# Talk:Drake equation/Archive 1

## Drake vs. Koran - Finding the Other Six Earths in the Universe As Mentioned in Koran

Koran says that God has created seven Earths, like the seven Firmaments He has created, one we live on & the rest of the six are unknown to us as to where they are. As per the Prophetic Hadith each Earth is inhabited by a human civilization & each civilization is accountable to God for their deeds as we are. As per the Hadith each has its Adam (ie. the first of a progeny on a planet who was created by God's Hand) & its Mohammad (ie., the last of God's Messenger to each Adam's progeny to guide them to His Paradise in the Hereafter) so in fact God created seven Adams & sent seven Mohammads & all the progenies of seven Earths will be together on the Plain of Accounting on the Day of Resurrection. God has revealed to us in Koran that: [{سورة الطلاق}*Q:65('The Divorce' or 'AtTalaq'):12) in which God says: (({It is}Alllah who created seven Firmaments & from the Earth likewise...,God's command descends between them...))((الله الذي خلق سبع سموات و من الأرض مثلهن... {يتنزل الأمر بينهن ...} لتعلموا أن الله على كلّ شئ قدير) & God says that He is telling us all this in Koran: (...that we may know that verily God is capable on {doing} everything) & (و أن الله قد أحاط بكل شئ علما) (ie. And that verily God encompasses {or knows} everything) ie. Seven Earths, on one we live, while the rest of the six, though unknown to humanity as to where they are, are known to God as to where they are, & as earlier stated as per Prophetic Hadith each Earth is populated with humankind & each has its Adam & its Mohammad & as earlier stated so in fact God created seven Adams & seven Mohammads & as earlier stated all the progenies of seven Earths will be together on the Plain of Accounting on the Day of Resurrection, for the successful to enter God's Paradise for Eternity.Ilaila (talk) 08:56, 23 January 2010 (UTC)

## Question

I'm trying to figure out what this means, and unfortunately my understanding of stats is weak. Can someone break this down for me and others?

When at the end, the current estimates plugged into the Drake equation give an N of 2.31 -- that's, as I understand it, saying that odds are there are 2.31 possibly-communicating civilizations in the Milky Way. Now:

Does that include us? In other words, does it mean that besides us there are probably 1.31 others? Or is the sample size so big that we haven't scratched the surface, and we're talking about 2.31 *more*?

I'm not taking the Drake equation as infallible, I'm just trying to understand what it means. -- Please help! 71.101.53.18 (talk)

N is an estimate of EXTRA-terrestrial (ie. alien) civilizations. But the result of 2.31 is far outweighed by the uncertainty factors in the parameters -- something which the article should mention more clearly. Even the order of magnitude of N is unknown. See Fuzziness ~~ Ropata (talk) 00:35, 25 May 2009 (UTC)
Thanks! -- that makes sense. I agree, that for a moderately-educated layman like me, conveying the range would definitely help understanding (if it's 2.31 +/- 1, that's a different animal than 2.31 +/- 20 or 3,000!) -- isn't there something about not reporting more digits than your sig figs allow for? (71.101.53.18 (talk) 03:41, 25 May 2009 (UTC))

## Typo? Close to novea

At discussing fl (the fraction of the above which actually go on to develop life) it says: "Lineweaver has also determined that about 10% of star systems in the Galaxy are hospitable to life, by having heavy elements, being far from supernovae and being stable themselves for sufficient time."

I gues that should be "by being close to supernovae"?

I'm not an expert in astronomy, but what it says now does not sound logical to me. Or somebody explain me the mechanism. ;-)

For the rest: impressive article!

Arjan202 (talk) 11:06, 26 June 2008 (UTC)

## Rare Earth refutation

This really begs to be contrasted with Ward and Brownlee's Rare Earth hypothesis, which many believes lays waste to the Drake Equation. Any thoughts?

Surely the Rare Earth hypothesis does not contradict the Drake eqn, but merely says that some of the parameters (notably fi) are a lot lower than originally thought. 80.3.112.87 22:56, 6 May 2007 (UTC)
Yes, it's sillly to say that the "Rare Earth" hypothesis "refutes" the Drake equation. What it does it does is to make a set of proposals for what the terms in the Drake equation are, and carry the calculation through to say the answer is that the expected number of other civilizations is <<1. The Rare Earth hypothesis doesn't even make sense without the Drake equation; it takes the Drake equation as a starting point.

Geoffrey.landis 15:56, 30 May 2007 (UTC)

## Drake overly optimistic?

What about the possibility that even if an alien civilization did exist, from what they could gather of our culture they wouldn't want to communicate with us? Was Drake being overly optimistic about us?

Why do you say that the currently observed value of N = 0? What are we, chopped liver? (Or are you saying that we are not able to communicate interstellarly?) ----

Does "fairly conservative" f_l, f_i, f_c and L has any meaning ? --Taw

f_l, f_i and L are the really contentious ones, I think. We can make a fair stab at guesstimating R* and f_p now, given recent advances in astronomy. -- The Anome

Existence of human race now acknowledged. -- The Anome

Claim that f_l = 1 is weird. In "planets which can potentially support life" in Solar System they usually list Venus, Earth and Mars. So f_l here is 1/3. Unless they say that only Earth is capable of supporting life. In that case n_e is way too high.

This whole thing is rather fuzzy and ill-defined, IMO. For example, if I were listing "planets which can potentially support life" for the solar system, Venus would emphatically _not_ be included. On the other hand, Europa, Callisto, and maybe Ganymede would be on there; these three moons are thought to have liquid water oceans under their crusts (Ganymede is the iffiest, Europa is almost certain). Uranus and Neptune may also have liquid water layers, though even if they do conditions there would be somewhat extreme for life as we know it and may not be suitable. Basically, IMO, we simply don't know enough about the universe yet to be proposing actual numbers for some of these variables yet. -BD

We certainly don't know enough to produce good numbers, but even guesses within a few orders of magnitude are better than nothing. It doesn't take much accuracy to make certain theories more or less likely than others, or to present interesting problems. In particular, the estimates given as "conservative" are sufficient to generate the Fermi paradox; if our guesses are two low, it's even more remarkable; if our guesses are way too high, Fremi becomes expected but then the low numbers themselves are hard to explain. --LDC

If there are a couple of orders of magnitude of flexibility to a couple of the terms in an equation like this, then I don't see how it can be reasonably used to suggest _anything_ with enough certainty to base a serious discussion on. I see the Drake equation as more of a suggestion of what we should be trying to find out in the future than as a useful analysis of life in the galaxy at this point, and wanted to make sure the article didn't give the wrong impression (ie, that "scientists say there should be aliens everywhere" or that "scientists say we're alone in the universe").

