redshift in different directions, and there is not, so we must be at the center, not the surface. Of course, there is no center to the surface of a sphere, and

there is no fourth spatial dimension.

The fun part is that any observer on the surface of a sphere might think
its at the center. Or, well, think about the great attractor, in space...

That observer would not think they were at the center if there were a velocity-distance relationship because the redshift would differ in various directions. It doesn't, so we must be at the center, not the sphere's surface.

Nope. Consider a spherical balloon with stars drawn on it. Consider an
observer anywhere on the balloon's surface. The balloon inflates at a
constant rate. The stars get farther and farther from each other, and
from the observer. The observer measures the redshift of the stars. He
notices the direction doesn't matter but concludes the star's redshifts
are proportional* to their initial distance from him. He concludes he's
at the center.

Consider a second observer on the balloon, anywhere except for the
location of the first observer. Following the same reasoning, this
observer *also* concludes he is at the center.

Consider a third, fourth... observer. They conclude the same thing. They
all observe they are at the center. Because the surface of the balloon
HAS NO CENTER.

(*) maybe not proportional since the light can travel along the 2D arc
path along the surface or the chord length "through" the balloon,
invoking the third dimension. I don't know which method more accurately describes the 3D "balloon surface" of the Big Bang universe. Two
slightly different models but both result in the observers' conclusion
of being at the center.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/8/2023 6:21 PM, Richard Hertz wrote:

On Friday, December 8, 2023 at 5:31:28 PM UTC-3, Chris M. Thomasson wrote:

<snip>

Everywhere and nowhere? ;^) Let me throw out a point wrt unit sphere centered at (0, 0, 0):

(1, 0, 0) this is on the surface, however is it the center? What about point (-1, 0, 0)? lol.

:^)

Be an arbitrary sphere, having a radius "1" be centered at (x₁,y₁,z₁) in a Euclidean 3D space.

It's mathematically TRUE that the infinite collection of (x,y,z) points that verify (x-x₁)² + (y-y₁)² + (z-z₁)² = 1
form part of a surface equidistant to the center (x₁,y₁,z₁).

The volume of the sphere is centered in (x₁,y₁,z₁), as well as THE SHELL OF THE SPHERE (outer layer of infinitesimal thickness) is centered in (x₁,y₁,z₁).

Think of the Earth, or the Sun.

Can't believe how deranged people have become. So ignorant, so clueless, without any visualization power at all.

I blame relativism, which has converted their adherents into drooling mutant cretins!

For instance, the points

x₁ ± 1, y₁, z₁
x₁, y₁ ± 1, z₁
x₁, y₁, z₁ ± 1

are three points contained in such surface, out of an infinite number of 3D points.

I have to ask myself: 1) Did you take your medications? ; 2) Did you really go to HS?; 3) Have you procreated?

1) It certainly appears you didn't take your medicine, at least not the antipsychotics.
2) I can't be sure but you didn't manage to get a high school education
in sciences.
3) I hope you didn't!

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/9/2023 7:31 PM, Laurence Clark Crossen wrote:

On Saturday, December 9, 2023 at 4:05:36 PM UTC-8, Volney wrote:

On 12/9/2023 2:17 PM, Laurence Clark Crossen wrote:

On Friday, December 8, 2023 at 8:05:59 PM UTC-8, Chris M. Thomasson wrote:

On 12/8/2023 7:43 PM, Laurence Clark Crossen wrote:

On Friday, December 8, 2023 at 7:29:30 PM UTC-8, Chris M. Thomasson wrote:

On 12/8/2023 1:53 PM, Laurence Clark Crossen wrote:

On Friday, December 8, 2023 at 8:40:27 AM UTC-8, Tom Roberts wrote: >>>>>>>> On 12/8/23 1:31 AM, Paul Alsing wrote:

[about the "center" of the SURFACE of a sphere] Why, it is both >>>>>>>>> everywhere and nowhere at the same time!

No. It is simply that the SURFACE of a sphere has no center WITHIN THE >>>>>>>> MANIFOLD (i.e. any putative "center" must lie on the surface). >>>>>>>>> It would depend on where you started peeling
Nobody said anything about "peeling". Don't do that, because it cannot >>>>>>>> be done -- the topology of S^2 is incompatible with the topology of R^2
(the plane). Likewise, any metric on S^2 is incompatible with any metric
on R^2.

