The Drake Equation

[SkinWalker]

Most theoretical speculations about the existence of extraterrestrial life begins with the Drake Equation and the Principle of Mediocrity. The latter states, simply, that we are not special and, not being special, life such as ours must exist elsewhere in the universe.

The Drake Equation, however, is more complicated. Nearly every fundamentalist UFOist (the hardcore UFO proponent that pushes his beliefs in extraterrestrials with a religious fervor, ignoring prosaic explanations for even the most spurious UFO events and accepting with blind faith the testimony of fellow believers) uses the Drake Equation in his argument. (I've used the masculine pronoun in my description of UFO proponents twice in this paragraph because they are almost always male). Even middle ground UFO believers and skeptics refer to this equation as evidence of the probable existence of life in other parts of the universe.

But what doesn't get discussed is the fact that there are varied opinions as to the final outcome of the equation!

Let's start with the equation itself:

<img src="http://home.earthlink.net/~ctfeagans/drake.jpg">

R* = the rate at which stars are formed in our galaxy per year

f_p = the fraction of stars, once formed, that will have a planetary system

n_e = the number of planets in each planetary system that will have an environment suitable for life

f_l = the probability that life will develop on a suitable planet

f_i = the probability that life will evolve to an intelligent state

f_c = the probability that intelligent life will develop a culture capable of communication over interstellar distances

L= the time (in years) that such a culture will spend actually trying to communicate.

Drake himself viewed N as a moderate number: not too large; not too small. His argument was that communication might be possible for a moderate number of civilizations, but they would find colonization and travel expensive endeavors. Regardless of another planet's version of economic means, materials and resources would have to be expended to create ships/technology/energy to move from one place to the next.

But what the Drake Equation doesn't cover is travel to other worlds. L, as noted above, refers to the time a capable civilization will spend trying to communicate. Wouldn't actually traveling to another planet of another solar system of, potentially, another galaxy be a whole different equation?

I have some other thoughts of the Drake Equation itself, but I'll hold off for now. This just struck me as an interesting topic since it has come up several times in several threads of late.

In fact, it might be interesting to discuss each of the factors of the Equation itself in a thread such as this. "The probability that life will develop" at all on a suitable planet is an interesting topic. What about the probability that a given culture of reasonable intelligence might endure the same fallible nature as humanity: competition among each other for prestige, power, etc. that leads to war? This, after all, would be an intuitive characteristic of natural selection/survival of the fittest. What about natural disasters such as volcanoes, asteroid impacts, and disease? Why wouldn't this need to be a subfactor for f_i or f_c?

 

[Ophiolite]

Recall that Drake did not intend his equation to be used primarily to calculate the number of galactic civilisations. Rather he wanted to provide a vehicle with which to discuss the variables that might control the emergence of such civilisations. It was to provide a focus for the first ever symposium on Extra-terrestrial life. So, your suggestion that we discuss each element in the equation brings us, rather neatly, full circle.

One of the strengths of equation is that it is general, and so can readily incorporate amendments to handle new understandings and awareness of new controls, as you suggest in relation to natural disasters.

If we are to discuss this may I suggest that we do so systematically, working through one function at a time. (Recognising that many will accidentally or deliberately disrupt this.)
Let me begin by simplifying this a little, or rather preventing the addition of unecessary complexity. The question of interstellar travel: this is not an issue.

When we think in terms of populating the galaxy, we need to compare the process with our ancestors move out of a small locale in East Africa to populate the world. It will be slow, ponderous, but inevitable. The peoples at each end of the migration will not be in direct contact. There will not be a Galactic Empire, anymore than there was a global one.

Within one thousand years, and probably a great deal less, we shall have technology that allows us to emigrate viable populations within an acceptable time frame to nearby planetary systems, which we should certainly have the technology to identify and evaluate. What technology?
Not space warps or FTL, but anything that can get us 'there' within a half century or so. Too long?
No. Four options make the time incidental:
1) Generation star ships.
2) Longer life spans
3) Deep Freeze
4) Send only emrbyos

 

[Quantum Quack]

It;s worth noting that for over 30000 yeasr aboriginals here in oz remained more or less the same as they were with out significant evolution of culture or knowledge.
Evolution of life is also dependent on many variables and to evolve sentience is no exception.
In other words you may have life but unless circumstances demand it evolution of that life beyond basic survival instinct would require certain circumstancial attributes.

