From: kqb@cbnewsl.cb.att.com (kevin.q.brown)
Subject: Misadventure as a Cause of Death
Organization: AT&T Bell Laboratories
Date: Tue, 21 Jul 1992 23:34:19 GMT

> From: alcor@cup.portal.com
> Message-Subject: Misadventure
> Date: Mon, 20 Jul 92 00:43:10 PDT

Misadventure As A Cause Of Death In An Immortal Population
by Hugh Hixon

Reprinted from *Cryonics* magazine, May, 1988.

     A year or two ago, I got hold of a galley proof for an article in 
*Longevity*, the life extension oriented newsletter put out by *Omni*.  The 
piece was kind of a short overview of the quest for immortality and was 
apparently intended to appear in *Penthouse*, *Omni's* parent magazine.  What 
caught my eye was the last paragraph:

     "Among the visionaries are those who talk of achieving immortality.  
     But eliminating death doesn't seem very likely.  After all, with a 
     five percent probability for accidents, the longest we could hope to 
     live -- even absent disease and decrepitude -- would be 600 years."

     *Not* true!  In fact, on close inspection, about all you can get from 
this statement is that there is a crisis in science education among 
journalists.

     Among other things, this seems to invoke some Cosmic Accountant who 
comes along and zeros out everyone celebrating their 600th birthday, an 
absurd thought.  And as to how the calculation was made in the first 
place, I can't even guess.*
-----------------------
*An estimate of 700 years is made by Dr. Alex Comfort in his *The Process 
of Aging*, (New American Library, New York, 1964):

     "If we could stay as vigorous as we are at 12, it would take about 
     700 years for one-half of us to die, and another 700 years for the 
     survivors to be reduced by one-half again."

Dr. Comfort does not show how he arrived at this figure.  The death rate 
(1981, *all* causes) for the 10-14 year age group is 29.6 per 100,000 per 
year.  This rate does not yield Dr. Comfort's result (see below to make 
calculation).  He would have had to use pre-1964 statistical figures that 
may include much higher childhood disease mortality.
------------------------

     It does raise an interesting question, though.  How long *can* we 
expect to live?  As it turns out, this is not a difficult question to 
answer, in a statistical sense.  We can use current mortality tables to 
supply real-world numbers.  Arguably, our life-styles will change in the 
future, but it seems reasonable that our lives should not be *more* 
hazardous than they now are.

     First, the math.  Given that you are part of a fixed group, say, 
everyone born in 1942, the death rate is normally expressed as deaths per 
100,000 population per year.  If the death rate does not vary with age 
(actually, it does, but one of the goals of immortalists is to eliminate 
aging; and besides, it's not relevant to this example), the death rate 
from some cause is, say, 500 per 100,000 population per year, and the 
population size is 100,000, then in the first year of the example, about 
500 people will die.  The next year, the population is 99,500, and 498 
will die, etc.  139 years in the future, half the population will still be 
alive, and of those, 250 will die in that year.  In 276 years, one-fourth 
the population will still be alive, and in that year, 125 will die.  In 
459 years, one-tenth will still be alive, and in that year, about 50 will 
die.  Et cetera.  It should be obvious from this example that it will be a 
long time before the last person in the group dies.  The probability of it 
being you is, of course, one in 100,000.  The proper mathematical 
expression is an exponential decay curve, which has the form,

               (1 - R[d])exp(t) = N

where:
               N = the fraction of the original group still alive
               t = time in years
            R[d] = death rate per year, expressed as a fraction

     To conform with established convention, I will set N = 0.5, and find 
the time *t* at which one-half the population is still alive.  This is 
commonly referred to as the *half-life* (t[1/2]) of the population.  The 
concept of a half-life is used very commonly as a simple measure of 
exponential decrease.  Perhaps the measure seen most often is that of 
radioactive decay, where one refers to the half-life of radioactive 
isotopes.  Please note that the concept of half-life is independent of the 
number of people, atoms, etc., in the sample.  Whether one is working with 
a group of ten people or a million, all other things being equal, both 
groups have the same half-life.  The only differences are that the random 
nature of statistics will make the decrease of the smaller group 
proportionally much more irregular, and that it is much easier to 
determine accurately the half-life of a large group.*
---------------------------
*  For other fractions of the population, use the following conversion 
table with the half-life values:
  
     For a remaining population of:   90%    70%    50%    30%   10%     1%
                                   ------------------------------------------
     Multiply the half-life time by:0.1520 0.5416 1.0000  1.737 3.322   6.644
---------------------------

     To do the actual arithmetic, even with a scientific calculator it is 
easier if the expression is changed to the form,

               t[1/2] ln (1 - R[d]) = ln 0.5

or,
               t[1/2] = (ln 0.5)/ln (1 - R[d]) = -ln 2/- R[d]

since
                 ln (1 - R[d]) = -R[d],  as R[d] approaches zero

thus,
               t[1/2] = 0.693147.../(r[d]/100,000) = 69315/r[d]

where r[d] is the death rate per 100,000 population per year, which is the 
normal mode of expression for the mortality tables I will use.  

