In 1961, astronomer Frank
Drake proposed a method of estimating the number of
civilizations in our Galaxy that could be detectable from
Earth. He wrote it as an equation, but it may be more useful
to think of it as a series of questions: How many stars are
born every year? What fraction of them have planets? How many
planets does each such star have? What fraction of those
planets can support life, and of those, how many planets
actually give rise to life? What fraction of those living
planets give rise to intelligent beings? And of all those
planets with intelligent beings, what fraction will produce
radio transmissions that would allow us to notice them, and
how long would they continue to transmit them?
These questions have definite answers; we
just don't know what most of those answers are. But the
answers to these questions are not beyond our reach. As we
build better and better telescopes, and as we learn more and
more about our own origins and that of our planet, the
answers to these questions will gradually be revealed. We may
know many of the answers within the next ten to twenty years.
Even back in 1961, it was obvious
that these were answerable questions, so a group of
scientists and engineers gathered together to discuss the
possibility of using astronomical techniques to search for
evidence of intelligent life beyond the Earth. They
have become known as The Order of the Dolphin.
They made educated guesses about the
answers to each of these questions, and tried to place
reasonable upper and lower bounds on the value of each
corresponding term of the Drake Equation. Since they had
little direct observational evidence to support their views,
they had to rely on their considerable experience in the
fields of science relevant to these questions, such as
astronomy, chemistry, and biology. And although their
estimates were based primarily on theoretical arguments, they
are still widely used almost four decades later; all our
explorations since then have not led to any major
disagreements with the ranges of values they determined.
The Order of the Dolphin chose to
concentrate on searching for civilizations that are similar
to our own, those that reveal their presence by making radio
transmissions. But no attempt was made to ask questions about
civilizations that are much older than ours, because such
questions did not seem relevant to the astronomical searches
they were proposing, and perhaps because at that point our
collection of known examples drops from one to zero.
Soon we will be making increasingly
accurate measurements of many of the terms, removing much of
the uncertainty. So it seems appropriate to investigate ways
of going beyond the original Drake Equation, to make educated
guesses about the civilizations that may have already passed
beyond the technologically adolescent phase where we are now.
This page includes a calculator, where you
can try out your own educated guesses about the answers to
each of the questions considered here, and see where your
guesses take you.
Popular values have already been entered in
all of the boxes, but you can change any or all of them.
Enter values as decimal digits, with or without a decimal
point. Be careful; if you enter zero for any term in the
Drake Equation, you are saying that we ourselves cannot
You can also enter values using floating
point notation: for example, 2e-3 = .002, 5e6 = 5000000, and
If you type in something that isn't a
number, or leave a box blank, your browser will probably give
you some kind of error message.
If you are using an older browser, the
calculator may not work. But the page should look very much
the same, so you can do the calculations manually.
This page contains many links to other
pages. If you follow any of these links and then come back to
this page, your browser might forget any numbers you may have
already entered here, and if so, you would have to re-enter
them. Links that lead away from this page (and which may open
a separate window) are marked like this:
This is the equation Frank Drake wrote on the
blackboard in 1961:
N = R fp
Each term to the right of the equals sign
represents one of the questions we asked earlier:
R is the rate of star formation within the
Galaxy, expressed in stars per year;
fp is the fraction of stars that form planets;
ne is the average number of planets each such
star possesses, which are capable of supporting life;
fl is the fraction of those planets where life
fi is the fraction of life-bearing planets
where intelligence arises;
fc is the fraction of intelligent life-bearing
planets where intelligent beings develop the ability to
communicate beyond their own world; and
the length of time, in years, that such communications remain
By estimating values for each of these
terms and multiplying them together, one arrives at:
the estimated number of detectable civilizations.
We begin with:
How many stars form each year within the
Milky Way Galaxy? The Order of the Dolphin estimated that
about one new star is born every year. This is an observable
quantity, and astronomers are reasonably certain that this
value is close to the correct one, but many tend toward
higher values, perhaps ten to twenty stars per year. More details...
Your estimate (stars per year):
What is the fraction of stars that form planets? The Order
estimated between one fifth (0.2) and one half (0.5); until
recently, there was little observational data to help with
this number, and there still isn't very much. (And for all
the terms after this one, there is essentially no data, so
other methods were used to arrive at numbers.) More details...
Your estimate (must be between 0 and 1):
How many planets does each stellar system contain, which
are capable of sustaining life? The Order estimated between
one and five. However, recent results indicate that our Solar
System may be uncommonly rich in the heavy elements that are
necessary for chemistry-based life-forms, so perhaps a lower
number may be appropriate. More
What fraction of those planets actually develop life? The
Order came to the conclusion that all planets capable of
sustaining life will eventually develop life, so they said
this number is around one. More
On what fraction of life-bearing planets do intelligent
beings arise? The Order agreed, all of them. However, recent
results relating to the role of orbital resonances in
planetary stability may point to a lower number. Also, some
researchers think that intelligence may often take longer to
develop than the amount of time available during the lifetime
of the parent star. So it might be reasonable to choose a
number lower than 1. More
On what fraction of planets carrying intelligent beings
will those beings develop the ability to communicate their
existence to others? (Note that this includes planets where
beings unintentionally announce their existence, by beaming
episodes of soap operas and such into the cosmos, as we do.)
The Order estimated this number to be between 0.1 and 0.2. More details...
Finally, what length of time, in years, will such
communicating civilizations typically remain detectable? This
period of time is not thought to be indefinitely long, even
if a civilization does not destroy itself. If we succeed in
running fiber-optic cables to every home on Earth, and
switching all our mobile communications to spread-spectrum
digital, we would become much harder to detect from far away.
The Order estimated between 1,000 and 100,000,000 years. More details...
Now, click this button to multiply these numbers together:
N = detectable civilizations.