So whilst life may be diverse through out the universe higher forms of sentient life may be quite rare.

 

[Ophiolite]

Why is this thread in pseudoscience?

 

[SkinWalker]

Good point, but I started the thread here since many of the proponants of ETI-UFO and alien visitation cite the Drake Equation as part of the body of evidence for their claims.

I was hoping that one or more of those individuals would post their views of it here, namely Starman and as well as several others.

I plan to post some more of my own views on it, but need to set some time aside to collect thoughts, info and actually do the typing..... I'm off to a class in Mesoamerican archaeology the moment.

 

[Starman]

Good point, but I started the thread here since many of the proponants of ETI-UFO and alien visitation cite the Drake Equation as part of the body of evidence for their claims.

I was hoping that one or more of those individuals would post their views of it here, namely Starman and as well as several others.

I plan to post some more of my own views on it, but need to set some time aside to collect thoughts, info and actually do the typing..... I'm off to a class in Mesoamerican archaeology the moment.

I have not been able to write much lately I have become so involved with work, full time school and family that it leaves little time to for me to visit my favorite forum. I will make an effort to do better.

The Drake Equation is due to our recent discoveries of new solar systems. It was not all that long ago that we thought we were the only solar system in the universe. We have discovered that life dose exist in adverse conditions such as we understand them.

The DE is a formula that has an answer of <1 or but not >0. I can prove this by saying look around you and observe the evidence. Yes I am referring to life on Earth.

So if we take the astronomical figure of similar solar systems in what we perceive as our Universe then it becomes quite obvious, life dose exist elseware in the Universe. I believe that where water is present in its liquid state, life is likely to evolve, life is more common than we think.

Once we take our own planet into consideration of how long it has taken life on this planet to evolve to the state of intelligent life that we know today this could serve as a formula to solve for intelligent life elsewhere with a conservative factor of + or - 10%. Within this calculation it would be possible that intelligent life on another planet may have technowledge way beyond what is known on Earth. We have proven many times in the past that we are ignorant and naive, this is evident by pondering the thought that the only life in the universe, only exists here on Earth.

It is my theory that the Universe its self is alive and intelligent. We have discovered that life is multi dimensional and yet what we unable to comprehend may be evident in the opposite spectrum. We know allot about the smaller dimension that exists within our scope. For instance micro biology informs us about life forms that are so small that they can only be seen under an electron microscope. Dust Mites for example they are very real even though we can not see them, we are naive to contemplate that the dimensional existence ends with us, just because, we can not visualize the larger life forms that encompass everything we conceive as our existence. Life has a repetitious tendency and if we look at our own existence as just one dimension of multidimensional life then and only then will we begin to understand our Universe.

 

[Ophiolite]

Welcome back Starman. I was afraid you might have been abducted by aliens.

The Drake Equation is due to our recent discoveries of new solar systems.

No. This is incorrect. Frank Drake developed the equation for a meeting in 1961(?) at Greenbank Observatory (?) on the topic of extraterrestrial life, and in particular intelligent ETs. You will agree this was well before the recent explosion of extra-solar planet discoveries.

It was not all that long ago that we thought we were the only solar system in the universe.

In the words of Tonto, from the old Lone Ranger joke "What do you mean 'we', white man."
I have been struggling to think of a single astronomer of significance in the last two hundred years who thought this. Can you name one? Or, by 'Not all that long ago' did you mean five hundred or a thousand years ago. I'm afraid that wont work either:

There are innumerable worlds of different sizes. In some there is neither sun nor moon, in others they are larger than in ours and others have more than one. These worlds are at irregular distances, more in one direction and less in another, and some are flourishing, others declining. Here they come into being, there they die, and they are destroyed by collision with one another. Some of the worlds have no animal or vegetable life nor any water. Democritus according to Hippolytus, Refutation of the Heresies I 13 2, in Diels and Kranz, Die Fragmente der Vorsokratiker, vol. 2, section 68 A 40, p. 94. Translation from Guthrie, A History of Greek Philosophy, vol. 2, p. 405.
Source:http://www.mlahanas.de/Greeks/ManyWorlds.htm

I believe that where water is present in its liquid state, life is likely to evolve, life is more common than we think.

