The Lake County Astronomical Society

Doing the Math

Matt Lowry

The power of numbers, and by extension the whole subject of mathematics, is phenomenal. Math takes us from the realm of guesswork into certainty; math gives us power over our physical world, allowing us to make predictions that are testable. And, when applied in certain ways, can lead us to ponder some of the most compelling questions about our very existence.

Take, for instance, two areas of thought -- the age-old pseudoscience of astrology and the considerably younger search for extra-terrestrial intelligence (SETI). Each is popular, and each has its own peculiar association with numbers.

As much as one-third of the U.S. population still adheres in some way to astrology, outdated and useless as it is. This is, in large part, due to a misunderstanding of basic mathematics. As a way to simply illustrate the incorrectness of astrology to my high school classes, I had them perform a simple test. Each student was to read through a description of each Zodiac symbol (there are 12 in all) and rate which one described them best, on a scale of 1 to 7 for accuracy. It should be noted that each symbol was represented by a number, as opposed to the symbol's name -- this was done to blind the students from knowing ahead of time which Zodiac symbol they were reading about.

The next day, I had the students pick the Zodiac number which they say described them best, and then we looked up on calendars to see which Zodiac symbol actually belonged to each student. Then came the kicker -- I showed my students the key, which matched up the numbers with the actual Zodiac symbols. The whole idea is for the students to see how close, if at all, they came to accurately describing themselves through astrology.

The result? Only 1 out of 42 students actually got it "right" -- that is, one kid picked the description that was their actual Zodiac symbol. When they saw the results, there were a lot of wide eyes and "whoas" throughout the room; the conclusion at that point was obvious. When applied as a tool to separate fact from fiction, numbers and mathematics can be most powerful.

Yet math can also inspire. Take the case of SETI. One of the more quanitifiable concepts associated with SETI is the famous Drake Equation, which is a mathematical way of estimating the number of technological civilizations that may exist in our galaxy. Here's what the equation looks like...

N = R* - fp - ne - fl - fi - fc - L

where N = number of civilizations in the Milky Way Galaxy whose electromagnetic emissions are detectable, R* = rate of formation of stars suitable for the development of intelligent life, fp = fraction of those stars with planetary systems, ne = number of planets, per solar system, with an environment suitable for life, fl = fraction of suitable planets on which life actually appears, fi = the fraction of life bearing planets on which intelligent life emerges, fc = fraction of civilizations that develop a technology that releases detectable signs of their existence into space, and L = length of time such civilizations release detectable signals into space.

At this stage, we have a rough handle on the values of R*, fp, and ne. Frank Drake himself estimates tthe value of R* at about 10/year. Discoveries of numerous (150+) extra-solar planetary systems within the last 15 years have given us an estimate of fp. And in mid-June, the news of the discovery of the first Earth-like planet beyond our solar system was announced -- this now gives more information on the possible value of ne. Of course, we don't truly have any solid idea of the values beyond these first three, and any guesses would be speculation.

But if you're like me, and you cannot resist speculating on such a fascinating question, you could always tinker with the numbers on your own using the Drake Calculator -- www.seti.org/science/drake-calc.html

In time, we'll gather more data and the terms in the Drake Equation will become better known. And perhaps, someday in the far future, our descendants will be able to do the math in a more satisfactory manner. Until then, we'll have to live with the uncertainty... and the inspiration to learn more.

Ad Astra -- Matt Lowry