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 15:32:36 GMT
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3736 times
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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!)
> '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.
> 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.
> 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.
> 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!
> 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.
Alternatively, when the wood fails to perform, you might try an iron.
Dave!
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