In 1980 Carl Sagan produced a well received book and TV series titled "Cosmos." Many of us remember the exquisite beauty of the images and sounds, but few of us remember his relatively less spectacular discussion of Frank Drake's mathematical model of the estimated number of highly evolved civilizations in our neighborhood. But the model affected our collective thinking more than the images and sounds did, for Carl Sagan is seen as the principle spokesman of the scientific viewpoint, and when he presents a mathematical model that shows that it is unlikely that ETs could ever visit here, many of us adopt that perspective without further analysis, for who are we to take on Carl Sagan? What he says often goes without question, but let's gently close that era now. New evidence has surfaced, and new conclusions flow from it.
Sagan's expertise is in astronomy. Mine is in the analysis of
computer and mathematical models for inherent bias. It was my
doctoral dissertation. I know whereof I speak on this issue. An
in-depth analysis of many models that were being used to influence
people's thinking revealed that many models make assumptions favorable
to a desired outcome, and that the conclusions of the model often
changed when alternative assumptions were considered. The same
applies to Sagan's presentation of the Frank Drake model of the
likelihood of intelligent life in the universe. I will explain
the hidden assumptions in the model and explore the conclusions
that follow when new data and alternative assumptions are considered.
We begin by understanding the Drake model. The question we are
interested in is "Are we alone in the Universe?" but
the question Sagan poses is, "What is N, the number of advanced
technological civilizations currently in our Galaxy?" Sometimes
the very question posed locks in bias, as in this case. Why do
we seek only technological nuts-and-bolts civilizations using
radio waves? There is much evidence that there are metaphysical
, spiritual and psychic dimensions to the ET phenomenon. Some
of the visitors seem to come through walls, others seem to appear
and dematerialize before one's eyes, and others seem to speak
through channels from non-physical dimensions. To discount all
these very real possibilities at the start certainly limits the
possible outcomes from the inquiry. Nevertheless, we will proceed.
The original formulation was in terms of subscripted variables,
multiplied together, but since subscripts are commonly associated
with eye-glazing-nod-off syndrome, I will refrain from their use,
with no loss in clarity. Further, I will simplify the model, combining
some factors together for ease of understanding. If you wish to
do some interesting modeling, use a spreadsheet that supports
scientific notation to implement the following equations. Then
you can plug in your own assumptions and get your own answers.
Here is the simplified model:
N=S*P*L*A*T
Each letter is a numeric variable. The first two are large
integers, the last two are fractions. We guess their values and
multiply them together. Here's what they mean:
N The Number of advanced technological civilizations now
in our galaxy
S The number of Stars in our galaxy
P The number of ecologically suitable Planets per star
L The fraction of suitable planets that actually harbor Life
A The fraction of living planets that on which Advanced
civilizations occur
T The fraction of advanced civilizations with which we co-exist
in Time
The model works like this: Estimate the total number S*P of possible planets in the Milky Way where advanced civilizations might occur and reduce that number by multiplying S*P by a series of fractions that eliminate all the impossible places. As Sherlock Holmes would say, "When you eliminate everything that is impossible, then what remains, no matter how strange, must be the truth,"
Here's a quick run-through of the model. Refer to the Base column
in the table at the end of this article. (Ignore factor G in the
first row for the time being.) We start with S, the number of
Stars in our galaxy, which is estimated to be about 4E11, which
is scientific techno-talk for a number that starts with a 4 and
is followed by eleven zeroes, i.e., about 400,000,000,000, or
about four hundred billion stars. Then we assume that maybe a
third of all stars have planets and that an average planetary
system has about three planets suitable for life, so that P, the
number of ecologically suitable Planets per star , is about one.
Then we assume that a third of the ecologically suitable planets
actually evolve life, so that L, the fraction of suitable planets
that actually harbor Life, is 1/3, and that maybe half
of the planets with evolved life continue to evolve into Advanced
civilizations. Ignoring factor T for the moment, we multiply these
numbers together and come up with 4E10, i.e., forty billion advanced
civilizations in the Milky Way. That's quite a few folks out there,
if the numbers are true.
But we have forgotten T, the fraction of advanced civilizations
with which we co-exist in Time. Why is this factor in the model?
