I wish to debunk the title of this article.
There is a common conundrum about racing a turtle (or tortoise) with a headstart, which is this:
1. Tortoise starts at point X ahead of you
2. By the time you reach X, turtle will have moved to further point Y.
3. By the time you reach Y, turtle will have moved to further point Z.
4. Ad Infinitum…
Regardless of how much faster you are, he’s always further ahead when you reach where he was and therefore in uncatchable.
This is neither scientific, nor a conundrum, as I will prove shortly.
Technically, this argument is a mathematical one, as in the realm of physical science, we would define the parameters of the race differently. Even still, if actual numbers are assigned to the problem above, they form a geometrically diminishing relationship which “collapses” to a point in time-space at which the human and turtle are even and cannot push past that point in time. A physicist might rather analyze the problem thus:
Assume Turtle has rate of motion R1. (say metres per hour)
His headstart is that of distance D. (say in metres)
Then, the Turtle’s Position, as a function of time: T(t) = D + R1*t
Assume Human has a rate of R2, where R2 > R1.
With no headstart, the Humans position, as a funtion of time: H(t) = R2*t
The Human will then pass the Turtle at T(t) = H(t)…
D + R1*t = R2*t
t = D/(R2-R1)
To give sample numbers, assume R1 = 60 metres/hr, D = 1000 metres, R2 = 7200 metres/hr.
According to the above equations, the human will catch the turtle at t = 1000/(7200-60) = 0.14 hr = 8 minutes, 21 seconds, at which point both contestants will be at 1008.4 m along the track. After which point the human will be in the lead.
Sorry to discount the title of this article.
