The numbers we deal with most often are the natural numbers: 1, 2, 3…. When it comes to money, we need fractions, what we call “rational numbers”. There are special numbers like pi, too. What all of these numbers have in common is that they are “real numbers.” You can order them in a row by size and you can do math with them. Some can be really large (like the US deficit) and some can be really small (like the percentage of Obama eligibility cases won by plaintiffs), but they are all real numbers.
In math there are some questions that cannot be answered by real numbers, like what number squared equals minus 1. For that, mathematicians created a special “imaginary number” and represented it with the symbol i. You can multiply real numbers by imaginary numbers, and you can add them too. When you add a real number and an imaginary number, the result is a complex number and it is written like “6 + 7i” where 6 is the real part and 7 is the imaginary part.
Here’s where birther math comes in. Birthers say that President Obama has spent millions of dollars in legal fees keeping his records hidden. They don’t have any facts behind these numbers; they just make them up, and they get bigger as the story gets told and retold. It is almost certain that Obama has had legal fees, since folks like Philip J. Berg have sued him, claiming all sorts of things from birth in Kenya to renunciation of citizenship in Indonesia. Berg calls Obama a fraud, and Obama has no choice but to defend himself against these charges. While this case, and all the others naming Barack Obama as defendant, have never gone to trial, being summarily dismissed, it stands to reason (even though some lawyers have offered their services pro bono) that there are some legal fees involved. These fees, while estimated, are real. The millions claimed by the birthers are not based on any factual foundation, and so they are imaginary. The result, adding the real part (call it R) and the birther imaginary part (call it B) is the complex number that the birthers cite as Obama’s legal fees: R + Bi.
Birthers, however, do not use the correct mathematical notation and simply add R and Bi and call it real. In the real world B=0.