Math Coinky-Dinks

I’m a math guy, so I know that most coincidences are nothing more than people making a big deal out of something that, in fact, is quite likely. I’m not impressed when two people at a cocktail party have the same birthday or when nearly 30% of the people at that same party have a street address that begins with the digit 1.

Nor was I impressed when the Oregon newspaper The Colombian printed a winning number for the state lottery in advance. The probability that the number they accidentally printed on June 27, 2000, which was 6-8-5-5, would actually win the Pick 4 game the following day was 1/10,000. Not likely, to be sure, but not out of the question.

But is it just a coincidence that Douglas Adams claimed that 42 is “the answer to life, the universe, and everything,” and that Oreo cookies can be obtained by pressing 42 on the vending machine in my office?

And is it just a coincidence that ELEVEN + TWO = TWELVE + ONE?

Well, yeah. Probably.

But something happened yesterday that was so strange, it cannot be brushed aside as mere coincidence.

My son Alex was home sick from school. Around two o’clock, he said, “Daddy, I smell blood.” I checked to make sure he wasn’t bleeding… then I checked to make sure that I wasn’t bleeding, either. There was no blood to be found. A couple of hours later, we went to pick up his twin brother Eli at school, and Miss Vanessa at after-school care told me that Eli had an accident.

“He fell and hurt his knee,” she said, “and there was blood everywhere.”

Blood? I asked what time that happened. “Around two o’clock,” she said.

Freaky.

With twin boys, I suspect that there will be similar coincidences in the future. For instance, I suspect that I will one day receive a call saying that both boys were caught in a co-ed dorm after curfew. How weird would that be?

But I’m not phased. Coincidences are very common in my family. For example, my mother and father got married on the same day!

To check out some truly random statistical coincidences, click on over to www.coincidenceithinknot.com.

The following joke is based on a fun math coincidence.

Saul: It’s -40 outside.
Paul: Fahrenheit or Celsius?
Saul: When it’s that cold, it’s impossible to tell the difference.

It’s just a coincidence that -40° F = -40° C.

Or is it?

Random Number Generation

While playing Nurikabe, my sons completed the following puzzle:

The puzzle itself isn’t very interesting, but did you notice the Puzzle ID? Exactly 1,000,000. The boys thought this was pretty cool, and I did, too. Yeah, yeah, I know, the occurrence of 1,000,000 shouldn’t impress me more than the appearance of, say, 8,398,176 or 3,763,985. But there are just under 10,000,000 unique 5 × 5 puzzles on the site, and only nine of them contain six 0’s. How lucky were we to get that random number?

Generating random numbers can be a difficult proposition, especially for a computer. This article from WIRED magazine — which describes a pattern that inadvertently appeared on lottery tickets, making it possible to predict winning tickets before they were scratched — shows how difficult it can be to generate numbers that appear to be random. (The article really is worth a read, especially for math geeks. Truth be known, WIRED is the only magazine that I read cover-to-cover every month.)

Robert Coveyou, a mathematician who worked on the Manhattan project, was an expert in pseudo-random number generators. He is most famously remembered for the following quote:

The generation of random numbers is too important to be left to chance.

Of course, Randall Munroe at xkcd has a foolproof method for generating a random number:

I would hate for you to need a random number and then have difficulty generating one. I’m here to help, so I present the…

MJ4MF Random Number Generator (PDF)

Creating the MJ4MF RNG is quite simple. Just follow these steps:

1. Download and print the PDF from the link above.
2. Cut out all six squares, one for each number 1-6.
3. For each square, make two folds: first, fold the paper to the center vertically; then, fold the paper to the center horizontally. The result of these two folds is shown, below left.
4. When all six pieces are folded, interlace them to form a cube. This is shown, below middle. The assembled cube is shown, below right.

Finally, a joke about random numbers.

A student is asked for the probability that a random number chosen between 0 and 1 will be greater than 2/3. The student answers 1/3. The teacher says, “Great! Can you explain to the class how you arrived at your answer?” The student says, “There are three possibilities: the number is either less than, equal to, or greater than 2/3, so the probability is 1/3!”

Holiday Gifts to Avoid for the Math Geek on Your List

There are lots of lists with suggestions for what to buy a math geek. Don’t believe me? Just do a Google search for “gifts for math geeks.”

As a public service, I’m providing a list of gifts that no one, under any circumstances, should purchase for a math geek. If you’re not a mathy person, take note. Every item on this list will only bring disappointment to the mathy people in your life. If you are a mathy person, print this list, and tuck it into your mom’s purse or leave it on your sweetie’s pillow.

Math Wall Clock

I’ve railed against this one before, and for good reason. Absolutely the worst math gift EVER. The expression for nine is 3(π – .14). Apparently the designer of this clock face isn’t aware that π has a non-terminating decimal representation. And the expression for seven is 52 – x² + x = 10, which has two solutions, 7 and -6. Let’s hope folks don’t start making dinner reservations for “negative six o’clock.” Sheesh.