The lower and upper bounds for all
these terms, as estimated by the Order of the Dolphin, lead
to the result that the number of detectable civilizations in
this Galaxy may only be a few dozen, or may be many millions.
These results, and the results that more recent investigators
have gotten, have led to a series of very sophisticated searches for evidence of intelligent
life beyond the Earth. Almost all of the funding for these
efforts comes from the pockets of private individuals,
companies, or philanthropic institutions.
The Drake Equation, as originally
envisioned, was intended to justify efforts to search for
evidence of extra-terrestrial intelligent life (SETI) by means of radio astronomy. But
we can go beyond its original use.
Consider what happens if we ignore the last term, L. Multiplying the other numbers
together, we get:
= R fp ne
where we define Rc
as the rate at which communicating civilizations arise in
this Galaxy, expressed as the number of civilizations per
year. Your estimates give this value:
new communicating civilizations arising every year.
Now, let us define an explorer civilization as
one which achieves the ability to communicate, and then
spreads beyond its home world, and continues to exist in one
form or another indefinitely after that. Let us then define
the fraction of all communicating civilizations that become
Optimists generally estimate this number equals one. More details...
Your estimate (must be between 0 and 1):
Now define Rx =
as the rate at which explorer civilizations arise,
expressed as the number of explorer civilizations arising per
Now click this button, so we can do some more figuring:
By your estimates, then:
explorer civilizations arising every year.
Therefore, the number of explorer civilizations that have
arisen in the last billion years is
and the number of explorer civilizations that have arisen
in the last million years is
[Note: here, we are using the American terminology, where
one billion = 109 = 1,000,000,000.]
By definition, explorer civilizations last forever, so all
of the ones that have arisen in the past are still in
existence; therefore, if we subtract these two numbers, we
get the number of explorer civilizations between one million
years old and one billion years old:
[Note to mathematically sophisticated readers: Of course,
we can use calculus to get where we are going here, but this
page is intended to be intelligible to people who aren't
comfortable with calculus.]
So the explorer civilizations between one million years
old and one billion years old outnumber the younger ones by a
factor of 999.
In other words, 99.9% or more of the explorer
civilizations in the Galaxy are more than one million years
old. (Unless, of course, you are a real pessimist, and
entered a zero in one of the boxes above.)
And as long as you assume that Rx
has not changed much in the last few billion years or so,
which seems like a fairly reasonable (but not necessarily
correct) assumption, then, by the same reasoning, most of the
explorer civilizations in the Galaxy should be more than one billion
From all of this, we can conclude that
the probability that the Earth will be discovered by a
relatively young explorer civilization, before being
discovered by old ones, is essentially zero. We can also
conclude that any extraterrestrial civilizations that exist
nearby, if there are any, are probably much older
than we are. It is highly improbable that there are any
nearby civilizations that are roughly contemporary with our
own. More details...
Let us go further. It seems safe to assume that explorer
civilizations will be even more aware of their surroundings
than we are. After all, our awareness of the Galaxy around us
is limited by the relatively primitive state of our observing
devices; civilizations that have much more experience in
space should be able to build much better telescopes.
We can already monitor the nearest stars for evidence of
the use of radio communications, and hopefully we will
someday be able to monitor the nearest stars for signs of
non-intelligent life as well. This should be possible because
living organisms, even very primitive ones, sometimes have
the ability to alter the atmospheres of their home planets;
such alterations might be detectable from great distances by
using instruments called spectrographs, mounted in very large
In the foreseeable future, we could build space telescopes
large enough to monitor the planets surrounding thousands of
nearby stars for signs of life, and it seems reasonable that
older explorer civilizations will be able to monitor many
more than this. Since we have shown that most explorer
civilizations could be many millions of years old, it is
conceivable that each such civilization could monitor a
significant fraction of the stars in the Galaxy.
Let us define yet another term:
the number of stars that are monitored regularly by each
explorer civilization, on average.
This number ought to be rather large, so just guess... The
default value in the box below is one million stars. There
are about a million stars within 400 light-years of us, and
this distance represents less than 1% of the diameter of our
Galaxy. Most of the bright stars you can see in the night sky
are less than 400 light-years away. More details...
Enter your estimate:
nmx = stars
monitored regularly by each explorer civilization.
Finally, how many stars are there in the Galaxy?
Astronomers say between 100 billion and one trillion. [As
before, we are using one trillion = 1012 =
Let us define:
the number of stars in the Galaxy.
Enter your estimate (must not be zero):
ns = stars
in the Galaxy.
Once more, click this button to recalculate:
Now earlier, we figured that there should be about
explorer civilizations that have arisen in the last
billion years. Let us use this number as the number of
explorer civilizations in the Galaxy, for the purposes of the
following calculations; it simplifies things somewhat. Let's
call this number:
=1,000,000,000 Rx =
number of explorer civilizations.
If you assume that explorer civilizations are evenly
distributed among the stars, then we can estimate how many
explorer civilizations are monitoring each star. It's just
the number of explorer civilizations in the Galaxy, times the
number of stars monitored by each, divided by the number of
stars in the Galaxy:
/ ns = explorer
civilizations monitoring each star.
So we have reached the conclusion that we are being
simultaneously monitored by that number of explorer
civilizations. Assuming, of course, that your estimates are
Note that the Earth's atmosphere
exists in a state of chemical disequilibrium, and has done so
for a significant fraction of its existence. If anyone out
there bothers to examine it spectroscopically, which is
possible to do from a considerable distance, it would stick
out like a sore thumb. So if the number above is much greater
than one, it would seem to imply that somebody out there has
known for a long time that there is life on our planet.
Let us take the above reasoning further. If we define nvx as the number of stars
that are actually visited by each explorer
civilization (in person or robotically or whatever), then a
similar formula will give an estimate for the number of
explorer civilizations that would be expected to visit our
Solar System. More
nvx = stars visited
by each explorer civilization.
