Excerpt from: http://hss.caltech.edu/~hanson/greatfilter.html
On the other hand, the historical step-by-step "march of progress" we
seem to see in the fossil record would seem to create difficulties for
the view that any one of these steps is astronomically unlikely. If a
step is so improbable, one might ask, then why did it happen so
quickly after its preceding enabling step? That is, if the expected
time for some step on any one planet is many trillions of years, they
why would it happen on Earth in only a few hundred million years?
After all, and the oldest known stars are now 15 billion years old,
our sun would seem to have another five billion years of life left,
and yet the longest known evolutionary step (from simple to complex
cells) only took about 1.7 billion years.
It turns out that this is probably not a problem, however, and it is
useful to understand why. Assume that a certain set of steps are to
be completed in a certain order within a certain total time window,
and that for each step there is some constant probability per unit time
of completing that step, given that the previous step has been
completed. If the probability of completing all the steps within the
time window is low, then for the cases where all the steps are in fact
completed, it turns out that the average time to complete each "hard"
step is unrelated to how hard that step is.
For example, say you tried to complete four tasks in an hour (all of
the "if you don't succeed at first, try try again" variety), where the
expected time to complete each task was .1, 1, 10, and 100 hours
respectively. Then in those rare cases when you did complete all four
tasks in the hour, the average time to complete the first task would
be about .1 hours, but the average time to complete each of the others
would be about 0.23 hours. All the hard steps, no matter how hard,
take about the same time, while easy steps take their usual time.
There would also be an average of about 0.23 hours to spare left over
after all the steps were complete. And since the distributions are
exponential, the standard deviation of each step size would be equal
to its average. Models where the window closing is also random give
This sort of model seems to apply to the evolution of life on Earth.
Since the Earth formed, there have been about five periods between
major evolutionary changes, periods of roughly equal duration.
Specifically, the earlist known fossils of simple single-cell life
appeared 1.0 billion years after the earth was formed, and then the
earlist known complex single-cell fossils appears 1.7 billion years
after that. 0.8 billion years later the tempo of evolution suddenly
picked up dramatically (perhaps with the introduction of sex [Schopf
95]), and then 0.4 billion years later we see the first fossils of
multi-cellular life [Knoll 95]. Finally, 0.6 billion years brings us
to where we are today.
To these five stages we might add two other discrete non- "try try
again" type steps: an initial step of getting the right sort of planet
around the right sort of star, and a final step of humanity either
succeeding or destroying itself. Together, these seven steps could
explain the Great Filter if the (logarithmic) average filter per step
was at least a factor of one thousand. That is, either there might be
a one in a thousand chance of passing a discrete step, or a one
trillion year expected time to complete a "try try again" step.
Of course we may find more steps as we get better fossil evidence, and
we may have slighted some step which happened to take a particularly
short time. And of course the Great Filter need not be distributed
evenly among these steps - just how much of the Filter rests in the
last step is the ominous question that motivates our analysis.
This model predicts that the expected time remaining until the window
of opportunity for life on Earth closes is about one billion years.
This model could therefore be confirmed by astronomical analysis
regarding expected durations until the Earth is fried by a runaway
greenhouse effect, by an unstable sun, a nearby supernovae, or by some
other disaster ahead in the sun's travels through the galaxy.