Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: the ugly contradiction at the heart of High School Geometry #35.3
Uni-text 8th ed.: TRUE CALCULUS

Replies: 24   Last Post: Nov 3, 2013 7:44 PM

 Messages: [ Previous | Next ]
 plutonium.archimedes@gmail.com Posts: 18,572 Registered: 3/31/08
Re: what a real rebuttal of AP's claim of a contradiction in the
heart of Geometry looks like #35.9 Uni-text 8th ed.: TRUE CALCULUS

Posted: Nov 2, 2013 11:35 PM

On Saturday, November 2, 2013 9:26:15 PM UTC-5, Wally W. wrote:
> On Sat, 2 Nov 2013 17:30:28 -0700 (PDT), Archimedes Plutonium wrote:
>

(snipped)

>
> >AP 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.
>
> >
>
> >What a Wally Walrus rebuttal should look like:
>
> >
>
> >(1) point has no length, width, depth
>
> >(2) line has length but no width and depth
>
> >
>
> >So, as points become more dense and more dense they become closer together.
>
>
>
> They don't *become* more dense. They always existed. How do you
>
> *create* points? From what do you create them?
>
>
>

> >Visualize a point as a tiny circle or tiny sphere.
>
>
>
> You want to give it size. It has none.
>
>
>

> >As you make them more and more dense they crowd together.
>
>
>
> I don't *make* points. How do you?
>
>
>

> >At some moment of density,
>
>
>
> A critical mass of points. Is there then a chain reaction to initiate
>
> a Big Bang?
>
>
>

> >the points are so close together that they touch one point to the neighbor point.
>
>
>
> Then there is no greater perception of density, right?
>
>
>
> This happens when they are 10^-603 units of distance apart? BTW: you
>
> never clarified whether this distance was measured in light-years or
>
> microns. There are 22 orders of magnitude difference at stack in this
>
> distinction.
>
>
>
> If you say points can be no closer than 10^-603 light-years apart,
>
> what do you say to someone who has defined points 10^-603 microns
>
> apart? They have points spaced 10^-625 light-years apart. Your minimum
>
> point spacing seems to be inadequate for their use.
>
>
>
>
>

> >This moment is called a continuum of points,
>
>
>
> By whom?
>
>
>
>
>

> >and although each point has 0 length,
>
>
>
> If you visualize a point as "a tiny circle or tiny sphere" then it
>
> does not have zero length.
>
>
>
> Tiny things have size.
>
>
>
>
>

> >when they touch one another, they begin to form a length.
>
>
>
> A length is associated with any distance between points, continuous or
>
> not.
>
>
>

> >That is what a real rebuttal begins to look like there Wally,
>
>
>
> Or not.
>
>
>

> >not your sentences of contrary to everything I write.
>
>
>
> Not everything.
>
>
>

> >But of course you never studied logic in school and all of this if foreign to you.
>
> >
>
> >AP
>
>
>
> Are we having fun yet?

I am because you show how crippled in mind the establishment mathematics is:

---------------------------------------
AP Claim:

(1) point has no distance, no width, no depth
(2) line has distance but no width and no depth

Contradiction: because a line composed of just points, all of which have no distance, or 0 distance when added up yields 0 distance.

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 distance. 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 distant that line is.

Distance is a measure of one point to another point because distance is point A, then empty space, then point B.

--------------------------------------------

Now Wally is incapable of a paragraph or longer rebuttal, for he can only handle short sentences and cannot form a rebuttal argument. So based on what Wally said above, here is his defense of the Establisment Geometry.

What a Wally Walrus rebuttal is beginning to look like:

(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 > So Zeno's arrow can't exist. It could never hold together in flight
>
> because it is not continuous.
>

So apparently a line for WW is continuous.

So 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 the 2 points in question.

So Wally is confused in thinking that distance is totally separate from length, when in fact it is a chose 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.

In the AP argument, the mechanism is the third entity of empty space that is combined with point and line.

--------------------------------------------------

Until Wally can provide that mechanism, he has failed to defend.

AP