Antonio Leon
"New Elements of Euclidean Geometry" Revised 2023
"Apparent Relativity" Revised 2023
Both books available free at Academia.edu

He demonstrates Euclid's 5th postulate, something supposedly ridiculous to claim, since many attempted to do this for over 2,000 years without success.

The non-Euclidean geometries take as a pretext the alleged inability to prove the 5th postulate to embark on their unproven claims.

Jeremiah Joseph Callahan already accomplished the same in his 1931 book, "Euclid or Einstein: A Proof of the Parallel Theory and a Critique of Metageometry"

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LaurenceClarkCrossen <clzb93ynxj@att.net> wrote:

Antonio Leon
"New Elements of Euclidean Geometry" Revised 2023
"Apparent Relativity" Revised 2023
Both books available free at Academia.edu

He demonstrates Euclid's 5th postulate, something supposedly ridiculous to claim, since many attempted to do this for over 2,000 years without
success.

The non-Euclidean geometries take as a pretext the alleged inability to
prove the 5th postulate to embark on their unproven claims.

Jeremiah Joseph Callahan already accomplished the same in his 1931 book, "Euclid or Einstein: A Proof of the Parallel Theory and a Critique of Metageometry"

Great! Show us the proof,

Jan

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You might first try to understand Callahan's proof if you need help. I'm kind of busy reading Leon's second book, which criticizes relativity.

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I think non-Euclidean geometry is recognizable as necessarily involving the reification fallacy, so it is not true. It is necessary to attribute qualities to abstract space to suppose that parallel lines meet. Contrary to Tom Roberts, in physics, one
cannot use models that involve reification fallacy because they cannot account for causation.

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LaurenceClarkCrossen <clzb93ynxj@att.net> wrote:

I think non-Euclidean geometry is recognizable as necessarily involving
the reification fallacy, so it is not true. It is necessary to attribute qualities to abstract space to suppose that parallel lines meet. Contrary
to Tom Roberts, in physics, one cannot use models that involve reification fallacy because they cannot account for causation.

FYI, all this talk of // lines meeting at infinity is obsolete.
In modern presentations Euclidean geometry is defined
as that geometry in which the Pythagorean theorem holds.
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,

Jan

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W dniu 17.03.2024 o 12:45, J. J. Lodder pisze:

LaurenceClarkCrossen <clzb93ynxj@att.net> wrote:

I think non-Euclidean geometry is recognizable as necessarily involving
the reification fallacy, so it is not true. It is necessary to attribute
qualities to abstract space to suppose that parallel lines meet. Contrary
to Tom Roberts, in physics, one cannot use models that involve reification >> fallacy because they cannot account for causation.

FYI, all this talk of // lines meeting at infinity is obsolete.
In modern presentations Euclidean geometry is defined
as that geometry in which the Pythagorean theorem holds.
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,

And communism can be shown to be the best. If an idiot
buys it...

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Jan just declared that parallel lines can be defined as not meeting at finite distances but meeting at infinity. Jan, we disagree. Callahan and Leon prove they don't meet at infinity. My explanation above is enough because making them meet requires
attributing qualities to space, which involves the reification fallacy.

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Callahan and Leon prove it if you look through the telescope by reading their books...

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What relativist or non-Euclidean geometer has ever directly replied to Callahan's book/argument?

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LaurenceClarkCrossen <clzb93ynxj@att.net> wrote:

What relativist or non-Euclidean geometer has ever directly replied to Callahan's book/argument?

<https://en.wikipedia.org/wiki/Jeremiah_J._Callahan>

Duquesne University tries to deny that they ever had such a president, <https://www.duq.edu/about/history/index.php>

Jan

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On 2024-03-17 19:58:02 +0000, J. J. Lodder said:

LaurenceClarkCrossen <clzb93ynxj@att.net> wrote:

What relativist or non-Euclidean geometer has ever directly replied to
Callahan's book/argument?

<https://en.wikipedia.org/wiki/Jeremiah_J._Callahan>

Duquesne University tries to deny that they ever had such a president, <https://www.duq.edu/about/history/index.php>

Jan

Really? "Rev. Jeremiah Joseph Callahan
President, 1931 - 1940" at the link you give.

--
athel -- biochemist, not a physicist, but detector of crackpots

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Why not listen (see above)?
Jan claims that it has been proven that parallel lines meet at infinity without giving proof.
No such proofs do not presume what they want to conclude.
Why don't they diverge at infinity?
Because Jan wants space to curve one way and not the other.

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Callahan, in Euclid or Einstein, says,
p.222 "he is himself struggling to give, in a hazy way, some kind of reality to his mathematics by clothing his formulae with some interpretation or other....clarity ends, and we step into a region of mistiness and fog. We certainly cannot consider
Einstein as one who shines as a scientific discoverer in the domain of physics, but rather as one who in a fuddled sort of way is merely trying to find some meaning for mathematical formulae in which he himself does not believe too strongly..."

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BTW Jan, when parallel lines meet at a distance, that's an optical illusion...

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Yes, Jan, we know about those. So there are no refutations of Callahan's proof because relativists are not able to.

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Einstein and his defenders are crackpots.
You can detect a crackpot by their inability to reason exhibited in their use of logical fallacies.

Callahan says,
Callahan page 285: "only another example of the lack of clearness of conception and love of the incongruous that everywhere characterizes the position of Einstein...how can we explain such a confused mentality in anyone professing himself to be a
scientist? ... Einstein is neither a physicist nor a metaphysician capable of dealing clearly with physical and metaphysical entities in a scientific way... he is hampered by a load of contradictory and absurd assumptions... above all he utterly lacks
the scientific sagacity or instinct to choose the proper physical, metaphysical and mathematical basis.... as a result his beginnings are as bad as his conclusions... even worse... is the absence of the power of criticism to enable him to see the glaring
contradictories which he is embracing, and the lack of logical insight to understand the use and force of language. No wonder then he blunders, and in floundering..."

LCC Skeptic of UFO's Bigfoot & Relativity

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Athel Cornish-Bowden <me@yahoo.com> wrote:

On 2024-03-17 19:58:02 +0000, J. J. Lodder said:

LaurenceClarkCrossen <clzb93ynxj@att.net> wrote:

What relativist or non-Euclidean geometer has ever directly replied to
Callahan's book/argument?

<https://en.wikipedia.org/wiki/Jeremiah_J._Callahan>

Duquesne University tries to deny that they ever had such a president, <https://www.duq.edu/about/history/index.php>

Jan

Really? "Rev. Jeremiah Joseph Callahan
President, 1931 - 1940" at the link you give.

Yes, and that is all they want to know about him,

Jan

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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.

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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.

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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.

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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.

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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.

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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.

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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)

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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.

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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

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