Sagan's Cosmos Revisited



©1996 Granite Publishing LLC

from Contact Forum
November/December 1996

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:

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.

Table of Assumptions and Results

   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 Forum, now The 5th World Journal.

Call 800-366-0264 to begin your subscription. Six issues, $24.

Subscribers regard this publication as one of the finest of its kind.