So what exactly is the Fermi paradox? The estimates for the parameters given in the article yield N=0.01, which doesn't seem to be excessively high. --AxelBoldt

See my examples now in the article -- The Anome

Being new here, I won't take the privledge of removing this particular statement, but I want to alert you that in all of my studies of genetics and molecular biology, I have never encountered the suggestion that outside mutagens (such as UV, as stated in this article) are necessary to produce the genetic variation that alows organisms to adapt to changing environments. I have only encoutered this idea in science fiction books from the 1950s or so (Asimov and Heinlein), and I think that this was just a bunch of speculation from biolgists of the time who had no idea of the mechanism of how mutations occur.

We now know that mutations occur by changes in the DNA sequence. We know that DNA must constantly be copied, and that any copying device has some error rate. We know that there are multiple DNA polymerases (copying enzymes) each with its own characteristic error rate. The error rate is itself an evolvable trait, even as it affects evolution. If it is necessary to have mutations for long term survival of a lineage (which I believe it is), then any lineage that ceases to have mutations will die out a la natural selection, and only the ones that have mutations will persist. Thus, even this trait (mutation rate) will acquire a sort of optimum, just as other traits do, and it will be adapted based upon the lifestyle of the organism and the environment that it lives in.

This may be based on a younger hypothesis that Sol's UV was the driving force behind the start of life, but I think that's just as discredited now. In any case, it's not cited, I added a "citation needed". Darekun 02:28, 18 October 2007 (UTC)

Too bad it probably won't be on the actuarial exam. It has a nice mnemonic to it, just think "pelican".

F_l=1 is quite optimistic, since it means every planet that can develop life does. -Padde 00:38, 15 April 2006 (UTC)

That seems to be based on the observation that as soon as Earth could develop earthlike life, it did; cases like Venus and Mars seem to be covered by the low n_e. Darekun 02:28, 18 October 2007 (UTC)

## Removed paragraph

Removed this paragraph: It's a very common misconception often spread by the popular media that the evidence supports the value of N equal to 1 - there's one human civilization in the galaxy. But the galaxy is just an arbitrary probed area - we could as well probe each two galaxies, each 100 galaxies, or each one thousandth of a galaxy - and the conclusion should be the same number of such civilizations per galaxy. According to this fallacious thinking, the evidence would have supported N equal to one half, one hundredth, and one thousand as well as exactly 1.

1. On the contrary, the popular media gives the impression that N is equal to hundreds, if not thousands of civilizations in our galaxy (Star Trek, Babylon 5, Star Wars, many sci fi movies and shows like the X-Files, stories of UFO and government conspiracies to cover up the "truth"... etc...).
2. The rest doesn't make sense due to the fact that we know of at least one civilization. Anything beyond that is speculation based on the equation here (some parameters we do know better than others). And if there is only one civilization between two galaxies (a lonely thought) that would give an N = 0.5 for each of those galaxies. There is nothing fallacious about that - it is just probability. I suggest a read of anthropic principle. --mav

This probably has changes some of the numbers, but not sure how. http://news.bbc.co.uk/1/hi/sci/tech/3588721.stm

Edward 12:23, 2 Apr 2004 (UTC)

Is there any source discussing what Drake meant by an estimate of 10 years as the value of L? Does such a pessimistic view reflect the fact that he was living during the Cold War, or did he think that in general a civilization that develops interplanetary communications will wipe itself out within 10 years? I mean, it took us humans decades to go from understanding light and using radio, to detonating a nuclear weapon.

Yes, I think it's at least generally assumed that he was thinking of nuclear annihilation. BTW we actually detonated a nuclear weapon before the development of our first radio system that had any reasonable chance of communicating with an interstellar civilisation (Trinity test in 1945, Jodrell Bank opened in 1947). Securiger 12:12, 4 Nov 2004 (UTC)

## Fuzziness

I do not think that our article adequately conveys the "fuzziness". As BD and someone else remarked above, the basic problem, is that for several of the parameters we really have no idea, or at least the range of plausible estimates varies by several orders of magnitude. And when you multiply variations of orders of magnitude several times, you end up with a huge range. This is occasionally hinted at in the article, but is never really made clear. Rather than listing several people's estimates and results, would it not be more useful to multiply out the ranges of estimates, to show the range of the results? (This is easier if we work in orders of magnitude - OoM being logarithmic we could then add instead of multiply - but that might lose some readers.) An example to explain what I mean:

Parameter low estimate high estimate ratio my comments
R* 10 20 2 The only parameter we have any real handle on, and it's already got a factor of 2:1
fp 0.1 0.75 7.5
ne .5 5 10 Up to here, it's wild estimates with at least some observational basis. All the rest are pure guesswork.
fl .001 1 1000 I think most people who argue for values close to 1 are making a common statistical inferential error; see "Anthropics and stuff" below
fi ${\displaystyle 10^{-7}}$ 0.5 ${\displaystyle 0.5\times 10^{7}}$
fc .01 .1 10 I can't believe our uncertainty in this is really so low. People just haven't been exercising their imaginations enough.
L 66 ${\displaystyle 10^{9}}$ ${\displaystyle 1.5\times 10^{7}}$
N ${\displaystyle 3.3\times 10^{-11}}$ ${\displaystyle 3.75\times 10^{9}}$ ${\displaystyle 1.125\times 10^{20}}$ Yes folks, that's 20 orders of magnitude.