I agree, except why do you say 'life is more common than we think'. A large majority of people seem to think the Universe is rife with not just life, but intelligent life. A significant minority (yourself included, I believe) think that some of them are visiting this planet. The expectation amongst most of the general public, and probably among most scientists, is that life is common, and intelligent life, not unusual.
I think what SkinWalker hoped to do with this thread was to examine that contention in more detail, using the Drake equation as a guide and starting point.

We have proven many times in the past that we are ignorant and naive, this is evident by pondering the thought that the only life in the universe, only exists here on Earth.

I agree we have proven this many times in the past, but not by rejecting the possibility of life on other planets. Quite the reverse. We have tended to 'people' just about anywhere and everywhere: Venus was supposed to have a climate and biology akin to the Carboniferous on Earth; Mars had a dying civilisation pumping water form the poles to an arid equator via canals; the sun had a society that could be glimpsed occasionally through the sunspots that gave us a view into its interior! The ignorance and naivety has been demonstrated when we postulate intelligent life elsewhere, not decry it.

It is my theory that the Universe its self is alive and intelligent. We have discovered that life is multi dimensional and yet what we unable to comprehend may be evident in the opposite spectrum. We know allot about the smaller dimension that exists within our scope. For instance micro biology informs us about life forms that are so small that they can only be seen under an electron microscope. Dust Mites for example they are very real even though we can not see them, we are naive to contemplate that the dimensional existence ends with us, just because, we can not visualize the larger life forms that encompass everything we conceive as our existence. Life has a repetitious tendency and if we look at our own existence as just one dimension of multidimensional life then and only then will we begin to understand our Universe.

Right....... Where does this 'larger' life form reside? Where is the 'seat of intelligence' of the Universe. How do we test your theory?

 

[Starman]

Welcome back Starman. I was afraid you might have been abducted by aliens.

No. This is incorrect. Frank Drake developed the equation for a meeting in 1961(?) at Greenbank Observatory (?) on the topic of extraterrestrial life, and in particular intelligent ETs. You will agree this was well before the recent explosion of extra-solar planet discoveries.

You are correct what I meant was that the recent discoveries have had a signifigent impact on the Drake Equation. Drake was involved with SETI and he worked on the equation to help further their cause.

In the words of Tonto, from the old Lone Ranger joke "What do you mean 'we', white man."
I have been struggling to think of a single astronomer of significance in the last two hundred years who thought this. Can you name one? Or, by 'Not all that long ago' did you mean five hundred or a thousand years ago. I'm afraid that wont work either:

What you are describing here is the exception to the rule. The astronomers were the brave few in the first century world who were brave enough to challenge the Church and its teachings whom the majority of the population followed. Only the brave like Bruno would stand up against the church and it's teachings he was labeled a heretic and burned at the steak.

I agree, except why do you say 'life is more common than we think'. A large majority of people seem to think the Universe is rife with not just life, but intelligent life. A significant minority (yourself included, I believe) think that some of them are visiting this planet. The expectation amongst most of the general public, and probably among most scientists, is that life is common, and intelligent life, not unusual.
I think what SkinWalker hoped to do with this thread was to examine that contention in more detail, using the Drake equation as a guide and starting point.

We are a minority as for believing in ETL. I would be surprised, to find we are in error.

I agree we have proven this many times in the past, but not by rejecting the possibility of life on other planets. Quite the reverse. We have tended to 'people' just about anywhere and everywhere: Venus was supposed to have a climate and biology akin to the Carboniferous on Earth; Mars had a dying civilization pumping water form the poles to an arid equator via canals; the sun had a society that could be glimpsed occasionally through the sunspots that gave us a view into its interior! The ignorance and naivety has been demonstrated when we postulate intelligent life elsewhere, not decry it.

Yes it goes in both directions to achieve moderation is the goal. Just because life may have existed on other planets in our solar system in the past which is highly possible doesn't mean life ever existed on our Star the Sun.

Right....... Where does this 'larger' life form reside? Where is the 'seat of intelligence' of the Universe. How do we test your theory?

I would look at the dust mite and ask; is it aware that it lives on a living creature at times? Or is where the Dust Mite exists, just a barren plane of existence with a dynamic topography.

Now let us examine how the structures of the Universe resemble the building blocks of life. Life is nothing more than the byproduct of organized energy. The Universe resembles the multi dimensional properties of matter.

