Drake Equation Statistics

The Drake Equation

If you aren't familiar with the Drake Equation, it was formulated by astronomer Frank Drake in 1961. It provides a probabilistic method of estimating the number of technical civilizations that might concurrently exist in our galaxy. It combines 7 parameters that make up the components of the estimate.

Our dilemma is that we don't know very well what values many of those parameters should have. We can come close to estimating the N^* star formation rate, but the original view of the paramater was to estimate the rate of sun-like star formation, as low as a value of 1 star per year. Now Red Dwarfs are being considered as possible life sustaining stars. So that rate of star formation paramater may be bigger than thought.

We know now that most stars (f_p) have planets. Most stars likely even have one or more planets in the life zone, that temperate zone where liquid water may exist. But the number of those planets that may be earth-like is small, just a few percent.

The values of the remaining parameters are largely unknown, though the percentages for number of planets that will develop life (f_l), percentage of those that will develop intelligent life (f_i), and percentage of those that will develop technology (f_c), are all likely small values.

We also have no idea how long a civilization, having gotten started, may last (L). We have been a technical civilization a very short time, yet we already have the potential to destroy ourselves. And nature can provide numerous methods of destroying life, such as plagues, massive solar flares, asteroid or even planetary collisions, and nearby super novae. So if we are a typical technical civilization, our predicament may suggest that the length of time a technical society exists could be rather short.

This post shows a version of the Drake Equation you may have never seen before. Rather that present the equation with the option to pick your own specific parameters for a trial run like the Drake Equation App, it lets you get serious about your study of the equation.

Instead of selecting specific parameters, this version lets you select ranges of parameter values to express you sense of how well parameters are known. Then the app picks the high, low, and two values within the range for each parameter, and calculates number of civilizations (Nciv) for each parameter combination.

The program then creates a histogram of Nciv values and turns them into percentages of the total number of estimates. It then creates a sum of percentage array and uses that to determine likely values for the number of concurrent civilizations in our galaxy. It provides the Maximum, Average, 90th percentile, 75th percentile, and 50th percentile values of Nciv estimates. When you see these statistics from thousands of samples, you can get a much better picture in your mind of how isolated we may actually be.

The statistical version of the Drake equation is presented below. Try out some parameter ranges and see what you can deduce.

The formulation of the Drake Equation used:

N = N* . fp . ne . fl . fi . fc . L N* Star Formation Rate/Year fp Percent of those stars with planets ne Average number of life-potential planets per star fl Percent of those that will harbor life fi Percent of those that will develop intelligent life fc Percent of those that will develop radio communications L Number of years a civilization will exist

Parameter Min Max N*, Star Formation Rate 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 fp, Percent of Stars With Planets 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% ne, Avg Number of Life Potential Planets Per Star 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 fl, Percent Of Those That Will Develop Life 1% 5% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 1% 5% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% fi, Percent Of Those That Will Develop Intelligent Life 1% 5% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 1% 5% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% fc, Percent Of Those That Will Develop Radio Communication 1% 5% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 1% 5% 10% 20% 30% 30% 40% 50% 60% 70% 80% 90% 100% L, Number Of Years A Civilization Will Last 10 yr 100 yr 500 yr 1000 yr 2000 yr 5000 yr 10000 yr 20000 yr 50000 yr 100000 yr 200000 yr 500000 yr 10 yr 100 yr 500 yr 1000 yr 2000 yr 5000 yr 10000 yr 20000 yr 50000 yr 100000 yr 200000 yr 500000 yr Click for Results