     We are now ready to crunch some numbers.

     For the year 1981 (Why 1981? -- because I could get tables for it), 
from *Vital Statistics of the United States**, the tables are listed by 
cause of mortality, and by age group in five year blocks.  I assume that 
our conquest of disease will be total, leaving only accidents, suicides, 
and homicides as causes of death.  I further assume that suicide is a 
treatable disease process, and eliminate that as a cause of death.
--------------------------
*  National Center for Health Statistics: *Vital Statistics of the United 
States, 1981* Vol. II, Mortality, Part A.  U.S. Department of Heath and 
Human Services (DHHS) Pub. No. (PHS) 86-1101.  Public Health Service, 
Washington. U.S. Government Printing Office, 1986.
--------------------------

     Death rate varies with age.  The two major factors seem to be 
experience and infirmity.  The older we get, the more experienced we are 
at avoiding accidents; and the older we get, the slower we get at avoiding 
accidents.  The curve bottoms out at the 40-44 year age group.  I will 
also use that age group for the homicide figures, even though the minimum 
is in the 70-74 year age group, on the grounds that at that age, who's 
*doing* anything that would make it worthwhile to kill them.  I also ignore 
the lower death rates for children and teenagers.  They're not out in the 
real world, yet, and besides which, we're only *that* young once.  And the 
number is, . . . 41.9 deaths per 100,000 in the white population (64.9 for 
males, 19.5 for females.  I do not wish to predict the future distribution 
of women into more hazardous occupations, or the appearance or 
disappearance of more or less hazardous occupations).  Which gives us a 
*half-life* for our population of 1654 years.

     So much for a maximum life span of 600 years!

     But this figure is based on *current* mortality.  Let's consider the 
impact of future medical technology (including nanotechnology) and squeeze 
the figures a bit.  A population half-life of 1654 years is for our 
current resuscitation technology (actually, for 1981), whether the 
accident occurs in the emergency room of a major metropolitan trauma 
center, or in the most inaccessible portion of Alaska's Brooks Range.  If, 
as at least one space satellite company proposes, a person can be located 
anywhere in the world with an accuracy of about 12 feet, with a cigarette-
pack sized transmitter, and if everybody is equipped with vital-function 
monitors, about the only people who will slip through the net are those 
with truly massive head trauma.  This is not a large fraction of 
accidents.  In fact, a short conversation with a friend of mine who works 
in Emergency Rooms confirms that actual destruction of the structure of 
the brain is not particularly common.  This leaves only serious homicides 
as a factor to consider.

     Estimating the rate on this kind of homicide is very difficult.  I do 
not believe that, in any society with competitive forces, homicide will 
disappear.  It certainly will get less common.  So I will grab a figure 
out of the air, more or less, and say that the sum of truly permanent 
fatal accidents and homicides will be *one* per 100,000 population per year 
(the aggregate figure (male and female) for white homicides is 8.9 in the 
40-44 year age block.).  This gives a population half-life of *69,315* 
years.  However, anyone who quotes this figure without including a 
statement of its very speculative nature is on their own.

     So much for the good news.  The bad news is that we are still in a 
time where most people die as a result of disease processes.  The 
calculations I have made here obviously apply to a benign future that 
(along with cryonics) may never come to pass.

     It *is* possible, however, to exert some choice.  A close examination 
of the causes of death in whatever population you may find yourself may 
allow you to take actions that will isolate you somewhat from the sources 
of risk (*thus placing you in a subgroup with a longer half-life!*) while 
still allowing you to enjoy life.  You can never get away from statistics, 
but as a thinking being, you can often choose which set of statistics will 
apply to you.  Thus cryonics.

     Finally, it should be pointed out that whatever death rate may apply 
to you, your chances of dying either last *or first* are equal, and equally 
unsatisfactory.  

     Y'all be careful, hear?
Newsgroups: sci.cryonics