The surface of a sphere simply has no center INTRINSICALLY. I explicitly
said one must NOT embed the surface into a higher-dimension space. >>>>>>>> Similarly, the manifold used to mode the universe we inhabit cannot be >>>>>>>> embedded in any higher-dimension space.

Most posters in this thread insist on embedding the surface of the >>>>>>>> sphere S^2 in a 3-D euclidean space, and point to its center in the >>>>>>>> space. They seem to have insufficient powers of abstraction to avoid >>>>>>>> doing that and to just consider the surface ON ITS OWN.

Tom Roberts

Unfortunately for you, any spherical universe would necessarily have a center, and you haven't been able to explain why it wouldn't. You are the dumbest fool.

A sphere would have a single origin point, and a radius. This point is >>>>>> contained in all the points in a 3d volume, and is unique for said >>>>>> sphere. Surface points in this volume wrt said sphere are different than >>>>>> the single origin point. There is no center on the surface.

Even if we are on the surface of a spherical universe, there should be a difference in a redshift in different directions, and there is not, so we must be at the center, not the surface. Of course, there is no center to the surface of a sphere, and

there is no fourth spatial dimension.

The fun part is that any observer on the surface of a sphere might think >>>> its at the center. Or, well, think about the great attractor, in space... >>

That observer would not think they were at the center if there were a velocity-distance relationship because the redshift would differ in various directions. It doesn't, so we must be at the center, not the sphere's surface.

Nope. Consider a spherical balloon with stars drawn on it. Consider an
observer anywhere on the balloon's surface. The balloon inflates at a
constant rate. The stars get farther and farther from each other, and
from the observer. The observer measures the redshift of the stars. He
notices the direction doesn't matter but concludes the star's redshifts
are proportional* to their initial distance from him. He concludes he's
at the center.

Consider a second observer on the balloon, anywhere except for the
location of the first observer. Following the same reasoning, this
observer *also* concludes he is at the center.

Consider a third, fourth... observer. They conclude the same thing. They
all observe they are at the center. Because the surface of the balloon
HAS NO CENTER.

(*) maybe not proportional since the light can travel along the 2D arc
path along the surface or the chord length "through" the balloon,
invoking the third dimension. I don't know which method more accurately
describes the 3D "balloon surface" of the Big Bang universe. Two
slightly different models but both result in the observers' conclusion
of being at the center.

Volney, you always flabbergast me leaving me speechless! To the contrary, there would be depth to the spherical universe. Our universe is not paper thin and not two dimensional.

Well, I tried to dumb it down to your level by using an example of a 2D "universe" because imagining a 3D "surface" is too difficult for you,
but you're too dumb to see that and think I am talking about the actual universe as a 2D balloon surface.

You're ineducable.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/9/2023 7:48 PM, Richard Hertz wrote:

On Saturday, December 9, 2023 at 9:05:36 PM UTC-3, Volney wrote:

On 12/9/2023 2:17 PM, Laurence Clark Crossen wrote:

On Friday, December 8, 2023 at 8:05:59 PM UTC-8, Chris M. Thomasson wrote:

On 12/8/2023 7:43 PM, Laurence Clark Crossen wrote:

On Friday, December 8, 2023 at 7:29:30 PM UTC-8, Chris M. Thomasson wrote:

On 12/8/2023 1:53 PM, Laurence Clark Crossen wrote:

On Friday, December 8, 2023 at 8:40:27 AM UTC-8, Tom Roberts wrote: >>>>>>>> On 12/8/23 1:31 AM, Paul Alsing wrote:

[about the "center" of the SURFACE of a sphere] Why, it is both >>>>>>>>> everywhere and nowhere at the same time!

No. It is simply that the SURFACE of a sphere has no center WITHIN THE >>>>>>>> MANIFOLD (i.e. any putative "center" must lie on the surface). >>>>>>>>> It would depend on where you started peeling
Nobody said anything about "peeling". Don't do that, because it cannot >>>>>>>> be done -- the topology of S^2 is incompatible with the topology of R^2
(the plane). Likewise, any metric on S^2 is incompatible with any metric
on R^2.

The surface of a sphere simply has no center INTRINSICALLY. I explicitly
said one must NOT embed the surface into a higher-dimension space. >>>>>>>> Similarly, the manifold used to mode the universe we inhabit cannot be >>>>>>>> embedded in any higher-dimension space.

Most posters in this thread insist on embedding the surface of the >>>>>>>> sphere S^2 in a 3-D euclidean space, and point to its center in the >>>>>>>> space. They seem to have insufficient powers of abstraction to avoid >>>>>>>> doing that and to just consider the surface ON ITS OWN.

