Subject:
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Re: Ahh infinity, how I love ye! Was Re: George Bush has legitimised terrorism
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Newsgroups:
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lugnet.off-topic.debate
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Date:
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Fri, 23 Apr 2004 18:15:21 GMT
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Viewed:
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3818 times
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In lugnet.off-topic.debate, Dave Schuler wrote:
> In lugnet.off-topic.debate, David Koudys wrote:
>
> > In other words, in theory there is an infinite number of points between A and B.
> > That's great for math and theories and such. However, if I were to get a
> > straight edge and draw a line between A and B on a piece of paper, the line
> > wouldn't take me an infinitly long time to draw, nor would it use up an infinite
> > amount of ink.
>
> True, but your formulation of this example is incorrect. The ink line is not
> made of an infinite number of infinitely small "points" of ink; rather, the line
> is made of a finite (but quite large) number of very small (but quite finite)
> particles of ink, each of which covers a tiny fraction of the space between
> point A and point B. That's why it doesn't take an infinitely long time to draw
> nor an infinite amount of ink.
>
> > The real world is finite. You can draw the arcs on spheres
> > showing an infinite concept, and dissimilate the infinite number of points of a
> > hyperbola thru a cone--in the end, however, the real world shows that the area
> > is finite, the line is finite.
>
> Well, the area is finite in three dimensions, but is unbounded in two. This
> means that although the area is not infinitely large in three dimensions, it is
> infinite in two dimensions. Similarly, the line you're positing isn't a line at
> all--it's a line segment, which is very different even in purely mathematical
> terms.
>
> But consider my example again. Take a sphere (it doesn't even need to be a
> mathematically perfect sphere--just one that doesn't have any major gaps in its
> surface. A marble or ball bearing will suffice.
>
> Shine a laser pointer (maybe from your long-neglected Rock Raiders set) against
> the surface of the sphere. Then start rotatating the sphere. When will you run
> out of surface? Barring such tangential events as loss of laser power, erosion
> of the sphere, or the eventual end of the universe, you will never run out of
> surface. But the surface is not finitely bounded (which is also why you tend
> not to fall off of the Earth when you pass the horizon!)
Yes, and I can sit in my swivel chair and spin from now until "the end of time",
never stopping the spin (excluding such contingencies as death and parts on
chair wearing out) but, again, that only works 'on paper'. IN real world
applications, I will die, the chair will stop spinning (due to fatigue). If
there was a path around the equator that one could walk, one could theoretically
walk around the world until the world stopped. But that's theory. Spin the
ball and point a laser at it. In the real world, after one revolution the laser
would be traversing the same path, therefore no infinity, and secondly, in the
real world, after a finite number of spins, either the ball bearing would have
disintegrated due to entropy and as you correctly pointed out the lasr would
eventually break down.
See, that's the differenc between theory and real world concepts. We can
discuss infinity and come up with ideas and equations only 'on paper' The
second you try to make a construct in the real world showing 'infinity', you
will fail for we live in a finite world. You can show concepts of infinity--"if
we could eliminate entropy and the fact that our universe had a beginning, then
this laser reflected off a spining ball-bearing would physically show us
something infinite."
But we don't have that in real-life applications.
>
> > 'Tis like that idea that if you throw a baseball at a tree--you should always be
> > able to divide the distance between the baseball and the tree by two, on to
> > infinity--therefore the baseball, in theory, would never hit the tree. Unless
> > you have a pitching arm like me, if you throw a ball at a tree in reality, the
> > ball hits the tree.
>
> You understand, though, that the paradox of Zeno's Arrow was eliminated by the
> mathematical concept of "sums of infinite series?" Additionally, it is now
> becoming apparent that space is not infinitely divisible, so the formulation of
> one-half-of-one-half-of-one-half-of-one-half... doesn't really hold water.
Thus a 'proof' showing that infinite cannot be concretely formed in a finite
world--only shown on paper in equations and theory.
>
> > If you take infinite number of monkeys with an infinite number of typewriters,
> > and infinite amount of time, one of 'em's bound to bang out the complete works
> > of Shakespeare.
>
> This commonly held notion is a conflation of the concepts of infinity and
> comprehensiveness. Something that is infinite need not be all-encompassing, so
> the monkeys could endlessly bang away at the keys and never even type out a
> single complete word, much less Hamlet.
I just always liked that expression--"throw infinite number of monkeys and an
infinite number of typewriters into a room..."
I think there would be an infinite amount of mess, myself. Thankfully this is a
theory and no one has to actually go in there and clean up the mess.
> > Well, the universe isn't infinite, time, as far as relative to us, is finite,
> > and there's only a finite number of monkeys and typewriters--"To be or not to
> > be" and the rest of the plays aren't going to be banged out by a chimp in the
> > real world
>
> Incidentally, the typing-monkeys model is very commonly (and very misguidedly)
> used in an attempt to refute evolution. Richard Dawkins discusses the thought
> experiment at length, and his "Blind Watchmaker" is well worth reading.
Still haven't picked it up, but have heard many conceptual notions about it. I
would not argue against evolution, now (may have in the past but that's neither
here nor there).
> > Fractal geometry--There's a square. Divide that square into 9 sections--3 x 3.
> > Take out the middle section. Each of the remaining squares also divide into 9
> > sections--3x3. Take out the middle square. Repeat to infinity. What you're
> > left with, in theory, is a square that has the same perimeter as the original
> > square, a.k.a. finite perimeter, but infinite divisions.
> >
> > In theory.
> >
> > If you took a piece of wood and did the same, probably wouldn't get to far, even
> > with nanotechnology--there is only so far you can go in the real, finite, world,
> > hence the 'finite' bit.
>
> This comes back to the realization that space isn't infinitely divisible.
> Additionally, you'd need to hypothesize an infinitely homogenous piece of wood;
> otherwise, you can't reasonably expect it to yield fractal symmetry!
Hypothetical != real world. (!= means 'not equals') In the history of the
world, it is my contention that there never has been this 'homogenous piece of
wood' ever grown capable of being divided into smaller and smaller pieces thru
infinity. At least, that's my contention. If someone out there finds a piece
of wood that is able to do this great feat, I will accede this point (oh, that
includes the iron listed below as well...)
> > I'm just saying. For me, the application of theories to the real world is where
> > the important bit lies. If the theory and the real world do not jive, then the
> > theory has to be modified.
>
> I am in infinite agreement on this point. Just be sure that you're objecting to
> the correct part, and be sure that your formulation of a given issue is correct.
> The "fractal wood" is a good example of a straw man, for instance, because
> you're requiring a finite, material object to behave in the manner of a
> conceptual infinity, and when the wood fails to perform you claim that the
> conceptual infinity has been disproven.
And you just made my point crystal clear--the finite material universe cannot
'make' an infinite object or demonstration, by the very nature of the finite
universe.
Conceptual infinity, therefore, can only exist in the realm of theories,
equations, and, as you put it, concepts. There can be no real-world
applications showing same. The second you state that, "We've set up this
demonstration to show infinity, but this demonstration has to work for an
infinite time..." you've left the real world and gone into concepts.
>
> Alternatively, when the wood fails to perform, you might try an iron.
>
> Dave!
About a 9 iron, I'd say... the ground breaks a little bit to the left, though.
I'd watch out for that.
Dave K
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