How Math Can Save the World
Do extraterrestrial aliens exist?
How can we prevent nuclear war and a major asteroid impact?
When is the world going to end?
What exactly is mathematics? Dictionary.com (used by those of us who spend more time online than at the library) defines it as “ the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. ” That ’s what mathematics is, but this article is much more concerned with what you can do with it, which is why mathematics goes far beyond the dictionary.comdefinition. Probably the most dramatic thing you can do with it saves the world.
The Drake Equation
I ’ m not sure whether H. G. Wells was the first to envision an invasion by a sentient alien race bent on world domination, but his classic sci-fi story War of the Worlds has been made into two successful movies and has spawned countless imitators.
Half a century ago, a group of scientists envisioned kinder and gentler aliens than the ones postulated by Wells. These scientists met in Green Bank, West Virginia, in order to found an endeavor is now known as SETI, the Search for Extra-Terrestrial Intelligence. One of the participants was Frank Drake, who proposed an expected - value calculation to estimate N, the number of civilizations in the galaxy with whom communication might be possible. This expected - value calculation was presented in the following formula, which is now known as the Drake equation:
R * represents the rate of star formation in the galaxy: how many new stars are created each year. Drake estimated this number as 10; better technology over the last fifty years has resulted in NASA estimating this number as 7.
f p is the fraction of those stars that have planets. Drake, with nothing to guide him other than the solar system, estimated this number as 0.5. Planet hunting has now evolved into fine art. More than 300 planets are known to exist outside the solar system, and our current technology enables us to find only really big planets. Drake ’ s estimates certainly a guess — for the time being, let ’ s keep the number as 0.5, with the understanding that it could definitely be higher. I don ’ t know whether any stars have been found that are known to have no planets.
n e is the average number of habitable planets per star that has planets. Drake estimated this as 2, but the consensus today is that this number is probably much smaller. The habitable zone, where the temperature of the planet is neither too hot nor too cold to support life, is generally fairly narrow. In addition, the parent stars must have a sufficiently long period of stability and must supply sufficient heavy elements to support life. There ’ s no consensus on this that I could find, but relatively few planets have been found in habitable zones.
f l is the fraction of habitable planets on which life develops. Drake used 1 for his estimate and recent arguments based on the length of time it took life to evolve on Earth have concluded that this fraction is greater than 0.13. The question boils down to this: given the right conditions, how inevitable is life?
f i is the fraction of planets with life that go on to develop intelligent life. Drake estimated this as 0.01. Nobody has a clue, and this guess is probably as good as any.
f c is the fraction of planets with intelligent life whose species evolve the ability to communicate with others and are willing to do so. Again, Drake guessed 0.01. Earth had intelligent life for hundreds of millions of years before a combination of events triggered the ascent of mammals, the eventual emergence of man, and the development of a technological civilization, so to me, this number seems high, but who knows?
L is the expected lifetime of such a civilization for the period that it can communicate across interstellar space. Drake guessed that this was 10,000 years. Our civilization has had this ability for less than 100 years, but for all we know, once the growth problems of civilization have been surmounted, such a civilization might last for millions of years.
H = N * f a * f g * f h
N is the number of civilizations able to communicate with us, as determined by the Drake equation; f a represents the fraction of those civilizations that are actually able to get here from wherever they are. There are any in the solar system, and, from all, we know of physics, getting here is a whole lot more difficult than Star Trek would have us believe.
This article makes you think about the possibility of other living existence in the universe and us as humans, we can think and create a different reality based on math. Think about that!
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