So there are several versions of the paradox, but the most basic one is, can you cross a room if you could only move half the distance to the other side ?
I got into an argument with my friend over this and I said you could indeed cross the room because the human body in the physical world has a hard limit for how close stuff like atoms and forces allow interaction.
Now I totally understand how this thought experiment works on something like a number line, but if semantics of walking across a room, is just what it means and has no deep (geometric for example) mathematical implications, there is no way you could physically do this. Who is right? Me or my friend ?
I got into an argument with my friend over this and I said you could indeed cross the room because the human body in the physical world has a hard limit for how close stuff like atoms and forces allow interaction.
Now I totally understand how this thought experiment works on something like a number line, but if semantics of walking across a room, is just what it means and has no deep (geometric for example) mathematical implications, there is no way you could physically do this. Who is right? Me or my friend ?
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In the limit of an infinite # of steps, you do.
It is simply the sum of an infinite geometric series with ratio 1/2 and that sum is 1.
That is the mathematical answer.
The physical answer is that you can't subdivide any distance indefinitely. You'll stop at Planck's length.
So, either way, you cross the room.
It is simply the sum of an infinite geometric series with ratio 1/2 and that sum is 1.
That is the mathematical answer.
The physical answer is that you can't subdivide any distance indefinitely. You'll stop at Planck's length.
So, either way, you cross the room.