Tom Roberts

Unfortunately for you, any spherical universe would necessarily have a center, and you haven't been able to explain why it wouldn't. You are the dumbest fool.

A sphere would have a single origin point, and a radius. This point is >>>>>> contained in all the points in a 3d volume, and is unique for said >>>>>> sphere. Surface points in this volume wrt said sphere are different than >>>>>> the single origin point. There is no center on the surface.

Even if we are on the surface of a spherical universe, there should be a difference in a redshift in different directions, and there is not, so we must be at the center, not the surface. Of course, there is no center to the surface of a sphere, and

there is no fourth spatial dimension.

The fun part is that any observer on the surface of a sphere might think >>>> its at the center. Or, well, think about the great attractor, in space... >>

That observer would not think they were at the center if there were a velocity-distance relationship because the redshift would differ in various directions. It doesn't, so we must be at the center, not the sphere's surface.

Nope. Consider a spherical balloon with stars drawn on it. Consider an
observer anywhere on the balloon's surface. The balloon inflates at a
constant rate. The stars get farther and farther from each other, and
from the observer. The observer measures the redshift of the stars. He
notices the direction doesn't matter but concludes the star's redshifts
are proportional* to their initial distance from him. He concludes he's
at the center.

Consider a second observer on the balloon, anywhere except for the
location of the first observer. Following the same reasoning, this
observer *also* concludes he is at the center.

Consider a third, fourth... observer. They conclude the same thing. They
all observe they are at the center. Because the surface of the balloon
HAS NO CENTER.

(*) maybe not proportional since the light can travel along the 2D arc
path along the surface or the chord length "through" the balloon,
invoking the third dimension. I don't know which method more accurately
describes the 3D "balloon surface" of the Big Bang universe. Two
slightly different models but both result in the observers' conclusion
of being at the center.

Fucking useless eater: You don't have a correct perception of the relativistic Big Bang universe! You, as many others retarded, fail even on this
visualization by using the balloon stupid example. Probably due to your ant size brain.

The correct visualization of an expanding universe since the BB should be THIS ONE, asshole:

1) You CAN'T VISUALIZE THE UNIVERSE FROM AFAR! There is NOTHINGNESS beyond the MBR spherical shell. You CAN'T EXIST IN NOTHINGNESS, idiot!!!!!

I see the answer I just gave applies to you as well. You are too
stooopid to understand a 2D equivalent to the 3D problem.

2) You can only TRY TO VISUALIZE THE UNIVERSE FROM WITHIN ITS SPHERICAL VOLUME.

The universe isn't spherical. It is a 3D hypersurface of a hypersphere.

3) The VOLUME of the spherical expanding universe IS COMPOSED BY INFINITE SHELLS, being that THE RADIUS (if exists in a 3D perception)

Nope. The universe isn't a sphere, it is a hypersurface that LOOKS LIKE
a sphere's center from any point within it.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/10/2023 11:50 AM, Volney wrote:

On 12/9/2023 7:31 PM, Laurence Clark Crossen wrote:

You're ineducable.

Kudos to Uncle Al.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/10/2023 11:39 AM, Volney wrote:

On 12/8/2023 6:21 PM, Richard Hertz wrote:

On Friday, December 8, 2023 at 5:31:28 PM UTC-3, Chris M. Thomasson
wrote:

<snip>

Everywhere and nowhere? ;^) Let me throw out a point wrt unit sphere
centered at (0, 0, 0):

(1, 0, 0) this is on the surface, however is it the center? What
about point (-1, 0, 0)? lol.

:^)

Be an arbitrary sphere, having a radius "1" be centered at (x₁,y₁,z₁) >> in a Euclidean 3D space.

It's mathematically TRUE that the infinite collection of (x,y,z)
points that verify (x-x₁)² + (y-y₁)² + (z-z₁)² = 1
form part of a surface equidistant to the center (x₁,y₁,z₁).

The volume of the sphere is centered in (x₁,y₁,z₁), as well as THE
SHELL OF THE SPHERE (outer layer of infinitesimal thickness) is
centered in (x₁,y₁,z₁).

Think of the Earth, or the Sun.

Can't believe how deranged people have become. So ignorant, so
clueless, without any visualization power at all.

I blame relativism, which has converted their adherents into drooling
mutant cretins!

