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.
— Anonymous

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

GRiN and Solve It

My boys have been asking to do Math Trivia before bedtime each night, and one of my favorite sites, GRiN: Good Riddles Now, has provided a treasure trove of fun puzzles that they can solve.

Here’s one of them.

There are 100 coins on the floor in a dark room: 90 coins show heads, the other 10 show tails. If you’re not allowed to turn on any lights, how can you divide the coins into two piles so that each pile contains the same number of coins showing tails?

GRiN was started by Justin Zablocki, a math major cum computer scientist who enjoys logic and puzzles. He created GRiN as a way to practice his web development skills and to “improve upon an underdeveloped entertainment category.” (Hear, hear!)

His favorite math joke?

Why does no one talk to π?
He’s irrational and goes on forever.

His favorite riddle?

A murderer is condemned to death. He has to choose between three rooms. The first is ablaze with raging fires, the second is full of assassins with loaded guns, and the third contains lions who haven’t eaten in three years. Which room is safest for him?

Keeping with today’s theme, here’s a math riddle quiz for ya. Enjoy.

1. How is the moon like a dollar?
2. A plane with 56 passengers crashes on the border between Canada and the United States. Where do they bury the survivors?
3. When spelled out, what is the first positive integer that contains the letter a?
4. In a race of 548 runners, you overtake the last runner. What place are you now in?
5. The first term of a sequence is a1 = 13. Every term thereafter satisfies a1 ∙ a2 ∙∙∙ ak = k! for k > 1. What is the 31st term of this sequence?
6. There are four cookies in the cookie jar. You take three of them. How many do you have?
7. If you remove the first letter, the last letter, and all the letters in between, what do you have left?
8. What is the next number in the sequence 1, 4, 5, 6, 7, 9, 11, …?
9. What is the product of all the digits on a telephone dialpad?
10. If you have 6 apples in one hand and 7 oranges in the other, what do you have?
11. What has a face and two hands but no arms or legs?
12. What occurs once in a minute, twice in a moment, but never in a thousand years?
13. A man has four daughters, and each daughter has a brother. How many children does the man have?

1. Both have four quarters.
2. You don’t bury survivors.
3. One thousand.
4. Trick question. It’s not possible to overtake the last runner, because you’d have to be behind him, in which case you’d be the last runner.
5. 31.
6. Three.
7. The mailman.
8. 100. The pattern of numbers are the positive integers that do not have a t in them when spelled out.
9. 0.
10. Big hands.
11. A clock.
12. The letter m.
13. 5. One son is a brother to each of the daughters.

Math in the Senate Election

With the election two days in the rearview mirror, three states remain undecided in their Senate election:

• Louisiana, which uses an archaic and easily manipulated run-off system;
• Alaska, where Mark Begich claims that there are many uncounted rural votes; and,
• Virginia, the Old Dominion — my home state — with Mark Warner and Ed Gillespie in an apparent dead heat.

As of this morning, Warner was ahead 1,071,283 to 1,054,556. That’s a lead of 16,727 votes with 99.9% of precincts reporting. Local newspapers have declared Warner the “apparent winner,” but no concession has been offered.

Why hasn’t Gillespie conceded yet? Perhaps it has to do with simple math.

While 0.1% sure doesn’t seem like a lot — and it’s not, if you’re talking about the amount of alcohol in a bottle of whiskey — it can represent a lot — like when you’re talking about the amount of alcohol in your blood.

It’s also a lot when you’re talking about millions of votes. If the 2,179,235 votes counted so far represent 99.9% of all votes, then the remaining 0.1% represents 2,181 votes. If Gillespie gets all of them, that would bring him within 14,546 votes of Warner. Were Gillespie to get all of the provisional votes that are yet to be counted — the number of which is unknown — well, he probably still won’t win, but I suppose you can’t blame a guy for trying.

And let’s not forget, we’re talking about politicians. For most of them, delusion is a normal state of existence.

A politician’s wife called him from the hospital. “Honey, I had triplets!” she exclaimed. The politician responded, “I demand a recount!”

To be fair, many politicians think realistically — they just don’t think very often.

A cannibal goes to the butcher shop and notices that mathematician brain is selling for \$1 a pound, but politician brain is selling for \$4 a pound. “Is the politician brain really that much better?” she asks the butcher.

“Not really,” he says. “But it takes a whole lot more politicians to make a pound.”

Car Talk Puzzlers

Tom Magliozzi

I make a point of not having heroes, but there are people I greatly admire. Tom Magliozzi, the co-host of Car Talk who passed away yesterday, was one of those people.

Not only was Tom able to make other people laugh, he was always laughing himself. He and his brother Ray hosted Car Talk from 1977-2012, making folks laugh — and think — for 35 years.

In case you haven’t noticed, laughing and thinking are two of my favorite activities.

Every week, Tom and Ray would try “frantically to come up with a mediocre new puzzler,” a logical or mathematical problem that wouldn’t have an immediately obvious solution. Sometimes I’d be able to solve them, sometimes I wouldn’t, but I’d always enjoy them… and I’d laugh out loud while Ray read the puzzler and Tom offered commentary.

