## Posts tagged ‘Venn diagram’

### The Weird I Before E Rule

I’ve always hated the I before E except after C rule. My hatred is simple: a rule is a “prescribed direction for conduct,” and, as far as I’m concerned, it should be accurate very close to 100% of the time.

The Triangle Inequality? That’s a rule that always works.

The sum of the angles of a triangle? It’s 180°, 100% of the time.

Ceva’s Theorem? Completely worthless, to be sure, but also completely correct.

But the I before E rule? I wasn’t sure how often it was inaccurate, but it only took a few seconds to come up with myriad counterexamples:

- weird
- science
- neighbor
- rein
- pricier
- deficient
- eight

That’s the thing, right? Math rules always work. Else we wouldn’t call them rules. But grammarians, philosophers, artists — pretty much anyone with a liberal arts degree — will call anything a rule that works some of the time.

So with some help from MoreWords, I created the following Venn diagram:

Let me ‘splain. No, wait… that would take too long. Let me sum up.

There are 5,443 words that contain either EI or IE. Of those,

- 3,562 correctly contain IE not following C
- 62 correctly contain EI following C

That is, of the 5,443 words containing EI or IE, **1,591 words** violate the rule by having **EI without a C** in front of it, and **162 words** violate the rule by having **IE with a C** in front of it.

Which is to say, only 66.6% of the words that contain either EI or IE adhere to the rule *I before E except after C*.

Put another way, **the rule is total bullshit**.

These numbers are consistent with an analysis from Language Log, which looked at about 8.7 million words randomly pulled from a month of the NY Times. It was found that 174,716 words contained EI or IE, but only 114,070 words correctly followed the rule, which means the rule held about 65% of the time.

One of the readers of Language Log commented that the rule works with the following amendment:

When the sound is long E,

it’s I before E,

except after C.

I’ll call bullshit.

I didn’t even have to think to come up with a list of words for which that modified rule fails:

- seize
- leisure
- either
- neither
- protein

Speaking of rules…

Philosophy is a game with objectives and no rules.

Mathematics is a game with rules and no objectives.

— AnonymousMathematics is a game played according to certain simple rules with meaningless marks on paper.

— David Hilbert

### Therapeutic Numbers

I was lying on my left side, my right leg awkwardly bent so that my right foot was flat on the floor in front of me, and my left leg was extended straight out underneath my bent right leg. There was a weight strapped around my left ankle, and I was lifting my left leg as high as I could. “How many?” I asked.

“Thirty,” said my physical therapist.

I’m not sure if she heard me gulp. I had only done eight so far, and already my thigh was screaming.

But that was nothing compared to the guy next to me. He was lying face-down on a table, his head and arms hanging off of one end. In each hand was a dumbbell, and he had to rotate his shoulder joint until his arms were parallel to the ground. After his first few, he asked, “How many?” She told him 30, too.

He did a few more, and his grunts were getting louder. “How many?” he asked again, but now with an air of incredulity.

“One-hundred fifty-two,” our therapist said. “That’s *always* the answer the *second* time you ask.” She smiled, then she looked at me. “I’m not sure why 152 is the number I pick.” It seemed reasonable that she’d want to explain her choice to me. After all, I am a numbers nerd. (Not a dweeb, geek, or dork. See below.) But then I realized she doesn’t even know what I do.

“It’s a fine number to pick,” I said. “After all, it’s evenly divisible by the sum of its digits: 152 / (1 + 5 + 2) = 19.”

She squinted a bit, and she raised one eyebrow slightly. I was undeterred.

“But 153 might be a better choice,” I continued. “It’s the sum of the first 17 counting numbers: 1 + 2 + 3 + … + 17 = 153. And if you raise each of its digits to the third power and then add them, you get 153 again: 1^{3} + 5^{3} + 3^{3} = 153.”

She now raised both eyebrows. Her head shook a little as she asked, “You just *know* that?”

“Yes,” I said. “And I often wonder how much useful information I could keep in my head if it weren’t filled with all this trivia about numbers.”

Then there was a long, silent pause. It probably would have been uncomfortable to a less mathematical, more socially adept individual. But not me. However, I felt bad when my therapist started to squirm, so I continued.

“What’s exceptionally cool, though, is that if you take any three-digit multiple of 3, and then add the third power of its digits, and then add the third power of the digits of the result, and keep doing that, you’ll always get back to 153.”

There was another long, silent pause.

The shoulder guy next to me finished his exercises. “What next?” he asked.

“How about some dumbbell presses,” she suggested.

“How many?”

She looked at me. “15*3*,” she said, with a little extra emphasis on the three.

### Flight of Fancy

Several weeks ago, after my team won the 2011 Grand Masters National Championship in Ultimate Frisbee (sorry, I just couldn’t resist saying that again), a teammate and I headed to the Dayton airport. The plane that was to take us to Dulles had a mechanical problem, though, so our flight, originally scheduled for 7:05 p.m., was delayed until 10:55 p.m. The following diagram sums up what it feels like to be stuck in the Dayton airport for four extra hours with only a Cinnabon to provide solace:

Then last night, after spending four days at the NCTM Interactive Institute for High School Mathematics, I headed to the Orlando airport. This flight was similarly delayed, though weather was the culprit this time. Although delayed only two hours, we departed too late to arrive to Reagan National before the airport curfew. Consequently, we were diverted to Baltimore-Washington International, where we could wait over an hour for a bus to drive us 75 minutes to Reagan National Airport, at which point we’d be dropped off at a closed airport and left to fend for ourselves. (Reagan National closes at midnight, and the DC Metro trains stop running at midnight.)

So I shared a cab with a pleasant young lady who lives near me in Virginia, and after sitting in a construction zone for 35 minutes and driving 46 miles, I finally arrived home. The picture below shows the taxi meter upon arrival. This is the greatest amount (by a lot) that I have ever seen on a taxi meter.

You might also notice the clock at the bottom of the picture. I arrived home at 1:25 a.m., only to be awoken at 6:56 a.m. to the sound of my Golden Retriever getting sick. Nothing says, “Welcome home!” quite like a nice pile of yellow doggy vomit on the bedroom carpet.

For my next trip, I plan to drive.

On the upside, at least I wasn’t stuck behind this guy:

When a statistician passed through the airport security checkpoint, officials discovered a bomb in his bag. He explained, “According to statistics, the probability of a bomb being on an airplane is 1/1000. Consequently, the chance that there are two bombs on one plane is 1/1,000,000, so I feel much safer if I bring one myself.”