Because it is possible that these civilizations grow, bloom, and
die isolated not only in space but also in time from other
civilizations. Atlantis, if it existed in Earth's past, could
not communicate with residual Martians living on Mars today, nor
could the presumably vanished ancient Martian residents of Cydonia
communicate with us today on Earth, assuming the absence of time
travel.
Visit any planet at any time in its billions-of-years of history,
and the probability that you visited on a day when an advanced
technological civilization was flourishing can be estimated as
the ratio of the number of years that such civilizations live
to the number of years that such planets exist. If advanced civilizations
flash on and off like fireflies in the night, then this fraction
is very small. We have been using radio astronomy for only 50
years, yet our planet has existed perhaps 5 billion years. We
might destroy advanced life on Earth at any time, so Sagan conservatively
estimates T, the fraction of the potential advanced civilizations
with which we co-exist in time, by dividing 50 by 5 billion to
get 1E-8, i.e., one chance in a hundred million.
Multiply our earlier number 4E10 by this fraction 1E-8, and we
get 13 other "fireflies" whose light shines concurrently
with ours in the blackness of space. But these civilizations are
also assumed to be distributed in space throughout the Milky Way,
which is 100 thousand light-years across, so it might take a radio
signal centuries to get to the nearest one.. We could radio the
other "fireflies" out there, but they are likely to
go out before they get our signal, and we are likely to be dark
before their response gets back. Thus, concludes Carl, we are,
in effect, alone in the universe Oh well.
From this result it follows that all abduction accounts must be
psychological aberrations, and all UFOs must be terrestrial and
explainable by science.
But not so fast. Some issues have arisen in this discussion that
have been conveniently brushed aside. Let us examine a few of
them and see the effects of addressing them a little more directly.
Let's work backwards and address the factor T for starters. It
seems a shade pessimistic to presume that our technological society
will wink out in a half-century. What if we learn to avoid nuclear
war? There is great progress being made now on the possible elimination
of all nuclear weapons on Earth. What if we save the ozone? We
have banned chemicals that are destroying it. What if we make
it? Can we get over the hump and have a continuously existing
advanced civilization for a million years or so? Even the stupid
dinosaurs lasted longer. If advanced civilizations can last that
long, then fraction T grows from 1E-8 to 0.02%, and the number
of concurrent advanced civilizations grows to nearly three hundred
thousand. (Refer to the column labeled "Set 1" in the
table at the end of this article.) This is much more than 13,
but there's more to come.
Consider factor A, the fraction of living planets that display
Advanced civilizations. Sagan assumes that 1% of all planets in
the Milky Way that harbor life do at some time develop advanced
civilization. This low figure comes from assuming that random
evolution from primordial slime is the only pathway to advanced
civilization. On some planets giant dumb lizards may still be
in charge. Humans rule Earth only through the unlikeliest of occurrences
in evolution and stray meteors over millions of years. Development
of intelligent folk like us should be equally unlikely elsewhere,
thinks Carl.
But, there is some circularity in reasoning going on here. If
advanced civilizations wink out like fireflies before they get
off their home planets, then natural evolution is the only pathway
to intelligence, and the probability of life becoming advanced
is low. But, if just one advanced civilization figures out how
to travel the vastness of space, then there is another pathway:
seeded jump-starts. Travelers from afar arrive on promising planets
and stay long enough to leave colonies, seeds, or genetically
altered beings. Neanderthals suddenly get displaced by Cro-Magnons,
organized city-states like Ur appear suddenly with little visible
prior preparation. If such processes occur, then the probability
of life becoming advanced on other planets may be relatively high.
Let's assume that intelligent civilizations can survive a million
years and that they travel space, affecting planets, so that 75%
of planets with existing life display advanced civilization at
some time. Then the model suggests that we coexist in time with
twenty million other advanced Milky Way civilizations, the nearest
of which should be no further than 45 light years away. (Set 2
below)
Now let's consider factor L, the fraction of planets that are
ecologically suited for life in every respect and, in fact, do
exhibit life. Sagan assumes that two out of three such planets
are entirely devoid of life. Imagine sun-drenched, balmy breezes
on dead oceans and lifeless shores. If advanced civilizations
ply the waves of the cosmic ocean looking for the promised land,
I would imagine that they would find it almost impossible to refrain
from planting some kind of life seed in such a fertile garden.
