I came up with this idea maybe a year and a half ago. I was taking a Philosophy course online and decided to make up something that made absolutely nosense but was logically correct. Anyway, I worked out this clever idea, and now it's driving me insane. If you asked anyone if it was right, they'd tell you it didn't make any sense, but I can't see what's wrong with it. So, I'm posting this in the hopes that someone smarter than me can prove it wrong.
Here's how it goes. Noone assumes that all change is instantaneous. In books, it's cliche to write that something, let's say a person's hand, moved faster than the eye could follow, almost appearing in some new place. We know, however, that the hand had to move through points between its beginning and end. But you can't measure these points. Let's say the hand started at point zero and ended up at point ten, moving in a straight line. At one point, the hand had to be at points one, two, and so on. But the hand still has to get from point zero to point one, so it has go through points one point one, one point two, and so on. Do you see where I'm going with this? No matter how little you divide up the distance, there will always be a gap that the hand magically teleports past. Thus, these changes are instantaneous, skipping over some points.
Please, someone prove this wrong. It's such a stupid idea, but I can't do it myself.
The Return
9 years ago
Posts
3 comments:
I think your problem is that you are trying to describe an analog phenomenon in digital terms. Yah, I know, cop out.
Cheers
It's calculus, man. Since the area that we're covering can be considered an infinite amount of points, what we take is the limit of our movement towards infinity in terms of time. So if our runner has to cover 1/2 the distance, then 3/4, 7/8, etc, the series converges to the limit one- then we merely have to take the distance one as a function of time and we can tell how fast he got there.
This is how we explain it, but it's a kind of cheating to give the phenomena we clearly see a name even if it doesn't make sense under the current rules. But that's the point of reason- to show things that are there, and to explain what we see in terms of other things that we understand. You can actually come up with tons of logically correct statements that are nonsense if the premises are different, or if you want to think about it a different way, if the world that the argument was brought forth in was different.
I just realized that since this post is three months old, I'm probably posting this to no-one, but what they hey, huh?
Points are meant to express only one dimension, not two. They cannot express linear movement. So, if you look only at points it would appear that the hand is skipping from point to point.
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