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From: Stathis Papaioannou <stathispapaioannou.domain.name.hidden>

Date: Sat, 23 Apr 2005 14:33:24 +1000

Jesse,

*>Stathis Papaioannou wrote:
*

*>
*

*>>Now, look at p(n) again. This time, let's say it is not k, but a random
*

*>>real number greater than zero, smaller than 1, with k being the mean of
*

*>>the distribution. At first glance, it may appear that not much has
*

*>>changed, since the probabilities will "on average" be the same, over a
*

*>>long time period. However, this is not correct. In the above product, p(n)
*

*>>can go arbitrarily close to 1 for an arbitrarily long run of n, thus
*

*>>reducing the product value arbitrarily close to zero up to that point,
*

*>>which cannot subsequently be "made up" by a compensating fall of p(n)
*

*>>close to zero, since the factor 1-p(n)^(2^n) can never be greater than 1.
*

*>>(Sorry I haven't put this very elegantly.)
*

*>
*

*>p(n) *can* go arbitrarily close to 1 for an arbitrarily long period of
*

*>time, but you're not taking into the account the fact that the larger the
*

*>population already is, the more arbitrarily close to 1 p(n) would have to
*

*>get to wipe out the population completely--and the more arbitrarily close a
*

*>value to 1 you pick, the less probable it is that p(n) will be greater than
*

*>or equal to this value in a given generation. So it's still true that the
*

*>probability of the population being wiped out is continually decreasing as
*

*>the population gets larger, which means it's still plausible there could be
*

*>a nonzero probability the population would never be wiped out--you'd have
*

*>to do the math to test this (and you might get different answers depending
*

*>on what probability distribution you pick for p(n)).
*

*>
*

*>It also seems unrealistic to say that in a given generation, all 2^n
*

*>members will have the *same* probability p(n) of being erased--if you're
*

*>going to have random variations in p(n), wouldn't it make more sense for
*

*>each individual to independently pick a value of p(n) from the probability
*

*>distribution you're using? And if you do that, then the larger the
*

*>population is, the smaller the average deviation from the expected mean
*

*>value of p(n) given by that distribution.
*

*>
*

*>>The conclusion is therefore that if p(n) is allowed to vary randomly, Real
*

*>>Death becomes a certainty over time, even with continuous exponential
*

*>>growth forever.
*

*>
*

*>I think you have any basis for being sure that "Real Death becomes a
*

*>certainty over time" in the model you suggest (or the modified version I
*

*>suggested above), not unless you've actually done the math, which would
*

*>likely be pretty hairy.
*

*>
*

*>Jesse
*

*>
*

Jesse,

It would be stubborn of me not to admit at this point that you have defended

your position better than I have mine. I'm still not quite convinced that

what I have called p(n) won't ultimately ruin the model you have proposed,

and I'm still not quite convinced that, even if it works, this model will

not constitute a smaller and smaller proportion of worlds where you remain

alive, over time; but as you say, I would have to do the maths before making

such claims. I may try out some of these ideas with Mathematica, but I

expect that the maths is beyond me. Anyway, thank-you for a most interesting

and edifying discussion!

--Stathis Papaioannou

_________________________________________________________________

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Received on Sat Apr 23 2005 - 00:38:23 PDT

Date: Sat, 23 Apr 2005 14:33:24 +1000

Jesse,

Jesse,

It would be stubborn of me not to admit at this point that you have defended

your position better than I have mine. I'm still not quite convinced that

what I have called p(n) won't ultimately ruin the model you have proposed,

and I'm still not quite convinced that, even if it works, this model will

not constitute a smaller and smaller proportion of worlds where you remain

alive, over time; but as you say, I would have to do the maths before making

such claims. I may try out some of these ideas with Mathematica, but I

expect that the maths is beyond me. Anyway, thank-you for a most interesting

and edifying discussion!

--Stathis Papaioannou

_________________________________________________________________

SEEK: Now with over 80,000 dream jobs! Click here:

http://ninemsn.seek.com.au?hotmail

Received on Sat Apr 23 2005 - 00:38:23 PDT

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