All of these parameters were taken from either our own article, or one of the ones in our extlinks. But I make no claim they are comprehensive, just an example. Securiger 12:12, 4 Nov 2004 (UTC)

(Is this table a comment on the section 'Current estimates of the parameters' in the main article? One problem with that section is no 'error bars' are quoted for the factors, there must be someone who has estimated the uncertainty in all the factors? Seems Sagan did this several times back in the early days of the Drake Equation.) —Preceding unsigned comment added by Albert.a.jackson (talkcontribs) 14:39, 10 December 2007 (UTC)

### Effects of personal bias

As an aside, having discussed this with quite a few people over the years, and read a few learned monographs on it, I have come to the conclusion that most people make up their minds beforehand - perhaps either wanting to believe that human life is especially unique, or wanting to believe that alien visitation is just a few years away - and then choose parameter ranges that satisfy those desires. The Drake equation tends to add excessive dignity to this process of biased, wild guessing. Really for at least four of those parameters, the only intellectually honest estimate is "we have no idea", which means the final answer is "we have no idea". Not very satisfactory, but true nonetheless. Securiger 12:12, 4 Nov 2004 (UTC)

(I totally agree with the statement above, but I think Drake would too, the equation was really only a 'talking point' and he has stated such himself. Some of the factors have almost infinite standard deviations. ) —Preceding unsigned comment added by Aajacksoniv (talkcontribs) 01:00, 12 December 2007 (UTC)

## Anthropics and stuff

Another point whilst I'm rambling on; our statement:

What evidence is currently visible to humanity suggests that fl is very high; life on Earth appears to have begun almost immediately after conditions arrived in which it was possible, suggesting that abiogenesis is relatively "easy" once conditions are right.

suffers from the Self-Sampling Assumption. We can in fact deduce nothing about fl from our own presence on earth, since our own presence somewhere is a given, or else we would not be making the observation in the first place. For example, suppose that the true value of fl is so extremely low that there probably exists only one planet in the Universe with life on it. Evidently then, we the observers are on that planet, and we know of one civilization (us) and no others, because there are no others. Now consider a parallel universe where fl is billions of times higher, but, for some reason, no contact has been established. Any given group of observers knows of one civilisation (themselves) and no others, for reasons unknown to them. The observations are identical in both cases; by observing the existence of your own civilisation, you can deduce nothing at all about fl. To cut a long story short, in estimating any of these parameters, you can't count yourself. (The exception is L; since it doesn't affect our ability to observe ourselves, we can use ourselves as an estimator for L. I think.)

Actually, not an exception. The L estimate will never stop increasing, because if it does, no one is left to make that observation.

The best that we can do is observe that there is another planet nearby where maybe life could have appeared, but apparently didn't, so fl is certainly less than 1. Note incidentally, that this is already implicitly taken care of in the definition of N, which is for extraterrestrial civilisations only; N does not include our own civ. Securiger 12:12, 4 Nov 2004 (UTC)

Another way of looking at the question is to ask how many degrees of freedom we have in estimating each parameter. For many of them, we have zero degrees of freedom, since we only have the one sample (ourselves). Thus, no valid estimate can be made, just various wild-ass guesses.Dogface 20:04, 28 July 2006 (UTC)

## What is N << 1 ?

What is this terminology used in the article? N << 1

How does it differ from N < 1 ?

N < 1 means N is less than 1 (possibly by an infinitesimal amount); N << 1 means N is much less than 1. Exactly how much "much less" means is a bit vague and usually determined by context. In some contexts, it means "so much less that within the limits of accuracy of our calculation, we can ignore it". In other contexts it can be taken to mean an order of magnitude less. Securiger 18:27, 15 Nov 2004 (UTC)

What you are saying is it should be

N approx zero, an infinitesimal. BernardZ 05:47, 6 March 2007 (UTC)

## 2?

for N not >>1, there should be some discussion of the conditional probability of the presence of a second civilization, given the presence of one (i.e. we know we are here, but we are interested if there is anyone else). dab () 14:52, 13 Jan 2005 (UTC)

I imagine that if N not >> 1 then it is independent of the number of civilizations observed. Just because our star system came up "heads", it wouldn't affect the chances of the other star systems. The only way I can conceive of it not being independent is the chance for intergalactic war between civilizations, and I don't remember us engaging in any genocidal space campaigns =P Intangir 08:32, 13 November 2005 (UTC)

However it probably would be argued to being a Poissonic distribution. Low probabilities and discrete values.

If we assume that the average number we can expect = X Then the probability is PR(N) =(exp(-x) * X^N)/N!

therefore the probability of no ETI life is Pr(0)=exp(-X)

therefore the probability of one ETI life Pr(1)=exp(-X)*X = X*Pr(0)

So we can say that Pr(N>0) = 1-Pr(0) Pr(N>1) = 1-Pr(0)-X*Pr(0)

You could say using the Anthropic principal that the Pr(N>0) could be anything say an infinitesimal as there would be no discussion on this question if N=0.

So what are the odds that some else is there. The odds that there is someone else is

Pr(X>1)/Pr(X>0)= 1- X/(1/Pr(0)-1) = 1 - X /(Exp(X)-1)

Odds knowing that Pr(N>0)
× Pr(N=1) Pr(N>1)
0.001 1.000 0.000
0.101 0.950 0.050
0.201 0.903 0.097
0.301 0.857 0.143
0.401 0.813 0.187
0.501 0.770 0.230
0.601 0.729 0.271
0.701 0.690 0.310
0.801 0.652 0.348
0.901 0.616 0.384
1.000 0.582 0.418

Of course I am simplifying it a lot. Another issue is as the universe gets older, I would expect the X to go up over time. BernardZ 23:57, 20 February 2007 (UTC)

## Michael Crichton on the Drake equation???

Removed the following from the article:

Michael Crichton denounced the Drake Equation as pseudoscience in the Caltech Michelin Lecture entitled "Aliens Cause Global Warming" (meant to be a serious lecture with a catchy title), 17 January 2003:

Cast your minds back to 1960. John F. Kennedy is president, commercial jet airplanes are just appearing, the biggest university mainframes have 12K of memory. And in Green Bank, West Virginia at the new National Radio Astronomy Observatory, a young astrophysicist named Frank Drake runs a two week project called Ozma, to search for extraterrestrial signals. A signal is received, to great excitement. It turns out to be false, but the excitement remains. In 1960, Drake organizes the first SETI conference, and came up with the now-famous Drake equation:
N=N*fp ne fl fi fc fL
Where N* is the number of stars in the Milky Way galaxy; fp is the fraction with planets; ne is the number of planets per star capable of supporting life; fl is the fraction of planets where life evolves; fi is the fraction where intelligent life evolves; and fc is the fraction that communicates; and fL is the fraction of the planet's life during which the communicating civilizations live.
This serious-looking equation gave SETI an serious footing as a legitimate intellectual inquiry. The problem, of course, is that none of the terms can be known, and most cannot even be estimated. The only way to work the equation is to fill in with guesses. And guesses-just so we're clear-are merely expressions of prejudice. Nor can there be "informed guesses." If you need to state how many planets with life choose to communicate, there is simply no way to make an informed guess. It's simply prejudice.
As a result, the Drake equation can have any value from "billions and billions" to zero. An expression that can mean anything means nothing. Speaking precisely, the Drake equation is literally meaningless, and has nothing to do with science. I take the hard view that science involves the creation of testable hypotheses. The Drake equation cannot be tested and therefore SETI is not science. SETI is unquestionably a religion. Faith is defined as the firm belief in something for which there is no proof. The belief that the Koran is the word of God is a matter of faith. The belief that God created the universe in seven days is a matter of faith. The belief that there are other life forms in the universe is a matter of faith. There is not a single shred of evidence for any other life forms, and in forty years of searching, none has been discovered. There is absolutely no evidentiary reason to maintain this belief. SETI is a religion.
One way to chart the cooling of enthusiasm is to review popular works on the subject. In 1964, at the height of SETI enthusiasm, Walter Sullivan of the NY Times wrote an exciting book about life in the universe entitled WE ARE NOT ALONE. By 1995, when Paul Davis wrote a book on the same subject, he titled it ARE WE ALONE? ( Since 1981, there have in fact been four books titled ARE WE ALONE.) More recently we have seen the rise of the so-called "Rare Earth" theory which suggests that we may, in fact, be all alone. Again, there is no evidence either way.
Back in the sixties, SETI had its critics, although not among astrophysicists and astronomers. The biologists and paleontologists were harshest. George Gaylord Simpson of Harvard sneered that SETI was a "study without a subject," and it remains so to the present day.
But scientists in general have been indulgent toward SETI, viewing it either with bemused tolerance, or with indifference. After all, what's the big deal? It's kind of fun. If people want to look, let them. Only a curmudgeon would speak harshly of SETI. It wasn't worth the bother.
And of course it is true that untestable theories may have heuristic value. Of course extraterrestrials are a good way to teach science to kids. But that does not relieve us of the obligation to see the Drake equation clearly for what it is-pure speculation in quasi-scientific trappings.
The fact that the Drake equation was not greeted with screams of outrage-similar to the screams of outrage that greet each Creationist new claim, for example-meant that now there was a crack in the door, a loosening of the definition of what constituted legitimate scientific procedure. And soon enough, pernicious garbage began to squeeze through the cracks.

Comment: Crichton is a film-maker and a thriller writer, do his comments really add to this article? In any case, he fails to understand the concept of falsifiability. The Drake equation is not the issue, the value of N is. The Drake equation is just a back-of-envelope calculation made about the Fermi paradox. Falsifiable hypotheses can be made by setting bounds on the value of N, and making observations that can falsify these hypotheses. For example, just just one otherwise-unexplainable signal (prime numbered pulses, for example) recieved by SETI@home would do the job of setting a lowerbound of N=2. Or the sighting of some Dyson spheres, or other examples of engineering capable of being seen from lightyears away. Alternatively, you could go round the galaxy, enumerating civilizations, a task which whilst lengthy (a few hundred thousand years) is entirely physically possible, given von Neumann machines and a lot of civilizational patience. -- The Anome 14:13, May 21, 2005 (UTC)

I agree, Crichton is way off the mark here: he appears to think that DE is same thing as e.g. the law of gravity. DE is used for estimation purposes, it is not a physical law. If we knew the real value of N, we wouldn't need DE, would we? Moreover, when he says that DE is not scientific, he is again off the mark, because it exactly follows the scientific approach to cracking hard problems, which is dividing them into smaller subproblems, separating well-defined ones from ill-defined ones along the way. GregorB 17:35, May 30, 2005 (UTC)
Wow - just lost a lot of respect for ol' Crichton. I'm not so concerned about the Drake equation - I agree with the substance of what Crichton says - it is a little silly, but as GregorB says, it wasn't meant as a law, just an attempt at an estimate. However, that attack on SETI is out of the ballpark ridiculous. His claim that "SETI is a religion" just doesn't make any sense. If SETI was a group of people who dogmatically believed in the existence of extraterrestrials, then they would be a religion. However last I checked, they were searching for extraterrestrial life, not assuming its existence. I see no distinction in that respect between SETI and particle physicists. No one would reasonably claim that particle physics is a religion because it involves searching for new particles that aren't known to exist! Religious groups don't spent millions on equipment to search for evidence of their beliefs - they just believe them. How did he miss that? Sorry, this doesn't have much to do with the article, but oh well. --Bmk 04:47, 7 July 2006 (UTC)

A new number for Ne could be 4 being that in our star system there are 2 planets and 2 moons which might develope life. They are Earth, Mars, and the moons Europa and Titan which may be developing life. Theoretically counting only ours as a primary source because we don't know how many planets are actually out there that are capable of creating life let alone sustaining it. Concluding the fact that the majority of the stars in the Milky Way are red dwarfs (which cannot have a planet around it because it would erode away any atmosphere on a planet). We took most of Drake's original numbers and added a few of our own and got N=8 so we think there are only 8 planets out there like ours that could communicate with us... comments please!!! need help with this one...!!!!

WP:NPOV states that various views must be represented fairly, proportionately and without bias. Crichton is not alone in his perception. I encountered this equation in a philosophy class in which it was labelled a pseudo-science. Shawnc 07:09, 17 December 2006 (UTC)

## Nitpick: lower bound on L

I changed the following from the article:

A lower bound on L can be estimated from the lifetime of our current civilization....

