## Archive for August, 2013

### Flatulence Funniness Formula

Little kids love flatulence.

I was reminded of this when my two five-year-old sons Alex and Eli, my wife Nadine, and I were playing Blokus at the dining room table, and one of us (who shall remain nameless) brought forth a sound slightly louder but a little less musical than a kazoo.

“Excuse me,” said the offending party. And then both boys giggled uncontrollably until they were out of breath and red in the face.

“Are farts funny?” Nadine asked, after they collected themselves.

“Well, they are,” Eli began, “but the older a person is, the funnier their farts are.”

“That’s true,” Alex agreed, “but it also matters how much they fart. The more often someone farts, the funnier it is.”

Intrigued, Nadine had a series of follow-up questions. “Are grandma’s farts funny?” she asked.

Both boys answered quickly and unequivocally in the negative.

“Are daddy’s farts funny because he farts a lot?” she then asked.

“Daddy farts a lot, and he’s also old — that’s why his farts are so funny,” Eli explained.

“But his stinky farts are **not** funny!” Alex insisted.

All of this pontification got me to thinking: someone ought to devise a formula to estimate how funny a fart is. Given my expertise, I decided that that someone should be me.

Alex and Eli had already identified three factors — frequency, age of offending party, and odor. In addition, I believe that sound quality, attractiveness of the offending party, and inappropriateness of the situation are also important criteria.

But I had no idea how these components should be incorporated. To do this justice was going to require some research.

According to the National Institutes of Health, an average person breaks wind between 14 and 23 times per day. (Wow!) So based on Eli’s belief that more often is funnier, but also based on my experience that there can definitely be too much of a good thing, it seems that a flatulence frequency slightly above average — maybe one fart every 40 minutes — would be funny, but significantly above average — such as one fart every 2 minutes — would be devoid of humor and, quite frankly, disgusting. Consequently, the **frequency (F)** in the formula below takes into account the number of rectal tremors released within earshot of another human being during the past hour (not counting the current infraction).

**Age ( A)** is a delicate issue in this analysis. Farts from very young kids can be funny, and I personally think that farts from really old people are hysterical. For people in between, age isn’t much of a factor — unless you’re a teenage girl, in which case the embarassment of a public toot would be too much to bear.

The **loudness ( L)** of a fart is measured in decibels, as is any sound. For a fart to be funny, it has to be loud. Silent farts are not funny — they can’t evoke laughter if no one hears them, and they most definitely aren’t funny if they fall into the silent-but-deadly category. But any sound over 130 decibels immediately causes ear damage, so the formula below assumes that no fart will be greater than 130 dB. It’s difficult for me to fathom that a fart could exceed that level — that would put it on par with a jackhammer or gunshot. (Great googly-moogly! If you’re reaching that standard, change your diet!)

The **beauty ( B)** of the offending party, measured on a scale of 1‑10, also has an impact. No one wants to imagine — or worse, actually witness — a supermodel letting one rip. But on the flip side, most of us are equally mortified by the thought of a repulsive person cutting the cheese. The formula therefore uses a quadratic relation, so that a person with middle-of-the-road looks receives higher marks.

As Alex said, stinky farts are not funny, so **smell ( S)** is a major concern. As it turns out, odor has four properties: odor concentration, odor intensity, odor quality, and hedonic tone. Biochemists use very detailed methods to measure each of these properties; for the purpose of this analysis, however, only odor intensity will be considered. A complex formula called the Weber-Fechner law ranks the odor intensity of a smell on a scale from 0 (no odor) to 6 (intolerable). You don’t need to use some complex formula; let your nose be your guide. If

*S*= 6, the formula below automatically zeroes out.

^{1}

Finally, the **inappropriateness ( I)** of the situation has to be considered. The formula below accepts values from 1 (“whatever, no big deal”) to 10 (“oh, no, you didn’t!”). Of course, this is a highly subjective factor. While it is certainly inappropriate for a groom to pass gas while reciting his vows on the altar, it’s a whole lot funnier than releasing an air biscuit while delivering the eulogy at your father’s funeral. So

*I*= 4.2 for the gassy groom, but

*I*= 9.9 for the guy who shows no respect for the deceased.

Put this all together, and what do ya get?

For the most part, the formula will return values in the range 0‑100, so it works sort of like a song rating on *American Bandstand*.

Yeah, it’s not perfect, and I’m happy to hear suggestions for improvement. But it works pretty well. A middle-aged (*A* = 45) woman with average looks (*B* = 6) who kills the canary for the first time that evening (*F* = 0) with a loud (*L* = 95) but relatively mild (*S* = 1) honk while playing Scrabble^{®} with her sister (*I* = 1) would score a 49.5; and having witnessed my mother and aunt bust a gut at this very scenario on numerous occasions, my instinct is that such a score is about right.