One final time, click this button to recalculate:
Now we can estimate how many explorer civilizations visit
each star, on average. It's the number of explorer
civilizations in the Galaxy, times the number of stars
visited by each, divided by the number of stars in the
/ ns = explorer
civilizations visiting each star.
Note that this is averaged over all stars. Of course, some
stellar systems may be considered relatively boring, because
their stars are doomed to blow up in a few million years or
because they don't have any interesting planets, and they may
not be visited very often. So the number of explorer
civilizations that visit interesting stellar systems
(like ours) may be larger than this.
In addition, recall that we limited ourselves to explorer
civilizations less than one billion years old, so the true
number may be larger still.
Although your estimates may indicate that we could have
many visitors, remember that these visits could be
distributed over a very long period of time. A large
numerical result does not imply that visits are happening
now, but may imply that many visits have taken place in the
To summarize, if we define Nx
as the number of explorer civilizations (of age ax years or
less) that monitor/visit each star, and nx as the number of stars monitored/visited by
each such civilization, we get
= R fp ne
fc fx ax
nx / ns
For a wide range of numbers that are considered reasonable
by researchers in relevant fields, this equation yields
results that are larger than one, implying that we should
already be under surveillance, and that we should have
already been visited. But it is important to recognize that
this equation may greatly underestimate the actual
numbers, because it does not take into account the
possibility that some explorer civilizations might begin to
multiply exponentially when they reach a certain age...
to "Are We Alone?"
to "A Conversation"
More details follow:
Drake Equation: Parameters
These are the parameters used in the Drake Equation:
R is the rate of star formation
within the Galaxy, expressed in stars per year.
This is the only parameter in the original
Drake Equation that is known with any accuracy. Astronomers
and astrophysicists have built up a detailed picture of the
life cycles of stars, and stars can be observed throughout
most of the stages of stellar life. The Order of the Dolphin
assumed that this number was around one star per year, but
recent results indicate the true value may be as high as ten
to twenty stars per year.
Some stars are probably unsuited for the
development of life-bearing planets. Very small stars,
although long-lived, may not produce enough heat to keep
their planets from freezing solid, and very massive stars
explode shortly after they form. It seems the Order of the
Dolphin assumed this factor into R, and considered only the birthrate of
"suitable" stars similar to the Sun, while others
prefer to include this factor in one of the later parameters.
Take your choice.
Recent results have indicated that the
Milky Way may be larger than once thought, and that it may be
a "barred spiral" rather than a "spiral"
galaxy. If it really is significantly larger, then the star
formation rate would have to be increased, because it is
calculated based on the number of stars in the Galaxy.
It should be noted that this parameter has
not necessarily been the same throughout time. There are
observations indicating that when the universe was about one
third its present age, the starbirth rate was substantially
higher than it is now. This may imply that most of the
Sun-like stars in this Galaxy are billions of years older
than the Sun, and that our civilization may be a latecomer.
fp is the fraction of stars that form planets.
The Order of the Dolphin estimated that this number lies
between 0.2 and 0.5, and this is still a popular range of
Most stars occur in binary or multiple star systems.
Because of orbital dynamics considerations, planets that form
in single star systems (like our own) are more likely to have
It is widely thought that most single Sun-like stars have
planets. Stars form from clouds of gas and dust, and such
clouds generally possess angular momentum (they rotate). As
the cloud particles orbit the central mass concentration that
will become the star, they collide with each other, gradually
averaging their angular momentum vectors (and their orbital
revolution axes) until they all orbit with the same axis of
revolution, forming a disk. Some of the particles will fall
into the star, and some will be blown away from the system
when the star ignites, but some remain within the disk. Such
protoplanetary disks have been observed around nearby young
stars, but they are not stable; the matter they contain has
to go somewhere, and much of it must eventually gather
together to form planets. (However, sometimes protoplanetary
disks are destroyed
before they can form planets.)
Astronomers have been trying to reduce the uncertainty in
this parameter by observing the presence of planets around
other stars. At the moment, this can only be done by
measuring tiny motions in the central star, and then
inferring from that the mass and orbit of the planet. Several
such possible planets have
been inferred, but there is some controversy over these
It would be far preferable to directly image distant
stellar systems, and count their planets. This requires very
specialized instruments, and may not be possible at all from
the surface of the Earth. There are now instruments on the drawing boards
to do exactly this, and the first may be launched in only a
few years. So we may have a fairly precise measurement of
this parameter within the next decade or two.
ne is the average number of planets each such star
possesses, which are capable of supporting life.
The Order of the Dolphin estimated that this is between
one and five. In 1961, relatively little was known about the
other planets and moons within the Solar System, but it was
assumed that planets in the zone where liquid water can exist
would be the most likely to be capable of supporting life.
Venus, Earth and Mars lie within or near this zone, so the
Order settled on three planets, plus or minus two.
Today we know a lot more about our Solar System. There are
now four widely-discussed possibilities: Earth, Mars, Europa,
and Titan. (Technically, Europa and Titan aren't planets, but
they are large, complex worlds, and it is
conceivable that life could arise in such places. So we
should count them as planets, at least as far as the Drake
Equation is concerned.)
We know the Earth is capable of supporting life, such as
it is, and we are now exploring Mars. We already know that
Mars once possessed substantial quantities of liquid water,
and many researchers think that life could have arisen there.
NASA is now engaged in a series of missions to Mars, and is planning
to launch spacecraft specifically designed to look for evidence that
life once existed there. And the discovery of the famous Martian meteorite has
brought this question into sharp focus. (For more details,
see An Exobiological Strategy For Mars
Europa , one
of Jupiter's large moons, has intrigued planetary scientists
ever since the Voyager spacecraft returned pictures of its
very young and bright surface almost two decades ago. Many
researchers suspected Europa had ice floes floating on an
ocean of liquid water, kept warm by the gravitational
influence of nearby Jupiter and other moons, and Arthur C.
