The nature of force

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">You have to concede that a "point particle" does have various obscurities. For if you take the function f(x)=arctan(x), then it is seen that the real line, for points x in (-inf,inf), maps into the interval (pi/2,-pi/2). Now, the real line looks "solid" to me on paper, having "no gaps", yet it is possible to place all points of the real line next to each other in an arbitrary small interval (epsilon, -epsilon). Hence, an infinite "solid" horizon of seemingly touching points fits into an arbitrary interval in a one-to-one manner. <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Are you saying that Tom's MIs, elysons and such exist in a one to one correspondence with the "real" numbers or to the "integers"?

A) - If they go as the real numbers ... then ... an MM particle can possess the required finite cross-section ... but ... so does all of space which in MM is filled. Hence, it is "solid"? ... and no movement is possible.

- On the other hand, if it exists in a one to one correspondence to the integers ... then ... an infinite number of constituents can exist in a finite volume ... but ... they do not cover a finite cross-section [which is the thing to be collided with]. They cover "0" cross-section because the integers are an infinitely smaller infinity than the real numbers as per Cantor.

Now, in the case of A, no movement is possible because everything is solid (the whole universe). While in B, no collision is possible because no cross-section is there to hit or be hit.

Do you understand what my argument is now, and why an exact description of "collide" is necessary? Since we are talking about fundamentals in the context of infinities, we must be in the realm of what corresponds to what on the number line. Maybe the elysium corresponds to the "real" numbers and the MIs to the "integers" ? Something like that ... ??

LB, If you do as you suggest and keep on looking for the answers in smaller and smaller(or larger and larger)things where do answers ever appear? And if they never do appear why look for them at all? This is what is in fact being done in science currently. The only goal seems to be doing the research to get the grant and getting the grant to do the research so more grants can be got yada,yada,

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by EBTX</i>

Are you saying that Tom's MIs, elysons and such exist in a one to one correspondence with the "real" numbers or to the "integers"?
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

I certainly believe that elysons, seen as objects, are infinitely countable. But since each object in the universe comprises an infinite number of constituents by definition, I'm tempted to say that all objects in the universe cannot be counted. Hence, as per cantor's "continuum hypothesis", all forms and objects in the universe would then have the same cardinality as the real line.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">all forms and objects in the universe would then have the same cardinality as the real line.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Then space is a solid and no movement is possible if elysons fill all space. There must be some "empty" somewhere for things to move around in a finite space without always running into something else. "Real" emptiness ;o)

This is where MM theory fails in my view. It cannot adequately define what a collision is ... as in "What is colliding with what?".

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by EBTX</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">all forms and objects in the universe would then have the same cardinality as the real line.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Then space is a solid and no movement is possible if elysons fill all space. There must be some "empty" somewhere for things to move around in a finite space without always running into something else. "Real" emptiness ;o)

This is where MM theory fails in my view. It cannot adequately define what a collision is ... as in "What is colliding with what?".
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Perhaps our understanding of empty space is somewhat incomplete. This is why I posted the example of the function f(x)=arctan(x), which describes an equivalence relation:

(-inf,inf) ~ (-pi/2,pi/2)

That is to say that an infinite horizon of seemingly "touching" points can be contracted into an arbitrary interval (-epsilon,epsilon). But isn't this remarkable? How can a seemingly solid entity such as the real line, which has no gaps, can be contracted into an arbitrary interval? Thus, by going from the limit point -pi/2 to pi/2 we actually traversed the distance between the limits points -inf to inf. Moreover, we have visited each point once.

Now, perhaps there is no such thing as empty space. The universe is filled with particles of arbitrary size, but these particles can form cloulds of higher subtance densities, yet there is never space between the particles. Motion then becomes an intricate process of particle clouds that "roll" into different positions continuously. Furthermore, "contact" always occurs, thereby allowing forces and other phenomena to propagate continuously throughout the continuum of particles without any magic jumps from one object to the other.


my 2 cents []

Jan

[Jan] " ... all forms and objects in the universe would then have the same cardinality as the real line."

Jan, I think you are right about that. And, IIRC, Dr. Van Flandern has opined on this issue and said something similar.

[EBTX] "Then space is a solid and no movement is possible if elysons fill all space."

EBTX, still having trouble with the concepts of infinity and infinite divisibility, are we? By this arguement oceans are solid and no motion is possible because because water molecules fill all oceans.

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These concepts are not entirely intuitive, so most of us have some problems comming up to speed on them. Well, don't worry. We can help you in that area. If you are really interested in learning ...

I'm going to re-post an example from another thread that might shed some light.

LB