Your%20Concerns%20(from%20quiz)

1
Your Concerns (from quiz)

• What (if anything) is wrong with Zeno's
  argument?
• What about the theory of types?

Later (minutes)

• Is Zeno the sixth patriarch or is he not?

• Significance in positioning the Tortoise upwind
  of Achilles?

Later (weeks)

• Use ordinary algebra to find how long it will
  take for Achilles to catch the Tortoise.

Right now
2
Achilles vs Tortoise (algebra)
Assume that Achilles runs with a speed of 1 rod
per second, so that his position is given by
A(t) position of Achilles over time 0 rods
from start (1 rod/sec) (t sec)
position
position
position
0
1
2
A(t)
1 rod/sec
1 rod/sec
1 rod/sec
Units?
3
Achilles vs Tortoise (algebra)
Assume also that the Tortoise runs with a speed
of 1/2 rod per second and has a head start of 10
rods, so that his position is given by
T(t) position of Tortoise over time 10 rods
from start (1/2 rod/sec) (t sec)
0
1
11
2
10
A(t)T(t)
A(t)
1 rod/sec
1/2 rod/sec
1 rod/sec
1 rod/sec
What is t when A(t) T(t)?
What is the time when the position of Achilles is
the same as the position of the Tortoise?
A(t) 0 rods (1 rod/sec) (t sec) T(t) 10
rods (1/2 rod/sec) (t sec)
(1 rod/sec) (t sec) - (1/2 rod/sec) (t sec)
10 rods
(1 rod/sec - 1/2 rod/sec) (t sec)

(1/2 rod/sec)(t sec) 10 rods
20 sec
(t sec) 10 rods / (1/2 rod/sec)