The Solar System resembles that of an Atom. Stable Solar system are of stable elements and unstable Solar systems are of unstable elements. Galaxies resemble that of a molecule. When we look at the structures of superclusters they resemble cell structure and so on.

Now the latest membrane theory sudjests that instead of the big bang there was a big slap, when two membrane universes collided our Universe was created.

Well if you take this hypothesis one step further and say that our Universe was the result of cell division, is this the answer to the expansion of the Universe?

If this theory is correct then the Universe should have periods of expansion at variable rates that do not make sense to the laws of physics, at some time in the future the cell our Universe will continue to divide and to grow until its own biological clock runs out.

Just a side note, what we perceive as solid mass is more space than actual matter. Think about it, even in water there is far more space than mass. So hypothetically if you existed in a realm where the molecules were the size of Galaxies and you were in a pool of liquid water, made of the same basic structures as we understand them only on a galactic scale in size, (i.e. a binary star system resembles that of a giant hydrogen atom a nuclease and one orbital.)

Ok now again if you existed in water constructed of molecules, the size of Galaxies, would the observer smaller than a atom of the structure notice or even be able to observe the matter? Or can the observer only sense space within the element?

 

[SkinWalker]

The Solar System resembles that of an Atom.

Only with rudimentary models found in earlier textbooks. The Heisenburg Uncertainty Principle doesn't apply to planets, as we can predict where they are now as well as where they'll be in time/space... can't do that with an electron.

 

[Starman]

Only with rudimentary models found in earlier textbooks. The Heisenburg Uncertainty Principle doesn't apply to planets, as we can predict where they are now as well as where they'll be in time/space... can't do that with an electron.

If the observer were the size of the atom, I would like to think he could predict the orbit of the electron.

Also when two orbiting bodies collide in a solar system do they not release energy. Could this not be compared to a photon?

It could be, that a photon is the result of a collision involving two or more electrons.

 

[Gambit Star]

I personally think Drake had to many whiskeys that night.

 

[SkinWalker]

In the Drake Equation, R* is often considered to be the best understood or easiest to deal with, since we have some solid data regarding the formation of new stars in the universe, how the coalesce from intergalactic clouds of hydrogen, helium, methane, ammonia, dust grains, etc.

We also know that only a fraction of these stars will be suitable for providing habitat for intelligent life or, in many cases, any life. The environment of the star itself has to be conducive for forming planets, these planets need to be within certain parameters of temperature and need to be in existence long enough to allow life to evolve, etc.

Life is certainly possible, even probable, in extreme environments, but conditions would need to have qualities of stability in order to allow intelligent life to evolve.

Current theories are that stars that have 1.4 times our own Sun's solar mass or more have a life cycle that is too short to produce viable planets. There is also an age qualification for stars, the older ones would have difficulty producing planets because of the lack of heavy metals produced in supernovae. These only eliminate about 1% of the stars from the equation to this point, but other factors have to be considered as well.

The proliferation of binary systems of stars eliminates more of the total due to continually shifting gravitational stresses, extreme temperature shifts, etc. that interfere with a stable planetary system forming. When we look at the Earth, the stability of the orbit, and the delicate nature of the zone we live it is unique. Otherwise we would note proliferations of life on other Solar worlds (not that it doesn't exist, but remember we're talking about civilizations not simply microbes). Apparently, at least half of the stars that aren't too old or too big belong to binary systems.

After including this as well as other factors, like stars that are too small, reside in regions of their galaxy that are deleterious to life -such as near the galactic core, and then R* goes from about 10 stars per year to much, much less. Shklovskii and Sagan (1966) estimated a rate of 10 stars per year, but Rood and Trefil came up with rates between 0.15 per year in the high range, and 0.005 per year in the low range -depending on what criteria was adhered to.

The vast majority of stars in the universe present very inhospitable environments to organisms if they have planets at all.

References:


Dole, S. (1970) Computer Simulation of the Formation of Planetary Systems. Icarus. Vol. 13, pp 494-508.
Hart, M. (1979). Habitable Zones About Main Sequence Stars. Icarus. Vol. 37, pp 351-357.
Rood, R., and Trefil, J. (1981). Are We Alone? The Possibility Of Extraterrestrial Civilizations. New York: Schribner's.
Shklovskii, J., and Sagan, C. (1966). Intelligent Life in the Universe. San Francisco: Holden-Day

 

[Starman]

In the Drake Equation, R* is often considered to be the best understood or easiest to deal with, since we have some solid data regarding the formation of new stars in the universe, how the coalesce from intergalactic clouds of hydrogen, helium, methane, ammonia, dust grains, etc.