Clarke even worked this idea into the plot of his book 2010:
Odyssey Two, and the two books later in the series. The Galileo spacecraft has
now sent us much more detailed pictures of Europa, lending
considerable support to this hypothesis. Most recently, the Galileo Extended
Mission has returned magnetic data
consistent with the presence of a conductive liquid under the ice. NASA is now planning to launch a new probe to examine
Europa much more closely. The Europa Orbiter Mission will utilize radar and other
techniques to measure the thickness of Europa's icy crust,
and the depth of any oceans. If oceans are found there, we
may eventually send a robotic submarine to look around
beneath the ice.
Titan, the largest moon of Saturn, may be most tantalizing
and mysterious object in the Solar System. It is larger than
Mercury and Pluto, and is nearly as big as Mars. It has a
dense atmosphere, even denser than our own, and may have
methane oceans and hydrocarbon rains. Most researchers think
Titan is too cold to have developed life, because liquid
water cannot exist there, but it is widely thought that
pre-biotic chemistry may be happening there at the very
least. If it is possible for life to develop in solvents
other than water, then Titan may have many surprises in store
for us. The Cassini spacecraft , launched in 1997, is now scheduled
to deliver a probe to the surface of Titan on January 14, 2005.
It is also conceivable that the giant gas planets in our
Solar System may be capable of supporting life. However,
these environments are so totally alien to us that we can
barely begin to speculate on these possibilities.
Within the next few decades, we should have determined
with some degree of certainty which planets and moons in our
Solar System are capable of supporting life, or ever were. So
we should be able to reduce considerably the uncertainty in
However, recent observations indicate that our Solar
System may be uncommonly enriched in the heavy elements
necessary for chemistry-based life-forms, so counting planets
within our Solar System may be somewhat misleading. It will
be necessary to look at planets in other stellar systems, and
instruments are being designed
to do this. If a planet can be imaged at all, then it should
be possible to obtain spectroscopic measurements, and such
measurements can reveal the presence and even the composition
of a planet's atmosphere. We may be making such measurements
within the next decade or so.
fl is the fraction of those planets where life
The Order of the Dolphin came to the conclusion that all
planets capable of sustaining life will eventually develop
life, so they assumed this number is around one.
It now appears that life on Earth arose very
quickly after the Earth had cooled enough to allow liquid
water to accumulate on its surface, so there is some
confidence in this number. Life appears to be almost
inevitable under the right circumstances.
fi is the fraction of life-bearing planets where
The Order of the Dolphin agreed, all of them. But it is
now thought that this number may be somewhat less than one.
Some planets may develop life, and then fail to sustain
it. This may have happened on Mars, and may be a common fate
for many planets.
Some planets may fail to recycle critical materials. For
example, if all available supplies of a particular material
become locked into rocks, and plate tectonics does not occur,
then those materials may become lost to the biosphere, and
the whole system can grind to a halt.
Many other things can go wrong. For example, some planets
may fail to develop feedback systems to maintain their
temperature in the proper range.
There has also been a lot of discussion on the role of
catastrophes in the development of life and intelligence.
Catastrophic events can cut life short, but can also
encourage the evolution of new species. Some planets might
experience catastrophes much more frequently than the Earth,
and some far less frequently. For example, it has been
suggested that the Earth is partially shielded from
devastating comet impacts by the presence of Jupiter.
There has also been much discussion of the role our Moon
plays in the stability of the Earth's biosphere. It appears
to be rare for a small planet to have such a large moon.
We also don't know how long it typically takes for
intelligence to develop. On the Earth, it took 4.55 billion
years, but it might take much longer on some planets, and
might happen faster on others. If it takes longer than about
ten billion years on a given planet, it will all be for
nought, because that's when Sun-like stars grow old and
destroy their planets.
It is commonly thought that intelligence, having adaptive
value, will eventually evolve on any planet that can produce
and maintain complex ecosystems for a sufficiently long time,
provided its star doesn't consume it first. So this number is
still frequently assumed to be close to unity, but we won't
really know if this is reasonable until we find some examples
of intelligent life on other planets.
fc is the fraction of intelligent life-bearing planets
where intelligent beings develop the ability to communicate
beyond their own world.
The Order of the Dolphin estimated this number to be
between 0.1 and 0.2, on the basis of the observation that
there may be planets where intelligent beings arise who never
develop a technological civilization, such as dolphins, and
also that there may be technological civilizations that take
great care never to advertise their presence.
The Order was just guessing here, and we can do little
better at this time.
L is the length of time, in years, that such
communications remain detectable.
The Order of the Dolphin estimated between 1,000 and
This period of time is not thought to be indefinitely
long, even if a civilization does not destroy itself. If we
succeed in running fiber-optic cables to every home and
business on Earth, and switching all our mobile
communications to spread-spectrum digital, we would become
much harder to detect from far away, and perhaps after much
less than 1,000 years.
This parameter is critical to the use of the Drake
Equation in relation to SETI searches.
If it is typically a small number of years, then it would be
very hard to find anything out there. The Order of the
Dolphin realized early on that most of the other parameters
tend to cancel each other out, leaving the Drake Equation
(short form): N = L.
There is a great deal of uncertainty in
this parameter, and we won't know at all what the true range
of values is until we have found a lot of civilizations out
there. But we can forget about this parameter, and explore
other variations on the Drake Equation, using the parameters
These are parameters we can use to go beyond
the original use of the Drake Equation:
or nvx as
fx is the fraction of all communicating civilizations
that become explorer civilizations, where an explorer
civilization is defined as one which achieves the
ability to communicate, and then spreads beyond its home
world, and continues to exist in one form or another
indefinitely after that.
