Re: Probability formula for life


dkomo <dkomo871@xxxxxxxxxxx> wrote:-

If there are 300 billion stars in an average galaxy and 100 billion
galaxies in the observable universe, the total number of stars is 3 X
10^22. Suppose we wanted to know to a certainty of 99.9999% that life
has formed at *least* once on some planet other than earth at one of
these stars. What would be the minimum average probability of life
forming at any of these stars? We can find a simple formula to answer
this question.

Let p_a = the average probability of a star supporting life

P = the probability of at least one other star in the universe
with life

Q = 1-P = the probability of no other stars than
the sun with life

We want to find p_a given P = 0.999999 (a certainty of 99.9999%)

The probability of a star *not* supporting life is

1 - p_a

So the probability of no other stars in the universe supporting life is

(1). (1 - p_a) ^ (N-1) = Q where N = 3 X 10^22

The -1 results because we're excluding our own sun, but N is so large
that N-1 is equal to N for practical purposes.

Taking the natural logarithm of both sides of equation (1), substituting
N for N-1, and dividing through by N we get

(2). ln(1 - p_a) = ln Q / N

Using the power series expansion for ln,

(3). ln(1 - p_a) = -p_a - p_a^2 / 2 - p_a^3 / 3 - ....

Since p_a is small, we can neglect all terms but the -p_a term.

So the final equation is

(4). p_a = -ln Q / N

Now, given P = 0.999999, Q = 1-P = 10^-6

p_a = - ln(10^-6) / (3 X 10^22) = 4.61 X 10^-22

This means that if the average probability that a star in the universe
contains a planet with life is no less than 4.61 X 10^-22, we can be
99.9999% certain that the universe contains *at least* one star (other
than our sun) with life.

Those are pretty good betting odds.

Note that the above analysis ignores *when* life develops at a star.
The analysis is not constrained to extant life. If life developed only
once at some other star 200 million years ago, then disappeared, that is
an example of a successful life event.

JE:-
Thanks for an interesting post.

I think that the popular human centric view (life on earth remains the only
life in the universe and ourselves the only cognitive life) remains as
primitive as the earth centric solar system dictated and brutally enforced
by early Christian belief systems. I don't think we are not the centre of
attention of an all knowing (but apparently vindictive) god, or anything
else. Darwin was the first to sever the umbilical chord provided by our many
tribal belief systems which granted us a welcome, privileged place in the
universe. What Darwin and Wallace taught us using their empirically testable
theories (neither was just a non testable belief) is that all life remains
connected, independent and naturally competitive. Each competing living
system remains subject to exactly the same laws of nature (sorry, no
privileges). What I find interesting to speculate on are the following:

1) What would cognitive life be like if it evolved on an earth like planet
but millions of years in advance of us.

2) What advances in cognitive knowledge could such an advanced civilization
evolve and what would constitute a morality within their communities?

3) Would such a civilisation be bothered to contact us even if they could
so? If not, why not?

Regards,

John Edser
Independent Researcher

edser@xxxxxxxxxxxxxx




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