A better link criticizing Callahan would be this provided by Anderton:
https://www.laphamsquarterly.org/roundtable/beware-cranks

At bottom, relativists dismiss Callahan on the basis of his failed attempt to trisect an angle, making that an excuse for not answering his criticisms of relativity and its non-Euclidean geometry.
Relativists don't refute Callahan because they are unable to.

We can dismiss Einstein and relativity even more easily.
He embraced the Lorentz Transformation, the purpose of which is to save the ether from the null result.
He discarded the ether.
He kept the LT for no good reason.

Einstein was a quack. So are you.

Jan says the intersection of parallel lines at infinity can be proven!
Parallel lines can only meet at infinity if one starts with irrational premises.

LaurenceClarkCrossen <clzb93ynxj@att.net> wrote:

> Jan says the intersection of parallel lines at infinity can be proven!
> Parallel lines can only meet at infinity if one starts with irrational
> premises.
>

Nope. You didn't pay attention.
Euclid's axiom says that given a line, and a point outside it,
there is one -unique- line through the point that doesn't intersect it.
(no matter how far you prolong it)
Taking the Pythagorean axiom instead this can be proven. [1]

'Points at infinity' and 'intersection at infinity'
are add-ons that have no place in the original Euclidean geometry,

Jan

[1] For the perhaps misled kiddies here:
In other words, the // axiom and Pythagoras' theorem/axiom
are fully equivalent. Take one, ant the other can be proven.
In still other words: Euclidean geometry doesn't contain
any actual infinities, only potential ones.

Yes, you did say that parallel lines can be proven to intersect at infinity:
You said, "The intersection at infinity, or better non-intersetction in the finite
can then be proven as a theorem.

The two definitions can be shown to be equivalent,"

No rational person would say the two do not contradict or that parallel lines that do not intersect in the finite intersect in the infinite, especially considering Euclidean geometry is about plane two-dimensional static geometry.

Please do give your proof!
That should be easy for you.

You have shown you are unable to show any relativist who ever refuted Callahan's proof for the 5th postulate, much less Leon's. In fact, relativists have never even tried.

On 03/19/2024 01:15 PM, LaurenceClarkCrossen wrote:
> You have shown you are unable to show any relativist who ever refuted
> Callahan's proof for the 5th postulate, much less Leon's. In fact,
> relativists have never even tried.

You know what's the sound of the tiniest violin in the world?

:)

You're mistaken about infinity not being in Euclid's parallel lines according to his article:

"He began by studying Euclid's postulate that a straight line has infinite length."

"THE PARALLEL POSTULATE"

Author(s): Raymond H. Rolwing and Maita Levine

Source: The Mathematics Teacher, Vol. 62, No. 8 (DECEMBER 1969), pp. 665-669

Published by: National Council of Teachers of Mathematics

Stable URL: http://www.jstor.org/stable/27958258

I think that the geometries opposed to Euclid do not contradict his because they depart from plane geometry. For example, a triangle with other than 180 degrees is not on a plane surface, nor are parallel lines that diverge or meet. please read the article and see what I mean!

Euclid's geometry is about plane geometry and the non-Euclidean's are not.

LaurenceClarkCrossen <clzb93ynxj@att.net> wrote:

> You're mistaken about infinity not being in Euclid's parallel lines
> according to his article:
>
> "He began by studying Euclid's postulate that a straight line has infinite
> length."
>
>
> "THE PARALLEL POSTULATE"
>
> Author(s): Raymond H. Rolwing and Maita Levine
>
> Source: The Mathematics Teacher, Vol. 62, No. 8 (DECEMBER 1969), pp. 665-669
>
> Published by: National Council of Teachers of Mathematics
>
> Stable URL: http://www.jstor.org/stable/27958258
>
> I think that the geometries opposed to Euclid do not contradict his
> because they depart from plane geometry. For example, a triangle with
> other than 180 degrees is not on a plane surface, nor are parallel lines
> that diverge or meet. please read the article and see what I mean!
>
> Euclid's geometry is about plane geometry and the non-Euclidean's are not.

Euclid's 5th postulate can (and was) given as:
===
5. If two lines are drawn which intersect a third in such a way that the
sum of the inner angles on one side is less than two right angles, then
the two lines inevitably must intersect each other on that side if
extended far enough. This postulate is equivalent to what is known as
the parallel postulate. (Wolfram)
===

The domain of Euclidean geometry is the open Euclidean plane.
No actual infinity is involved, [1]

Jan

[1] You can extent Euclidean geometry by adding a 'point at infinity'.
This is called projective geometry, and it is something else.
(and also irrelevant for disproving general relativity)

