The Drake Equation

Short science fiction by Torn MacAlester


Drake equa­tion devel­oped the equa­tion:  n_0=R*f_p*n_e*f_l*f_i*f_t*L_0 where R is the rate of star for­ma­tion, f_p  is the frac­tion of stars that have plan­ets, n_e aver­age num­ber of plan­ets per star that could sup­port life, f_l is the frac­tion of plan­ets that have life, f_i is the frac­tion hav­ing intel­li­gent life, f_t  is the frac­tion that devel­ops suf­fi­cient tech­nol­o­gy, and L_0 is the life­time for the civ­i­liza­tion. The para­me­ter n_0  is the num­ber of civ­i­liza­tions in the galaxy. This equa­tion is a series of para­me­ters when mul­ti­plied togeth­er account for all the fac­tors lead­ing to a civ­i­liza­tion capa­ble of inter­stel­lar com­mu­ni­ca­tions. Despite a lot of tan­ta­liz­ing clues, we have only one exam­ple, us. As a result, we can set the num­ber of civ­i­liza­tions in the galaxy capa­ble of inter­stel­lar com­mu­ni­ca­tions to be at least one.

We’ll take a quick review of the terms of the Drake equa­tion, mak­ing note of some con­nec­tions with civ­i­liza­tions on the Kar­da­shev scale. In lat­er arti­cles, we’ll take a deep­er dive into each of these terms and extend them as necessary.

Terms from astrophysics:

The first term, R, is the stel­lar for­ma­tion rate. It is a term that can be com­put­ed from astro­physics. A con­ser­v­a­tive val­ue is about 1.5 to 3 stars being formed per year. We will explore how advanced civ­i­liza­tions, such as a Type 3 galac­tic civ­i­liza­tion, could change this num­ber to suit their needs.

The sec­ond term, f_p, is the frac­tion of stars that have plan­ets. This is cur­rent­ly esti­mat­ed at approx­i­mate­ly 1.  All stars seem to have plan­ets. Advanced civ­i­liza­tions, such as a Type 2 stel­lar civ­i­liza­tion, could alter this number.

The num­ber of plan­ets that could sup­port life per sys­tem, n_e, is the third term. Esti­mates are from 0 to 4. It all depends upon the life zones. Some plan­ets might be out­side of the life zones but still have envi­ron­ments that meet the con­di­tions. Obvi­ous­ly, advanced civ­i­liza­tions could alter this number.

Terms from biology:

The frac­tion of those worlds hav­ing life, f_l, is spec­u­la­tion. Right now, because of what we have in the solar sys­tem, the val­ue is about 0.25 if we con­sid­er Earth, Mars, Europa, and Ence­ladus hab­it­able. Suf­fi­cient­ly advanced civ­i­liza­tions will push this num­ber to 1 and increase the val­ue of n_e.

The long path from life to intel­li­gent life is estab­lished by the para­me­ter f_i. Geo­log­i­cal­ly and bio­log­i­cal­ly speak­ing, we have no idea the val­ue of this num­ber. We could take it as a chance to sur­vive a mass extinc­tion, how­ev­er such an extinc­tion might increase the prob­a­bil­i­ty of intel­li­gence aris­ing before the next extinction.

Terms based upon other factors:

Anoth­er impor­tant con­sid­er­a­tion if the rise of tech­nol­o­gy. The para­me­ter f_t  is the frac­tion of intel­li­gent species devel­op­ing the tech­nol­o­gy nec­es­sary for com­mu­ni­ca­tions with the stars. Using our own Earth as the exam­ple, only us out of all the var­i­ous hominids devel­oped the advanced tech­nolo­gies nec­es­sary for stel­lar com­mu­ni­ca­tions. That does not count all the var­i­ous civ­i­liza­tions that rose with­in the emer­gent homo sapi­ens that died out before the tech­no­log­i­cal hur­dles could be over­come. Any val­ue will be at best a guess.

Last­ly, we look at the life­time of a civ­i­liza­tion capa­ble of inter­stel­lar com­mu­ni­ca­tions, L_0. This is the hard­est to assess. But we can real­ize that this num­ber could like­ly be any­thing from sec­onds to bil­lions of years. For us, the pos­si­bil­i­ty of radio com­mu­ni­ca­tions began around 1900, so con­ser­v­a­tive­ly, we can say 122 years.

Extending Drake’s equation to class 1, 2, and 3 civilizations:

We can mod­i­fy Drake’s equa­tion by adding six addi­tion­al terms, f_1,L_1,f_2,L_2, and f_3, L_3 for the frac­tion of civ­i­liza­tions at the said lev­el and the aver­age life­time of the same. These para­me­ters give the num­bers , , and . of civ­i­liza­tions that make it to type 1, type 2, and type 3 civ­i­liza­tions: n_1=\frac{n_0}{L_0} f_1 L_1 , n_2=\frac{n_1}{L_1}f_2L_2 , and n_3=\frac{n_2}{L_2}f_3L_3. This is the sci­ence of the Drake equa­tion applied to sci­ence fic­tion. The life­time of a civ­i­liza­tion depends on the civ­i­liza­tion type. There are also fac­tors which depend upon the num­bers of civ­i­liza­tions of var­i­ous types present in the galaxy or in the local area.