Not anymore than A2 + b2 = c2. Both equations do not have values plugged in, however, both are valid equations.
Aw we learn more about the universe, the numbers can and will be filled in. When I was in school, I remember a professor telling me he never expected up to discover planets outside of our own solar system since the distances were so vast and the parent star would "drown out" and light being reflected from those planets.
Now we suspect planets are the norm instead of the unusual. So again comes the naysayer who says, "we don't see systems just like ours". Heck we are only beginning to search (and it is an awfully big universe).
So why do we search?
IMHO, We search because that is in the nature of the human spirit. So how do you measure the human equation? I think back to all the threads where I heard over and over the incessant argument that the government should not fund space exploration or SETI, or particle physics, etc.
Exploration is who we are! Without that drive to push the frontiers of knowledge, science, arts, literature, engineering, etc. we would never have left the trees in the first place. This is the reason I get so upset when I see the loss of a museum or library. We as a species are diminished when our heritage (the who we were/are) is forever lost. All of us are going to die someday, but our writings, art, philosophy, music, discoveries, etc. will live on long past our short-lived selves. I am reminded of a quote from the movie the Dish; it makes our spirits soar.
I also hear this question quite often; if they are out there, why have we not heard from them of seen evidence for them?
We are all quite aware just how far it is "out there". With the speed of light being the fundamental limit for baryonic matter, it will be next to impossible to travel between the stars (at least under our current level of physics knowledge). So the universe may be populated with little isolated bits of intelligence all wondering if any other species are out there.
Just in the past few years we have advanced far enough in our technical prowess to both "announce" to the universe we are here (radio waves) and to receive the same from another species. With that in mind and the speed of light being a constant in a vacuum, the expanding sphere of radio noise heralding our presence has only gone about 60 light years or so. So there may be an entire galactic community out there but our "knock" hasn't yet hit the door so to speak.
Also there may be thousands of intergalactic signals bouncing around but we have not yet found the right frequency or built sensitive enough equipment to receive them. We really are kind of in the back woods of this galaxy 2/3rds the way down one of the spiral arms. So have we been visited? I don't think so, How would a race even know we were here to come and visit us with out us heralding ourselves first. So far, radio is the only way we have done that, and its not gotten very far out there yet.
So on to SETI:
While SETI is indeed a long shot, we do have one example of a species that sends signals out into interstellar space: ourselves. This means that intelligent life in the universe is possible and proven. Further, it is possibly detectable if that intelligence uses any form of EM radiation to communicate as we have for years. It is therefore not without merit.
Most SETI searches are not looking for a radio signal "beamed" directly at us. They are looking for that expanding shell of radio noise that a tool building civilization would produce, not unlike our own. The assumption (and yes I do realize its an assumption) is that electromagnetic energy (EM) is the most efficient means of conveying information over vast distances. Gravity waves may also accomplish the same thing, however, we do not yet have that capability. So this leaves us with EM.
I personally believe for a race to become technologically advanced, it must have the ability to store and convey information over long distances. Since radio waves (I am including any EM in this such as RADAR, TV, microwave, etc.) are still the best method for accomplishing this, any other race would use/do the same. For about the past 60 years we have been isotropically radiating EM across a huge RF spectrum into outer space. What SETI is looking for, is another species that is doing the exact same thing we are; unintentional radiation of EM into outer space.
So, why have we not seen anyone yet?
First: There are two real sources of noise that limits the radio astronomer's ability to search for very weak signals. The Galactic noise halo interferes with us below 1Ghz and noise due to earth's atmosphere interferes with us above about 10Ghz. This pretty much keeps all SETI searches (at least radio ones) between 1 and 10Ghz. Between the two, the noise is around the 2.7K Cosmic Microwave Background from 1.4 to 7Ghz. This is why most of the SETI searches are around the frequencies that the OH (hydroxyl) and H (hydrogen) molecules masers emit. This is the so-called water hole. OH H (tell me scientists don't have a sense of humor)
Second: Where do we look? There are literally millions of stars within reach of our radio telescopes. This is quite an undertaking. So we scan large portions of the sky in hopes of seeing that very faint signal that tells us we are not the only species pushing our way up the tool building ladder.
Will SETI ever be finished even if we here nothing?
Not finished per say: But in total absentia of any confirmed signal we will have a better understanding of just; a) how hard the search will become or b) the possibility we really are alone.
However, if we do find that extremely narrowband signal heralding the fact we aren't the only intelligence in this vast universe, I think it would further our understanding of our relationship with this universe. With C being the fundamental limit (speed) of communication, "talking" with another race would be quite impracticable. Not much of a conversation if you have to wait 3000 years for a reply to your hello. Still we would know as a species that we were not the only organisms contemplating the existence of the universe. Finding another intelligent race would definitely redefine our place in the universe.
I remember a story, I think it was by Asimov, that had as a plot point the difficulty of communicating with someone on Neptune. With the 8-hour turn around time, it was impossible to get anything done by phone. The protagonist's mother, by contrast, had no trouble with it; she just chatted away with her pals on Neptune all day long. Her secret was just to talk and to listen by periodic turns. In principle it takes eight hours to get a response to a question, but if you both just keep talking, you find that many of the answers show up ahead of time anyway.
... the noise is around the 2.7K Cosmic Microwave Background ...
A sneaky bunch of aliens would use that frequency.
Thank you again for reminding us of why you are truly one of FR's finest!
It is not the critic who counts: not the man who points out how the strong man stumbles or where the doer of deeds could have done better. The credit belongs to the man who is actually in the arena, whose face is marred by dust and sweat and blood, who strives valiantly, who errs and comes up short again and again, because there is no effort without error or shortcoming, but who knows the great enthusiasms, the great devotions, who spends himself for a worthy cause; who, at the best, knows, in the end, the triumph of high achievement, and who, at the worst, if he fails, at least he fails while daring greatly, so that his place shall never be with those cold and timid souls who knew neither victory nor defeat.
Theodore Roosevelt, "Citizenship in a Republic"
Speech at the Sorbonne, Paris, April 23, 1910
"Not anymore than A2 + b2 = c2."
This is a stunningly poor analogy.
We know exactly what a and b are physically. We further know that they are the only factors influencing c. And we have a darn good understanding of geometry.
The Drake equation is an assumption, no more, no less, unlike The Pythagorean Theorem you mention.
N = N* fp ne fl fi fc fL
The first two factors are measurable. The next two potentially measurable in the future, though non trivial to ascertain. The rest are, as mentioned, wild assumptions. And as yet another flaw, there is little reason to believe that this equation contains all of the important factors involved in such a determination, even as mere assumptions.
For example, does galactic location make a difference? One would think so, though again this is an assumption. Older stars and those near the galactic center would be by terran standard less likely to harbor life. Should there not be an N1, N2, N3, ... Nn for each generation of star? And also an Nc, Na, No for stars near the center, in the arms, and "other" in our galaxy?
And frankly we know exactly one case of life, let alone intelligent life, developing. The effort to draw conclusions with such a limited data set is bound to fail. Or, to take a reasonable comparison, the Drake Equation is rather the equivalent of studying but one human being and deriving a set of equations explaining all human behaviour.