Alright, Wally did good in trying to defend the establishment old decayed contradictory Geometry taught in High School and Colleges, by trying to shift the focus from "length" to that of "distance". So that a point has no length, but that 2 points can have a distance.
Which would be the argument most would make, even John Baez when he is not stalk mocking. And I have to say, Wally really caught me off guard there, for I never thought I would have to distinguish between length and distance.
As Wally said:
WW> The distance between Point A and Point B is given by the Pythagorean > > Theorem, regardless of how many points exist between these two points. >
But unbeknownced to Wally or establishment geometers the distance argument is far worse than the length argument since the "empty space between two points" is made immediately aware of. For if we select any two points, A and B in the plane and compute the distance, as WW says, we are not measuring how many points lie along the path from A to B but rather, we are measuring "empty space between A and B".
So with the distance argument we arrive at the contradiction at the heart of modern day Fake Geometry far earlier than if we do the length argument.
In the length argument I have to appeal to finite and infinity borderline to resolve the contradiction to obtain a microinfinity that gives a "empty space composed of infinite numbers".
So I compliment WW for at least trying to defend the establishment of their fakery geometry which they indoctrinate innocent High School kids and College students with their phony baloney of a Euclidean Geometry of continuity, and always another point between any two points, and their continuum and their line with length but points without length.
All that geometers need do to fix their contradictory fake geometry, is recognize that three items exist-- point, empty space and line. To stop being lazy and recognize that finite has a borderline with infinity which demands an empty space between two successive points.
So, people can be like Jennifer Murphy that want to run and hide from new true ideas and want to forever teach people old fake ideas. Who want to indoctrinate young students to pollution, rather than debate and question ideas. At least Wally made an attempt to defend although he failed which is far more than can be said for John Baez (Brian Q. Hutchings, where did you pick up that name-- some character in literature??) or said for Jennifer Murphy and her camps of suppression training.
Kids deserve better education than seeing a mocking John Baez or a suppressionist Jennifer Murphy. Kids deserve to see the logical arguments for and against geometry of line with length.
Sure, a lot of money is at stake for every High School and College at this moment is using a textbook of geometry that is mostly fake geometry. But change has to start somewhere when your teaching is fakery. And Usenet is a good place to start that wholescale change of getting the fakery and phony old geometry out of schools.