The Pfeifer Equation

The Drake Equation

The Drake Equation, which looks to estimate the number of extraterrestrial civilizations in our galaxy that have the capabilities to communicate with us is shown below:

N = R_* • f_p • n_e • f_l • f_i • f_c • L

N = the number of civilizations in the galaxy which we could communicate with

Factors (and Drake's original estimates):

• R_* = the average rate of star formation in our galaxy (1 star per year)
• f_p = the fraction of stars that have planets (0.2 to 0.5)
• n_e = the number of habitable planets per star (1 to 5)
• f_l = the fraction of habitable planets that do develop life (100%)
• f_i = the fraction of planets with life that develop intelligent life (100%)
• f_c = the fraction of civilizations that develop detectable technology (0.1 to 0.2)
• L = the average length of time which detectable civilizations are around (1000 to 100,000,000 years)

Results:

When all of Drake's factors are multiplied together, the value of N ranges from N = 20 to N = 50,000,000. This outcome indicates a great deal of uncertainty. Interestingly, three of Drake's estimates, namely R_*, f_l, and f_i, do not affect the result since they equate to 1. Nevertheless, Drake's range of values for N implies that there should be life somewhere in our galaxy that we could theoretically communicate with. At the same time, it is easy to see that the equation can take on a plethora of values depending on the chosen estimates. This lack of precision has caused some to question the usefulness of the equation.

If the Pfeifer Equation were written in this format, it would look like this:

n = [P(ts) • P(hz) • P(mf) • P(a) • P(c) • P(lf) • N_s • PPS] + k

n = the number of life inhabiting planets currently in the Milky Way galaxy

Factors (and Pfeifer's estimates):

• P(ts) = probability of planet being Terrestrial or Super Earth (0.3371)
• P(hz) = probability of planet being in the habitable zone (0.0147)
• P(mf) = probability of planet having a magnetic field (0.7)
• P(a) = probability of planet having a life supporting atmosphere (0.1)
• P(c) = probability of planet containing essential chemicals (0.01)
• P(lf) = probability of life forming on a habitable planet (1/universe)
• N_s = the number of stars in the galaxy (200,000,000,000)
• PPS = the number of planets per star (1.3652)
• k = the number of planets known to have life (1, The Earth)

Differences between the Equations:

Before diving into the differences in factors and estimates, it is important to note that the Drake Equation and the Pfeifer Equation are not attempting to estimate the same thing (N ≠ n). The Drake Equation is estimating how many detectable intelligent civilizations are in the Milky Way, while the Pfeifer Equation is estimating how many life-inhabiting worlds are in the galaxy. The Pfeifer Equation is not concerned with intelligent life at all. It simply evaluates whether other life exists and how prevalent it is. Drake saw planet habitability and the formation of non-intelligent life as common, as seen in his estimates for n_e and f_l. Essentially, he estimated that stars with planets would have on average 1 to 5 planets with life. The orange factors in the Pfeifer Equation compute the probability that an individual planet is habitable, and the red factor determines the proportion of habitable planets which develop life. f_l from the Drake Equation and P(lf) from the Pfeifer Equation represent the same thing. However, Pfeifer strongly disagrees with Drake's estimate of 100%. Pfeifer believes that the probability of life forming on a habitable planet is once per universe. This does not mean that it is impossible, but rather that the likelihood is extremely close to zero. Evidently, the two equations have some serious discrepancies.

To understand more about why Pfeifer chose the factors and estimates that he did, visit the factors and estimates pages.

Made by Nicholas Pfeifer