For instance, the points

x₁ ± 1, y₁, z₁
x₁, y₁ ± 1, z₁
x₁, y₁, z₁ ± 1

are three points contained in such surface, out of an infinite number
of 3D points.

I have to ask myself: 1) Did you take your medications? ; 2) Did you
really go to HS?; 3) Have you procreated?

1) It certainly appears you didn't take your medicine, at least not the antipsychotics.
2) I can't be sure but you didn't manage to get a high school education
in sciences.
3) I hope you didn't!

The problem concerning a high school science education has to do with
those who think the only aspects worthy of learning are the ones that
directly impact the narrow subdiscipline that interests them. They take
up space in the room and more or less pay attention where the topic of
the day sounds as though it may have something to do with their
interest (these days usually some subdiscipline of electronics.)

By sitting through a course that lay claim to knowledge of the
contents of the course they usually have just enough to be
dangerous, more often not even that.

Then there's the other set that got excellent grades because they
have excellent memorization and testing sills. The only thing they
can do is to teach the same topic so long as they don't actually
have to explain anything. I had an algebra and geometry teacher like
that in high school. As has been said many times before, some students
learn because of a teacher, others despite the teacher. That leaves of
those who never actually learn anything at all.

The premise for a public education in the USA has always been to take
the children out of the factories and as Dewey said "to make good
citizens."

What I see here is a lot of the worse outcomes.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/10/2023 2:28 AM, Chris M. Thomasson wrote:

On 12/9/2023 10:45 PM, Chris M. Thomasson wrote:

On 12/9/2023 9:33 AM, Volney wrote:

On 12/8/2023 11:05 PM, Chris M. Thomasson wrote:

[...]

The fun part is that any observer on the surface of a sphere might
think its at the center. Or, well, think about the great attractor,
in space...

Exactly. No matter where you are on the surface of a sphere, it LOOKS
like you are at the center.

Same with the 3D universe. No matter where you are, it LOOKS like
you're at the center.

Another point... Think of a 3d point in a 4d system where any "true"
3d point has a w component of zero, ala:

(x, y, z, w), fine... vec4, okay:

vec4 point_4d = { 1, 1, 1, 0 };

Is a "pure" 3d point. However:

vec4 point_4d_oddball = { 1, 1, 1, 0.000000001 };

is not a "pure" 3d point at all, not in any way shape or form! A 4d
observer at that point with a non-zero w component, would be able to
look at the 3d world as a sort of alpha blend, in a sense. It could
see right through things, and walk right through walls... Eve ones
made of lead. ;^)

Too much pondering here? lol. :^)

In a land far far away... The 4d observer, with a non-zero w point in
its 4-ary vector, would be able to stand on the surface of a planet,
look down and see right through said planet into space on the other
side... Everything looks like an alpha channel/blend of sorts, it would
be able to see things akin to a 3d person drawing 2d plans. It would be
able to walk right through walls that exist in points that have zero for
a 4d component, w = 0... It would be able to see in every room, see
inside of people, look down and see space look up and see more space... Sorry, I wrote that for fun. Try not to call me a 100% kook? ;^) lol.

I like the description of what it would look like if a 1 meter diameter
4D hypersphere with its x,y,z coordinates of its center were in the room
you are and its w coordinate going from negative to zero to positive.
First you'd see a point which rapidly would grow into a sphere, continue growing but slower until it was 1 meter diameter, then it would shrink
to a point and wink out of existence.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/10/2023 2:12 PM, whodat wrote:

On 12/10/2023 11:50 AM, Volney wrote:

On 12/9/2023 7:31 PM, Laurence Clark Crossen wrote:

You're ineducable.

Kudos to Uncle Al.

Maybe his famous rant about Archie Plutonium needs to be modified to be
about Laurence. He would post a rant about him if he was here to do so.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/10/2023 2:09 PM, whodat wrote:

On 12/10/2023 11:39 AM, Volney wrote:

On 12/8/2023 6:21 PM, Richard Hertz wrote:

On Friday, December 8, 2023 at 5:31:28 PM UTC-3, Chris M. Thomasson
wrote:

<snip>

Everywhere and nowhere? ;^) Let me throw out a point wrt unit sphere
centered at (0, 0, 0):

(1, 0, 0) this is on the surface, however is it the center? What
about point (-1, 0, 0)? lol.

:^)

Be an arbitrary sphere, having a radius "1" be centered at (x₁,y₁,z₁) >>> in a Euclidean 3D space.