I don't think that's estimating a lower bound, because our civilization might have a longer lifetime than the average (expected) lifetime. Maybe "pessimistic value of L" would be more accurate? Wmahan. 05:53, 2005 Jun 15 (UTC)

I think it would make a decent lower bound in that we are not dead yet and do not expect to be dead next year. Our technology is futher expected to outlive us (at least in detectble terms). But throwing the value of L away I think the deravation of the equation with respect to R* and L needs a bit more fleshing out for the less geek of readers. The stated goal of counting civlazations which we should be able to detect would seem at first anyway to call for a count of stars of the proper type at the proper distance. The rest of the equation is pretty simple as its all fractions of fractions of fractions, but I think the years aspect of the equationneeds further explination in the article. Dalf | Talk 06:43, 14 October 2005 (UTC)
Yes, but if we use Earth's civilization to estimate L, that's not much of a sample space. The paragraph currently in the article: "The value of L can be estimated from the lifetime of our current civilization from the advent of radio astronomy in 1938 (dated from Grote Reber's parabolic dish radio telescope) to the current date. In 2007, this gives an L of 69 years." is absurd, and should read "at least 69 years" or "69 years and counting". Moreover, the number 69 has no use in an example of the equation, any more than producing the equation with all other variable values estimated based on this one-sample (our solar system) empirical method, which would yield (using the equally absurd 69 for L): fp = 1.0, ne = 1.0 (minimum), fl = 1.0, fi = 1.0, fc = 1.0 and thus: N = 6 × 1.0 × 1.0 × 1.0 × 1.0 × 1.0 × 69 = 414. I suggest either removing the paragraph concluding that using 69 is logical for L (and the 0.0000001 conclusion for N), or, add my above example of the equation, showing that using our solar system and present history (the extremely pessimistic value 69 for L), the number for N is at least 414. Anybody's thoughts? Gekritzl 22:11, 23 June 2007 (UTC)

## Different version of the equation

It seems to me that the equation with "R* is the rate of star formation in our galaxy" gives an estimate of the number of civilizations that come on line each tear.

The astronomy book "Horizons: Exploring the Universe", by Michael Seeds gives a different version of the equation:

N = N* x f_p x n_LZ x f_L x f_i x F_S (6 terms instead of 7)

where

N = number of communicative civilizations in the galaxy
N* = # of stars in the galaxy - NOT the number of new stars/year
f_p = fraction of stars with planets
n_LZ = # planets of star in life zone
f_i = fraction that evolve intelligence
f_L = fraction of planets suitable for life
F_S = fraction of star's life that has a technoligal civilization

Needless to say, with the number of stars in the galaxy in there instead of the number of new stars/year, the result is much larger. He gives the pessimistic result 0.00002 and the optimistic 10,000,000.

Also, another point - f_i is normally limited to <= 1, i.e. at most one intelligent per planet. But there could be more than one per planet. Earth could evolve other intelligent species later. Bubba73 04:36, 22 Jun 2005 (UTC)

P.S. On second thoght, I guss the two versions are pretty much equivalent. One thing, near the end of the article for the current estimates, in the body it lists f_i as 0.01 but 1E-7 is used in the calculations.

Also, it should be noted that the number of intelligent civilizations is extimated to be considerably higher than the number that we can communicate with. Bubba73 04:54, 22 Jun 2005 (UTC)

I agree with the point that it's useful to also post the verion of the equation using N* instead of R* as the initial variable in the equation. In fact, I already made this addition; I'll go back and add your reference.

I'll quibble with your point that "with the number of stars in the galaxy in there instead of the number of new stars/year the result is much larger". It's not larger, because making this change means you have to divide the lifetime of the civilization by the lifetime of the galaxy, so the end result comes out the same. Geoffrey.landis 19:18, 30 May 2007 (UTC)

## What is N, really?

Should N be the number of communicative civilizations out there (ie right now)?

As currently phrased in the article, the equation instead gives the rate at which new stars are forming which will someday house communicative civilizations times the average length of the civilizations. Of course, these civilizations take time to blossom, that the equation does not take into account the age of the galaxy should be a clear indicator that N is not the number of communicative extraterrestrial civilizations in our galaxy right now (this follows from the observation that a relatively young galaxy with the same rate of star formation would be treated identically to our own). It seems the our version of the equation somehow misrepresents the equation. Either what we are representing N as meaning should be changed, or some of what the terms represent need to be changed, though it would seem to be the former, judging from the above post. Of course we aren't the first to make this mistake, it seems to be everywhere so...

...maybe I'm wrong. Maybe there is some analysis (which is missing from the article) which shows that the age of the galaxy is somehow already taken into account. Or maybe the Drake Equation relies on the assumption of a relatively 'steady-state'(ie all terms in the equation have been the same for billions of years) galaxy, much older than the average time it takes for civilizations to evolve (i think that only in such a case would the rate*length = current number of civilizations).

...or maybe this is a valid criticism of the equation which others somewhere have pointed out. (ie the Fermi Paradox solution which posits that we are among the earliest civilizations).

Anyone know which it is? Intangir 06:17, 13 November 2005 (UTC)

## I think the Current Estimates Section Should be removed

The current estimates section should be removed or at least edited to indicate that it's mostly baloney. To the reader, it seems to indicate that current evidence suggests those values are more or less correct while in fact they just certain people's opinions of what the values ought to be. In science, there are not supposed to be experts and the opinion of one person should be given no more weight than the opinion of any other. As the links at the bottom of the document and discussion in this section show, there is wide spread disagreement over the values.

Also, I have taken several astro classes in which the Drake Equation is discussed and never heard claimed values that remotely approach for resemble those ${\displaystyle f_{i}}$. The claim neither gives a citation for the figure or explains why radiation dosage must be as low as Earth. Indeed, much of the experimentation regarding the formation of life seems to indicate that higher doses of certain sorts of radiation may actually encourage the formation of life.

Many astronomers, Frank Drake included, seem to believe that we really don't have any good ideas of any of the values other than R*. With future space missions such as Kepler and TPF we may get a better idea for ${\displaystyle f_{p}}$ and ${\displaystyle n_{e}}$. Everything else is guesswork, not science, and it shouldn't be presented like it is.

How about ranges for values instead? Are there papers that say things like "well, the laws of physics say it can't be less than X, and if it were more than Y then the stars at night would outshine the moon"? Otherwise, I think consensus figures are a good idea, as long as they have an adequate disclaimer. --noösfractal 17:32, 24 August 2005 (UTC)
Ranges are even worse unless we are going to put what the actual ranges are given the unknowns (in which case the ranges will be so large 0-1 for example as to only confuse the matter). I think a discussion of what sort of considerations are made when thinking about each number is worthwhile. I think doing an example where the numbers used are called out as being guesses (or perhaps two examples one that generates a really high value and oen a really low). Using talking about the numbers Drake used originall is also ok since that is historically accurate and not claiming any values for the number but simply stating the ones that Drake used. Dalf | Talk 06:47, 14 October 2005 (UTC)

I agree with the original poster, this section is absolute bollocks. If anything, current estimations place N above 10,000.

