X-Message-Number: 5879
Date:  Tue, 05 Mar 96 11:39:07 
From: Mike Perry <>
Subject: SCI.CRYONICS infinite survival

Eli Brandt, #5871, writes:

>Mike Perry writes:
>>Even though a condition of total invulnerability is never reached
>>(and it would be unrealistic to think it could be reached),
>>the overall probability of dying is only about 2%, i.e. there is a 98% 
>>chance of literally infinite survival. 
>
>"Literally infinite" in the mathematical model, where you can view the
>whole process /sub specie aeternitatis/.  In the world, you can at
>best claim unbounded rather than infinite survival.  Furthermore, such
>a claim is a claim about the future for all time, and a strong one at
>that (is it likely that there is *no* non-zero lower bound on risk?).
>This makes it hard to support empirically.
>
I'm not sure what is meant here by "unbounded" vs. "infinite" 
survival (more than one possibility comes to mind), but I can explain 
what these concepts mean to me. First, I hope it will seem 
reasonable to speak about the probability of survival for *finite* 
intervals of time. S(D, D+n), say, is the probability that person P, 
alive at date D (in years), is still alive (survives) at date D+n. 
(For simplicity I'm assuming D and n are integers.)
Clearly, then, S is nonnegative, <= 1, and is a decreasing function of n,
so long as we 
assume there is *some* chance of dying within any given year.

If the probability of dying within any one year is independent of that of 
dying within some other year, then we can calculate the probability 
of survival over a range of years. (In fact, in a future free of 
aging, we might expect the probability of dying to be independent in 
this way, i.e. death would mainly be from accidents and not from a 
progressively deteriorating condition, as today.) For D up to D+n, 
then, the probability of surival is the product 
of S(D+m, D+m+1) where m ranges from 0 to n-1. For the case I 
consider in my previous posting, S(D+m, D+m+1) = 1-1%*2^-m, and the 
product is.very nearly equal to 1 minus the sum of 1%*2^-m where m ranges 
from 0 to n-1, which in turn is 1 minus 2%*(1-2^-n). Interestingly enough, we 
see that, as n goes to infinity, this approaches 1 minus 2% or 98%, 
which brings us to the subject of infinite survival.

Eli Brandt says, "In the world you can at best claim unbounded rather 
than infinite survival." To me, a "claim of infinite survival" would 
be supported by an assertion as follows:

there exists q>0 such that S(D, D+n) >= q for all n >=0.

In this case, by letting r be the least upper bound of all such q, 
and remembering that S is a decreasing funciton of n, we see that

limit as n approaches infinity of S(D, D+n) = r >0,

and we can 
reasonably identify r as the "probability of infinite survival."

"Unbounded survival" on the other hand, to me would signify only that

for all n>= 0, S(D, D+n) > 0, 

or in words, "no matter how large n may be, there is some, nonzero 
chance that person P, alive at date D, will still be alive at date 
D+n." (Technically, that assertion is true now, though the 
probability involved is negligible if n, say, is > 130 and D+n is not 
much larger than 1996.)

Anyway, I see nothing forbidding the possibility that someday, 
according to then-accepted (and presumably well-tested) laws of 
physics, it will seem reasonable to make assertions like S(D) = 98%,
where by S(D) I mean the limit, as n goes to infinity, of S(D, D+n). 
In other words it could be reasonable to 
make claims about infinite as opposed to unbounded survival, 
according to the way I view the matter. True, a claim like "S(D) = 
98%" might seem a very tall one to make now, but someday we'll have 
greater understanding of cosmological issues and can hopefully 
project the future with more confidence than today.

Eli Brandt asks, "is it likely that there is *no* non-zero lower 
bound on risk?" This is a good question; in effect, unless the 
risk can be pushed to zero over infinite time, it must catch up to 
you eventually, or to use our notation, for infinite surivival, a 
necessary condition is that S(D+n, D+n+1) go to 1 as n goes to 
infinity. In other words, as n goes to infinity there must be a 100% 
likelihood of survival or zero risk of dying over any one year. (And 
this condition, while necessary, is not sufficient, but the risk of 
dying must also go to zero not too slowly with n.)

To make a stab at answering this question
(whose real answer we don't know and may
not have a reasonable handle on for some time) I'll say that, at 
least in an unbounded, potentially infinite universe, a 
zero-approaching risk is a possibility. Clearly it must 
always be possible to lower any previous risk of death. One way to do 
this might be to store increasing copies of identity-critical 
information. By the time the sun explodes, say, your redundant 
information will be so well-dispersed that a sufficient subset will 
survive the cataclysm. More generally this seems to be a way around 
the "fluctuations and dissipations theorem" of physics that asserts 
that catastrophes of arbitrary magnitude have some chance of 
happening and will happen eventually in any given locality.

Mike Perry



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