Relativity's Geometry is a Castle Made of Sand.

[Laurence Clark Crossen]

Callahan shows that non-Euclidean geometry is extremely unlikely. The non-Euclidean geometers take as a pretext the failure of Euclidean geometers to prove the parallel theory. However, the parallel theory is highly probable. The problem has only been that it has not been proven with the same rigor that Euclid's earlier postulates were. Additionally, the non-Euclideans would require a new foundation for their own geometry because theirs is not based on Euclid's. They have not begun to do this. Callahan gives the correct proof of the parallel postulate by re-ordering a few of Euclid's propositions.

[Laurence Clark Crossen]

Page 107 of Euclid or Einstein: "But if non-Euclidean Geometers had either critical acumen or mathematical insight they would not be non-Euclidean Geometers, trying to hold together the incongruous disarray of ideas that goes by the name of non-Euclidean Geometery."

[Laurence Clark Crossen]

Wikipedia:

" Mathematical workCallahan was an academic who studied Euclidean geometry. The first volume of his book Euclid or Einstein? A Proof of the Parallel Theory and a Critique of Metageometry claimed to have proved Euclid's fifth "parallel" postulate, by re-ordering the logical structure of Euclid's Elements. Callahan proved that for any point not on a given line, there exists a parallel line in the plane so determined and through the point that does not intersect the given line. Euclidean geometry requires the existence of a unique parallel line satisfying the specified conditions--which Callahan did not prove. The second volume purported to refute the theory of relativity."

On Wednesday, March 6, 2024 at 10:42:12 AM UTC-8 Laurence Clark Crossen wrote:

[Laurence Clark Crossen]

The Wikipedia article cited a Time article, "Angle Trisected?"=

"Given: Any angle whatever. Required: to divide any angle into three equal parts, using only straight lines and circles in the construction. Thousands of mathematicians have sought to solve that problem. It is comparatively easy of solution with a peculiarly linked chain or by means of complex curves which no compass can draw on a flat surface; but impossible, mathematicians generally agree, with the simple tools of straightedge and compass.

Last week the new, bland, stiff-collared president of Duquesne University in Pittsburgh, Very Rev. Jeremiah Joseph Callahan.* declared "the problem can easily be solved by plane geometry." He said he had done it in less than two months after the June semester closed. His mathematical reputation (his book Euclid or Einstein? on parallelism is to be published next month) gives prestige to his statement. The Callahan trisection depends "on the geometry of a plane figure that is not treated in Euclid, or in those modern works that are based on Euclid. When certain theorems concerning this figure are demonstrated, the problem of the trisection of the angle is quite simple." But what the figure is and what the theorems, President Callahan, like the Bostonian trisectors, would not disclose last week. He too wanted copyright first. He was at Chippewa Falls, Wis. for the 75th anniversary celebration of Notre Dame Church, where once he preached. A friendly man, medium tall, 53, a horse back rider when he has time & opportunity, he was amused at the excitement over his statement. Said he: "Trisection has no special practical applications. . . . It is a matter of pure science or, rather, pure mathematics."

On Wednesday, March 6, 2024 at 10:42:12 AM UTC-8 Laurence Clark Crossen wrote:

[Laurence Clark Crossen]

Callahan on Einstein: " Einstein is an analytical mathematician seeking to give a physical interpretation to the conclusions of his mathematical process. In this he is hampered by a load of contradictory and absurd assumptions of the school that he follows, which throws him in to all manner of difficulty. Einstein has such a faculty for embracing both sides of a contradiction that one would have to be of the same frame of mind to follow his thought, it is so peculiarly his own. The whole Relativity theory is as easy to follow as the path of a bat in the air at night. "

On Wednesday, March 6, 2024 at 10:42:12 AM UTC-8 Laurence Clark Crossen wrote:

[Laurence Clark Crossen]

The above quote in Wikipedia came from: https://www.hellenicaworld.com/USA/Person/en/JeremiahJCallahan.html

[Laurence Clark Crossen]

Callahan p. 161 on Riemann: "a translation made by a close follower of Riemann... It is such pedantic and flatulent language (pure macrology) that has drawn a veil of mystery around a certain class of modern scientists, who seem to use language only to cloak their thoughts, or lack of thoughts, except to the initiated, and to those outside the mystic realm the impression that the secrets thus  mumbo-jumboed must contain profound and weighty mysteries, before which they can only stand agape or bow down in humble wonder."

On Wednesday, March 6, 2024 at 10:42:12 AM UTC-8 Laurence Clark Crossen wrote: