Creation ex nihilo

[Skarp] " ... the smallest particle has no size by which we can chop yet one more time."

You actually don't have a clue what infinitey is, do you? No real particle can have zero size, so I can <u>always</u> take someone's "smallest particle" and cut it in half.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by tvanflandern</i>
<br />I doubt you mean (A) because it is pretty absurd. So I'll address my answer to (. The <i>infinite</i> series 1 + 1/2 + 1/4 + 1/8 + ... has a finite sum of exactly 2. Proof: any proposed sum less than two can be shown to be exceeded. But no number of terms can ever exceed 2. Moreover, there is a one-to-one correspondence between this series and steps in crossing the street, where we first go half way, then half the remaining distance, and so on forever. No matter how many steps we take, there are always an infinite number of "half the remaining distance" steps left, although the other side is a finite distance away by construction.

Consider a particle occupying some volume of space. It is composed of ever smaller and smaller particles such that each particle has less than half the mass of the particle containing it, all the way to infinitesimal (infinitely small). So by another one-to-one correspondence with the series above, the total mass (the sum of masses on an infinity of smaller scales at a single point in space) is still finite, not infinite. -|Tom|-<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Tom, I remember coming across this series as a kid, before I knew anything about finite or infinite series. There was something about it that always bothered me.

The way it was presented was that if you stood two feet from the wall, and walked halfway there on each step, you would never get there because you could always divide the remainer of the distance in half. But then we would try it and in kid's terms would say that's a bunch of bs, because by the 8th step our foot was touching the wall. Another variant was to take a piece of paper and fold it in half. While there is always something left to fold in half, the reality of the situation was that you could never fold it more than about 8 or less times, no matter how large a sheet of paper you used. Again you "bumped up against the wall". With the clarity of the child, again we would say "that's baloney."

The math that explains this phenomenon is of course finite and infinite series. The finite series as you say, has a limit and an exact sum, whereas the infinite series doesn't. That all makes perfect sense, but it still didn't prevent our foot from hitting the wall.

Ok, so now let's talk about this notion that the universe is infinite in scale in both directions: small and large. In the "large" direction, it's a little easier to imagine that for every possible arrangement of objects from particles through galaxies through clusters of galaxies to anything you can imagine, I can sort of see how the notion of "infinitely large" might work out. But for the "infinitely small" side of it, I keep coming back to the fact that our foot hit the wall in a mere 8 steps.

We can imagine anything we want, and we can certainly divise a mathematical scheme to explain it, but that's an altoghether different thing than saying that it really has some actual physical reality.

In fact, the notion of the infinitely small with the same form as the medium and infinitely large quite frankly strikes me as "baloney."

rd

JR, cosmicsurfer,

Keep in mind that Skarp is not serious about this discussion. At least, not in the usual way. When he "mistakenly" confuses Tom's meaning, it is not really a mistake. When he talks about the difference between is and {{{is}}}, he is just obfuscating.

I proclaim in mock astonishment that he doesn't understand infinity, but I'm pretty sure he does. There is a learning opportunity here; the real question is how to take advantage of it.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by rderosa</i>
Ok, so now let's talk about this notion that the universe is infinite in scale in both directions: small and large. In the "large" direction, it's a little easier to imagine that for every possible arrangement of objects from particles through galaxies through clusters of galaxies to anything you can imagine, I can sort of see how the notion of "infinitely large" might work out. But for the "infinitely small" side of it, I keep coming back to the fact that our foot hit the wall in a mere 8 steps.

We can imagine anything we want, and we can certainly divise a mathematical scheme to explain it, but that's an altoghether different thing than saying that it really has some actual physical reality.

In fact, the notion of the infinitely small with the same form as the medium and infinitely large quite frankly strikes me as "baloney."<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">rd, I had the same problem, but for a different reason. I can grasp and accept the idea of infinite composition(adj.), but the infinite composition(v.) (or decomposition in the case of dividing the distance to your wall) in a finite time interval is impossible. This is where the scale dimension becomes important. In a previous post I explained how the scale dimension allows us to treat all intervals as finitely divisible at each scale. So the distance between your foot and the wall cannot be infinitely divided at our scale. But there are infinitely smaller scales each having its own smallest distance. The key is that as you move towards the wall, you are crossing a finite number of distance intervals at each scale but doing so over the entire infinite range of scales <b>simultaneously</b>.

JR

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Larry Burford</i>
<br />Keep in mind that Skarp is not serious about this discussion. At least, not in the usual way.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Those who come to this discussion without a background in the study of infinities are at a severe disadvantage, and tend to rebel at the notion that infinities have applicability to the real world. It is a natural first reaction. But as long as they don't take it to the extreme that Fopp did and start to question logic itself, I prefer to give each of them the benefit of the doubt.

What we can't do here is teach "Infinities 101". We can provide the references and answer questions, but it is up to the participants to inform themselves or not, according to their personal priorities.

What we do face is that most thoughtful people have already confronted these issues and come up with some sort of answer that comforts them, usually one of the big three: God did it, it's beyond human comprehension, or infinity concepts explain it. Once a position is adopted, it can be very difficult to detach a person from his choice because he/she has built life-changing decisions around his answer, and because people don't like to admit error to themselves (much less to others) because if they see themselves as capable of big mistakes, they would have to continually question all their choices. They have not learned the answer of scientific metod, which is to test hypotheses in such a way that one's own biases cannot influence the outcome. That way, one's own fallibilities are less of a factor in what one accepts to be true.

I appreciate your challenging illogical statements. But attributing motives is something we should try not to do because it brings out emotion instead of a determination to make one's reasons persuasive. If someone does become so much of a troll as to disrupt the discussions, we can deal with that. But as for questioning the meaning of "is", jrich is probably right about it just being a misunderstanding, and Skarp can always argue that he is just imitating presidential behavior. [}] -|Tom|-

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">You actually don't have a clue what infinitey is, do you? No real particle can have zero size, so I can always take someone's "smallest particle" and cut it in half. <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote"> Your missing the point. There are no particles in an infinitely composed universe like the one described in Meta Model. Just as 1 + 1/2 + 1/4 + 1/8 + 1/16 ........ = 2. 1 - 1/2 - 1/4 - 1/8 - 1/16 ........ = 0. We are talking about a complete infinity, and not a finite one like you keep describing. You can always have a particle that can be cut in half, because you can't do it infinitely, but if you should happen to do it infinitely, you will end up with nothing left to cut. Meta Model says it's been done, it has always been a done deal. So my expectation is (nothing) at all by way of the Meta Model