How is it possible to travel any amount of distance when their is an infinite number of increments between where you are trying to go?
- Jeffrey KLv 610 months ago
Each increment is infinitesimally small so it takes an infinitesimal amount of time to travel thru each of them. This forms an infinite series that converges to a finite number.
For example, (1/2)+(1/4)+(1/8)+....... = 1
- cosmoLv 710 months ago
The time to cross each increment is infinitesimal
- D gLv 710 months ago
That is a stupid question. You pick a distance. You can then divide it up infinitely small DD oesnt change the original distance
- Ray SLv 710 months ago
periodic quantum leaps in and out of normal space-time.
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- davidLv 710 months ago
Read Xeno's paradox in Wikipedia. The original conjecture was that you travel 1/2 the distance. Then you travel 1/2 of what is left. Then travel 1/2 of what remains --- etc.
so you travel 1/2 + 1/4 + 1/8 + 1/16 ... etc for each section
total traveled is 1/2, 3/4, 7/8, 15/16 etc where 1 would represent the entire trip.
... the amount remaining after 1st is 1/2, after 2nd 1/4, ... 1/8, ... 1/16, ... so you can see the remaining part of he trip is constantly less and less === if it gets to 0 that means that the trip is complete ... so, will it get to -??
- ElizabethLv 710 months ago
Let's suppose I cut a cake evenly into 4 pieces. I take a triangular spatula, and remove one piece. I've extracted 1/4 of the cake.
Now I divide the cake into a million slices and use my spatula to extract 1/4 of the cake. Ok, it might now be 0.250010 of the cake, but it is still about a quarter of the cake.
No matter how small I theoretically make each slice of cake, my spatula will extract about 1/4 of the total.
The point is that you could argue that if you divided the cake into a infinite number of slices, each slice would have no volume, and therefore my spatula would extract no cake. And whilst this is mathematically interesting, physicists would ask you to redo the maths or adjust the process so you actually get the correct real world result where my spatula removes 1/4 of the cake as the solution.
Thats why we have limits and infinite series that tend towards to a result. Mathematical solutions are not necessarily physical solutions.
- Chris AncorLv 710 months ago
- yet-knish!Lv 710 months ago
I think the problem lies in that word, 'infinity'. We can't really understand what that is. We think of it as a very, very, very large number, because that's all our minds can fathom; but it's not. A number implies a boundary, but infinity is the absence of boundaries. You can say there is an infinite number of increments, but you never reach that; you can never reach infinity. And the increments become smaller and smaller the more of them there are. So if you want to say there are "an infinite number" of increments, then you also have to say the increments become infinitely small...and you can cross over an infinitely small increment. But if you counter that with the argument that you never reach infinity, so you never reach an increment of zero length, then you also have to admit that you can never reach an unlimited number of increments either, and therefore the supposed problem of crossing an infinite number of increments doesn't exist. You can't treat an infinite number like it's a number; you can't have it both ways.
- PopeLv 710 months ago
The question reads a lot like Xeno's paradox, and I never understood why that got so much attention either. The finite distance and the infinite number of increments are held up as though they were contradictory. Where is the conflict?
If there is a least increment among those you mention, then the total distance must be at least as far as the least increment times the number of increments. Yes, that would be an infinite distance. However, since the number of increments is infinite, there does not have to be a least increment.
- 10 months ago
Either space and time are both smooth and continuous, or they are both discrete. I'm banking on the latter. Either way, in either case, movement is still possible.