It's mathematically TRUE that the infinite collection of (x,y,z)
points that verify (x-x₁)² + (y-y₁)² + (z-z₁)² = 1
form part of a surface equidistant to the center (x₁,y₁,z₁).

The volume of the sphere is centered in (x₁,y₁,z₁), as well as THE >>> SHELL OF THE SPHERE (outer layer of infinitesimal thickness) is
centered in (x₁,y₁,z₁).

Think of the Earth, or the Sun.

Can't believe how deranged people have become. So ignorant, so
clueless, without any visualization power at all.

I blame relativism, which has converted their adherents into drooling
mutant cretins!

For instance, the points

x₁ ± 1, y₁, z₁
x₁, y₁ ± 1, z₁
x₁, y₁, z₁ ± 1

are three points contained in such surface, out of an infinite number
of 3D points.

I have to ask myself: 1) Did you take your medications? ; 2) Did you
really go to HS?; 3) Have you procreated?

1) It certainly appears you didn't take your medicine, at least not
the antipsychotics.
2) I can't be sure but you didn't manage to get a high school
education in sciences.
3) I hope you didn't!

The problem concerning a high school science education has to do with
those who think the only aspects worthy of learning are the ones that directly impact the narrow subdiscipline that interests them. They take
up space in the room and more or less pay attention where the topic of
the day sounds as though it may have something to do with their
interest (these days usually some subdiscipline of electronics.)

This sounds like a variant of what Odd Bodkin and others noted: Why are
so many cranks electrical engineers?

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Am 11.12.2023 um 04:21 schrieb Volney:

I have to ask myself: 1) Did you take your medications? ; 2) Did you
really go to HS?; 3) Have you procreated?

1) It certainly appears you didn't take your medicine, at least not
the antipsychotics.
2) I can't be sure but you didn't manage to get a high school
education in sciences.
3) I hope you didn't!

The problem concerning a high school science education has to do with
those who think the only aspects worthy of learning are the ones that
directly impact the narrow subdiscipline that interests them. They
take up space in the room and more or less pay attention where the
topic of
the day sounds as though it may have something to do with their
interest (these days usually some subdiscipline of electronics.)

This sounds like a variant of what Odd Bodkin and others noted: Why are
so many cranks electrical engineers?

This is so, because electrical engineers have a MUCH better
understanding of magnetism and electricity than usual physicists.

Since everybody who dares to criticise mainstream physics is called
'crank' (or: psycho, Nazi, crackpot, nutcase...), physicists call all electrical enigineers 'crank'.

But much worse than the electrical cranks are the other variants of
engineers (like e.g. myself), who simply refuse to accept illogic nonsense.


TH

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/10/2023 9:42 PM, Volney wrote:

On 12/10/2023 2:12 PM, whodat wrote:

On 12/10/2023 11:50 AM, Volney wrote:

On 12/9/2023 7:31 PM, Laurence Clark Crossen wrote:

You're ineducable.

Kudos to Uncle Al.

Maybe his famous rant about Archie Plutonium needs to be modified to be
about Laurence. He would post a rant about him if he was here to do so.

That would prove irresistible!

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/10/2023 9:21 PM, Volney wrote:

On 12/10/2023 2:09 PM, whodat wrote:

On 12/10/2023 11:39 AM, Volney wrote:

On 12/8/2023 6:21 PM, Richard Hertz wrote:

On Friday, December 8, 2023 at 5:31:28 PM UTC-3, Chris M. Thomasson
wrote:

<snip>

Everywhere and nowhere? ;^) Let me throw out a point wrt unit
sphere centered at (0, 0, 0):

(1, 0, 0) this is on the surface, however is it the center? What
about point (-1, 0, 0)? lol.

:^)

Be an arbitrary sphere, having a radius "1" be centered at
(x₁,y₁,z₁) in a Euclidean 3D space.

It's mathematically TRUE that the infinite collection of (x,y,z)
points that verify (x-x₁)² + (y-y₁)² + (z-z₁)² = 1
form part of a surface equidistant to the center (x₁,y₁,z₁).

The volume of the sphere is centered in (x₁,y₁,z₁), as well as THE >>>> SHELL OF THE SPHERE (outer layer of infinitesimal thickness) is
centered in (x₁,y₁,z₁).

Think of the Earth, or the Sun.

Can't believe how deranged people have become. So ignorant, so
clueless, without any visualization power at all.

I blame relativism, which has converted their adherents into
drooling mutant cretins!