The estimates give no rational for their values. Shouldn't they be based on hard data and give the expected error or confidence interval or something like that. For instance with the discovery of Gliese_581_c and the information in Extrasolar_planet we now have earth, mars, venus, and Gliese 581c as the only known possibly habitable planets. (venus and mars are a stretch, and Gliese 581c has too little data to make a call on but it is a possible life supporting planet.) out of 229 extrasolar planets + 8 solar planets = an experimental ratio of 4 / 237 habitable planets per known planet. Similarly the current experimental value for the ratio of stars containing habitable planets is 2(sun and Gliese) / the number of stars. We also have an experimental value for the number of stars that contain planets(given current detection methods). I took some stats classes, but am more than a bit rusty, and of course I suspect that our current sampling method is no where near random but a trained statistician could probably come up with some numbers for the experimental means, standard deviations, errors, and the current confidence level of our testing method. I'm sure the errors would be huge(given such small sample sizes and non random sampling methods) but it would be nice to get some real statistics behind these estimations. Would anyone be willing to write down some math that would give estimates of the values for which we have some data? Anytime the experimental data gets updated the math can be rerun to give a more current estimate. --Dave1g 07:05, 28 April 2007 (UTC)

## Possibility of other life

Has the possibility that non-intelligent ET life-forms exist been documented? That would be M = N * (1 / L) * (1 / fc) * (1 / fi). We know that N >= 1, so M must be very high. I guess a flaw with this is observer bias, i.e. N could be less than 1. Neurodivergent 19:27, 11 January 2006 (UTC)

## Value of L

Doesn't the value of L (67 years) assume we'll go extinct tomorrow? L should be based on the life expectancy of the species, assuming we'll keep using this technology. The doomsday argument might be helpful, although flawed for various reasons. Neurodivergent 19:41, 11 January 2006 (UTC)

I have many problems with this equation.

1. "fc is the fraction of the above which are willing and able to communicate". These should be broken into seperate parts. The ablity to communicate and the willingness to do so are not congruent.
2. "L is the expected lifetime of such a civilization". Since it's been pointed out that technology and knowledge go with a civilization this should be changed to "expected evolutionary lifetime of a sentient species"(eg: The Roman Empire is long gone but much of their technology, culture, and knowledge is alive and well in almost all current cultures)
3. It doesnt take into account many of the smaller events here on Earth that may have led to the formation of life. Such as, the Earth's magnetic core. As well as, though probably less important, the moon's affects and the rate of rotation.

"(Note, however, that in the year 2001 a value of 50 for L can be used with exactly the same degree of confidence that Drake had in using 10 in the year 1961.)"

Is this supposed to mean 10,000 or 50,000? It doesn't make any sense if not... 82.32.65.149 10:06, 10 May 2006 (UTC)

The article is about a historical equation created by one person, right? Is there a place to argue about the details of what makes up the equation? ADyuaa 23:17, 8 January 2007 (UTC)

I don't understand why the value of L is the number of years that a civilization is capable of radio communication. Wouldn't it make far more sense that L would be the proportion of the length of the life of a star that a civilization is in radio communication mode. Thus if the average life of a star is 10 billion years and the average life of radio communication civiliations is 10,000 years (making us a very, very young civilization), the odds of any given star at a given time (assuming 100% develop radio civilizations) being a radio transmitter is 1 in 1,000,000 (10,000 divided by 10 billion). Given that the other factors in Drake are less then one and that there only 600 million stars with 5,000 light years and 10,000 looks highly optomistic as the length of a civilization and the fact that SETI has not found anybody is not very surprising. TedA 07:09, 18 August 2007 (UTC)

The units don't work out for that - given the other terms, it needs a time unit to produce a number of civilizations. However, it now says "L is the length of time such civilizations release detectable signals into space.", which works. - Darekun 03:29, 18 October 2007 (UTC)

I haven't seen anything about the end of L being due to using something better than radio as we know it now. (For example, a message using the orbital angular momentum of single photons would be a single photon - we couldn't even detect a pulse of fifty copies.) Is there nothing encyclopedia-worthy about the idea yet? - Darekun 03:29, 18 October 2007 (UTC)

Question: In mathematics, when any number of variables is multiplied together,if one of the variables equals Zero, the result is Zero. So, doesn't plugging a zero into this equation also make the answer zero? Joeylawn 05:33, 12 March 2006 (UTC)

No worries there: none of them is zero, or we wouldn't be here. -Padde 00:37, 15 April 2006 (UTC)

Someone changed the value of f_p to 10.5 from 0.5. That's impossible, f_p is the fraction of stars that have planets and so must be less than or equal to 1.

## Notation

fi = fc = 0.01 is poor notation. It suggests that fi and fc are intrinsically equal for some reason. I have fixed this. Padde 00:36, 15 April 2006 (UTC)

If anyone is interested Fermi Paradox is on peer review. I'd like to get some feedback to get it back to FA status. Marskell 10:32, 28 April 2006 (UTC)

## Literature

If I remember right, the Drake Equation is mentioned in Sphere by Michael Crichton. I don't have a copy of it to hand, so I can't check it though :'( --H2g2bob 00:43, 26 May 2006 (UTC)

## Gary Bates a reliable reference?

The following reference is currently in the article:

• {{#invoke:citation/CS1|citation

|CitationClass=book }} Can someone verify that this is a reliable reference? A quick look at the amazon (UK) reviews [1] makes me doubt it. It was added by 68.85.27.47 (talkcontribs) back on the 25 february 2006 [2]. Mike Peel 21:05, 6 August 2006 (UTC)

## Roddenberry's fudge

I think putting this fake equation in the opening section is confusing to a casual reader - in an article named for an equation, the first thing on the page that looks like a mathematical construct should be the subject of the article!

