This week in Pop Science, we transition into analysis of the beloved* Big Bang Theory* on CBS. As you might imagine, there’s quite a few scientific references to analyze in any given episode of a show *about* science. According to Metro.co.uk, there are 12 seasons and 279 episodes chalked full of opportunities for identifying discrepancies and accuracies between legitimate science and scientific vocabulary dressed up for television.

One reference to real-world math and science that stood out to me occured in the opening scene of the 20th episode of season two, titled “The Hofstadter Isotope.”

The show’s main quartet, Sheldon, Leonard, Howard, and Raj, are having Thai food around their shared apartment’s coffee table while debating plans for the rest of the evening. When Howard suggests a trip to a bar to flirt, Leonard quips that the likelihood of picking up girls is nearly zero.

In response, Howard proffers the Drake equation as a counterpoint, suggesting that a seemingly unlikely incident (encountering communications from an alien lifeform) is actually of greater statistical probability than one might expect, much like their chances of socializing with the opposite sex. For his purposes, the Drake equation was altered to represent the number of girls willing to sleep with them.

Sheldon’s explanation of the real Drake equation is actually pretty accurate. You can hear it for yourself here.

In the YouTube video “What Is The Drake Equation?” from the sister channel of HowStuffWorks, BrainStuff, Josh Clark breaks down the elements of the equation. Clark says that the Drake equation describes the potential number of planets that could contain life able to communicate with us, the human race. In other words, the equation offers an estimate of how many advanced alien civilizations might exist in the Milky Way.

In 1961, Frank Drake debuted his famous equation at the first conference of SETI (Search for Extraterrestrial Intelligence), as a response to the Fermi paradox. The paradox, named after Enrico Fermi, addresses the contradiction that arises when considering the vast number of the planets in the universe in comparison to the number of apparent advanced life forms.

Just looking at it, the equation seems as complicated and prestigious as Sheldon’s description of it, but it really only involves the multiplication of a few fractions fractions. The formula is as follows:

N = R_{*} x f_{p} x n_{e} x f_{l} x f_{i} x f_{c} x L

When asked if he was familiar with the Drake equation, he responds, “The one that estimates the odds of making contact with extraterrestrial life by calculating the product of an increasingly restricted series of fractional values, such as those stars with planets, and those likely to develop life? N equals R times FP times NE times FL times FI time FC times L?”

In truth, Sheldon’s summary is reasonably accurate, although general. Clark’s video dictates that the variables equal the following values:

N = number of detectable intelligent civilizations (in the Milky Way)

R_{*} = rate of star formation

f_{p }= fraction of those stars that have have orbiting planets

n_{e} = number of planets capable of supporting life

f_{l} = fraction of those life-supporting planets where life *has *evolved

f_{i}* _{ }*= fraction of life that develops intelligence

f_{c} = fraction of intelligent life that develops detectable communications

L = longevity of communications

For further explanation of the variable listed, check out the YouTube video linked above.

As you can see, Sheldon did a fairly good job of describing this obscure formula. The one minute error that can be identified is that Sheldon mistakenly asserts that the Drake equation “estimates the odds of making contact with extraterrestrial life,” instead of the equation predicting the *number* of extraterrestrial life forms *capable* of making contact.

This may seem an irrelevant distinction to make, but it is a mathematical distinction nonetheless.

In order for the equation to be closer to meeting the specifications of Sheldon’s summary, the value of N would have to be divided by the total number of planets in our galaxy. That is to say, N number of detectable, intelligent civilizations out of the X billion number of planets in the Milky Way galaxy.

Although no exact estimate for N exists, the value of N increases all the time, shearly because of the ever-increasing number of planets developing in the universe.

So, whether you’re searching for a date like Howard or an advanced alien civilization, the universe is vast and chances are you won’t be alone forever.