About The Author
D. R. Prescott has written a novel, a collection of short stories, a nonfiction book, a collection of essays, planetarium show/display scripts, two family histories, technical articles and business plans as well as written for and edited several newsletters.
Awards and published work include Writers' Journal, Long Story Short, Taj Mahal Review literary journal, The Orange County Register, Writer's Digest, and Writing.com and four books among other challenges.
As a former aerospace executive and planetarium program director, Prescott currently writes and explores life in Orange, California.
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Since 2008, Prescott has been a regular contributor of
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O R D E R   T O D A Y !
Once Upon An Equation...
by D. R. Prescott

What purpose does it serve to estimate how many communicative civilizations there might be in the cosmos and, once calculated, search for those civilizations?

Frank Drake started it all back in the 1960’s with what has become known as the Drake Equation. You can find a number of variations of his basic equation where factors have been altered for a number of reasons. In all its variations, it is a fairly straightforward mathematical exercise. The version here is for purposes of comparing it with another equation, the Rare Earth Equation, both of which have been slightly modified from their original forms.

Equation 1:
N = N* fp ne fi fc fl fL

N = number of communicative civilizations in the galaxy
N* = number of stars in the galaxy
fp = fraction of stars with planets
ne = number of planets per star that are capable of sustaining life
fl = fraction of planets where life develops
fi = fraction of planets where intelligent life evolves
fc = fraction of intelligent life that can communicate
fL = fraction of the planet's life during which the communicating civilizations live

The main variations of Drake’s Equation are in the first and last terms. Here, for the first term, we use N*, defined as the number of stars in the galaxy, whereas other versions of Drake’s Equation use R as the rate of suitable star formation in the galaxy per year. That change spawns another change in the last term of the equation. We use fL as the fraction of the lifetime of a planet that is marked by the presence of a communicative civilization while other forms use L, the lifetime in years of a communicative civilization.

Estimates of the number of stars within the Milky Way Galaxy range between 200 and as high as 500 billion, depending who you are reading at the moment and when the text was written. To get the estimating juices really flowing and provide the greatest possible optimism, we start off with 500 billion stars.

While the existence of extra-solar planets use to be a matter of some conjecture, it has become fairly apparent with the recent spate of planetary discoveries that planets, fp, seem fairly common as stars form. We are not asking if the planets are Earth-like. We are just making the assumptions that planets of any type form for some period of time as a part of the star formation process. Let’s say for fun that half (0.5) of all stars in the galaxy have some planets, regardless whether they are habitable or not.

The number of planets per star that are capable of sustaining life (ne) is a subject of much debate. If we look at our own solar system for evidence, it would appear that the answer would be somewhere between 3 and 5 when you consider the possibilities of Earth, Mars, Europa, Titan and, maybe Venus, if it had a different rotational period that allowed it to cool off. While a lot of optimistic people might use 3, we only know of one to date. Remember, this term means life, not necessarily complex life. Using 1 is a very good bet in our solar system.

The troubled waters of making bold estimates become murkier when attempting to set a value for the fraction of planets where intelligent life evolves (fi) and develop the means (fc) to communicate across interstellar distances. Conventional wisdom seems to place these variables between 10 and 20%. For these controversial terms, we’ll use a conservative 1% for planets where intelligent life does arise and 10% of that number who actually acquire the capability to communicate. It seems reasonable that intelligent life might be rare but, once intelligent life is established, the capability to communicate would likely come sooner or later.

Estimating fL takes us into the never-never land of estimating our own future. Using the Earth as an example, projecting the fraction of a planet’s life during which the communicating civilizations live is tenuous at best. We have had the ability to communicate with radio signals for less than a hundred years. Some courageous estimators place this factor at 10,000 years. If we manage to destroy our communicative ability, if not the entire species, in the next few years, the fraction would be 1/100,000,000th. Let’s give us 1,000 years of communicating ability, hoping to err on the conservative, not pessimistic or overly optimistic.

The final result is obtained by multiplying these factors together to get a number of intelligent, communicating civilizations, N, within the galaxy. Using our rather arbitrary values, we would expect to find 5 intelligent civilizations with the desire to communicate with us. If we assume that our civilization and hence others will survive for an average of 10,000 years, then our estimate climbs to 54 planets spewing radio signals, laser beams or other things back and forth across our galaxy.

In the early days, enthusiastic estimates soared to one million civilizations! No wonder SETI@home has over 2 million people about the globe putting their personal computers to work in the largest scientific computing effort in the history of the species-searching for that first contact! It is of no small import that this is the largest computing exercise ever attempted on Earth. The success of this distributed computing experiment has profound benefits in other areas of scientific investigation and, in fact, the technology is being used by other disciplines.

Before we draw conclusions on the validity of the search for extraterrestrial intelligence (SETI) using Drake’s Equation and the implications of finding it or not finding it, let’s explore another idea. Peter D. Ward and Donald Brownlee of the University of Washington published a fairly popular work, Rare Earth. In that book, they challenge the optimistic view that the universe is teeming with intelligent life capable of communicating with each other and us across interstellar distances. They give readers another equation that is virtually irresistible to compulsive number crunchers. Their equation has more variables, posing some rather interesting challenges to an optimistic estimate for ET.