I'd suggest trimming that section out and placing it in a 'trivia' or 'culture' section, below the main content. Radagast 04:04, 4 December 2006 (UTC)

## Equation vs. Variables

Why is the Drake equation considered bad science? From what I can see, it's just a multiplication of probabilities which seem quite reasonable. People who argue with it seem to be mostly quibbling over the estimates of the variables. What's the problem with the equation itself? Maybe we currently have no way of knowing most variables, but we come closer to figuring them (at least some of them) out daily, and it becomes a good guideline of other factors to estimate (scientifically) to determine N. ADyuaa 23:10, 8 January 2007 (UTC)

## R*

Shouldn't R*, obviously, be the total number of stars in the galaxy?

No, it's correct as Drake wrote it. I added to the main section the other version of the formula, which calculates the same number in terms of N*, the number of stars in the galaxy. The two equations are identical if you define the average rate of star formation R*, to be equal to the number of stars in the galaxy divided by the age of the galaxy. Geoffrey.landis 19:31, 30 May 2007 (UTC)
I was wondering about this too. If this were the definition (R* = dN*/dt), where dt is the age (change in time) of the galaxy, shouldn't R* be defined as the average rate (or joint rate) of both formation and destruction of stars? This definition assumes that the number of stars in the galaxy N* refers to all stars that have been formed and destroyed in the history of the galaxy. Daniel.kho 11:49, 7 September 2007 (UTC)

## Move Crichton to SETI?

I added some discussion of the section with Michael Crichton's critique of SETI, but it occurs to me that this might fit better if it is moved to the SETI article, since it's really a comment about SETI, not about the Drake equation. Should it be moved to the SETI article? Geoffrey.landis 19:58, 30 May 2007 (UTC)

## Assumptions about intelligent life's form

This entire equation seems to have (at least) one really glaring fallacy. It requires making a gigantic assumption about the prerequisites for an environment to evolve intelligent life. I mean the very basis of evolution is that life adapts to the environment, not the other way around.

What's to say life has to evolve in conditions even remotely similar to earth? Or even on a planet for that matter? Intelligence could eventually evolve in some complex system that isn't even anything close to what we think of as biological, and it hardly requires ANYTHING other than a complex systems for evolution to take place on a large scale. There are surely plenty of non-planetary systems (not to mention planetary one's discounted here like gas giants) that would have enough complexity to allow evolution to potentially take place.

I tried to scan through the entirety of the talk page and didn't notice anything addressing this. I don't have anything to reference for this, but I wouldn't mind seeing it addressed in the article as well.

Jbrownos (talk) 21:20, 6 December 2007 (UTC)

This is one of the most important criticisms of the Drake equation, and is noted in the article. It doesn't make the equation wrong, however. It simply feeds into fp, ne, and fl - if you can have life in exotic environments, you just change the value of the relevant fractions and the number of possible sites. The talk page isn't usually used for stuff like this, being about the article, not a forum. Michaelbusch (talk) 21:24, 6 December 2007 (UTC)

## Criticism

Does this count as criticism? http://xkcd.com/384/ There's a wikipedia article about this webcomic, so I guess it is relevant: http://en.wikipedia.org/wiki/Xkcd --217.86.19.19 (talk) 11:03, 15 February 2008 (UTC)

I believe the criticism section is for constructive, meaningful critics, not just somebody who called the Drake equation "bullshit." The reference under the in fiction header seems appropriate. ~ Booya Bazooka 16:05, 15 February 2008 (UTC)
I'm not sure that was the point of the comic, but then I'm not Randall Munroe. But if we're going to call it criticism, then surely the alt-text is more relevant than the comic itself. --Iustinus (talk) 22:20, 15 February 2008 (UTC)
Or better yet, the artist's blog entry on the subject. Jruderman (talk) 05:02, 21 February 2008 (UTC)

There are better sources for criticism of the Drake equation than Munroe. That should be obvious. The comic is pretty funny though...I suppose there's no way to include it (even if Munroe would change the licensing), due to NPOV issues. --C S (talk) 21:47, 20 February 2009 (UTC)

## Disabled?

Looks like vandalism stemming from the xkcd webcomic. Kjl (talk) 18:53, 28 February 2008 (UTC)

## L should be proportional

Why is L measured in years? Doesn't that make the answer meaningless? The equation is supposed to tell us how many alien species are out there right now, but nowhere is "now" plugged into the equation. L should be "the proportion of the age of the universe that a civilization will be in a signal-emitting phase". This would then give the chance - at any random point in time - that there will be another civilization out there to listen to. In effect, dividing the result by the age of the universe (in years, if L is in years) cancels out the years unit introduced by measuring L in years. Obviously this makes the final number really really small, but that isn't my problem. 14:05, 5 March 2008 (UTC)

Hi! The lifetime has unit 'years' since the star formation rate is in 'stars/year'. The basic idea is that the average number around at any time is (how many form per unit time) * lifetime. So if 0.01 civilizations form every year, and they last 500 years, then there should be about 5 at any time. The unit 'years' is arbitrary and does not change the number at all. If you change to 'stars formed per second' (or fortnight, or any other unit), as long as you measure the lifetime in the same units, you get the same answer. LouScheffer (talk) 16:04, 5 March 2008 (UTC)

Ok, the unit cancels out, I see. Thanks. 79.69.241.8 (talk) 01:55, 21 March 2008 (UTC)

## Correct Figure?

Drake states here[3] that "We used to think N was about 10,000. Now I think it could be a great deal larger." Which would make the entire historical and current estimates part of this page wrong - it says N=2 or 10... This[4] wiki page gives N as ~10,000. I think someone with more knowledge should have a look at corecting that and trimming the estimates section a bit.MrFire (talk) 01:19, 11 March 2008 (UTC)

## Europa & Jupiter

Given that theoreticaly the gravitational effects of Jupiter on Europa could cause core heating leading to liquid oceans on a volcanic ocean floor. Also theoreticly enabling the development of life... The Drake equation requiring R underestimates the possibilities. Indeed any body orbiting another with suficient mass could potentialy support life. Any body in or out of a solar system of relative size could carry a moon that harbours life irrelivent of what we would consider light.. --92.234.248.209 (talk) 04:12, 24 May 2008 (UTC)JBJ UK

A further level should be added to the Drake Equation to take this possibility into account. The potential of a rogue or orbital gas giant or body providing a surragate to a orbital body is not one that can be ignored. A solar system may not be needed!

