Beating Asafa - Zeno's Paradox

Meet Asafa Powell, the 100m current record holder. If chased by a lion, he’ll make the first 100 meters in 9.74 seconds so find another partner for that dangerous backpacking trip to Africa...
EDIT: Since this post Usain Bolt has done it in 9.58 seconds.

Meet Maya, my 1.5 year old daughter (I have another 3.5 year old son named Yoav). When she runs, her feet twist inwards and her upper body leans forward in a scary angle, so an observer will probably define her running as a controlled crash.

Now here’s a scenario for you: a race between Asafa and my kid.
Let’s use round numbers.
Powell runs ten meters a second (I hope he won’t accidentally browse to this blog ‘cause he’ll probably kill me for that). My kid controlled-crashes one meter a second. Since my kid is in kindergarten, and Asafa is world famous, he foolishly agrees to grant her a ten meters lead. Ready. Set. Go!

1 second after the gun fires, the amused runner will close the lead, but my kid will manage to advance 1 meter in that time.
Current status: My 1.5 year old kid still has a 1 meter lead over the current record holder.

100 milliseconds later, the smiling Jamaican will pass this meter, but my daughter will manage to advance another 10 centimeters in that time.
Current status: My 1.5 year old kid still has a 10 centimeters lead over the current record holder.

10 milliseconds later, the optimistic sprinter will pass this small distance, but my 1.5 year old will manage to advance another 1 centimeter in that time.
Current status: My 1.5 year old kid still has a 1 centimeter lead over the current record holder.

1 millisecond later, the frustrated athlete will pass this tiny distance, but my cute underdog will manage to advance another 1 millimeter in that time.
Current status: My 1.5 year old kid still has a 1 millimeter lead over the current record holder.

Etc…

Can Asafa Powell ever catch up, or was he acting foolishly by agreeing to grant my daughter this lead?

~~~
p.s. Engraved on my tombstone: "I hope it’s not just 42…"

16 comments:

Anonymous said...

Hejsa!

I am sure he is a perfect example of the adult, who will not torture cute kids, hence he will never overtake her.

(Being a mathematician, I know that's not the answer you were looking for. But hey!)

Lise A

Uri Kalish said...

;)

rlowe1980 said...

haha!! nice one!! but uhh Asafa Powell is a promoter for nutritional supplements that I sell (Nutrilite)...

but if he does lose the race to your daughter, I would deffintely tip my hat to her...

:-P

Graham said...

I love using this example at the pub after a few beers, it confuses the masses. The other one I like is the one about a tree falling in the forest, if there is nobody around to hear it, was there a noise. Great fun
Regards
graham

Uri Kalish said...

:)

Uri Kalish said...

As you might have guessed, the sprinter will beat my daughter, but in order to do that he must first close the gap and run this distance:
10 meters + 1 meter + 10 centimeters + 1 centimeter + 1 millimeter + …

A little bit counter-intuitive, but although this series of positive numbers is infinite, the sum of all these numbers is finite. In this case it is 11.11111… meters (11+1/9 meters).

So the answer is that Asafa Powell will pass my daughter after 11+1/9 meters. He can keep his medals for now…

Blog Directory said...

Great post and great food for thought, wish i could think like this sometimes.


Chris

Lordmanilastone said...

that was really hard for me to decipher at once, to be honest, here's a toast to this brain tickling post,... I will be back soon again, but with a shovel...^^

Blogger Gabby said...

That was a witty post Uri!
Great thinking :)

Keep it up

!!!Cheers!!!

Alban, Teacher of God said...

I am sure, your kid will get disqualified should she suddenly change gears and make 20 meters a second.

In terms of the neuro-electrical impulses in his brain, he certainly will never catch up with your daughter. He only sees a past image of her. The question is where this image is.

If it is in his mind, he is hallucinating.

Uri Kalish said...

Blog Directory, Lordmanilastone, Blogger Gabby & Alban,

Thanks!

p.s. You can also check out my previous posts…

Infonistacrat said...

Love this post! Its a great twist on the one I love to use on people, to wit: If you cut your journey to anywhere in increments of 1/2 of the total distance left, theoretically you will never get to where your going. For the unenlightened, this is a baffling proposition!

j4ur14 said...

i saw something tike this in my first year at university. Asafa was a hare and your daughter was a turtle. Nice chasing problem.

MoneyMoose said...

This is just a variation of a famous problem developed by a Greek mathematician, Zeno.

It's interesting to think about although not practical whatsoever. Within two seconds Asafa will be at the 20m mark while your daughter will be at 12m. That's a win if it's anything.

Uri Kalish said...

@MoneyMoose,
Yes, it is a twist on Zeno’s Paradox (look at the post title).

dennis hodgson said...

I see that you've already provided the answer. Zeno's answer is based on the widely held belief that the sum of an infinite series must be infinite, but this isn't the case. Take the series 1/2 + 1/4 + 1/8 + 1/16...1/2^n, where n is the position in the series. The sum tends towards 1 but never quite reaches it.