Optimists generally estimate this number equals one.
We have no examples of explorer civilizations as defined
here, but we may become one ourselves. Once a civilization
spreads beyond its home world, which we may be mere decades
away from doing, then all its eggs no longer reside in one
basket, and it should be able to continue spreading in spite
of any catastrophes which may befall any one planet.
It can be argued that the vast distances between the stars
will prevent civilizations from spreading beyond their home
stellar systems. But as Gerry O'Neill
pointed out nearly three decades ago, the surface of a planet
is a really terrible place for an advanced technological
civilization to grow. Once a civilization develops the
ability to build worlds of its own design, then travelling
between the stars, even at non-relativistic speeds, becomes a
The value you assume for this parameter will presumably be
based on the degree of optimism you hold for the fate of the
human race. If you believe that we and our descendents will
remain trapped within the gravitational well of our Sun until
it swallows us up, then you will probably choose a low value
for this parameter (like zero). But if you believe it is
inevitable that we will spread into space indefinitely, then
you will probably choose a higher value (like unity).
ns is the number of stars in the Galaxy.
Astronomers say this is between 1011 and 1012.
Out of all the parameters we examine here, this is one of the
few that is known with any degree of certainty.
As stated above, some researchers
think the Milky Way may be substantially larger than once
thought, and may contain even more than 1012 stars.
nmx is the number of stars that are monitored regularly
by each explorer civilization (of age ax
This number will probably depend on the age of each
explorer civilization. Older ones should be able to monitor
At the moment, we can monitor exactly zero planets beyond
our Solar System. We have only been doing astronomy in space
for a relatively short time, and we have not yet been able to
muster the resources needed to build the really large space observatories
needed to examine planets around other stars. But this will
come to pass shortly.
Once this happens, then the historical trends of astronomy
are expected to continue for the indefinite future: We will
be able to see farther and farther into space with each
passing year, and the depth of our vision should continue to
follow an exponential curve.
Historically, astronomers double their depth of vision
(the distance to which they can see a given type of object)
every few decades or so. This is because it takes about that
long to figure out (technologically and financially) how to
build an instrument twice as big as the previous one, and
because it takes about that long to prepare the questions
that arise from the answers provided by the previous
In recent decades, this trend has slowed somewhat, because
we are nearing the physical limits on instruments that can be
deployed on the Earth's surface, and getting instruments into
space has been very expensive. But now we have finally
entered the era of space astronomy .
If we ever become a true spacefaring civilization, with
the ability to build and maintain very large space facilities
using materials from space, then we should have no trouble
doubling the size of our astronomical instruments at the
traditional pace. Furthermore, since the zero-G environment
of space does not place any inherent limits on the size of
space structures, we should be able to continue doubling for
many generations. And any other spacefaring civilization out
there should be able to do the same.
Assume for the moment that we will develop the technology
to allow us to spectroscopically examine the atmosphere of
one nearby extrasolar planet around the year 2000, and that
we will double the distance at which we can do this every
twenty years. Every time we double the distance, we can see a
volume of space eight times larger, so we can see eight times
as many planets. Therefore, in the year 2000 we can see one
planet, in 2020 we can see eight, in 2040 we can see 64, in
2060 we can see 512... and in the year 2300, we can see 815,
or about 1013 planets. That's about how many
planets there probably are in the entire Galaxy, and in only
three hundred years of looking. Three hundred years doing
space astronomy is practically no time at all for a typical
Of course, we may not be able to continue doubling at that
rate for three centuries. (If we did, we would be building
space telescopes hundreds of kilometers across.) But the
point remains: Really old explorer civilizations, which could
be many millions of years old (and which may be able
to deploy deep-space observatories far from home), should
have little trouble monitoring a significant fraction of the
planets in this Galaxy.
nvx is the number of stars that are actually visited
by each explorer civilization (of age ax
or less) (in person or
robotically or whatever).
As above, this number will probably
depend on the age of each explorer civilization. Older ones
should be able to visit more stars.
However, the ability to visit other stars does
not necessarily imply a desire to do so. Some
ancient explorer civilizations may choose not to travel, for
whatever reason. Monitoring planets telescopically is a
passive activity, not requiring that you leave home, but
travelling between the stars is another matter entirely.
It has been proposed that advanced civilizations may
explore distant stellar systems using intelligent robotic
probes, commonly called von Neumann probes (after John von Neumann , an
early thinker on self-reproducing automata). Such probes
could maintain themselves, and even reproduce themselves,
using raw materials found during their wanderings.
It could be that virtually all interstellar exploration is
done by von Neumann probes. Such probes could reproduce like
bacteria, multiplying their numbers in a characteristic
period of time (the generation time). A single von Neumann
probe could produce 1012 progeny, one probe for
every star in the Galaxy, in only forty generations. Even if
the generation time is as long as one million years (you have
to include the time it takes for each probe to travel to
another star), it would only take forty million years for the
descendents of a single probe to visit all the stars in the
Galaxy. This is a short time in the scheme of things.
Since we don't see these things all over the place, some
conclude that there are no von Neumann probes. But we should
not jump to this conclusion; it could be that all of the von
Neumann probes ever deployed were programmed only to observe,
and not to interfere with living planets. This would seem to
imply something about the motives of all advanced
civilizations that deploy such devices (if there are any).
is the nearest extraterrestrial civilization? And how old is
We have defined explorer
civilizations to be those that have spread beyond their
home world, and continue to exist indefinitely after that.
Therefore, the number of explorer civilizations must increase
Let us define the age
of an explorer civilization as the number of years since it
became one. Since we have not quite reached that status
ourselves, but could become one in the next century or so if
we put our minds to it, we may wish to consider ourselves
almost of age zero.
