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 Post subject: infinitesimal possibilities given infinite trials
PostPosted: Sun Jun 24, 2007 10:17 pm 
Thanks for the reply in http://www.nutters.org/user/famous/mess ... 5929381.62

but i would like to take the idea a bit farther.

Specifically, w.r.t. monkeys and shakespeare, and the origins of life.

You make the point repeatedly that if the probability of an even is p>0, then given infinite trials, it will certainly happen, and happen an infinite number of times.

That seems to break down when p is 'infinitesimal'. Which is sort of like saying k * &inf; = &inf; but infinitesimal * &inf; = undefined.

If, then, the mathematics tells us that infinitesimal possibilities, which are not strictly 0, have a p<1 even given infinite trials, then the next question would appear to be:

Quote:
is the possibility of the origin of life small or infinitesimal?


I'm not sure if math and/or science can answer that one.

I'll ignore, for the moment, the possibility of the origin of life being 0 :)


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PostPosted: Mon Jun 25, 2007 7:25 am 
well i don't know it too, but i would certainly say that 1 + 1 is not always 2


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 Post subject: Re: infinitesimal possibilities given infinite trials
PostPosted: Tue Jun 26, 2007 6:23 pm 
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Joined: Mon Jul 10, 2006 6:57 am
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Location: Sydney, Australia
anon again wrote:
You make the point repeatedly that if the probability of an even is p>0, then given infinite trials, it will certainly happen, and happen an infinite number of times.

If the probability of an event P is finite and greater than zero, then it will happen an infinite number of times given an infinite number of attempts. If, on the other hand, the probability of event P is greater than zero but infinitesimal, it will happen a finite number of times given an infinite number of attempts.

I don't know of any real-world applications of infinitesimal numbers. There's no way to reach either the infinite or the infinitesimal using finite numbers and operations such as addition, subtraction, multiplication and division. I don't see how science could possibly conclude that the probability of an event was infinitesimal, since that conclusion would require infinite measurement. Empirical studies would simply conclude that the probability was "immesurably low".


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