first. This, however, seems unlikely. Therefore, I shall try to disprove Zeno’s statement with an example, using proof by contradiction.
If Achilles is travelling at twice the speed of the tortoise and the tortoise travels 1 metre a second and has a 1 second head start, then the following sequence occurs.
Time /seconds
Achilles /metres
Tortoise /metres
1 2 3 4 5
0 2 4 6 8
1 2 3 4 5
9
Tortoises are slow!
8
7
6
5
4
3
2
Slow and steady doesn’t win!
1
0
0
1
2
3
4
5
6
Achilles (metres)
Tortoise (metres)
Graph showing the data in the table above
Achilles, therefore, catches up with the tortoise at 2m and overtakes at the 3 second point, he is travelling at double the speed, so makes up the distance quickly.
I will now demonstrate Zeno’s paradox with the same example, but using a different set up for the problem. The start point for each successive time interval, , is the time at which Achilles has caught up to the point where the tortoise was at t-1.
Time (seconds)
Achilles (metres)
Tortoise (metres)
1
0 1
1
1.5
1.5
1.75
1.5
1.75
1.875
1.75
1.875
1.9375
1.875
1.9375
15
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