Multiple Civilization Lifetimes
If there are other civilizations, they are not likely to have equal lifetimes. There is a variety of internal and environmental events that can shorten lifetimes. I think the failure rate may be high in the early life of civilizations, as they create and encounter problems they are ill-equipped to deal with. The failure rate probably falls as experience in coping with threats grows, leading to an increase in the average lifetime of civilizations. One can expect this to occur with growing cooperation against internal threats to the stability of a civilization among groups initially having conflicting aims. It also can be expected to come from greater cooperation in handling external threats such as epidemics, volcanoes, and cometary impacts, and with the suppression of internal threats to the planet's ecosystem.
Such a variation of failure rate with age will lead to a distribution of lifetimes. For a simple approximation, then, the Drake equation can be calculated for individual sample lifetimes taken from a failure curve. If, for example, ten per cent of civilizations have a lifetime of 10,000 years, the calculation for this lifetime can be made for ten per cent of the stars created. Similarly for the other lifetime percentages that bring the total to 100 per cent. The totals for each lifetime can then be added together to produce the total number of civilizations that might be expected to be present now.
The effect of variation in lifetimes is the generation of different types of planet numbers that have to be added together in some way. If the Drake Equation produces a civilization count of less than one, this can be taken as the probability of a civilization being present now. The probability is 0.4 if the civilization count is 0.4. The effect can be thought of as four civilizations appearing during the course of time that would have been filled by ten civilizations in sequence. That is, there will be significant gaps between the emergences of civilizations, that need to be taken into account when summing the contributions of different lifetimes.
Another way of looking such number like 0.4 is that out of 10 planets with potential for a civilization, 4 will actually have a civilization. Thus, if one looks at the cumulative calculation, the total will be 40 per cent of that which would be calculated for a result of one planetary civilization being always present.
If the number of civilizations is one, this would means that there is always one civilization living out its lifespan somewhere in the Galaxy.
When the civilization count is greater than one, then the lifetimes of civilizations will overlap. In investigating concurrent alternative lifetimes, some simplification can be gained by assuming that civilizations emerge regularly with no gaps between civilizations, and that civilizations overlap by regular amounts. The number of civilizations overlapping gives the number of extraterrestrial civilizations in existence now. If their lifetimes are 50,000 years, overlapping civilizations may have been appearing at 5,000 year intervals during the prior 50,000 years. The earliest is now 50,000 years old, the youngest is 5,000 years old. There are ten civilizations that differ in age by five thousand years.
On this basis, the calculation has been made for two scenarios. Both assume ten different lifetimes ranging from 1,000 years to 10 million years. The first assumes that each lifetime is representative of 10 per cent of the population. The second assumes that civilizations with lifetimes of 1,000 years make up 20 per cent of the population, with the percentage decreasing down to 2 per cent at a lifetime of 10 million years. The calculations are done for different estimates as to the fraction of planets with simple life forms that evolve into a civilization. The results are shown in Table 1.
Table 1 Effect of Failure Curve on Number of Civilizations
| Civilization Fraction | Flat Failure Curve | Shaped Failure Curve |
| 0.00000001 | 0 | 0 |
| 0.000001 | 5 | 1 |
| 0.00001 | 54 | 15 |
| 0.0001 | 540 | 149 |
| 0.001 | 5,400 | 1,485 |
| 0.01 | 54,000 | 14,651 |
The flat failure curve gives higher numbers because there are many more long life civilizations.
On the basis that the galaxy is a uniform cylinder 1,000 light years thick and 100,000 light years in diameter, 54,000 civilizations spaced uniformly would be spaced 526 light years apart. For the lesser numbers, the spacing would be greater than 1000 light years.