The Definition of Points                                                  ~v~~ In the swansong of modern math lines are composed of points. But then we must ask how points are defined? However I seem to recollect intersections of lines determine points. But if so then we are left to consider the rather peculiar proposition that lines are composed of the intersection of lines. Now I don't claim the foregoing definitions are circular. Only that the ratio of definitional logic to conclusions is a transcendental somewhere in the neighborhood of 3.14159 . . . ~v~~ Please look up the difference between define and determine . In a theory that deals with points and lines (these are typically theories about geometry), it is usual to leave these terms themselves undefined and to investigate an incidence relation P on L (for points P and lines L) with certain properties Then the intersection of two lines /determines/ a point in the sense that IF we have two lines L1 and L2 AND there exists a point P such that both P on L1 and P on L2 THEN this point is unique. This is usually stated as an axiom. And it does not define points nor lines. This is interesting observation ))) But how do you define difference between define and determine ? Can definition determine and can determination define? Lester Zick has problem with circular definitions and you used term point in your determination to determine it. Maybe you want to say that in definition you can't use term you define to define it and in termination you can use it to determine it. I think it's time to call Determinator ))) He is the only one who can help us! hahahahahahaha

In a theory that deals with points and lines (these are typically theories about geometry), it is usual to leave these terms themselves undefined and to investigate an incidence relation P on L (for points P and lines L) with certain properties Then the intersection of two lines /determines/ a point in the sense that IF we have two lines L1 and L2 AND there exists a point P such that both P on L1 and P on L2 THEN this point is unique. This is usually stated as an axiom. And it does not define points nor lines. Here is one problem that is much biger that definition of point. How do you define definition ? If you have a definition of definition you can't prove that it is a really stuff becouse you don't know what definition is before you defined it. I can as well say that definition is a big red apple and it is true by definition. You can't prove that definition is not a big red apple becouse you don't have definition of definition other then this. Since I defined definition first, from now on definition is big red apple )))

My huge gripe is the way so many people have attempted to replace physics with mathematics. That's Lester's problem. He thinks vectors are Really Out There - not just handy ways of talking about forces or velocities. He thinks dimensions are Really Out There - not just handy ways of locating _object_s like roads and furniture. But he rejects lines made of points because he knows points have zero size - and how can you construct something out nothing? He rejects SR because it doesn't agree with his experience of time and space, so it must be wrong. But he believes that Science is Math, and Math is Truth (unlike whatever it is that mathematikers practice, which he says is mere guesswork.) So he has to interpret the SR math so that it agrees with his notions of what's Really Out There and with his experience. In order to do this, he invents his own notations and his own interpretations of mathematics. He's the most curious blend of idealist, materialist, and empiricist I've ever seen. He's quite amusing - until he starts pissing on people who try to help him make sense of his nonsense. [...snip the rest, with which I generally agree, except your slur on theoretical physicists. It's their work which has produced those very useful models that you use in your work. It's also corrected the ad-hoc models constructed by engineers, which have repeatedly led to more or less lethal disasters, and which the engineers couldn't explain until they decided to argue fine points of mathematics in their attempts to analyse the data.] HTH

                                  The Definition of Points                                                 ~v~~ In the swansong of modern math lines are composed of points. But then we must ask how points are defined? However I seem to recollect intersections of lines determine points. But if so then we are left to consider the rather peculiar proposition that lines are composed of the intersection of lines. Now I don't claim the foregoing definitions are circular. Only that the ratio of definitional logic to conclusions is a transcendental somewhere in the neighborhood of 3.14159 . . . ~v~~ Can you prove that non-circular definition of existence exists?

[...] What is your background in mathematics, Lester? You have asked: what is the empty set . The empty set was my only source of amusement in my proofs class. Proofs of what pray tell? Certainly not the truth of your assumptions. Bob has similar difficulties. He knows quite a lot whereof he cannot demonstrate the truth but prefers to assume it instead. ~v~~

                                   The Definition of Points                                                  ~v~~ In the swansong of modern math lines are composed of points. But then we must ask how points are defined? However I seem to recollect intersections of lines determine points. But if so then we are left to consider the rather peculiar proposition that lines are composed of the intersection of lines. Now I don't claim the foregoing definitions are circular. Only that the ratio of definitional logic to conclusions is a transcendental somewhere in the neighborhood of 3.14159 . . . ~v~~ My impression is that Euclid defined a line, not in terms of points, and never claimed a line was made up of points, but defined a line as a geometrical _object_ that has only the property of extensibility (length, where length can be infinite). He uses points in his proofs specifically as intersections of lines, if I remember correctly, and makes no attempt at describing or explaining their density in a line. (You gotta lot of 'splainin to do, Euclid!).