```X-Message-Number: 19127
Date: Sun, 19 May 2002 20:25:29 -0700
Subject: Death probability with backups (was Re: CryoNet #19109 - #19118)
References:  < var s1 = "20020519090002.81933.qmail"; var s2 = "rho.pair.com"; var s3 = s1 + "@" + s2; document.write("<a href='mailto:" + s3 + "'>" + s3 + "</a>"); >
From:  var s1 = "tim"; var s2 = "fungible.com"; var s3 = s1 + "@" + s2; document.write("<a href='mailto:" + s3 + "'>" + s3 + "</a>");  (Tim Freeman)

From: "Brett Bellmore" < var s1 = "bellmore"; var s2 = "tir.com"; var s3 = s1 + "@" + s2; document.write("<a href='mailto:" + s3 + "'>" + s3 + "</a>"); >
>Nah, I've actually looked at that. Given the speed of light as an absolute,
>there's no way the volume and mass available to you can continue to increase
>exponentially, as that scheme requires

The scheme only requires a linear increase in the number of backups.
Call the probability of one backup failure in one year "f", and assume
you make "b" backups per year.  Then your probability of eventual
death from backup failure is no more than

integral   f ** (b * x) dx
0 to inf

Here I disregarded the fact that you can't die twice, so this
overestimates the probability of death.  Evaluating this integral
gives me an overestimated death probability of

-1 / (b * log f)

(This is positive because log f is negative.)

Plugging in some easy numbers, if one backup fails per year with
probability 1/e =~ 1/2.7 (which is a pretty flakey backup), and you
make 10 additional backups per year, then the eventual death
probability from backup failures over all of time is no more than 1 in
10.

This still doesn't give you immortality unless you find some way to
keep the universe from running down, or to accomplish infinite
subjective time in a running down universe.  But it does give you
significant time to study cosmology and physics to work around those
problems.

I'm more worried about failing to get there from here, or perhaps
becoming too obsolete to be relevant by then.  Let's focus on more
important problems, guys.

--
Tim Freeman
var s1 = "tim"; var s2 = "fungible.com"; var s3 = s1 + "@" + s2; document.write("<a href='mailto:" + s3 + "'>" + s3 + "</a>");
GPG public key fingerprint ECDF 46F8 3B80 BB9E 575D  7180 76DF FE00 34B1 5C78

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