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:
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. [Footnote: 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 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. [Footnote: For other fractions of the population, use the following conversion table with the half-life values. For a given percent remaining population, multiply the half-life by the amount given.]
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 (U.S. Department of Health and Human Services Pub. No. 86-1101), 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. 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?
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