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.

Far Side

Thanks, Joel.

Mural

I recall with great fondness watching Cosmos with my Grandfather. To a curious 10 year old boy, the show was amazing; and it was one of the few shows Grandpa even bothered to watch on television.

He grew up during the depression on a small, dust bowl ravaged farm in rural Oklahoma. I suspect his family was too poor to migrate to California like everyone else. In the 6th grade he quit school so he could help support his parents and sisters. Although his education was cut short, many years later Carl Sagan captivated this man with lessons on physics and astronomy. Sagan brought out in my grandfather a child-like wonder about the Universe.

Almost thirty years later, as I watch Cosmos for the first time, again, I am left with the same wonder. Sagan was a master story-teller. Not only could he explain complex theories so that almost anyone could understand them, but he also presents them in a way which leaves me hungry for more knowledge.

There are already much more eloquent and insightful tributes to Dr. Sagan here than I am capable of, so I have kept my commentary brief. That being said, I would like to share a piece of artwork I photographed recently during my 20th High School reunion. I found this mural in the Science Hall of U.S. Grant H.S. in Oklahoma City. The school is scheduled for demolition sometime in 2007, and this painting will most certainly go with it.


Travis Church, Texas

Apple Pie Recipe

Here's an old recipe, tried and true.

I often bring up Sagan's quote when people say they've "built a PC from scratch" and such. Of course, I don't say it to make a philosophical or cosmological point of any sort, but to be the sort of linguistic jackass you know me as.

Neven, Florida

Originally posted to The Missing "O" on March 03, 2006.
Also see Neven's Flickr page.

Carl Sagan brings to mind two things.

1. Seeing the film Contact with my mom several years ago and finding it to be a vaguely spiritual experience (this coming from someone whose thoughts on religion are basically in line with Carl's).

2. Watching a few episodes of Cosmos with the authors of this site and some other high school friends on a weekend visit to Boston (during the 2004 DNC, in fact) and discussing how it was one of the most subversive television pieces ever created.

Carl, I should probably spend some more time with you. But these are good memories, so thanks.

Chris, in Chicago

From Japan

Thank you. Yes, thank you indeed.

I am so grateful to Doctor Carl Sagan for his many gifts to us. One of his greatest talents was making the cosmos accessible, but more importantly, he made the infinite vacuum PERSONAL.

When I read, or hear his praises, they are often sung by people who sound like they are reminiscing about an old friend, colleague or family member. He has had this effect on me as well.

I am no scholar, and at the time of my first viewing of "Cosmos", I had little to no knowledge of physics, astronomy, the history of mathematics or the science of the stars. A few years later after reading more of his work, he has taught me how to love to learn. He shares his passion and wisdom as if I was sitting with him in a quiet restaurant, asking him wide-eyed questions about it all.

This intellectual journey; asking questions, using skepticism, exploring the possibilities of the cosmos is exploring our history in its most raw form. When Carl made the cosmos accessible, he made the dust and gas our ancestors and our future just as hopeful as it was when the first microbes began multiplying.

I have a lot of faith in his words. And in turn, I have a lot of faith in us all.

Ashley

Thank You Dr. Sagan

Thank you for being a tremendous and positive influence on a young girl that thought she was the only geek in the universe.

Thank you for opening a lot of eyes.

Thank you for your enthusiam!

Thank you for teaching me. I am still learning, it's amazing that your show is still running on the Science Channel and is still as wonderous as it was.

Here is a piece of art made for you.


- Susan Anastasia

Sagan's Contributions to Us

I regularly followed his TV appearances because he had such a simple yet deep understanding of our universe and could speak in terms that was straight-forward and logical. Other than that I knew little about him. However, he was explaining the sheer beauty and majesty of it one evening and it struck me as how insightful he really was as a person and scientist. He had stated that if anyone doubts the existence of a higher being or creator all one had to do was look up at the night's sky-filled array of stars. To do this he suggested you pick a clear night, lie down flat on your back, relax and stare up at the multitude of bright stars peppered across the sky. Just lie there for awhile taking it all in and realizing how incomparable a scene that was. asking yourself the question: Was it a random act or was it purposely designed and created by a superior intelligence, an infinite being we call God. To any unbeliever, he posed that challenge.

- Art Murray