We also know that only a fraction of these stars will be suitable for providing habitat for intelligent life or, in many cases, any life. The environment of the star itself has to be conducive for forming planets, these planets need to be within certain parameters of temperature and need to be in existence long enough to allow life to evolve, etc.

Life is certainly possible, even probable, in extreme environments, but conditions would need to have qualities of stability in order to allow intelligent life to evolve.

Current theories are that stars that have 1.4 times our own Sun's solar mass or more have a life cycle that is too short to produce viable planets. There is also an age qualification for stars, the older ones would have difficulty producing planets because of the lack of heavy metals produced in supernovae. These only eliminate about 1% of the stars from the equation to this point, but other factors have to be considered as well.

The proliferation of binary systems of stars eliminates more of the total due to continually shifting gravitational stresses, extreme temperature shifts, etc. that interfere with a stable planetary system forming. When we look at the Earth, the stability of the orbit, and the delicate nature of the zone we live it is unique. Otherwise we would note proliferations of life on other Solar worlds (not that it doesn't exist, but remember we're talking about civilizations not simply microbes). Apparently, at least half of the stars that aren't too old or too big belong to binary systems.

After including this as well as other factors, like stars that are too small, reside in regions of their galaxy that are deleterious to life -such as near the galactic core, and then R* goes from about 10 stars per year to much, much less. Shklovskii and Sagan (1966) estimated a rate of 10 stars per year, but Rood and Trefil came up with rates between 0.15 per year in the high range, and 0.005 per year in the low range -depending on what criteria was adhered to.

The vast majority of stars in the universe present very inhospitable environments to organisms if they have planets at all.

References:


Dole, S. (1970) Computer Simulation of the Formation of Planetary Systems. Icarus. Vol. 13, pp 494-508.
Hart, M. (1979). Habitable Zones About Main Sequence Stars. Icarus. Vol. 37, pp 351-357.
Rood, R., and Trefil, J. (1981). Are We Alone? The Possibility Of Extraterrestrial Civilizations. New York: Schribner's.
Shklovskii, J., and Sagan, C. (1966). Intelligent Life in the Universe. San Francisco: Holden-Day

What if Space is only relative to the observer. Life may exist on a Galactic scale that we can not comprehend.

If the observer were small enough to stand on the Nucleus of an Atom and if the Nucleus were the size of the Earth, the observer would perceive the mass under the observers feet, the rest would appear to be space to the observer.

The observer may be able to see orbiting electrons and light from other nearby atoms, however the observer could not conceive what the structure was that the atom was apart of.

I would hypothesize that as with most things in nature speed is related to size. The smaller the faster.

Space time as we understand them, is a different frame rate in this case relative to the observer the electron would slow in its orbit due to the observer being accelerated to a faster time frame rate at this level of existence. As the observer is accelerated the motion of lets say an atom of Uup 115 the orbital electrons would appear to slow due to this acceleration of the observer.

As for the forces of attraction within the Nucleus, they act as gravity on a micro level to prevent our observer from flying off into the void around the atom.

For now when I refer to the other atoms in the distance being observed as light I am referring to light in the inferred part of the electromagnetic spectrum.

To this observer what we perceive as mass is observed as space and not a solid entity.

Science can be complicated if that is what one wants to do, complicate things. Because I lack the math and chemistry to complicate things I try to use general observations to apostolate conclusions.

1. Nature has shown to be repetitive in the grand order of things.

Originally Posted by geistkiesel
Starman,You will be interested in knowing that that electrons, for instance are always measured as point particles. The wave nature of the electrons is an ad hoc temporary modification of electron motion to expain two - hole diffraction. You can get a wavy ethereal glob of mass through two holes easier than getting a single particle through two holes. The wave-partickle duality of the electron is just another slothfully constructed confession of ignorance. 'They' can't see that the electron is a complex structure with parts and sub-parts. The standard model does not recognized no considered the possibility that the e;ectron has the intirisic ability to generate its own spin state ,+,1./ Thuis isn;t doens as acoin flip, the spin state just idly keeps flippin to the iopposite state +-+-+-+-+-+- These states are what detemine the direction taken by an electron when transitioning thouigj stern-gerlch magnetic field/gradient volumes, but I would be prepared to expel predictons of simple spherical volume morphology for protons, neutrons and so on, and especially when boiund in atomic structures. For all the quarks and other strangeness predicted the probabilities are more likely that the arributes assigned to quarks for instance as a 'particle' is a definable system for process of storing internal energy such that the particle doesn't blow up and become a mini-big-banger.