Below are two of my favorites, but you can find the full list of puzzlers at the Car Talk web site.

This first one sounds so simplistic, but most folks get tangled up in the details. Share it at your next department meeting, and see how many colleagues can solve it. You’ll be disappointingly surprised!

A store paid \$6.75 for a shirt, and they then sell the shirt for \$12. A man visits the store, buys the shirt, and pays with a \$20 bill. The clerk gives the customer \$8 in change, as expected. But unbeknownst to the clerk, the bill was counterfeit — instead of Andrew Jackson’s picture on the bill, it’s got Michael Jackson’s! In total, how much did the store lose on the entire transaction?

That one reminds me of the Marilyn Burns horse problem: You buy a horse for \$50, sell it for \$60, buy it back for \$70, then sell it again for \$80. Did you make money, lose money, or break even?

This next one is a classic that’s taken many forms. Finding a solution isn’t too hard… finding the simplest solution may take a little effort, though.

You have a four-ounce glass and a nine-ounce glass. You have an endless supply of water. You can fill or dump either glass. You can measure six ounces of water using these two glasses. What’s the fewest number of steps in which you can measure six ounces?

RIP, Click. I’m sure you’re already making people laugh and think upstairs.

Word + Letter = Math Term

On a recent Sunday Puzzle on NPR, Will Shortz gave a letter and a word, and the contestant was to guess the name of a popular TV show using an anagram of the letters (“Coming to TV This Fall: Anagrams,” Oct 12, 2014). For instance,

M + NAMED

This struck me as an interesting puzzle format. My only criticism is that it just wasn’t mathy enough.

But I’m not a problem maker, I’m a problem solver… so rather than cast aspersions at the puzzle, I’ll instead use the format to offer my own version.

Each of the 26 letters of the alphabet has been paired with a common English word. An anagram of the pair will yield a common math word. How many can you find?

1. A + ERA
2. B + AGLARE
3. C + BITES
4. D + NOTICER
5. E + EDGERS
6. F + SAUCER
7. G + LEAN
8. H + OPERABLY
9. I + TANGLER
10. J + INDUCTIONS
11. K + SEW
12. L + POSE
13. M + RIPS
14. N + AIMED
15. O + PINT
17. Q + AURES
18. R + ENVIES
19. S + RECITED
20. T + HAM
21. U + RAIDS
22. V + EXERT
23. W + ROPE
24. X + SEA
25. Y + PENTHOUSE
26. Z + ORE

I don’t believe in providing an answer key, but you can find some help at Math Words, and you can click over to More Words if you run into real trouble. But give it the old college try before seeking assistance. Honestly, you’ll feel better about yourself if you solve these on your own.

Halloween Math Jokes (Best Of)

I’d like to put together an entire collection of Halloween math jokes, but I don’t have the energy to write it.

I think I’ll use a ghost writer.

Did you hear about the ghost who earned 14% on his math exam?
He made a lot of boo-boos.

The following is blatantly stolen from all the other sites who blatantly stole it from somewhere else…

I’ve published a post with Halloween math jokes for the past several years.

Got any good Halloween math jokes? Please share!

True Inequalities

It’s true that Bertrand Russell once stated he could prove anything, given that 1 + 1 = 1. What’s likely not true is that someone challenged Russell to prove that he was the Pope, and he responded by saying, “I am one. The Pope is one. Therefore, the Pope and I are one.”

Whatever. Even apocryphal, it’s a fun story. Who needs truth, anyway?

Ask the poet (Keats) who said that what the imagination seizes as beauty must be truth.

He might also have said that what the hand seizes as a ball must be truth, but he didn’t, because he was a poet and preferred loafing about under trees with a bottle of laudanum and a notebook to playing cricket, but it would have been equally true.

— Douglas Adams, Dirk Gently’s Holistic Detective Agency

The following inequalities are — under some circumstances — true.

1 + 1 = 1

See above. (Were you even paying attention?)

1 + 3 = 1

This inequality comes from an athletic shirt that I own. What happens when one large, hungry fish meets three little fish? One large fish leaves with a full belly. (In case you can’t see it in the picture, there are four sets of small fish bones in the big fish’s belly.)

10 + 10 = 100

Binary much?

1/10 = 20%

Middle school teachers will cringe at seeing this seemingly incorrect fraction-to-percent conversion, but it’s true if you’re looking at a nutrition label. Eat 10g of low-fat Swiss cheese with 1g fat and 9g protein, and 20% of your calories come from fat.

10 + 4 = 2

On a calculator? No. On a clock? Yes. Move 4 hours past 10 o’clock, and it’s 2 o’clock.

1/2 + 1/3 = 2/5

More for middle-school teachers to cringe about. But if you play sports and want to compute your shooting, passing, or batting average, this equation is totally legit.

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

MJ4MF (offline version)

Math Jokes 4 Mathy Folks is available from Amazon, Borders, Barnes & Noble, NCTM, Robert D. Reed Publishers, and other purveyors of exceptional literature.