For instance, the points

x₁ ± 1, y₁, z₁
x₁, y₁ ± 1, z₁
x₁, y₁, z₁ ± 1

are three points contained in such surface, out of an infinite
number of 3D points.

I have to ask myself: 1) Did you take your medications? ; 2) Did you
really go to HS?; 3) Have you procreated?

1) It certainly appears you didn't take your medicine, at least not
the antipsychotics.
2) I can't be sure but you didn't manage to get a high school
education in sciences.
3) I hope you didn't!

The problem concerning a high school science education has to do with
those who think the only aspects worthy of learning are the ones that
directly impact the narrow subdiscipline that interests them. They
take up space in the room and more or less pay attention where the
topic of
the day sounds as though it may have something to do with their
interest (these days usually some subdiscipline of electronics.)

This sounds like a variant of what Odd Bodkin and others noted: Why are
so many cranks electrical engineers?

In my father's day (early 20th century) The most popular discipline was mechanical engineering. I predict that rocket science will be next, of
course I won't be around to see it.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Am 11.12.2023 um 15:18 schrieb whodat:

This sounds like a variant of what Odd Bodkin and others noted: Why
are so many cranks electrical engineers?

In my father's day (early 20th century) The most popular discipline was mechanical engineering. I predict that rocket science will be next, of
course I won't be around to see it.

No, the 'Next Big Thing' will be 'Flying Saucers'.

Rockets are a thing from the past.


TH

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Am 05.12.2023 um 00:22 schrieb Tom Roberts:

On 12/4/23 3:10 PM, Laurence Clark Crossen wrote:

The Big Bang and the Center of the Universe The velocity-distance
relationship interprets the redshift-distance relationship as caused
by the Doppler shift of starlight. This relationship is the same in
every direction from Earth. This requires we are at the center of
the universe.

Nope! In a homogeneous and isotropic universe this would hold at any location, and THERE IS NO "CENTER".

The center is me (or you).

The reason: as we see 'the universe' this universe is not universal, but identical to what relativity calls 'past light cone'.

This past light cone is always the past light cone of the observer in
question and that is me (or you or whoever else).


'The universe' is actually a picture we receive from the past.

And what we see is a set of events, which didn't happen at the same
time, but the longer ago the further away.

That IS (!!!!) the set of of events located on our own past light cone.

This is actually a picture and does not reflect any kind of reality.

So our picture from the past has a center, which we call 'big bang'. And
from there it does expand in all directions (and so forth).

But that's no big deal, because it is not real anyhow.

...

TH

--- SoupGate-Win32 v1.05
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On 12/12/2023 1:20 AM, Chris M. Thomasson wrote:

On 12/10/2023 7:40 PM, Volney wrote:

On 12/10/2023 2:28 AM, Chris M. Thomasson wrote:

On 12/9/2023 10:45 PM, Chris M. Thomasson wrote:

On 12/9/2023 9:33 AM, Volney wrote:

On 12/8/2023 11:05 PM, Chris M. Thomasson wrote:

[...]

The fun part is that any observer on the surface of a sphere might >>>>>> think its at the center. Or, well, think about the great
attractor, in space...

Exactly. No matter where you are on the surface of a sphere, it
LOOKS like you are at the center.

Same with the 3D universe. No matter where you are, it LOOKS like
you're at the center.

Another point... Think of a 3d point in a 4d system where any "true"
3d point has a w component of zero, ala:

(x, y, z, w), fine... vec4, okay:

vec4 point_4d = { 1, 1, 1, 0 };

Is a "pure" 3d point. However:

vec4 point_4d_oddball = { 1, 1, 1, 0.000000001 };

is not a "pure" 3d point at all, not in any way shape or form! A 4d
observer at that point with a non-zero w component, would be able to
look at the 3d world as a sort of alpha blend, in a sense. It could
see right through things, and walk right through walls... Eve ones
made of lead. ;^)

Too much pondering here? lol. :^)

In a land far far away... The 4d observer, with a non-zero w point in
its 4-ary vector, would be able to stand on the surface of a planet,
look down and see right through said planet into space on the other
side... Everything looks like an alpha channel/blend of sorts, it
would be able to see things akin to a 3d person drawing 2d plans. It
would be able to walk right through walls that exist in points that
have zero for a 4d component, w = 0... It would be able to see in
every room, see inside of people, look down and see space look up and
see more space... Sorry, I wrote that for fun. Try not to call me a
100% kook? ;^) lol.

