What Does The Drake Equation Say?

The Famous Drake Equation

Noted astronomer Frank Drake first wrote his famous alien prediction equation in 1961. It is a combination of factors that can be used to predict the number of concurrent civilizations living in the Milky Way galaxy in our time. The equation is:

N = R^* * fp * ne * fl * fi * fc * L
where:

R*	Galaxy star formation rate per year
fp	fraction of those stars that have planets
ne	number of planets in the life zone
fl	fraction of those planets that will develop life
fi	fraction of those planets that will develop intelligent life
fc	fraction of those planets that will develop technology (radio telescopes)
L	length of time intelligent civilizations exist

If you want to play with the equation, check out the Drake Equation web page. It lets you try your own numbers and see what is predicted. You'll likely learn in experimenting with the equation that to get many concurrent civilizations you have to input very generous parameters.

It seems a relatively simple equation, just a bunch of numbers multiplied together. But the proper numerical values for those parameters are hard to determine, and many simply aren't known.

For example, according to the Drake EQ Wiki, at the time of the development of the equation the rate of sun-like star formation (1st term, R^*) was thought to be about 10, or 10 stars per year. But a real unknown was the number of stars that had planets (ne in the equation). At that time no extrasolar planets were known.

Since that time, reasonable numbers for some parameters have been filled in, some in a civilization supportive way, and some in a less supportive way. We've discovered thousands of planets around other stars, and it seems that most if not all stars likely have planets. That's good, civilization-wise.

On the other hand, the optimistic number for sun-like star formation (10 per year), is more likely nearer only 1 per year. That's bad, civilization-wise.

It also appears, though the results are likely biased because earth-sized planets are harder to see, that our planet is a bit smaller than average. The predominant size seems to be perhaps 3 to 5 times larger than earth (in mass), being called super earths. And while we think Jupiter is large, there are a lot of Jupiter sized and bigger behemoths out there.

So while we are forming a view that most stars have planets, and statistically most have at least one planet in the life zone, that planet may be nothing like earth. So what percent of stars have earth-like planets in the right place? It's only a guess at this point.

If we even knew how many earth-like planets there were in the respective stars' life zones, what percentage of those planets would develop intelligent life? Intelligent life has only existed on our planet for a few tens of thousands of years, while the planet is some 4.5 billion years old. Does that suggest it is rare?

We don't even know what may have led to the existence of our planet's intelligent life. Was it an inevitable event? If so, why is it so recent a happening?

Did the multiple extinction events on our planet interfere with the development of intelligent life, or did they clear the way for intelligent life to form? We don't know.

But the current thinking is that given what we know of the distribution of planet sizes and types, the number of life supporting planets that could harbor technological species may be rather small.

Why Aren't the Parameters Better Known?

Many of the parameters are still poorly known because as in many areas of science, some of what you learn raises even more questions. So it's hard to access whether you can pin down some things or not.

As to the equation, the first parameter, R^*, or the rate of star formation, is better known. Unfortunately, for the aspect of supporting more civilizations the news isn't so good.

The fraction of stars having planets (fp) is much better known, and that bodes well for the support of civilizations. It's now thought that nearly all stars have planets.

The fraction of planets having life (fl) and the fraction of those having intelligent life (fi) are still completely unknown, though more cautious (small) numbers are now considered the best bet.

On the plus side, at the time of the equation only sun-like stars were considered as likely harboring life supporting planets. But with discovery of the TRAPPIST-1 star system and its amazing family of planets, there's new interest in planetary systems around Red Dwarf stars.

Why? There are billions of them in our galaxy. They outnumber sun-like stars several fold. That vastly opens up the number of potential planets. If red dwarfs can be considered, the rate of star formation number may be functionally bigger than the more basic sun-like assumption.

There are potential problems with including red dwarfs in the equation. It appears that red dwarf stars often are not well behaved, oft producing massive solar flares. Those would likely play havoc with life on the planets in the life zone, which with red dwarfs is quite close to the respective stars. How do you predict, with this new knowledge, the percentages of planets in the life zone that might have life? It's not so easy.

