totally sweet problem

[Waiting for Lunch]

Imagine that your worst enemy lives in a house by a river. You decide to get rid of him/her, and hire an army of superninjas to assassinate him/her. This army of ninjas lives in the "Totally Sweet House" across the river, and is made up of endless numbers of invincible ninja warriors. If your enemy is alive at 1:00 pm, ninja 1 will instantaneously cross the river and cut off his/her head. If (s)he's alive at 12:30 pm, ninja 2 will instantaneously cross the river and cut off his/her head. If (s)he's alive at quarter past twelve, ninja 3 will instantaneously cross the river and cut off his/her head. If (s)he's alive at 1/8 (of an hour) past twelve, ninja 4 will cross the river...etc. Keep dividing the fraction-of-an-hour past twelve by two, and there will be another ninja for each of these new times. When does your enemy die?

And who kills him/her?  

[Deppfan]

The enemy never dies  

[-Less than Graceful-]

Ninja 4 cuts off her/his head, assuming he/she has only one head he/she will be killed by ninja 4.  

[Khalida Nyoka]

This is the concept of a mathematical limit. The person would appear to never be killed, but at some point the fraction will be so close to zero, that a ninja will kill the "enemy."

Not that this is even technically philosophy. More of a game.  

[Waiting for Lunch]

Khalida Nyoka

This is the concept of a mathematical limit. The person would appear to never be killed, but at some point the fraction will be so close to zero, that a ninja will kill the "enemy."

Not that this is even technically philosophy. More of a game.

Well, maybe, but don't limits and infinity have everything to do with philosophy?

The idea is, that there will always be another fraction that is just a little closer to zero, and that, no matter which of the infinite number of ninjas you pick, there will be one before it. That means that none of the ninjas can have killed your enemy. (S)he was never killed (props for deppfan!). But the ninjas always do what they're hired to do. So, somewhere down the line, the "infinitieth" ninja will come along. This ninja will be assigned the time that is 1 "infinitieth" after twelve pm. What is 1 "infinitieth"? It's smaller than any fraction ever. Really. There isn't a fraction small enough to equal it. If you try to calculate it (by dividing by two quite a lot) your fraction will keep getting closer to zero. We assume that, if you eventually get to one over infinity, you will reach zero. So, the "infinitieth" ninja will kill your enemy at 12:00 exactly. But, the problem is, you can never get to infinity! So, let me restate one of my questions:

We know that your enemy is killed at 12:00, but...

Who kills your enemy?

This is where the philosophy comes in. wink  

[Deppfan]

Waiting for Lunch

Khalida Nyoka

This is the concept of a mathematical limit. The person would appear to never be killed, but at some point the fraction will be so close to zero, that a ninja will kill the "enemy."

Not that this is even technically philosophy. More of a game.

Well, maybe, but don't limits and infinity have everything to do with philosophy?

The idea is, that there will always be another fraction that is just a little closer to zero, and that, no matter which of the infinite number of ninjas you pick, there will be one before it. That means that none of the ninjas can have killed your enemy. (S)he was never killed (props for deppfan!). But the ninjas always do what they're hired to do. So, somewhere down the line, the "infinitieth" ninja will come along. This ninja will be assigned the time that is 1 "infinitieth" after twelve pm. What is 1 "infinitieth"? It's smaller than any fraction ever. Really. There isn't a fraction small enough to equal it. If you try to calculate it (by dividing by two quite a lot) your fraction will keep getting closer to zero. We assume that, if you eventually get to one over infinity, you will reach zero. So, the "infinitieth" ninja will kill your enemy at 12:00 exactly. But, the problem is, you can never get to infinity! So, let me restate one of my questions:

We know that your enemy is killed at 12:00, but...

Who kills your enemy?

This is where the philosophy comes in. wink

So, did I get it completely right, or is there some other part to it?  

[Khalida Nyoka]

I'll say this then:

Whatever ninja that would be the first to correspond to the micro-second range of times after 12:00 would be the one to kill them. As far as mechanical systems are concerned, the fastest they can move (therefore, the smallest time range worth considering) is in the range of 10's of microseconds. Therefore, once we'ved reach 10^(-6), we are physically close enough to zero, and that ninja will do it.

If you are only going with mathematics, and are not accepting of physical aspects, then they will never actually die. Mathematical infinity is impossible to reach by definition.  

[iMonochromatic]

Khalida Nyoka

I'll say this then:

Whatever ninja that would be the first to correspond to the micro-second range of times after 12:00 would be the one to kill them. As far as mechanical systems are concerned, the fastest they can move (therefore, the smallest time range worth considering) is in the range of 10's of microseconds. Therefore, once we'ved reach 10^(-6), we are physically close enough to zero, and that ninja will do it.

If you are only going with mathematics, and are not accepting of physical aspects, then they will never actually die. Mathematical infinity is impossible to reach by definition.

"I'm really sorry about your hand"

Exactly what I was going to say! We did a similar problem in Maths a while back, only it wasn't so graphic: "A rabbit is given a large piece of lettuce measuring (I can't remember what number went here)squared. If the rabbit eats half each day, how many days will it take for the rabbit to eat the lettuce?" Of course, if it eats half each time, mathematically, the rabbit would keep halving what is left, even if the numbers are minuscule. Obviously in real life, a rabbit wouldn't be able to cut lettuce leaves precisely in half, but hey.

"Next time you want to hit me, use a baseball bat or a crowbar, okay?"
- Jacob Black, Eclipse