I like the description of what it would look like if a 1 meter
diameter 4D hypersphere with its x,y,z coordinates of its center were
in the room you are and its w coordinate going from negative to zero
to positive. First you'd see a point which rapidly would grow into a
sphere, continue growing but slower until it was 1 meter diameter,
then it would shrink to a point and wink out of existence.

Well, so far, that is how some of my 4-ary vector field experiments
actually look/act like! The problem is that I am having trouble
visualizing points that have a w component that is non-zero. My n-ary
vector field helps! But its still strange. I can see how a "ghost" point
with a non-zero w component effect points in the 3d world, but its still
odd to me. I actually have no idea where to plot a 4d point that has
zero x, y, z components, and a non-zero w! Say,

(0, 0, 0, 1) ? Where do I plot that sucker!

Only points with w=0 can be observed by 3D beings. In my example, the hypersphere with a diameter of 1 will be nonexistent until its center coordinate becomes w = -1. At that time a single point (with w=0)
hypersurface appears. As w of the center increases, the number of points
with w=0 and thus "real" increases. When the center is at w=0, the
hypersurface is at a maximum and appears as a sphere with diameter 1. As
w increases the sphere shrinks and when w=1 it is a point and then vanishes.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/13/2023 1:03 AM, Volney wrote:

On 12/12/2023 1:20 AM, Chris M. Thomasson wrote:

On 12/10/2023 7:40 PM, Volney wrote:

On 12/10/2023 2:28 AM, Chris M. Thomasson wrote:

On 12/9/2023 10:45 PM, Chris M. Thomasson wrote:

On 12/9/2023 9:33 AM, Volney wrote:

On 12/8/2023 11:05 PM, Chris M. Thomasson wrote:

[...]

The fun part is that any observer on the surface of a sphere
might think its at the center. Or, well, think about the great
attractor, in space...

Exactly. No matter where you are on the surface of a sphere, it
LOOKS like you are at the center.

Same with the 3D universe. No matter where you are, it LOOKS like
you're at the center.

Another point... Think of a 3d point in a 4d system where any
"true" 3d point has a w component of zero, ala:

(x, y, z, w), fine... vec4, okay:

vec4 point_4d = { 1, 1, 1, 0 };

Is a "pure" 3d point. However:

vec4 point_4d_oddball = { 1, 1, 1, 0.000000001 };

is not a "pure" 3d point at all, not in any way shape or form! A 4d
observer at that point with a non-zero w component, would be able
to look at the 3d world as a sort of alpha blend, in a sense. It
could see right through things, and walk right through walls... Eve
ones made of lead. ;^)

Too much pondering here? lol. :^)

In a land far far away... The 4d observer, with a non-zero w point
in its 4-ary vector, would be able to stand on the surface of a
planet, look down and see right through said planet into space on
the other side... Everything looks like an alpha channel/blend of
sorts, it would be able to see things akin to a 3d person drawing 2d
plans. It would be able to walk right through walls that exist in
points that have zero for a 4d component, w = 0... It would be able
to see in every room, see inside of people, look down and see space
look up and see more space... Sorry, I wrote that for fun. Try not
to call me a 100% kook? ;^) lol.

I like the description of what it would look like if a 1 meter
diameter 4D hypersphere with its x,y,z coordinates of its center were
in the room you are and its w coordinate going from negative to zero
to positive. First you'd see a point which rapidly would grow into a
sphere, continue growing but slower until it was 1 meter diameter,
then it would shrink to a point and wink out of existence.

Well, so far, that is how some of my 4-ary vector field experiments
actually look/act like! The problem is that I am having trouble
visualizing points that have a w component that is non-zero. My n-ary
vector field helps! But its still strange. I can see how a "ghost"
point with a non-zero w component effect points in the 3d world, but
its still odd to me. I actually have no idea where to plot a 4d point
that has zero x, y, z components, and a non-zero w! Say,

(0, 0, 0, 1) ? Where do I plot that sucker!

Only points with w=0 can be observed by 3D beings. In my example, the hypersphere with a diameter of 1 will be nonexistent until its center coordinate becomes w = -1. At that time a single point (with w=0) hypersurface appears. As w of the center increases, the number of points
with w=0 and thus "real" increases. When the center is at w=0, the hypersurface is at a maximum and appears as a sphere with diameter 1. As
w increases the sphere shrinks and when w=1 it is a point and then
vanishes.