And the big question we can't yet answer is about the L parameter, the number of years technological civilizations last. We intelligent humans have a history of civilization on this planet of 10,000 years or so. But that's not our technological civilization history. That has only existed for 100 years give or take. And with human caused global warming, WWI and WWII, nuclear weapons, and our frequent brushes with more war, we don't know if we'll make 200 years, 1000 years, or 10,000 years before we do ourselves or our planet in. So what is a good estimate for the L parameter? Who knows? I suspect if we make it 200 years without causing a catastrophic disaster, our changes of long existence goes up considerably. But how many technical civilizations don't get past their technological burst of development?

How to Pick the Parameters

The DrakeEQ page on this site lets you try your hand at picking some parameters, and see what predictions are forthcoming. But that's pretty hit or miss.

I decided to take a different tack. Since specific parameters for each of the 7 terms are just unknown, I thought it better to think of parameter ranges. Those are better known, or known with more confidence. So I decided to work with parameter ranges rather than specific parameters, using ranges that seem to be commonly considered reasonable.

I created a small program using the Euler Toolbox programming language. With the program I created a range of each of the 7 Drake Equation variables, based on the best information I could find. I had the program compute the predicted result for each combination of the parameters within the best guess ranges, nearly 80,000 estimates with my parameter resolution.

Then the program made a histogram of the predictions, and converted those into a percentage of the total number of predictions. Finally, the program created a cumulative sum of the prediction percentages, a form of presentation I found most informative.

You can play with this parameter range version of the Drake equation by making a copy of this Drake Equation Spreadsheet. Once you have the copy of the Google Spreadsheet, you can change the range parameters as you wish, and the spreadsheet will perform nearly 17000 trials with different parameter combinations from the ranges you provided. Summary results are always shown below the range parameters.

The numbers I picked for the parameter ranges are listed below. Recall that the equation is:

N = R^* * fp * ne * fl * fi * fc * L
where:

Param	Min	Max	Desc
R*	0.5	5	star formation rate
fp	80	100	fraction that have planets
ne	1	5	num planets in life zone
fl	1	20	fraction that will develop life
fi	.1	5	fraction that will develop intelligence
fc	10	70	fraction that will develop technology
L	500	10000	years tech civilizations exist

Drake Equation Predictions (Percentages)

The percentage of the parameter set yields for each number of concurrent civilizations is presented above, truncated to 100 concurrent civilizations. The horizontal axis shows the predicted concurrent civilization count for all parameter sets, and the vertical axis shows the percentage of occurrence that of each predicted value. While the maximum number of civilizations produced by this set of parameters was 1750, as the graph illustrates the bulk of solutions yielded much smaller expectations. High population numbers only come about when every parameter in the multiplicative factor is favorable.

As a matter of fact, the most predicted value from all parameter range combinations was -- zero concurrent civilizations. A total of 22 percent of the solutions predicted zero concurrent civilizations. That's a bit disappointing, but it also means nearly 80 percent of the parameter combinations indicated at least one other civilization in concurrence with us.

The resulting graph produced by computing a cumulative sum of the individual prediction percentages is presented below:

Drake Equation Cumulative Percentages

90th Percentile

The horizontal axis shows the number of predicted concurrent civilizations, and the vertical axis shows the cumulative percentages. For example, according to the graph, 90 percent of the predictions from the varied combination of parameters were for 116 concurrent civilizations or less. The average number from all predictions came to be 41 concurrent civilizations, based on the parameter ranges used in the experiment. However, that average is from a highly skewed distribution.

Drake Equation Cumulative Percentages

75th Percentile

The above graph stretches the data out a bit, extending out to 200 concurrent civilizations. On this graph you can see that 75 percent of the parameter sets gave solutions of less than 36 concurrent civilizations. That doesn't seem so many, a bit disappointing. But they were obtained using pretty commonly accepted parameters.