On 03/24/2024 07:09 AM, J. J. Lodder wrote:
> LaurenceClarkCrossen <clzb93ynxj@att.net> wrote:
>
>> You're mistaken about infinity not being in Euclid's parallel lines
>> according to his article:
>>
>> "He began by studying Euclid's postulate that a straight line has infinite
>> length."
>>
>>
>> "THE PARALLEL POSTULATE"
>>
>> Author(s): Raymond H. Rolwing and Maita Levine
>>
>> Source: The Mathematics Teacher, Vol. 62, No. 8 (DECEMBER 1969), pp. 665-669
>>
>> Published by: National Council of Teachers of Mathematics
>>
>> Stable URL: http://www.jstor.org/stable/27958258
>>
>> I think that the geometries opposed to Euclid do not contradict his
>> because they depart from plane geometry. For example, a triangle with
>> other than 180 degrees is not on a plane surface, nor are parallel lines
>> that diverge or meet. please read the article and see what I mean!
>>
>> Euclid's geometry is about plane geometry and the non-Euclidean's are not.
>
> Euclid's 5th postulate can (and was) given as:
> ===
> 5. If two lines are drawn which intersect a third in such a way that the
> sum of the inner angles on one side is less than two right angles, then
> the two lines inevitably must intersect each other on that side if
> extended far enough. This postulate is equivalent to what is known as
> the parallel postulate. (Wolfram)
> ===
>
> The domain of Euclidean geometry is the open Euclidean plane.
> No actual infinity is involved, [1]
>
> Jan
>
> [1] You can extent Euclidean geometry by adding a 'point at infinity'.
> This is called projective geometry, and it is something else.
> (and also irrelevant for disproving general relativity)
>
>

I think that "Relativity" with an interpretation that
"L-principle of SR is light's speed is an E-spacial constant",
that the Light-principle is an Einstein-spacial, everywhere
local, constant, and that "Equivalence principle is up
to terms, mass-energy equivalency in the E-spatial
rotationally while Galilean linearly", then, first of all
that otherwise there are various notions of what the
principles of Relativity are, that the notions above are
Einstein's theory of Relativity that he arrived at if not
so much his first take or the usual mantras, the second,
that infinity does get involved, because of all the
higher-order moments, and it being about singular points,
about 0, 1, and infinity.

Why Einstein introduces two terms, "spacial" for SR and
"spatial" for GR, is a thing, that most don't know there's
a difference, and when things besides light are at rest,
there isn't, yet, that's usually only an abstract situation.

It's like if Einstein's idea about the clock face is that,
"if all of a sudden, time stopped moving and I moved away,
the clock face would also stop", and it's like, "well yeah,
Einstein, that would mean time stopped".

And it's like, "if I, Einstein, saw a women drop her glasses
on the train, it would be an arc", it's like, "Einstein, you
would see her as an arc, too".

So, I think most people's thought experiments in relativistic
dynamics, usually leave out properties of continuity, which
has also that usual formalisms of geometry, often leave out
a postulate of continuity, yet, it was kind of noticed to be
necessary and since Hilbert it's sort of included.

Is it Mach-ian? Einstein's later, greater theory, Relativity,
has the L-principle and an EQ-principle, and separate E-spacial
and E-spatial, and doesn't need much fixing, only rather the
mathematics that Mathematics _owes_ Physics, of higher-order
moments, to arrive at a fuller continuum mechanics, and very
much so to arrive at though that light's speed c can be in
natural units, "1", that c_g, gravity's, remains, "infinity".

So, I think most people's developments with or against Relativity,
have it that it's not what Einstein arrived at and maintains
as his last word, as out of "Out of My Later Years".

So, geometry has also a "postulate of continuity".

Obviously, Wolfram describes two lines that must intersect because they are not parallel since the sum of the angles is less than 180 degrees. You are a dunce at geometry!

As far as infinity being in Euclid, I have already proven it. His lines were infinite and every authority agrees with me. You are making a stupid mistake.

LaurenceClarkCrossen wrote:

> Obviously, Wolfram describes two lines that must intersect because they
> are not parallel since the sum of the angles is less than 180 degrees.
> You are a dunce at geometry!
>
> As far as infinity being in Euclid, I have already proven it. His lines
> were infinite and every authority agrees with me. You are making a
> stupid mistake.

we disagree. The shooters wore boots because they had trouble tying their
shoe laces, This was coordinated by at least three countries agencies.

The reason why ISIS and Al Qaeda still exist is because US and certain
other members of NATO give them shelter and aid. They could not survive in
such a hostile environment as the Mideast without state sponsorship.

not at all, these isis/ alquada are honeypots to attract and catch "free
fighters" from europe and usa.

Donald Trump on terrorists: ‘Take out their families’

''Radical Islamists'' from Langley, Virginia... The usual bullshit about
radical islamists when we know that these radical islamists handlers are
the CIA-MOSSAD-MI6 and of course the SBU. Ukraine by the way is full of
arab terrorists from ISIS... But then again don't mention indeed that we
know that USA and ISRAEL created and finance these radical islamists
across the Middle East and Central Asia to do their dirty jobs... Then
again it was to be expected that nobody would dare to talk to us about the
REAL TERRORISTS which are in Washington DC and a certain Middle East
country pretending fighting terrorists while treated them in hospital when
wounded ...

I don't believe a word the collective West (including Israel!) says. They
just made up a new ISIS.

https://www.r%74.com/russia/594893-putin-terrorist-attack-meeting/

LaurenceClarkCrossen <clzb93ynxj@att.net> wrote:

> Obviously, Wolfram describes two lines that must intersect because they
> are not parallel since the sum of the angles is less than 180 degrees. You
> are a dunce at geometry!

The two versions can be proven to be equivalent.

> As far as infinity being in Euclid, I have already proven it. His lines
> were infinite and every authority agrees with me. You are making a stupid
> mistake.

So you still have not understood the difference
between an actual and a potential infinity?

Consult Aristotle,

Jan