## Archive for October, 2018

### Math Words for National Dictionary Day

Want to start today the right way? Say, “Good morning!” to Alexa today, and she’ll respond:

Good morning! It’s National Dictionary Day. Ever wonder what the shortest word is? Technically, it’s a toss-up between the single letter words

andI, but sinceais always capitalized, I’d sayIis just a little shorter.a

Is there anything more powerful than a language arts joke to get the day off to a good start?

I have no words to describe today. I do, however, have a ton of obscene gestures.

So, what’s the shortest **math** word? Technically, *e* and *i*, but if you don’t like constants, then you’ll have to settle for the three-letter words *set* and *box*.

And what’s the longest math word — at least based on the list at Math Words? It has 17 letters, and you’ll get a big hint if you check the time.

What two math words, both having the same number of letters, are equally appropriate to describe a triangle whose sides are congruent?

And what’s the funniest math word? Personally, I think it’s *syzygy*, but according to Tomas Engelthaler, it’s *logic*. In Humor Norms for 4,997 English Words, Engelthaler and Hills (2017) describe a method for determining which words are funniest. I emailed Engelthaler to ask which math word is funniest, and he responded as if it were a completely reasonable question. Without hesitation, he shared a list of math words and their humor rankings, and these five were at the top of the list:

- logic
- math
- theory
- science
- graph

The overall funniest English word, according to Engelthaler’s research? *Booty*. Go figure.

While you may not think that any of those words, mathy or otherwise, are laugh-out-loud funny, this isn’t debatable; it’s based on science.

If you take issue with this research, you’ll need to discuss it with Engelthaler and his colleagues. Please write to him directly to say that you’re bumfuzzled, that his research is malarkey, or that you think he’s a nincompoop.

### Mr. Consistency, Khris Davis

If you flipped four coins, the probability of getting exactly one head would be 0.25.

But the probability of doing that four times in a row is much lower, somewhere closer to 0.0039, or about 1 in 250.

Now, imagine flipping 100 coins four times, and getting the same number of heads each time. The odds of that happening are only slightly better than impossible. In fact, if every person *in the entire world* were to flip 100 coins four times, it would still be highly unlikely that this would ever happen.

That’s how rare it is, and it gives you some idea of what Major League Baseball player Khris Davis just pulled off. The Oakland Athletics outfielder just finished his fourth consecutive season with a batting average of .247. That’s right — the same average four seasons in a row.

Davis had some advantage over our coins, though. For starters, he wasn’t required to have the same number of at-bats every year. Moreover, batting averages are rounded to three decimal places, so his average wasn’t *exactly* the same during those four years; it was just really, really close:

**2015**: .24745 (97 hits in 392 at-bats)**2016**: .24685 (137 in 555)**2017**: .24735 (140 in 566)**2018**: .24653 (142 in 576)

How could something like this happen? According to Davis, “I guess it was meant to be.“

Perhaps it *was* predestination, but I prefer to put my faith in numbers.

Empirically, we can look at the data. From 1876 to present, there have been 19,103 players in the major leagues. The average length of an MLB career is about 5.6 years, which means that an average player would have about three chances to record the same batting average four seasons in a row. It’s then reasonable to say that there have been approximately 3 × 19,103 = 57,309 opportunities for this to happen, yet Khris Davis is the only one to accomplish this feat. So experimentally, the probability is about 1 in 60,000.

Theoretically, we can look at the number of ways a player could finish a season with a .247 batting average. In 2007, the Phillies’ Jimmy Rollins recorded an astounding 716 at-bats. That’s the most ever by a Major League Baseball player. So using a sample space from 1 to 716 at-bats, I determined the number of ways to achieve a .247 batting average:

- 18 hits, 73 at-bats
- 19 hits, 77 at-bats
- 20 hits, 81 at-bats
- 21 hits, 85 at-bats
- 22 hits, 89 at-bats
- 36 hits, 146 at-bats
- …
- 161 hits, 652 at-bats
- 161 hits, 653 at-bats
- …
- 177 hits, 716 at-bats

And, of course, there are the examples above from Davis’s last four seasons.

It’s interesting that it’s not possible to obtain a batting average of .247 if the number of at-bats is anywhere from 90 to 145; yet it’s possible to hit .247 with 161 hits for either 652 or 653 at-bats. I guess it’s like Ernie said: “That’s how the numbers go.“

All told, **there are 245 different ways to hit .247** if the number of at-bats is 716 or fewer.

That may sound like a lot, but consider the alternative: there are 256,441 ways to **not** hit .247 with 716 or fewer at-bats.

So, yeah. No matter how you look at it, what Davis did is pretty ridiculous. Almost as ridiculous as what happened to Saul…

Saul is working in his store when he hears a voice from above. “Saul, sell your business,” the voice says. He ignores it. His business is doing well, and he’s happy. “Saul, sell your business,” the voice repeats. The voice goes on like this for days, then weeks. “Saul, sell your business.” Finally, Saul can’t take it any more. He finds a buyer and sells his business for a nice profit.

“Saul, take your money, and go to Las Vegas,” the voice says.

“But why?” asks Saul. “I have enough to retire!”

“Saul, take your money to Las Vegas,” the voice repeats. It is incessant. Finally, Saul relents and heads to Vegas.

“Saul, go to the blackjack table and bet all your money on one hand.”

He hesitates for a moment, but he knows the voice won’t stop. So, he places his bet. He’s dealt 18, while the dealer has a 6 showing. “Saul, take a card.”

“What? The dealer has…”

“Saul, take a card!” the voice booms.

Saul hits. He gets an ace, 19. He sighs in relief.

“Saul, take another card.”

“You’ve got to be kidding me!” he pleads.

“Saul, take another card.”

He asks for another card. Another ace, 20.

“Saul, take another card,” the voice demands.

But I have 20!” Saul shouts.

“TAKE ANOTHER CARD, SAUL!”

“Hit me,” Saul says meekly. He gets another ace, 21.

And the voice says, “Un-fucking-believable!”