Merely visiting the planet would probably introduce life accidentally.
Sagan uses an L value of 33%, which reflects his evolutionary
bias. Let us consider setting it to 90%, and leaving our other
values as we have set them most recently. The model now shows
fifty million concurrent civilizations, with the nearest not farther
than 27 light years away. (Set 3 below) That's encouraging, but
there's more.
Factor P is the number of ecologically life-suitable Planets per
star. Sagan assumes that one-third of all stars have planets,
and that those that do have planets may have on average two that
are ecologically suitable for life. Recent results from the Hubble
space telescope have shown planets around several neighboring
stars. Ice has been discovered on Europa, and it is expected to
be warm water down below, ideal for life. Residues and chemicals
that could only have been formed by living organisms have been
extracted from two Martian meteorites by two separate scientific
teams from two countries. From our sample of one solar system,
it seems that P is likely to be at least three. Plugging P=3 into
our model yields over 160 million concurrent civilizations, the
nearest of which should be no further than 16 light years away,
certainly a feasible distance for a civilization to cross occasionally
in a million years, using technology we can imagine. (Set 4 below)
Factor S, the number of stars in the Milky Way, may be adjusted
by the Hubble space telescope, but for now we will leave it alone.
But there is another factor that is implicit in the Drake model,
but not expressed. That is G, the number of Galaxies from which
intelligent beings may come. Sagan and Drake assume the value
of one for this factor, without expressing it. Why? Because intergalactic
travel would take much more time than interstellar travel, and
we don't live long enough to even do that, so why even consider
intergalactic travel?
From the viewpoint of Contact Forum there are some important
reasons to consider extragalactic visitors, and one is that many
contactees report that their visitors hail from Andromeda,
our nearest neighboring galaxy. Another reason can be discerned
by looking clearly at the evidence for extraterrestrial presence
on Earth, something that Sagan seems unwilling to do. Psychological
aberrations do not leave scars. Hallucinations do not occur to
multiple individuals in identical ways. Swamp gas does not create
pregnancies in women who have had hysterectomies. Misidentified
aircraft do not cause spontaneous healings of cancer.
Something real is going on. Intelligent life of some kind is interacting
with life on Earth. It comes from somewhere or sometime. Therefore
it got here and it knows how to traverse space and/or time. Many
of the reported characteristics of UFO encounters are consistent
with time manipulation. Many contactees are told that we do not
understand time. If the visitors manipulate time and space, then
the distance between galaxies should be no great barrier to cross.
Thus if any visitors are here, it is quite possible that they
could be from any place and any time.
What do such thoughts do to our model? If we multiply factor G
onto what we have, then we are most likely swimming in an alien
tide. The Hubble space telescope recently found hundreds of thousands
of galaxies in one small section of the sky. If we set G to 1E5
and multiply it onto our model, then there may be as many as 16
trillion concurrent civilizations capable of visiting us. (Set
5 below) The fact that only a few hundred of them seem to be actually
visiting us I take to be somewhat of a snub, really. Are we that
uninteresting? Perhaps Carl has an opinion on that.
As a final exercise on your own, take a current estimate of the
number of galaxies in the universe and use it for factor G, along
with Sagan's original values for the other factors. You will see
that merely opening to the possibility that the visitors can cross
the vastness of space is sufficient to cause the model to suggest
that there are probably millions of other advanced societies able
to visit us.
Assuming further that travel through time can be achieved, then all the civilizations throughout time and space may be capable of observing us, and we should expect our environment to be literally humming with ET activity at all times.
Base | Set 1 | Set 2 | Set 3 | Set 4 | Set 5 | |
G | 1 | 1 | 1 | 1 | 1 | 1E+5 |
S | 4E+11 | 4E+11 | 4E+11 | 4E+11 | 4E+11 | 4E+11 |
P | 1 | 1 | 1 | 1 | 3 | 3 |
L | 33% | 33% | 33% | 90% | 90% | 90% |
A | 1% | 1% | 75% | 75% | 75% | 75% |
T | 1.0E-08 | .02% | .02% | .02% | .02% | .02% |
N | 13 | 2.7E+05 | 2.0E+07 | 5.4E+07 | 1.6E+08 | 1.6E+13 |
©1996 Granite Publishing LLC
This article appears in the 1996.4 issue of Contact
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