Their basic premise, which they dub the Rare Earth Hypothesis, is that life may be widespread in the Universe, but animal life is rare and intelligent life is even rarer. It took nearly four billion years before complex metazoans appeared on Earth. According to the Rare Earth Hypothesis, a lot of things had to happen just right for animal life to arise-plate tectonics, a large moon, the right rotation, the right distance from a relatively stable star, the right mass of the star, stable planetary orbits, just the right amount of ocean and Jupiter-sized neighbors to sweep out planet-busting asteroids and comets. As with Drake’s Equation, the insight is in the details. Fleshed out, the Rare Earth Equation is:

Equation 2:
N = N* fp fpm ne ng fi fc fl fm fj fme

N = Number of communicative civilizations in the Milky Way
N* = number of stars in the Milky Way Galaxy
fp = fraction of stars with planets
fpm = fraction of metal-rich planets
ne = planets in the stars habitable zone
ng = stars in the galactic habitable zone
fi = fraction of habitable planets where life does arise
fc = fraction of planets with life where complex metazoans arise
fl = percentage of a lifetime of a planet that is marked by the presence of complex metazoans.
fm = fraction of planets with a large moon
fj= fraction of planets with Jupiter-sized planets
fme = fraction of planets with a critically low number of mass extinction events

While this equation looks formidable, it is also straightforward multiplication like Drake’s Equation. However, it leads to some disconcerting nuances when going boldly where no number cruncher has gone before. It should be noted that Ward and Brownlee did not generate a specific estimate from their new equation. Should we take a lesson from their lack of quantification and settle for their algebraic symbolism and seductive rationale? Can’t do that; it would take all the fun out of it!

The terms, N*, fp, ne and fi have definitions in common with Drake’s Equation. There is little argument between the two equations about basic definitions. To satisfy our number crunching compulsion, we will use the same values as we did in the Drake equation for all these variables. For compulsive number-crunchers, that’s 5 x 1011 stars in the galaxy, of which 50% are estimated to have planets, where 1 planet will be in the star’s habitable zone and 1 percent of those where intelligent life does arise. Multiplying those four terms together, you’ll find that we have reduced the possibilities from 500 billion stars to a mere 2.5 billion where we might search. Well, that certainly sounds encouraging! But, wait! There’s more.

A fairly rare occurrence in our universe is material heavier than hydrogen and helium. Our Sun has a fairly high in metal content compared to many other stars. In fact, out of 174 stars studied by astronomer G. Gonzalez, our sun had the highest metal content. While far from conclusive, it would appear from this study that our Sun might be a fairly rare star. Since the heavier elements are made in the crucibles of stars, the existence of metal-rich planets is likely related to the metal presence in their star. Considering the rarity of metals in our galaxy, Ward and Brownlee introduce a new term for the fraction of metal-rich planets, fpm. We will use 0.005 for this variable to recognize this scarcity. We are suddenly down to a mere 12.5 million possibilities, taking some of the wind out of our estimating lungs.

Another major difference between what appear to be common variables starts with the term, fc. Changing it from “where life does arise” to “where complex metazoans arise” is a huge change in the way we think. While complex metazoans are life, microbial life to animal life is a giant hurtle. The Rare Earth authors take the position that life (microbes/bacteria) may be prolific throughout our galaxy, while animal life (complex, multi-celled) may be extraordinarily rare, hence, the term Rare Earth Equation. While we use the conventional wisdom of 10% in the Drake Equation, we will apply a very conservative 5 per cent, or 0.05. Well, now we have narrowed it down to 625,000 possible stars out of 500,000,000,000!

The idea of a habitable zone in our galaxy is something not considered directly in the Drake Equation. The galactic center is packed with stars, and probably black holes, making the development of life, and especially complex animal life as we know it, most likely difficult. So, if we believe that the center of our galaxy is totally inhospitable to complex life, what about the rest of our 100,000 light year wide home? If we discount double star systems where orbital eccentricities might make the development of animal life dicey at best and eliminate the more crowded areas where disasters may be the rule rather than the exception, we might be bold enough to say that perhaps 20 per cent, or 100 billion stars in our galaxy are within the galactic habitable zone, the variable, fg. However, multiplying again we are left with 125,000 possibilities.

If the advancement from microbial to animal life requires even part of what the authors suggest, the fraction of planets where complex metazoans (fc) arise may be very small indeed. How long do they last? The fraction a planet’s lifetime where complex metazoans are presence on a planet around a suitable star is a guess at best. We will be conservative for the lifetime of complex life on a given planet (fl) and set that value at 0.02. Now, we are down to 2,500 possibilities.

The fraction of planets with a large moon (fm) seems at first glance an easy thing to imagine since we know that one exists, ours. Yet, having a large moon around a metal-rich planet within the animal habitable zone (AHZ, a term as opposed to the MHZ, microbial habitable zone) of its star is more of a stretch. Is a 0.05 too high to continue our estimating madness? Maybe. Throwing caution to the solar wind, we’ll use it anyway. Out of 2,500 possibilities, applying fm there are now only 125.