Since it seems reasonable to
assume that Rx has been roughly constant in recent times, at least
for the last billion years or so, then explorer civilizations
should be evenly distributed across the age spectrum. The
number of explorer civilizations between one million and two
million years old should be roughly equal to the number
between two million and three million years old, and so on.
Therefore, the explorer
civilizations between 100 million and one billion years old
should outnumber explorer civilizations between 10 million
and 100 million years old by a factor of ten, should
outnumber explorer civilizations between one million and 10
million years old by a factor of a hundred... ...and should
outnumber explorer civilizations between 1000 and 10,000
years old by a factor of 100,000.
To put it another way, less
than one in 100,000 explorer civilizations should be less
than 10,000 years old.
Assume for the moment that
there exists a nearby explorer civilization, less than 100
light-years from here, that is no more than 10,000 years
beyond us. That would imply that there should be, within that
volume of space, at least nine others that are between 10,000
and 100,000 years old, at least 90 others that are between
100,000 and one million years old, at least 900 others
between one million and ten million years old, at least 9000
others between ten million and 100 million years old, and at
least 90,000 others between 100 million and one billion years
old. That's a total of at least 100,000 explorer
civilizations occupying a spherical volume of space 200
light-years across. Since this volume of space is known to
contain only about 15,000 stars, this would imply that
explorer civilizations outnumber stars in this Galaxy by a
factor of a least six. This is nonsensical, so our initial
assumption must be invalid, and the average distance between
young explorer civilizations (of age 10,000 years or less)
must be considerably greater than 100 light-years.
Obviously, the nearest
explorer civilization should be very old. But how old? This
depends greatly on the nature of Rx. Throughout most of these discussions we have been
assuming that it has remained roughly constant in recent
history, but this is just an approximation. This number
varies throughout the history of the universe; obviously, it
was once equal to zero, and becomes non-zero as explorer
civilizations arise, so it is a function of time. What is the
shape of that function? Is it a monotonically increasing
rate, corresponding to the gradual enrichment of the cosmos
in the heavy elements necessary for life? Or did it increase
for a while, level off, and then decrease, corresponding to
the similar behavior in the rate of star formation? We really
The Drake Equation, and the
other equations here that go beyond it, assume a steady-state
universe. Our universe is manifestly not
steady-state, but the steady-state assumption is not too
unreasonable over time scales of up to a billion years or so,
and besides we cannot do much with these equations without
it. So it is reasonable to say that the nearest explorer
civilization should be many millions of years old, with the
older ages being more likely, but once you get up into the
billions of years, you have to stop somewhere. It is not
reasonable to say that explorer civilizations between one
billion and ten billion years old will outnumber the ones
between 100 million and one billion years old by a factor of
ten, because there probably aren't any that are ten
billion years old (and if there are any, they are probably
exceedingly rare, because Rx
started out small.)
The universe is now thought to
be between about 8 billion and 15 billion years old, and most
researchers think it's more than 11 billion years old
(because we can observe stars which appear to be that old).
So how long did it take for the first planets
suitable for life to arise? And on them, how long did it take
for the first life to arise? And how long did it
take for the first explorer civilization to appear?
Obviously, it is possible to write modified versions of the
equations we are already using to explore these questions,
but the parameters within these equations are much more
uncertain than the highly uncertain parameters we have
We can be reasonably certain
that our planet, and its Sun, formed when the universe was
already billions of years old. But could similar planets have
arisen much earlier, say, less than a billion years after the
Big Bang? We know that there were stars in existence this
early, and that some of them were pumping heavy elements out
into space. So perhaps this is possible.
Intelligent life arose on the
Earth about 4.55 billion years after it formed. Could there
be planets out there where intelligent life arose more
quickly? We really don't know; 4.55 billion years could be
unusually long, or unusually short, or quite typical.
At this point, all we can say
is this: We cannot rule out the possibility that there may be
civilizations out there that are several billion years older
than our own.
Before Frank Drake wrote his
equation on the blackboard, others were thinking about the
ideas embodied within it. One of these early thinkers was
physicist Enrico Fermi.
Fermi spent much of World War
II at Los Alamos, where he helped develop the atomic bomb.
One of the side benefits of the Manhattan Project was the
gathering together of a great number of brilliant minds in an
isolated setting where the distractions of civilization were
scarce, which resulted in a lot of spare time being consumed
in intellectual discussions unrelated to nuclear destruction.
Thanks to Fermi, some of that spare time was spent talking
about putative alien civilizations.
Fermi realized that
intelligent life ought to be widespread throughout the
cosmos, and should have been so for a very long time. He also
realized that the first spacefaring civilization to arise in
our Galaxy should have already spread to every part of the
Galaxy. But if that is the case, he asked, "Where are
they?" This has become known as the Fermi Paradox.
In those days, it was commonly
believed (at least in America) that aliens had never visited
our planet. Widespread popular belief in UFOs was still years
in the future. Fermi (and probably most of his colleagues at
Los Alamos) assumed the lack of evidence for alien visitation
was due to a complete lack of visits. But given what they
suspected about the abundance of intelligent life in the
universe, this did not seem to make sense.
A number of ideas have been
put forth to resolve this apparent paradox. One of the most
popular is the "ET
Hypothesis", which posits that we are being
visited, and that UFO sightings (as well as abductions,
cattle mutilations, crop circles, etc.) are the evidence.
Needless to say, this hypothesis is controversial and highly
problematical, and most serious scientists won't get anywhere
Another popular idea is that
we are completely alone in the Galaxy, or that any other
civilizations are so rare and distant that they have not
gotten anywhere near here as yet. This is entirely possible,
but reflects a rather pessimistic view of the questions
embodied in the Drake Equation.