Geistkiesel ”


This is indeed interesting, not to mention where do photons come from? Light has mass due to its ability to assert a force. The electron omits this mass so therefore a photon is one such sub-particle of the electron.

Energy also contains mass due to the fact that when it is compressed it takes the form of a solid object
2. The very small is related to the very large.
Ok, the idea is to link quantum physics to general relativity theory. The system of the atom is to similar to that of a solar system, this should not be ignored. Also if a body of mass collides with an orbital in the solar system will it not change the orbit of the object? Light is mass and energy and the effects of such interactions are the same at the atomic level as the planetary level. If the sun in our solar system were to receive an impact by a body of the same mass as the sun would it not release a great deal of energy similar to splitting the atom?


3. What we observe as space, is some kind of mass on a galact

ic level. If an observer is the size of the universe, the universe might appear as a solid object.

4. The multidimensional universe is the existence of mass of different sizes. Time is related to the size of mass the larger the body of mass the slower the passage of time the smaller the body of mass the faster the passage of time.

5.Time is affected by what we describe as gravity. This force has different wave properties at different mass levels. The strong force is an identical type force to gravity only much stronger. As we all know time slows as you travel from the source of attraction of gravity. Time increases as you travel closer to the source. The stronger the force, the faster the passage of time as related to a control frame of reference.
Ok, that is fine for the Bohr model of an atom. However, the Bohr model is merely a simplification. It is no longer acepted as the way an atom truly behaves. The electrons are not flying about in strictly defined orbits, but are in fact flying about everywhere. True, there are electrons that have specific energies and spins, but they do not stay within any particular orbit around the nucleus. This nullifies the entire solar system analogy. It cannot be ignored that at such small scales, matter behaves (more noticeably) in the ways described by quantum theory. If you want to get technical all matter obeys those rules it is simply much less apparent in the macroscopic world. ”

Ok would you agree that the nucleus of an atom is spherical in shape?

Why do so many place so much on the irregular orbit of the electron?

Our solar system is stable with orbitals (planets) in nearly circular orbits.

Solar Systems with elliptical orbital have many changes that effect the path of other orbital when they come too close to one another.

This could explain the irregular orbit of the electrons.

The focal point of this thread is; what we perceive as space could be part of a solid structure of mass, it is relative to the observer.

If the observer is too small or large in size, what the observer can conceive is limited.

 

[SkinWalker]

What if Space is only relative to the observer. Life may exist on a Galactic scale that we can not comprehend.

Your post was interesting, but I would say that there are an infinite number of hypothetical realities, but I think it's only useful to discuss the reality that we can measure or examine. Once observations of the relative nature of space can be tested, then we should enter them into discussions such as this.

I don't say that to be close-minded, but more to maintain some parameters of discussion. The Drake Equation itself, is that attempt. A boundless, post-modernist discussion would eventually degrade into a, "what's the point?" attitude.

 

[Starman]

Your post was interesting, but I would say that there are an infinite number of hypothetical realities, but I think it's only useful to discuss the reality that we can measure or examine. Once observations of the relative nature of space can be tested, then we should enter them into discussions such as this.

I don't say that to be close-minded, but more to maintain some parameters of discussion. The Drake Equation itself, is that attempt. A boundless, post-modernist discussion would eventually degrade into a, "what's the point?" attitude.

I agree this subject goes beyond this thread. Yet it is related by the fact that Life as we understand it may exist at levels beyond our comprehension.

And as you stated there is not enough knowledge about my hypothesis to consider it even close to reality yet I have always wanted to state what I thought of our existence.

The whole Religion thing just doesn't do it for me.

The Drake equation is a good example of a formula that will be more useful in the future than at present. As we make more discoveries it will prove to become more valuable.

The equation is very general in nature, I have looked a ways to improve it and have concluded that it is the best mathematical expression for projecting the amount of intelligent life in our Universe.