--92.234.248.209 (talk) 04:16, 24 May 2008 (UTC)JBJ

## Why is the unit of L years?

Years are an arbitrary number created by humans to coincide with our planet's patterns. Someone could argue that the unit of measurement should be seconds or minutes and if we used those numbers that would radically alter the equation. Why did Drake pick years in his equation? Maybe I missed something in the article, but it seems like a problem.24.22.28.146 (talk) 03:43, 23 August 2008 (UTC)

No, the units make no difference, since the lifetime of the civilization is also measured in years. So if the units were zlotls, which is 1/10 of a year, then the star formation rate would be 10 times lower, but the lifetime would be 10 times longer, and the anser the same. This holds for any unit of time you might choose. LouScheffer (talk) 12:58, 23 August 2008 (UTC)

## Probabilities

It appears that given the right conditions organic compounds are created by natural processes. Life (including bacteria, viruses and similar) can evolve to make use of almost any environment on Earth (and survived on the camera that stayed on the moon), however hostile. While the process by which organic compounds "become life" is presently unknown, having happened once, is likely to occur again - and, likewise more complicated life forms, and sentient beings albeit with increasingly lower frequencies.

To what extent can the "necessary criteria for life to emerge" be calculated - the orbited star's (or moon's planet's) lifespan and energy etc output (short-lived stars emitting much energy are unlikely to have life bearing planets) the relevant temperature ranges/minimum quantities of water and carbon etc? These should be easier to calculate than the probabilities (as "sufficient time has already elapsed"). Jackiespeel (talk) 17:21, 14 October 2008 (UTC)

## Contact

"Eleanor Ann Arroway ... in one scene of the 1997 motion picture based upon the Carl Sagan novel, she misstates her Drake Equation result by several billion." If I recall correctly, then she actually multiplies the Drake equation by the number of galaxies in the visible universe, so I don't think she was quite that far off in her estimate. Mike Peel (talk) 21:49, 24 December 2008 (UTC)

## Disputed neutrality: "SETI is unquestionably a religion"

This is the opinion of a popular science fiction writer. A quote like this from a science fiction writer is hardly a fact. Opinions have no business being stated as fact in wikipedia articles (See NPOV). I recommend rephrasing this, citing it as Michael Crichton's opinion, or removing it from the article. 199.111.176.245 (talk) —Preceding undated comment was added at 01:26, 13 December 2008 (UTC).

• The section in question Criticisms was in flagrant violation of many Wikipedia policies. There certainly may be a “Criticisms” section in Wikipedia articles—even widely accepted theories will have mainstream, respectable detractors and skeptics. But writing about dissenting viewpoints does not somehow create an "equal opportunities" scheme for fringe viewpoints. Over ten million Americans believe the Apollo Moon landings were faked. Notwithstanding the fact that this is a widely shared view, reliable sources state that the landings were real. Accordingly, Wikipedia strictly adheres to this view in our Apollo 11 article. Widespread, particularly famous fringe theories may be discussed and these are sometimes given their own articles (such as Apollo Moon Landing hoax conspiracy theories), but even then, Wikipedia does not depart from a mainstream view as to what is fact and what is discredited opinion.

This entire issue is, at this very moment, being discussed here on Jimbo’s talk page as a result of POV-pushing by a certain editor on Cold fusion. The cited criticism by Michael Crichton, who is a science fiction author, is a fringe view that is not shared by most reliable sources. Wikipedia is a mainstream encyclopedia that represents scientific points of views. The fact that Wikipedia always endeavors to maintain a neutral point of view does not mean that equal standing must be afforded to minority viewpoints—even if those views are those of an author who has sold many books—when those views are wildly contrary to the vast preponderance of reliable sources. Clearly, most reliable sources state that SETI is unquestionably science. The offending section has been deleted. 03:48, 30 December 2008 (UTC)

In addition to the source of the quote being a science fiction writer and not a scientist, I would add that Crichton in particular does not have great credibility compared to other science fiction writers like Arthur C. Clarke, Isaac Asimov, etc. If any of those guys were to have said SETI was a religion, you could reasonably argue that's worth including...but Crichton? Give me a break. --C S (talk) 21:42, 20 February 2009 (UTC)

## 1960

The 1960 date seems to be based on faulty information from Michael Crichton that someone added to this article. Does anyone have a source for this date besides Crichton? Drake himself said he worked on it in the 1950s, and as everyone is aware, it wasn't "published" until November, 1961. Viriditas (talk) 10:03, 2 March 2009 (UTC)

## "Sagan" equation

I admit that I know nothing about this topic, but is it fair to say it is "mislabeled" the Sagan equation? Many mathematical concepts could have diverse names. Maybe "it is also sometimes called" might be better. —Preceding unsigned comment added by 131.182.172.229 (talk) 20:55, 30 April 2009 (UTC)

## A question...

Who was it that said the chance of any intelligent life forms, much less a civilation, forming or being created, is 1 in a googol, or another really big number? Was that Drake?70.136.142.54 (talk) 03:36, 11 July 2009 (UTC)

I think the answer to the question "How many intelligent species exist in our Galaxy?" is probably zero. At least it seems that way from here. XAlpha (talk) 18:11, 3 August 2009 (UTC)

## Reasoning behind my edits

Just a quick run down of why these changes were made:

Removed:

"One reply to such criticism is that experiments by SETI scientists do not attempt to address the Drake equation for the existence of extraterrestrial civilizations anywhere in the universe, but are focused on specific, testable hypotheses (i.e., "do extraterrestrial civilizations communicating in the radio spectrum exist near sun-like stars within 50 light years of the Earth?")."

Because:

Besides having no verifiable reference, this is not a rebuttal of the criticism lodged against the Drake equation, and in fact has nothing to do with the Drake equation whatsoever. This may be SETI defending it's own internal policies but nothing in this unverified statement claims to disagree with criticism of the Drake equation. In other words, it isn't a "reply to such criticism".

Moved:

"A deeper objection ..." up to join the other criticism

Because:

This could have been misinterpreted as being part of the rebuttal to criticism where it was placed.

## Reappearance number

a history channel show recently reported that chromium stainless steel was invented in the Sung dynasty; and that the technology was lost, but re-appeared a thousand years later (Germany, 1945). this fact, and others, suggests that nr has estimable bounds. does anyone have references? -- 99.233.186.4 (talk) 20:16, 8 November 2009 (UTC)