A third hypothesis is that
intelligent life is widespread, as many researchers
suspect, but that we cannot see blatant evidence of it for
some reason. A number of suggestions have been put forward to
explain how this could come to be, including what has come to
be commonly called The Prime Directive. But all
possible explanations for this hypothesis have one thing in
common: They must apply to every civilization out
there, without exception. If even a small fraction of
extrasolar civilizations violates an interstellar quarantine,
we should find evidence, and we don't; this would seem to
imply that someone is enforcing our isolation. In any case,
we can be reasonably sure of one thing: Nobody is
aggressively appropriating all of the available resources in
the Galaxy at an exponential rate, even though this would
seem to be possible to do.
possible in this universe, anyway?
It is a widely held belief
among scientists that some things are simply not possible. In
other words, there exist physical laws that limit
what you can do, and as long as you remain within this
physical universe, you cannot violate those laws. It is
conceivable that we have no idea what those ultimate laws
really are, or that they may indeed be unknowable in some
sense, but until we see evidence that a really elegant
physical law has been violated, Occam's razor would seem
to demand that we stick with it.
One physical law that is
directly related to the subject at hand is that associated
with the speed of light. If it truly is impossible to travel
faster than the speed of light, and if it truly is
energetically very expensive to travel near the
speed of light, then this places severe constraints on all
discussion of interstellar travel. But if it is possible to
circumvent this limit in some way, then the whole tone of the
Methods of traveling quickly
and cheaply between the stars are a common staple of science
fiction, and are collectively known as FTL
(Faster-Than-Light). Popular FTL methods include warping
space and wormholes. These methods are essential to most
science fiction stories that involve interstellar travel, and
indeed were invented so that it would be possible to
tell compelling space travel stories. But so far, these
inventions must be viewed only as literary devices,
and not actual technologies.
Some who believe in the ET Hypothesis as an explanation for UFOs say that such
observations constitute evidence that FTL is possible, but
this is a logical fallacy. Even if UFOs are real, and even if
they come from beyond our Solar System, this does not
constitute proof of FTL, because it is already known that
interstellar flight is possible without FTL.
Nobody has ever actually seen
anything move faster than light. Indeed, since we see with
photons, and nobody has ever come up with a way of having
photons get from a FTL vehicle to your eye, one would not expect
to see such things even if they exist. Of course, some people
say they have been told (perhaps by some alleged
extraterrestrial) that FTL is possible, but this is only
hearsay evidence. And some people claim to have traveled by
means of FTL to other worlds, but one can think of a number
of explanations for this kind of experience; even if such
people are not deluded, and have really met aliens
and "experienced" such travel, this does not
constitute proof of FTL, because one would expect alien
visitors to have a sufficiently advanced technology so that
they could give a human any kind of "experience"
they desire, without any need for that human to actually
But perhaps the biggest
problem with FTL is that it appears to be incompatible with
the belief that intelligent civilizations are widespread. If
intelligent life is commonplace, and if FTL is possible, then
one would expect this technology to be possessed by a wide
variety of different species of intelligent creatures,
perhaps with widely varying ethical notions, and then one
would have to come up with some compelling explanation for
why none of these species produces any individuals
inclined to littering or grafitti. (Or, you have to postulate
that some external agency has a 100% success rate in keeping
joyriders away from quarantined planets.)
The principle of Occam's razor is a cornerstone of modern
scientific thought. Named for William of Occam (also spelled
Ockham), a 14th century philosopher, it is a principle of
parsimony. Given a choice between two or more viable
explanations for some phenomenon, Occam's razor cuts away the
more complex explanations in favor of the simplest.
For example: For centuries, astronomers attempted to
devise mechanistic models to explain the complex motions of
the planets through the sky. Unfortunately, they were hobbled
for many years by a philosophical compulsion to make the
heavens perfect. Since everything in the sky was observed to
go round and round, it was thought that everything had to be
made from perfect circles. But in order to make the models
match the observations, it became necessary to put more and
more circles into the models, and they evolved into horribly
complicated monstrosities, having wheels within wheels within
wheels.... It wasn't until Kepler came along that a simple
model was derived, based on ellipses instead of circles. But
people then had to redefine their notion of
simplicity before they could accept Kepler's laws.
Occam's razor is frequently wielded by those who wish to
speculate on the nature of extraterrestrial intelligence. But
it seems quite likely that we may have to redefine our notion
of simplicity, perhaps many times, before we will find any
truth with this tool.
For a more comprehensive discussion, see What is Occam's Razor?
At present, the only method we have for
searching for planets outside our Solar System is by looking
for the gravitational effects they have on the stars they
orbit. This can be done by using Doppler shift observations
to measure very small movements of the star. However, this
method is fraught with difficulties, and many of the results
remain controversial. And in any case, this method cannot
tell you if a given planet harbors life.
It would be highly desirable to see planets
directly, but unfortunately, this is extremely difficult.
Extrasolar planets lie very near their stars when viewed from
Earth, and they tend to be concealed within the glare of the
star. Planets are many orders of magnitude dimmer
than the stars they orbit.
When the image of a distant star is focused
onto the image plane of a telescope, the image of the star
does not focus to a point. Instead, it focuses to a small
disk, of finite size, and this disk is enlarged by various
effects. In most telescopes in current use, this disk is
large enough so that the images of any planets orbiting that
star will appear inside the star's image disk, and
be completely obscured.
There are several phenomena that cause the
image of a star to blur into such a large disk. The worst is
the blurring caused by looking through the Earth's
atmosphere; while there are techniques for partially
counteracting this effect, it is far better to eliminate it
completely by placing the telescope above the atmosphere, in
Another effect that can cause the star's
image to enlarge is commonly referred to as glare.
