I was reading Parallel Worlds the other day, and it brought up a thought that was pretty awesome: If a point is infinitely small, then there would be an infinite amount of points in a very small distance. It is impossible to cross infinite measurements, so how is movement possible? The author then parenthetically stated that it could be solved through calculus that it is possible to cross an infinite measurement in a finite time. Any thoughts? -Zack

i'm sure you've heard in rudimentary math classes the paradox of the 1/2 distance phenomenon. if i walk towards you covering half the distance between us over any finite interval, mathematically it will be impossible for me to reach you during a finite period. however, we know that if you try this experiment, i will reach you eventually. basically i think that the concept of "infinite" within finite space is only for calculation and realistically fails to describe macroscopic reality. however, at very small sectors of comparison, i can see how the infinite is a necessary rationale for describing space.

there's this thing you'll inevitably learn about called the "integral". its a math operation. basically what you do is you take a space (like any 2D shape) and cut it into squares (because squares or rectangles are easy to find the area of). the best approximation you can get for that area is by making your rectangles infinitely thin so they are essentially almost lines. this set of infinite rectangles spanning one interval in one dimension (such as x) and a function (such as y = blah) in another is called the integral. it's an infinite measure of a finite region of space. this can be expanded (as i learned only this year) to 2D and 3D space with double and triple integrals. i think that this concept is capable of describing how we can move, because inevitably though the distance crossed is "infinite", the infinite nature of it is very "small" and we somehow cross it. i'm only suggesting this, i may be totally wrong. its a complex idea

i'm thinking perhaps it works like this. [--------] A..........B the distance between the brackets is defined to be finite, like say 2 inches. but there's an infinite number of points between. we say finite amount of time (such as 2 seconds to cross 2 inches) but if dividing finite space into infinite points is acceptable, why not divide that finite amount of time into infinitely small fragments of time advancement. then: i think maybe movement takes place not in a series of finite states, but smooth, infinite rate of change that explains how one can go from A to B in a "finite" amount of time. infinite space between, infinite time elapsed, however A and B are boundary states that we can describe in finite terms such as "inch" and "second" though each inch and each second can be divided into infinitely small pieces.

Ah, the 1/2 distance converging phenomonon is a tricky one, I might talk to my dad about it again. You may well be right ss.

The 1/2 distance phenomenon you speak of is called Zeno's Paradox, if I remember correctly. If traveling from A to B, you could always change your mind and travel to some point C, past point B. Then you'll reach B on your way to C. If you think of all movement in such terms, you technically never get where you're going. I don't remember much about calculus from last year, but I'm sure that it explains such things.

Yeah, Zeno of Elea stated the original paradox about 2500 years ago, then various philosophers tried to tackle it in various ways with various flaws. It's become pretty much accepted over the last century or so that the paradox is based on a few false assumptions, though.