Zeno revisited

Is it not so that this issue is similar to the issue of how many angles can dance on a pin head? That was an important issue a some time in the past for some reason so maybe it would be a good thing to find out why it mattered then and not now.

nderosa,

I have to disagree with your contention that if the distance between X and Y is the "smallest possible distance", then they are necessarily touching. I think it is obvious (to everyone except perhaps yourself) that the phrase "smallest possible distance" means "smallest possible non-zero distance" or "smallest possible distance without touching".

Of course even assuming your interpretation and dispensing with the point particles leads to logical problems. The dimensions of the smallest particle must all be multiples of the smallest distance with at least one dimension equal to the smallest distance. The only geometry that can satisfy that requirement is a sphere with a diameter equal to the smallest distance. However, if 2 or more spheres are touching there will be some space between them with dimensions smaller than the diameter of the spheres. Therefore, there can be no smallest distance.


JR

Hello Neil,

You seem to be arguing for equality between the smallest possible size of particles and the smallest possible distance those particles can move.

It isn't immediately apparent to me that there should be any relationship between space and scale, nor that the ratio of any hypothetical minimums of each should be unity if there is a relationship.

===

BTW, I agree that the universe is what it is, and that if there is a smallest possible size, well, then there is (a smallest possible size). But I can see no reason to deduce a smallest possible size at this time.

I also see no way to ever prove that the universe is infinite in scale. Or infinite in the (probably independent) time or space dimensions. But at this point in our development logic seems to demand it.

Some day we may be digging around on a scale trillions of magnitudes smaller or larger than human scale and find the place where the railroad tracks actually meet.

Then the fun starts - we get to figure out "why?". With a little luck we will be up to the task by then.

===

Your book sounds interesting. Don't let a little criticism deter you.

Regards,
LB

{Larry) < BTW, I agree that the universe is what it is, and that if there is a smallest possible size, well, then there is (a smallest possible size). But I can see no reason to deduce a smallest possible size at this time.

I agree. I guess my point is that without empirical facts, one deduction is as good as another

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by nderosa</i>
<br />I guess my point is that without empirical facts, one deduction is as good as another.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">"Deductions" are conclusions drawn from premises and reasoning in logical syllogisms. The principal idea that separates the Meta Model from all other modern cosmologies (e.g., Big Bang, Quasi-Steady State, Plasma Cosmology, Variable Mass Cosmology) is that MM uses only deduction starting from primary physical principles, whereas all the others use induction from some empirical facts. So only MM is well-positioned to deal with such matters as Zeno's Paradoxes precisely because it requires no empirical facts to do so.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Van Flandern postulates a universe which is infinite in five dimensions, and that "scale" is one of the dimensions.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">This is a case in point. MM has no such postulates. The number and infinite extent of the five dimensions are deductions from first principles, and are not based on assumptions or empiricism of any kind.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">On the small scale, the smallest known particle can be an infinitely large universe on some smaller scale. On the large scale, a "wall of galaxies," trillions upon trillions of them, might be a mere light wave in the quantum world of some larger scale. That's it, except to say that you can repeat that statement an infinite number of times and it would always be true!<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Many people have had this same idea about the universe. Can you put into words why you think this is implausible?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">My objection to this hypothetical construct is that you can't use something as a starting point that you don't know for certain.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">But you did not address Jrich's fine argument that answered your objection very well, I thought.

I think you need to induce your intellect to wrestle with this "superman" of an intellectual problem and work on eliminating whatever biases you may have consciously or unconsciously brought with you to the wrestling arena. If we all allowed our biases to influence our judgment, no two humans could ever reach agreement about matters on which they disagree.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">in Van Flandern's model, X, Y, and Z are assumed to be infinitely small points—thus he arbitrarily assumes to be true precisely that which is necessary to prove his hypothesis.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">There is some misunderstanding here because "indefinitely small" (but still finite) is very different from "infinitely small" (infinitesimal). In my example that you cited here, I used the former, not the latter. -|Tom|-

Hello Neil,

Ah, but we do have some empirical facts. At any given time we have knowledge of something which is recognized as the current "smallest thing".

* First there were "elements" (earth, air, etc). (Maybe it even goes goes back further than that?)
* Then there were "atoms" (hydrogen, helium, etc.).
* Next there were "sub atomic particles" (protons, electrons, etc).
* Finally we get to now, where there are quarks (up, down, etc).

At each stage there was someone willing to step forward and say "this current smallest thing is actually the smallest POSSIBLE thing". Of course they were wrong.

We are still waiting to see if quarks are going to follow the same pattern. There is evidence that they do indeed have components.

===

Now, three or four examples of something is NOT proof. But the pattern is clear. It seems to me that it offers a solid reason to favor the "scale is infinite" deduction over the "scale is finite" deduction.

At least until we actually find that spot where the tracks meet.

And the more examples we find of the current "smallest thing" turning out to be composed of yet smaller things, the more likely it will be that the infinite scale deduction is actually correct.

But no matter how many examples we do in fact find, we will never be able to say with certainty that the then-current smallest thing MUST have components.

===

And that brings up another interesting point. Suppose that the current smallest things (quarks right now) actually are the smallest possible thing. How could we KNOW for sure? Even after looking for components and failing for a million years, we couldn't positively eliminate the chance that someone might succeed tomorrow.

So we will also never be able to say with certainty that the then-current smallest thing must NOT have components. Even if it doesn't.



Regards,
LB