Ideally, all of the light that enters an instrument should
follow the designed light path, ultimately arriving at the
detector where all of it is absorbed at 100% efficiency. But
in any real-world optical system, light does not always go
where the system designer desires. No material object is
completely black, so a small amount of the light entering the
instrument will be reflected and/or diffracted into paths
that the designer of the instrument did not intend, and a
small amount of the light arriving at a given light detector
will be reflected elsewhere rather than being absorbed. This
happens within electronic image detectors, photographic
emulsions, and even the human eye; when light strikes a light
receptor within your eye, a small amount of it can bounce
around inside the eye and within the retina itself,
eventually striking other receptors, so the light from even a
point source, if bright enough, will be detected by more than
one receptor (try looking [very!] briefly near the Sun
sometime, and before your eyes instinctively blink shut,
you'll see this effect). Similarly, when a photographic plate
is used to take a picture of a field of stars, the image of a
given star will become larger as the exposure time is
increased, because more and more photons are bouncing around
inside the photographic emulsion before being absorbed. In
addition, electronic image detectors sometimes experience
charge leakage from one pixel to the next, and this is can
also result in the enlargement of images. This type of glare
is difficult to eliminate completely, but by careful design,
it is possible to use various nulling techniques to reduce
this type of glare to any desired degree, short of
perfection, in a sufficiently large telescope.
A third effect that can enlarge the image of
a star is the most fundamental, that of diffraction. A
phenomenon known as Fraunhofer diffraction causes the light
from a star, or even from a point source, to spread out into
a disk of finite size, known as the Airy disk; the size of
this disk corresponds to an angular resolution of 1.220 w
/ a radians, where w is the wavelength of
the light being observed and a is the diameter of
the telescope aperature. If the image of a planet falls
inside the Airy disk of its star, then there is no way of
separating the two. And even if the image of a planet does
not fall inside the Airy disk of its star, the image of the
planet can still be obscured, because Fraunhofer
diffraction causes a small amount of the star's light to be
distributed well outside the star's Airy disk. Fortunately,
as long as two objects are separated by a non-zero distance,
it is always possible to design a telescope that will
separate their images far enough for them to be resolvable
(but it may require a very large telescope).
Once you have a telescope that can separate
out the image of a planet from its parent star, then the
possibilities open up. By examining the colors of the light
from an object, it is possible to derive a large amount of
information about that object. One can often tell what kinds
of materials a planet is made of, and whether it has an
atmosphere, and if so, what the composition of that
These kinds of measurements can sometimes
tell you whether or not a planet carries life. We know this
because the Earth's atmosphere has a detectable signature of
life: it is in a state of chemical disequilibrium, containing
large amounts of free oxygen, and life is the only known
natural process that can produce such a state. If we
see an atmospheric composition at a distant planet that we
cannot explain as a non-living natural phenomenon, then that
may indicate the presence of life.
A number of efforts are underway to build
instruments to image extrasolar planets, and make
measurements of them. The first attempts to do so will be
undertaken by ground-based observatories, such as the Keck Observatory in
Hawaii. But because they are handicapped by the Earth's
atmosphere, they may not find very many planets, and may not
be able to provide very much information about them. For
these kinds of searches, the future lies in space.
The first space-based instruments
specifically designed to look for planets are already being
designed, and may be launched within the next decade.
For more details, see:
The Exploration of Neighboring Planetary
Systems (ExNPS) Study
NASA's Origins Program
Other Solar Systems?
Darwin Mission - Lists of Extra-Solar Planets
SIRTF (Space Infrared Telescope Facility)
Search for Extra-Terrestrial Intelligence (SETI)
The first systematic search for extraterrestrial
intelligence, using the techniques of radio astronomy, was
conducted by Frank Drake in 1960. It was named "Project
Ozma" , after the princess in L. Frank
Baum's Oz books.
Since then, many searches have been undertaken, using
better and better equipment. Searches are also being
conducted for signals outside the range of radio astronomy.
A number of tantalizing signals have been seen, but none
could be verified; they were one-time transient events. Those
parts of the sky have been occasionally re-examined, and they
For details on recent and current SETI activities, see:
SETI League, Inc.
Small SETI Observatory
Cosmic Search Magazine
A very comprehensive document, published by NASA in 1977: The Search for Extraterrestrial Intelligence, SETI
Scientific American: Article: The Search for
Extraterrestrial Intelligence: 1/97
The Telson Spur: Field Nodes -- Visions (2):
contains a very large number of relevant links.
SETI - References for List of Searches
SETI etc. (W6/PA0ZN)
SETI League Technical Manual shows
you how to build your own SETI receiver, as does:
SETI@home allows you to
participate in SETI searches from your own home, even if you
don't have your own radiotelescope! SETI@Home provides a screensaver program that you can run on your
own computer, which automatically downloads and analyzes
SETI data collected by the world's largest radiotelescope,
the 1000 foot dish at the Arecibo Observatory.
For an excellent recounting of the early history of the
field, and of The Order of the Dolphin,
Is Anyone Out There?, by Frank Drake and Dava
Sobel, Delacorte Press, New York, 1992. ISBN 0-385-30532-X.
The Order of the Dolphin
In early November, 1961, a group of scientists and
engineers met at the Green Bank Observatory to discuss the
possibility of using the techniques of radio astronomy to
detect evidence of intelligent life outside our Solar System.
The Drake Equation was first
At the end of their three day meeting, they decided that
the group should have a name. Inspired by John Lilly's tales
of dolphin intelligence, they agreed to be known as The Order
of the Dolphin. They were:
Su Shu Huang
J. Peter Pearman
It should be noted that many of the ideas
discussed at this meeting had already appeared in a seminal
letter by physicists Giuseppe Cocconi and Philip Morrison
entitled "Searching for Interstellar
published in the journal Nature (volume 184, no.
4690, pages 844-846, September 19, 1959).
Morrison was undoubtedly influenced by his
Los Alamos colleague, Enrico Fermi, who was thinking about
these ideas during the early 1940's. See The Fermi Paradox, above.
Also at this site:
The Many-Worlds Interpretation of Quantum Mechanics
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on September 26, 2001.
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