The fraction (fj) of solar systems with Jupiter-sized planets is pretty straightforward. Since the recent extra-solar planetary discoveries have resulted in Jupiter-sized or larger planets (mostly because our detection techniques are that limited but we are getting better daily), the vacuuming effect of large gas giants protecting smaller metal-rich earthlike planets is fairly plausible. We will be bold enough to say that 80 per cent of planets that have planets will have Jupiter-sized planets. That helps, leaving only 100 stars left where intelligent, communicative life might exist.

The last variable in the Rare Earth Equation (fme) has subtle implications. The fraction of planets with critically low number of mass extinction events must have a stable orbit and, more importantly, be in a solar system where the other planets in that system also have stable orbits for a long enough time to permit life to develop. In addition, the Jupiter-sized planets must do their job while not disturbing the planetary incubator they are protecting. A dose of luck is also involved over billions of years since it is necessary that the life bearing planet avoid being hit by a huge, planet destroying object. On top of all those necessary ingredients in the life recipe, the parent star itself must be fairly stable over a long period of time. Since we have no real idea of where to peg this value and because we have no inhibition about taking a shot at it, let’s use the same value as we used for the last variable-0.01.

Anyone who has done a bit of arithmetic will recognize that, when multiplying all these fractional variables together, the closer to zero any one of the factors becomes, the closer to zero the result will be. Change a factor to zero and your answer will be zero, which would mean that there are no intelligent civilizations capable of communicating over interstellar distances within our galaxy. We know that isn’t true. We can do it, so there is one.

Now that we have mustered the wherewithal to estimate the individual factors for the Rare Earth Equation, we have been in drooling anticipation of the answer? Using the values we selected, the math gives 1 intelligent civilization in our galaxy. Well, what about other galaxies and there are billions. We know there is one intelligent, communicative civilization in the Milky Way Galaxy. Why limit these equations to our galaxy? Could we raise the number of stars in our calculation to account for a billion, trillion or whatever number of galaxies that you estimate within a given radius about the Milky Way? Are some of our factors too high? Are some too low? You, and everyone else, be the judge.

Would extraterrestrial civilizations be interested in communicating? If they exist, have they learned that it is wise to keep a low profile as Dr. Hawking recently suggested? Or, are they not there at all? After thousands of years (and it grows by the hour) of computer time spent trying to find a signal, none has surfaced…yet. What if an artificial signal, optical or radio, is found? What if none ever surfaces? What would either answer mean to us?

If an artificial signal is found and proven to be of extraterrestrial origin, the impact on our civilization will be noteworthy. The message will probably be a lecture rather than a conversation unless the sending species has managed to overcome the universal speed limit (the speed of light) permitting a real time dialog. Incidentally, it has been suggested that there is really no reason to communicate across space with optical or radio signals if time is not of the essence. Simply doing what we already have done gets the job done. Pioneer and Voyager are our emissaries to the stars and perhaps other civilizations. Sending a message affixed to a space craft would likely be more efficient since communication across interstellar distances by radio or lasers is pretty much limited to a one-way conversation.

Perhaps the greatest impact might be that we will feel less lonely in a universe that is not very user-friendly to complex life forms. Some politicians and scientists will argue that we must try to make contact and benefit from the scientific and technological knowledge of a civilization that is at least equal to or, much more likely, more advanced than, our own. Others may rage that we must get ready to defend ourselves. Budgets may be increased for research, space and/or defense programs. Society will work feverishly to interleave this new piece of information into belief systems, rationalizing our position in the universal pecking order.

Unless the signal has significant technical or philosophical content, little more communication will happen. A two-way conversation will definitely take longer than near-sighted political terms, is likely to extend far beyond human life spans and even outlive our civilization entirely. If the signal originates thousands of light years away, the civilization that sent it might be gone by now, or lost interest eons ago.
What if we are all alone in space and time?

Imagine what that would mean! It could mean that the human species is very, very special as many people think. Animal life is an exceptional occurrence in nature. The Earth would be the cradle of sentience. Everything we have learned and developed would become more valuable. We would be the only known keepers of consciousness, hence intelligence, in the Universe! Are we the Universe expressing itself? What an awesome responsibility!

What purpose does it serve to search for extraterrestrial life? If the SETI proponents are right about the abundance of intelligent life in our galaxy, our lives may get very complicated and very interesting, very quickly. If they are wrong and the Rare Earth Hypothesis is closer to the truth, we will have no help, or interference, from other intelligent life forms beyond Earth to carry the torch of sentience. A definite outcome, either way, will profoundly affect us. We must keep looking even if the answer is negative because it is part of what we are-an inquisitive, intelligent life form in search of others. In fact, a negative answer may be more profound.

Good hunting searchers, inquiring Earthlings want to know!

© Copyright 2010 D. R. Prescott (donprescott at Writing.Com). All rights reserved.
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' Copyright 2008 D. R. Prescott (UN: donprescott at Writing.Com). All rights reserved. D. R. Prescott has granted Writing.Com, its affiliates and syndicates non-exclusive rights to display this work. Questions or Comments? E-mail to prescottdc@sbcglobal.net
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