Just a Complex Thought of the Day?

Question

It is possible to cross an infinite space. Take any distance, say the distance from one hand to the other. Halve that distance, then halve that half, and repeat forever. The number can be halved for all time. Now think as each half as a point. That would mean there are an infinite number of points between your hands. Yet you can cross that distance. Mathematically sound theory.
I also want to note that i am no scientist, or mathematician so this may be wrong. Let me know.

Answer 1

This is a lot like the paradox of Zeno.

Excerpted from mathforum.org

A runner wants to run a certain distance - let us say 100 meters - in a finite time. But to reach the 100-meter mark, the runner must first reach the 50-meter mark, and to reach that, the runner must first run 25 meters. But to do that, he or she must first run 12.5 meters.

Since space is infinitely divisible, we can repeat these 'requirements' forever. Thus the runner has to reach an infinite number of 'midpoints' in a finite time. This is impossible, so the runner can never reach his goal. In general, anyone who wants to move from one point to another must meet these requirements, and so motion is impossible, and what we perceive as motion is merely an illusion.



Ok, back to my answer.

The key to answering this question is to realize that adding up an infinite amount of numbers doesn't necessarily mean the answer is infinity. Here's a clever way to see this.

Take an ordinary sheet of paper. Now tear it in half. Take one of those halfs, and tear that in half. Take one of the new smaller pieces, and tear it in half. Continue this forever.

At the end, you'll have an infinite number of tiny, tiny pieces of paper. But what do you get when you add them all together?? 1 whole piece of paper!! The same is true for space. Add up all of those tiny, tiny points you created and voilia, you have the distance between your two hands!

Answer 2

This is an arithmetic series, following the formula ar^(n-1). An arithmetic series is convergent for |r| (i.e. -1 Then this series would converge to a single point. You can do it the long way (10+ 5 + 2.5 + 1.25 + ... ) You would get a single, stationary point, not an infinite number (well, it may well have an infinite number of decimal places, but it is not infinitely large)

Answer 3

This is just a version of Zeno's paradox, which is described here:
There are two points that resolve this:
- Each of these individual segments is finite, and takes a finite amount of time. However, the shorter the segment, the shorter the time it takes to traverse.
- An infinite series of decreasing quantities can be summed. In this case, although you can logically analyze the motion into an infinite number of steps, each step takes less and less time. The total amount of time taken to do all steps is still finite.

Answer 4

Think of it as a converging series you'd study in high school calculus. True there are infinite numbers of segments, but the segments get smaller sufficiently fast enough that you can add them forever and they converge to a finite number.

Example, try adding 1/(n^2) for a long time: 1+(1/4)+(1/9)+... and you'll see that it converges.

Answer 5

technically no if it is infinite then you would not know where the end or the begining is so how would you know where the halfway point would be and if you dont know where the halfway point is how can you find the halfway point from that, but hey i am not a mathematician nor a physicist either but thats my theory on your question

Answer 6

You can break any space into an infinite number of parts, that doesn't mean that the space itself is infinite.

Answer 7

Learn Physics, Maths, Series and Limits: you will have your answers and stop spending time in philosophical paradoxes (although they are fun and I love them!)

Answer 8

why do u have this time to spare. Ur thooughts aren't nnormal. I like it

Answer 9

Why not just place the object on the table with one hand and pick it up with the other hand!!!!!!

Answer 10

sounds ok, but infinite space suggests never-ending: and the space between your hands as a beginning and end.. so, maybe its not ok.. i dunno.. got me thinking now.. come on mathematicians: get ya geeky headgear on and tell us the answer!