Alright, let me compliment WW for at least attempting to defend establishment Geometry with their contradiction of point and line. At least he tried, by saying that distance is different from length, but as it turns out, his is just a different word choice for both length and distance cause the contradiction at the heart of Old Geometry.
What I am displaying below is the difference between saying a line has distance but no width nor depth, as compared to saying a line has length but no width or depth.
In the case of length, the contradiction appears slowly because we must muster the finite and infinite borderline which yields the inverse of the macroinfinity as the microinfinity which is the empty-space of infinite numbers that composes the empty space. So in the argument of length as contradiction, we must add up many tiny holes between successive finite numbers.
In the case of a distance as the contradiction we get one huge empty space between two finite points immediately. So in the distance contradiction the distance between point A and B on a line is not how many number points exist between A and B, but rather the distance is the empty space between A and B. And in the case of length argument, I need to add up all the tiny holes between successive points for a total length.
So when WW injected distance rather than length, sort of caught me off guard for a moment but then I realized distance makes the demand for "empty space" that much stronger of a demand.
On Saturday, November 2, 2013 11:40:13 PM UTC-5, Wally W. wrote: > On Sat, 2 Nov 2013 20:35:41 -0700 (PDT), Archimedes Plutonium wrote: >
> > > > The distance between Point A and Point B is given by the Pythagorean > > Theorem, regardless of how many points exist between these two points. >
Well, you said it. distance in geometry is point A to point B where the in between is not points, but is ** empty space**.
The distance argument is far shorter because we need no infinity borderline to yield empty space. A distance argument has empty space as its argument.
So here are the two arguments of Contradiction:
AP length claim:
(1) point has no length, width, depth (2) line has length but no width and depth
Contradiction: because a line composed of just points, all of which have no length, or 0 length when added up yields 0 length.
How to correct the Contradiction? Find the finite to infinity borderline which gives a microinfinity which acts as "empty space between two successive finite points" thus giving the two points a length. So that a line in Geometry, True Geometry is a finite point with empty space and then the next finite point with empty space and then the next finite point with empty space for however long that line is.
AP distance claim:
(1) point has no length, no width, no depth (2) line has length but no width and no depth
Now we use the concept of distance rather than length, as if distance is separate from length. Now distance is measured by point A to point B with various calculations such as the distance formula and the end result is that the distance is A, empty space between A and B, B. So in distance we have just one huge empty space which we thence call the length of A to B.
Contradiction: because geometry has no distance nor length without empty space between points A and B. Distance is a measure of one point to another point because distance is point A, then empty space, then point B.
How to correct the Contradiction? Find the finite to infinity borderline which gives a microinfinity which acts as "empty space between two successive finite points".
So far Wally's attempt to defend old establishment Geometry for their contradiction at the heart of geometry is to wiggle waggle a difference between length and distance. But as it turns out, distance is one huge empty space between two points and length is a series of microinfinity lengths that compose a overall length for the line in question.
What a Wally rebuttal is beginning to look like so far is this:
(1) point has no distance, no width, no depth (2) line has distance but no width and no depth
WW > They (points) don't *become* more dense. They always existed. How do you > > *create* points? From what do you create them?
WW > A length is associated with any distance between points, continuous or > > not.
WW > Yes. (A line is continuous.) >
So WW made a valiant attempt to defend Old Geometry with a switch of words of distance compared to length but the flaw remains, and the contradiction remains, because the distance between point A and point B is not tallied by how many other points are in the path of the distance but how much empty space resides between points A and B.
So Wally is confused in thinking that distance is totally separate from length, when in fact it is a choice of words, whether we want to call it distance or want to call it length.
So Wally still has failed to defend establishment Geometry, for he needs to offer a mechanism of how points can turn from no distance or no length into points having distance and having length. He needs to provide a mechanism.
For that is Old Geometry, the establishment geometry which believes that you can have points as no length or no distance yet create a line composed of nothing but points that has a length and a distance.
In the AP argument, the mechanism is the third entity of empty space that is combined with point and line. In order for Wally and the establishment Geometry to win, they must come up with a mechanism that turns points of no length into points that have length, so the line can have length.