Drake Equation Cumulative Percentages

50th Percentile

Blowing up the resolution a bit more, you can see there there's a 50 percent chance that the number of concurrent civilizations is less than 10, maybe even 7 or less, given the parameter ranges used. So a full one-half of the parameter combinations came up with less than 10 concurrent civilizations.

What Makes These Predictions So Low?

So what happened to the favorable estimates you use to see discussed so often?

One thing to consider is that the Drake Equation, though not complicated, is a multiplication of all of the factors. Even if all factors except one were super optimistic, having just one low parameter in the mix could significantly lower the predicted outcome.

For example, one big thing is the lower rate of star formation that is assumed now. Another is the likely lower estimate for the number of livable planets in the life zone of stars. There are plenty of planets in the life zone, but what kind of planets are they? Gas giants with no definable solid surface? Super earths whose properties we know little about? Planets close to violent red dwarfs with their massive flares?

We still don't know how life started on this planet, so it's very hard to predict how easy it is for life to start elsewhere, and what are the necessary conditions. The one thing we do know is that life started very early in this planet's existence. By the end of the first half-billion years of our 4.5 billion total, life was emerging.

So that would lead to an optimistic belief that life can start easily on other earth-like planets. But we see that of the number of planets discovered, that's a small percent, with perhaps less than 5 percent of planets that are earth-like. And then a fraction of those in the life zone, and a fraction of those around non-volatile stars.

What Part has the Moon Played?

Our planet/moon system is pretty unusual, in that the moon is so large compared to the planet. The moon is fully 1/4 the size of earth. There are other moons of that size and even larger in our solar system, but all of those big moons are around the gas giant planets.

The moon is a very stabilizing force for our planet, keeping the spin axis consistently aligned. Evidence from Mars studies show that Mars' pole direction has varied considerable at times in the past, having large effects on the seasons. Is that lunar added stability a factor in the start and development of life on our planet?

When the moon was first formed, it was much closer to the earth than it is now. Astronomer Hakeem Oluseyi said that instead of the tides in that era being measured in feet, they would have been measured in miles. So the early moon really stirred up the oceans and seas. Was that a significant factor in the early start of life? It may have helped considerably in getting the necessary chemicals for life together.

As to moons around the known extraterrestrial discovered planets, we have no data. Do most planets have moons? Are most moons too small to be consequential?

Even More Things that are Unknown

One thing to consider is that we do have life forms on earth that exist in very inhospitable environments. So perhaps life can start in conditions much less like earth than we suppose. The question about these extremophiles is did they originate in those hostile environments, or evolve from life started in gentler conditions to little by little become extremophiles? We don't know enough to make predictions about that.

Another issue is the difficulty of predicting how common intelligent life is. On this planet, intelligent life didn't arise until just the last 100,000 years or so. A very recent phenomenon. That could lead to a pessimistic sense of how often intelligent life appears.

A more optimistic factor is that it appears water is actually quite abundant in our Milky Way. Even in our solar system, Earth is 3/4 covered in water, Mars was once heavily endowed with water, Europa has more water than Earth, Ganymede has an underground ocean, Enceladus is spewing water, Titan has mountains of ice, Triton, even Pluto. So life may actually be very abundant, though perhaps most of it existing in ice covered planets or subterranean oceans. That's exciting, but it's hard to imagine how intelligent creatures living in an ocean are going to be inspired or able to create radio telescopes.

One silver lining that might exist is that though many Jupiter and larger size planets are close to their respective stars, crowding out any earth-like planets, they may have Mars to earth sized moons. These moons may harbor life. But we don't have numbers on that.

Another important parameter that could change things dramatically is the L parameter, the number of years a technological civilization exists. I put in a range of from 500 to 10000 years. But should it be more like 5000 to 50000? That would dramatically up the likely number of concurrent civilizations.