The Irreverent Blog of Mathematics

By Logan Evans

A private letter to my mother

Journalists claim that for every equation you put in an article, you lose half your audience. In equation form, this is

$$ p = \frac{P}{2^n} + m $$

P is the prospective audience, n is the number of equations in the article, p is the final number of readers, and m is your mother, if she's still alive.

I want to write a private letter to my mother, but I want to display the letter publicly. Let's also suppose that I'm a noob and can't use public key encryption (because I'm really bad with 100 digit primes... they make me feel soggy). According to the journalism powers that be, I just need to put enough formulas into this essay to halve my audience enough times so that $ 1 > \frac{P}{2^n} $. I realize that this is an inequality, not a true equation, but I don't think those journalism powers are aware of the difference, so I'll include it in my final count.

There are between 500 million and 1.8 billion English speakers in the world (in equation form, if n is the number of English speakers, then $ 5.0 \times 10^8 \le n \le 1.8 \times 10^9) $, but this is an overly egotistic estimate for my potential readership. A lower estimate that is still equally conceited would be to use the circulation figures of the most popular newspaper as my potential readership P. According to all-knowing Wikipedia, hallowed be its name, the most popular newspaper is The Wallstreet Journal at 2.1 million copies distributed every week. So, here's a high school math problem (that should reduce my readership by half... go away pesky readers). Letting $P = 2.1$ million in my first equation, find the smallest $n$ such that the following inequality is true:

$1 > \frac{2.1 \times 10^8}{2^n}$

(Actually, I'm not sure if this would be a high school problem. High school curricula designers seem to have a phobia of inequalities. Not sure why... maybe they're afraid of making students think too hard and spontaneously combusting... yes it can happen! It happened to this girl I liked in tenth grade chemistry class when she was putting on hairspray while trying to boil a cup of water over a Bunsen burner... the teacher put an inequality on the board that claimed that the water temperature was always LESS THAN 101 degrees C).

I'm inherently lazy and don't want to solve the problem I posed yet, so in procrastination, I'll ask myself this: why might journalists have such a terror of equations? I once asked my imaginary friend Bob the Journalist how he would feel about losing half of his audience for any given article. He told me that he would rather lose an arm and a leg. Coincidentally, Worker's Compensation has a limit to how much they will pay out if someone gets injured. The payout for someone who gets mutilated to death is exactly the same as if that person loses an arm and a leg. Thus,

$$ one person = arm + leg$$

That's why

$$ Worth(American\ Citizen) = 2 \times Worth(not\ an\ American\ Citizen) $$

because we've got two arms and two legs.

In contrast to Bob the Journalist, a scientist who puts equations into his or her paper has more of a sour grapes philosophy about losing half of his or her prospective audience. They'll say, "I didn't want those people to read my article anyway. They wouldn't appreciate the nuances of my art. A wine ignoramus can't tell the difference between an amontillado and a sherry, and those people wouldn't have been able to distinguish my work from a Jackson Pollock painting! And they've got cooties!" For those few readers who are still reading (you shall be disposed of presently), here is that English statement translated into mathglish:

$$ amontillado \stackrel{?}{=} sherry $$

$$ math \stackrel{?}{=} Pollock Painting $$

[get a picture of a math professor's chalk board. Caption: This is either worth a million dollars... or it isn't]

Now that I've halved my audience a sufficient number of times, I can safely preach to the choir and complain about how it's absurd to think that so many people are so scared of equations that they will stop reading anything with an equation in it. Presumably, most people reading anything other than Shonen Jump and Cosmo Girl! have had some high school math, and I would hope that it's not completely erroneous to assume that high school students see equations in their math classes. Avoiding equations on the assumption that readers are unable to handle them is like assuming that students don't learn anything in their math classes. Hmm... that might not be a completely unfounded assumption...

Perhaps journalists make the same assumption about their audience that Jay Leno makes about his audience: people are incapable of handling anything involving brain waves. I personally feel that this is a bad approach. If someone is a zombie, then you should hack, slash, blow up, or otherwise dismember that person. Don't say, "Oh... you want brains? Er... here's a squishy ball. Go play."

Presumably, high school classes should prepare teenagers for life in the broad world. If life in that broad world assumes that everyone failed their high school math classes, then what is the point of having teenagers take math in the first place? After all, any babysitter will tell you that it's easier to waste time having kids watch TV than it is to teach them how to factor a quadratic equation. I'm sure it would be easier, and more fruitful, to change all high school math classes into Desperate Housewives Appreciation Class. After all, Desperate Housewives, unlike high school algebra, teaches kids useful life skills.

Anyway, I finally pulled out a calculator to solve the math problem I posed above. I started with $n=1$, then $n=2$, and used the recurrence of $n_{i+1} = n_{i} + 1$ (this is a fancy way of saying that I tried all of the numbers in my calculator until I got lucky with a solution, but I said that using 3 equations!). In the end, the solution is $n=22$. So, I need 22 equations in order to make certain that no one except my mother is reading this essay. So far, I have used 13 equations. (In Mathglish, letting "s" represent the number of equations that have appeared thus far, $s = 13$).

But now $s = 14$

Wait! But now $s = 15$

But now $s = 16$ It's a paradox! [include a picture of two ducks (get someone to draw it)... the caption will be "a pair of dox going for a swim"] Let's look at a tally of how large my audience could possibly be by this point. Again, letting $P = 2.1 \times 10^6$, then, $ \frac{2.1 \times 10^6}{2^{18} + 1} = 9 \ge x \ge 5 = \frac{2.1 \times 10^6}{2^{19} + 1}$

I had to use an obnoxious inequality like this to avoid the paradox of expressing the thing that I'm counting in the form of the thing that I'm counting (that sounds trippy). At this point, I need to get rid of four more readers.

$$ a^2 + b^2 = c^2 $$

is scary enough to get rid of two of you.

Stating that $ a^n + b^n = c^n $ gets rid of one more (keep in mind, this is Fermat's Last Theorem, so for any whole number $n$ greater than two, you will be unable to find integers for $a$, $b$, and $c$ to satisfy the equation).

Finally, $1782^{12} + 1841^{12} = 1922^{12}$ gets rid of the last of you! Don't let the door hit you!

Oh, how lonely it is to be writing an article with such a small audience. In any event, it's just you reading this, Mom. So, here's your letter.

Dear Mom,

$x$

Love, Logan

P.S. $x$ is not strictly a member of any set of numbers. Instead, $x$ is a variable that is intended to represent anything you want it to represent.