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Re: Boxcar Randy In Reference To Tomislav Strelar

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Posted by technicolor/">technicolor on September 11, 1998 16:26:21 UTC

: : Everyone, thanks for your help : : I have one further question. My original question was how could two trains collide seeing that there are an infinite amount of points between the two trains. I would think the trains would continue to travel along this string of infinite points never reaching its destination ( the collision). But here is another way to look at it. As the trains came closer and closer towards each other, the amount of space remaining between the trains would shrink. Now if we were to magnify this remaining space, and zoom in at the same rate the space is shrinking, we could maintain a view of this empty space. So... how would this empty space ever disappear, Or how would this empty space ever close and allow the trains to touch?

: Please read my followups from your last question. : If you do, you'll see that we could reach a point when "zoom" isn't possible (like when you zoom a digital picture, and see only one pixel). That "pixel" is the minimum distance. I am saying all along that there isn't infinite nubmer of points (the movement IS composed of discrete steps) : I WILL stay at that theory no matter what the rest of you think.

: Please consider this example. : For example, let's take two trains, and use "pixel" or "quantum" of space as the smallest element one can travel. That "pixel" CAN'T be divided. : Red train starts at 0 "pixel" with speed 8 pixel/s, and blue train starts at 12th "pixel" from start with speed 4pixel/s. : Let us now see what happens at 3 sec of elapsed time. : The red train is at 0(startpoint)+8(red's speed)*3(amount od seconds elapsed)=24 pixels from startpoint. : The blue train is at 12(blue's startpoint)+4(blue's speed)*3=24 pixel from startpoint. : As you can see the red train is after 3 seconds in line with blue. : Surely after that the red train would come in front of the blue one. : This explanation of Zeno's paradox is only valid with movment represented in discrete steps like the above example. : So in real life there must be such quantization of space because only then would the red train (faster speed) eventualy come in front of the blue one (slower speed).

: I hope I helped.

Tomisla

That is a very interesting theory about the pixel effect. I would have substituted "pixel" for "particle". However it is true that an infinite number of points can exist between point "A" and point "B". Hypothetically lets imagine a two-dimensional line one-meter long. We could cut this line in half, take the remaining portion of the line and cut it in half, then take THAT remaining portion and cut it in half. It would take an infinite amount of steps if we were to keep dividing the line in half. Now lets look at the space between the trains as if it were the line. We could divide this space into an infinite amount of points. Now lets attribute a number to the space. If the distance between the trains is 10 meters, obviously we can divide 10 an infinite number of times. Through how many points must an object travel to reach its destination…. I dunno? :0)

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