On the other hand, a man of any age who releases a silent-but-deadly (*L* = 0, *S* = 6) would score a 0 regardless of his looks, his age, how long since his last incident, or the situation. And that feels right to me, too. That sick SOB! How dare he?

And lest you think you’ve read all the way to the bottom with not a single joke, don’t dismay! Here’s a joke that’s both mathy and relevant to the rest of this post. (Be afraid… be very afraid.)

What do you call a math teacher who never farts in public?

A private tooter.

^{1} It occurs to me that (a) I’ve spent entirely too much time doing the research for this post and (b) I now know more about flatulence than I ever wanted or needed to.

### Longest Side of a Right Triangle

I’m rather tall — between 5’11” and 6’4″, depending on which convenience store I’m leaving — but my wife is quite a bit shorter. One of her great laments was our decision to install a tall toilet in our main bathroom when we had it remodeled. I love it, but her feet dangle three inches off the floor when she uses it.

This morning, she knocked on the door while I was in that bathroom. “Are you in there?” she asked.

“Yep,” I said, “and it feels like the longest side of a right triangle in here.”

She was about to ask, “What?” Then she saw it was a set-up, so she didn’t. But I don’t need no stinkin’ straight man; I delivered the punch line anyway:

High pot in use.

The typical set-up for that punch line usually goes something like

What do you call a kettle of boiling water on top of Mount Everest?

A better set-up is

What do you call a kettle of boiling water in a hangman’s rope?

because then the punch line is, “High pot in noose,” which sounds more like the real term.

But based on this morning’s incident, I think the best set-up may be

What do you call a tall toilet in an occupied bathroom?

Whatever, pick your poison. It’s not like any of ’em is gonna win you a free beer at the next improv comedy night.

### Vi Hart, Sierpinski, and the Chaos Game

My kids love to spend the last 20 minutes before lights out doing math with daddy. Often, as an alternative to reading another chapter from the *Magic Treehouse* series, they will ask, “Can we do bedtime math tonight?”

Unfortunately, the materials at Bedtime Math quickly lost their luster — if not for Alex and Eli, at least for me. The problems are based on current events, but they are little more than traditional textbook exercises. Sorry, that’s just not the math to which I’d like my sons to be exposed.

So instead, I’ve been developing my own ad hoc bedtime math curriculum. Last night’s lesson was the Binary Trees video from Vi Hart’s Math Doodling series.

For 3 minutes, 48 seconds, the video had the boys’ rapt attention. When it ended, Eli turned to me. “Well, *that was pretty cool*,” he said.

This afternoon, we explored an extension.

- Draw equilateral triangle
*ABC*, any size you choose, on a sheet of paper. - Randomly pick a point
*Q*on the same sheet of paper. - Now, randomly pick a vertex
*A*,*B*, or*C*, and place a dot at the midpoint of the segment that connects*Q*to that vertex. (But don’t draw the segment. That’ll just make things messy.) - Again, randomly pick a vertex
*A*,*B*, or*C*, and place a dot at the midpoint of the segment that connects the previous point to that vertex. - Repeat Step 4 thousands of times, or at least enough times to see a pattern emerge.

We played this game for a little while using a 12-sided die to determine the randomly selected vertex. A roll of 1-4 chose *A*, 5-8 chose *B*, and 9-12 chose *C*. Interest was starting to wain after 20 rolls, so we paused for a question:

Notice that most of the points occurred within the triangle. If we continue rolling and drawing points, do you think any more points will occur outside the triangle?

The answer is **no**. All points will occur within the triangle.

If you haven’t seen this game before, it’s called the Chaos Game. And if you don’t have interest in rolling a die 2,496 times to see what happens, you can open the Chaos Game spreadsheet. The values in column B are the *x*-coordinates of the points, and the values in column C are the *y*-coordinates. Change the values in B1 and C1 to pick a new starting point, and hit F9 on a PC or fn+F9 on a Mac to generate a new set of data.

Cool, huh?

### Math in Great Literature

I’ve been reading a lot recently. And not just math books. In fact, I just finished reading a book on antigravity — I couldn’t put it down.

Though the books I’ve been reading are known as great literature, they have a lot of great math, too. From Lewis Carroll, we have the following gem…

The four branches of arithmetic are ambition, distraction, uglification, and derision.

But let’s not forget about A. A. Milne, who didn’t write the following joke based on improper logical thinking, though he easily could have…

Winnie the Pooh and Piglet receive a box from Eeyore. In the box are 10 sweets and a note. The note says that they are to divide the sweets evenly — 7 for Pooh, and 7 for Piglet. “How is that possible?” asks Piglet.

“I don’t know,” replies Pooh. “I don’t even want to think about it. But I’ve already eaten my 7 sweets.”

And speaking of that tubby, little cubby all stuffed with fluff…

What is Winnie the Pooh’s favorite math subject?

Tiggernometry.