I see I was inconsistent. In my replies replace "diameter" with "radius" everywhere.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/13/2023 4:04 PM, Chris M. Thomasson wrote:

On 12/12/2023 10:03 PM, Volney wrote:

On 12/12/2023 1:20 AM, Chris M. Thomasson wrote:

On 12/10/2023 7:40 PM, Volney wrote:

On 12/10/2023 2:28 AM, Chris M. Thomasson wrote:

On 12/9/2023 10:45 PM, Chris M. Thomasson wrote:

On 12/9/2023 9:33 AM, Volney wrote:

On 12/8/2023 11:05 PM, Chris M. Thomasson wrote:

[...]

The fun part is that any observer on the surface of a sphere
might think its at the center. Or, well, think about the great >>>>>>>> attractor, in space...

Exactly. No matter where you are on the surface of a sphere, it
LOOKS like you are at the center.

Same with the 3D universe. No matter where you are, it LOOKS like >>>>>>> you're at the center.

Another point... Think of a 3d point in a 4d system where any
"true" 3d point has a w component of zero, ala:

(x, y, z, w), fine... vec4, okay:

vec4 point_4d = { 1, 1, 1, 0 };

Is a "pure" 3d point. However:

vec4 point_4d_oddball = { 1, 1, 1, 0.000000001 };

is not a "pure" 3d point at all, not in any way shape or form! A
4d observer at that point with a non-zero w component, would be
able to look at the 3d world as a sort of alpha blend, in a sense. >>>>>> It could see right through things, and walk right through walls... >>>>>> Eve ones made of lead. ;^)

Too much pondering here? lol. :^)

In a land far far away... The 4d observer, with a non-zero w point
in its 4-ary vector, would be able to stand on the surface of a
planet, look down and see right through said planet into space on
the other side... Everything looks like an alpha channel/blend of
sorts, it would be able to see things akin to a 3d person drawing
2d plans. It would be able to walk right through walls that exist
in points that have zero for a 4d component, w = 0... It would be
able to see in every room, see inside of people, look down and see
space look up and see more space... Sorry, I wrote that for fun.
Try not to call me a 100% kook? ;^) lol.

I like the description of what it would look like if a 1 meter
diameter 4D hypersphere with its x,y,z coordinates of its center
were in the room you are and its w coordinate going from negative to
zero to positive. First you'd see a point which rapidly would grow
into a sphere, continue growing but slower until it was 1 meter
diameter, then it would shrink to a point and wink out of existence.

Well, so far, that is how some of my 4-ary vector field experiments
actually look/act like! The problem is that I am having trouble
visualizing points that have a w component that is non-zero. My n-ary
vector field helps! But its still strange. I can see how a "ghost"
point with a non-zero w component effect points in the 3d world, but
its still odd to me. I actually have no idea where to plot a 4d point
that has zero x, y, z components, and a non-zero w! Say,

(0, 0, 0, 1) ? Where do I plot that sucker!

Only points with w=0 can be observed by 3D beings. In my example, the
hypersphere with a diameter of 1 will be nonexistent until its center
coordinate becomes w = -1. At that time a single point (with w=0)
hypersurface appears. As w of the center increases, the number of
points with w=0 and thus "real" increases. When the center is at w=0,
the hypersurface is at a maximum and appears as a sphere with diameter
1. As w increases the sphere shrinks and when w=1 it is a point and
then vanishes.

Still not sure if an 3d observer could see a 4d object with a non-zero
w. Afaict, it seems like you are taking w on a range of -1...1. Say:

x = 0
y = 0
z = 0
w = -1...0...1

When w is at the center and is actually equal to zero, 3d observers can finally see it. A fun part is that a 4d observer would be able to see
the 4d object moving, and it would be able to see completely inside the
3d realm (aka alpha blend) its moving through wrt its (x, y, z) components.

I sometimes wonder if the w component can be very small yet non-zero to
a point where a 3d object might be able to notice something, akin to paranormal activity wrt the 3d object. That is a fun one to ponder on...
:^)

The hypersphere is moving in the w dimension and has a finite radius in
all dimensions including w, of 1. When its center is at w= -1, a single
point at w=1 (relative to the center) is visible. As w of the center
increases but is still negative, parts of the hypersphere have w=0 and
become visible as a sphere. For example, when the center is at w= -0.5,
parts of the hypersphere with w=0.5 (total w=0) are visible. When the
center is at w=0, a sphere with radius 1 is visible. As w becomes
positive the reverse happens. At w=1 only a single point (w = -1
relative to the center) is possible, after which (w>1) it vanishes.

--- SoupGate-Win32 v1.05
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