Kevin (erf_) wrote,
Kevin
erf_

just when I thought I was free from calculus for a couple of months, it attacks me in my sleep.

I'm not a math person, so I was a bit surprised when I thought of this really freaky calculus question as I lay awake in bed last night. (Michelle, who is a math person, helped me work out the kinks this afternoon.) Here it is:

What is the probability of someone being born at any exact moment in time in a given year?

This question isn't as simple as it seems, since "exact" implies that the answer must be accurate to any number of digits, e.g. June 3, 2003, 12:00:00:00:00....

We know from elementary school math that the first step to solving a problem like this is to find the units. So let's see...since we're trying for absolute accuracy here, we'll assume that there is a unit that is the smallest possible unit of time and is one infinity-th of any other unit of time. Let's call it the phukasecond, since I've always wanted to use "phuk-" as a prefix.

Now on to the second step: finding an equation. There are 365 days in a year, 24 hours in a day, 60 minutes in a second, 60 seconds in a minute, 1000 milliseconds in a second, etc. The odds of being born on a given day in a given year are 1/365, the odds of being born on a given hour in a given year are 1/8760, the odds of being born on a given minute in a given year are 1/525600, and so on. Thus, our answer should come in the form of 1/x, where the more accurate time we want, the bigger x will get.

Thus, I know from AP Calculus that our equation should be:

I spent way too much time making this

Now here's the problem: The laws of calculus state that the limit of 1/x as x approaches infinity is zero. That would mean that as x approaches infinity, 1/x approaches 0/1. Therefore, the chance that you will be born at any exact moment in a year is as close to zero as you can get without actually being zero.

However, each and every one of us was born at some exact moment in time.

Contradiction? Michelle doesn't think so. According to her, yes, each and every one of the ten billion or so people on earth was born at an exact moment in time. However, there are a theoretically infinite number of exact moments in time, and 10,000,000,000/infinity is still pretty much equivalent to 1/infinity.

But still. We were all born, despite the odds against our existence being literally as high as odds can go without being impossible.

Against these odds, there is no way we could exist. Yet we do. Why?

Any answers (perhaps by someone with more experience with probability and calculus than Michelle and me) would be greatly appreciated.

(Not only did we not get a decent answer, I never got to use "phukaseconds" in my explanation. GRRRRRRR.)

Anyhow...we can deduce from these conclusions that the odds of any two people being born at the exact same moment in time in a given year is as close to impossible as you can get without being impossible.

Doesn't that make you feel special?

Also: Sauch can really shake that ass. o_0

[edit] The people at Kyhm's have some pretty interesting answers to this question.
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