The Drake Equation

N = R_* f_p n_e f_l f_i f_c L
Where,
N = The number of civilizations in The Milky Way Galaxy whose radio emissions are detectable.
R_* = The rate of formation of stars suitable for the development of intelligent life.
f_p = The fraction of those stars with planetary systems.
n_e = The number of planets, per solar system, with an environment suitable for life.
f_l = The fraction of suitable planets on which life actually appears.
f_i = The fraction of life bearing planets on which intelligent life emerges.
f_c = The fraction of civilizations that develop a technology that releases detectable signs of their existence into space.
L = The length of time such civilizations release detectable signals into space.

From SETI's Carl Sagan Center for the Study of Life in the Universe - try out their Drake Equation Calculator.


There are a lot of moments in Cosmos that widened my perspective when I first watched the series. Episode 12, Encyclopedia Galactica, is filled with such moments. In the clip below, just before he launches into his vision of the Encyclopedia Galactica, Sagan addresses the probability of intelligent life in the galaxy using the Drake Equation.

Even for a person with a rudimentary understanding of mathematics like myself, the Drake Equation is a simple way to explore the potential for life in the vast Milky Way, which is always a good time. In the clip, Sagan walks us through the equation, demonstrating just how hard it is to know whether we are alone and unique in the universe, or just pedestrian intelligent life. It ends with a humbling thought:

So if civilizations do not always destroy themselves shortly after discovering radio astronomy, then the sky may be softly humming with messages from the stars, with signals from civilizations enormously older and wiser than we.

He goes on from there to succinctly summarize the central plot of Contact, and leaves us reflecting on the great value of radioastronomy and it's potential to aspire us to take to the stars:

If there are millions of technical civilizations in the milky way, each capable of radio astronomy, how far away is the nearest one? If they're distributed more or less randomly through space, then the nearest one will be some two-hundred light-years away, but within two-hundred light years, there are hundreds of thousands of stars. To find the needle in this haystack requires a dedicated and systematic search.

There are many cosmic radio sources having nothing to do with intelligent life, so how would we know that we were receiving a message? The transmitting civilization could make it very easy for us if they wished. Imagine we're in the course of a systematic search, or in the midst of some more conventional radio observations, and suppose one day we find a strong signal slowly emerging. Not just some background hiss, but a methodical series of pulses. The numbers: 1, 2, 3, 5, 7, 11, 13. A signal made of prime numbers; numbers divisible only by one and themselves. There is no natural astrophysical process that generates prime numbers. We would have to conclude that someone fond of elementary mathematics was saying, "Hello." This would be no more than a beacon to attract our attention. The main message would be subtler, more hidden, far richer. We may have to work hard to find it.

But the beacon's signal alone would be profoundly significant. It would mean that someone had learned to survive technological adolescence, that self-destruction is not inevitable, that we also may have a future. Such knowledge, it seems to me, might be worth a great price."

If that doesn't open up your mind, well, you must have it closed pretty tightly.

Patents.

Thanks to Google's new Patent Search, I was able to uncover an original Carl Sagan invention.

Along with Akiva Bar-Nun and Simon Bauer, Sagan filed the Pressure Wave Synthesis of Aminocarboxylic Acids for a patent on October 2, 1970.


How does it work?

A homogenous vapor phase method for preparing aminocarboxylic acids by subjecting a gaseous mixture of compounds containing the elements of hydrogen, oxygen, carbon and nitrogen (with the latter two in reduced compounds), which are optionally mixed in an inert carrier gas to pressure wave heating and rapid expansion wave cooling. The products from the heating and cooling process are immediately withdrawn from the reaction chamber into a dilute aqueous solution of a mineral acid wherein the aminocarboxylic acids produced from the process are recovered.

The patent was awarded on March 28, 1972.


While this is the only Sagan patent I found in Google's records, the search giant did show that he had influence in getting other inventions patented.

You may remember these from Cosmos:

Hypercube model
Polyhedral model

A Year Science

In annual tradition, the Editors at Scientific American publish an article at the end of each year summarizing that year's scientific developments.

'The Year in Science' published on December 20, 1997 starts off with the death of Carl Sagan but quickly moves to focus on his impact on science.

To quote:

The year 1997 began on a somber note, just days after the death of astronomer Carl Sagan. In many ways, though, the year's events went on to celebrate Sagan's life. There were steady advancements in a variety of disciplines. But perhaps the most stellar happenings of the year took place in Sagan's own specialties, namely astronomy, cosmology and space science.

As if in tribute to Sagan, Comet Hale-Bopp blazed across the early summer skies, its fiery tail observed by the most sophisticated observatories and millions of amateurs--armed with telescopes, binoculars or the naked eye. 1997 also marked the 40th anniversary of the Space Age, which began officially when a startled world awakened to beeping signals from the Soviet Union's Sputnik I on October 4, 1957. In the years that followed, Sagan was a pivotal in the conception and planning of unmanned space probes, many of which are still returning important data.

Two spacecraft inspired by Sagan, Voyager I and Voyager II, which were launched August 20 and September 5, 1977, arrived at halfway points in their 40 year missions. Both reached the very fringes of the solar system in 1997, and headed into interstellar space. In their first decade, these vessels returned important images and data from Jupiter, Saturn, Uranus and Neptune. Since 1989, both have patroled the outer solar system. And in February 1998, Voyager 1 will pass the Pioneer 10 spacecraft, making it the most distant human-made object in the universe.

All of these spacecraft are equipped should they chance upon intelligent life elsewhere in the cosmos. Pioneer 10 carries Sagan's famous plaque, which bears human greetings. And both Voyagers contain a gold record describing the location of Earth and human civilization. (Perhaps DVD compact discs, which only came to market last year, would now be more appropriate.)

To read more about Sagan's impact on sciene in '97, check out the Scientific American article.