Acme’s Klein Bottle Wine Bottle

You can take my word that this is a bad gift, or you can listen to the designer. The manufacturer describes it by saying, “As impractical as it is elegant.” Fact. The description is a litany of flaws: “Wine is trying to go down while the air is trying to go up the spout. Result is slow filling. Pouring wine out is equally frustrating.” And, “Not only are these difficult to fill and empty, but cleaning them is a real challenge.” And the piece de la resistance, “They’re easy to tip over, especially when empty.” On the flip side, their web site includes this gem, too: “Now with a LIFETIME GUARANTEE — you will live your entire life, or your money back.”

A better yet equally geeky option is the Klein Bottle Opener, which is practical if you’d like to use a non-orientable manifold to get the liquid out of a boundaryless compact two-manifold homeomorphic to the sphere. Unlike the Acme Klein Bottle, this tool works very well, and you look super cool using it. (Be careful; there are cheaper versions of this item that are only decorative. They won’t open bottles.)

xkcd: volume 0

Okay, sure, this hard-copy volume has “a lot of doodles, notes, and puzzles in the margins,” but, really, you’re paying for a bunch of comics that are available for free at xkcd. What’s more, the math geek on your list has already read all of these comics! (If not, then she isn’t a true math geek. Please call 1-877-NOT-GEEK, and we’ll revoke her license immediately.)

Want a book your math geek will really love? Might I recommend Math Jokes 4 Mathy Folks? (Okay, that was even too shameless for me.)

Infinity Symbol Cuff Links

Need a synonym for geeky? How about dorky, nerdy, dweeby, techy, or studious? Want an antonym for geeky? Try stylish.

Math geeks don’t want silver cuff links. More importantly, they don’t need them. Honestly, what would they wear them with? Plaid flannel shirts don’t have cuff link holes. And for $195, do you really want to buy something that will collect dust in his dresser drawer?

Up and Down — That’s Collatz For Ya

The Collatz Problem goes by many names — some call it the 3n + 1 problem, though it’s also called the Hailstone Problem, Hasse’s algorithm, and others. The Collatz Problem can be stated as follows:

Let a₀ be a positive integer. Then, a_n = 0.5a_n – 1 if a_n – 1 is even,
and a_n = 3a_n – 1 + 1 if a_n – 1 is odd.

The Collatz Conjecture states that no matter what number you start with, the sequence will eventually reach 1. Originally posed in 1937 by Lothar Collatz, the problem is still unsolved.

Randall Munroe stated the following truth about the Collatz Conjecture at xkcd.com:

In line with this week’s earlier post about the MJ4MF Humorous Math Poem Contest, the following poem about the Collatz Conjuecture comes from poet and retired mathematician Joanne Growney. Growney uses a slightly different statement of the Collatz Problem; in her version, a_n = 1.5a_n – 1 + 0.5 if a_n – 1 is odd.

A Mathematician’s Nightmare
by JoAnne Growney

Suppose a general store —
items with unknown values
and arbitrary prices,
rounded for ease to
whole-dollar amounts.

Each day Madame X,
keeper of the emporium,
raises or lowers each price —
exceptional bargains
and anti-bargains.

Even-numbered prices
divide by two,
while odd ones climb
by half themselves —
then half a dollar more
to keep the numbers whole.

Today I pause before
a handsome beveled mirror
priced at twenty-seven dollars.
Shall I buy or wait
for fifty-nine days
until the price is lower?

Confounding Factors

My colleague Julia is preparing a talk about factoring for an elementary audience, and she created the following problem to use as a warm-up:

Take a two‑digit number ab, and find the least common multiple of a, b, and ab. For example, if you take the number 35, then LCM(3, 5, 35) = 105. For which two‑digit number ab is LCM(a, b, ab) the greatest? (The notation ab is used to indicate the two‑digit number with tens digit a and units digit b, which is equal to 10a + b. This notation is used to distinguish the two‑digit number ab from the product ab.)

Here are some math jokes about factors:

What do you call an amount that exactly divides a recipe for a sweet confection?
A fudge factor.

What do algebra equations and British television have in common?
An X Factor.

Sadly, both of those are my original jokes. Sorry. To cleanse your palate, check out one of Randall Munroe’s original jokes about factoring:

Five Online Math Favorites

According to Google, there are more than 121 million results for “math.” The following is an unordered and incomplete list of some of my favorite math things on the web.

1. I laugh out loud at the comics on xkcd.com, but I think my favorite joke on the site is the disclaimer that appears at the bottom of every page.

Warning: this comic occasionally contains strong language (which may be unsuitable for children), unusual humor (which may be unsuitable for adults), and advanced mathematics (which may be unsuitable for liberal-arts majors).

But if you insist that I choose just one of Randall Munroe’s cartoons, I’ll pick Fields Arranged by Purity.

2. I used to watch really old, really bad movies with my father on Sunday afternoons (but only when the Steelers weren’t playing, of course). The following is a clip that I remember, now ubiquitous on YouTube.  

Ma & Pa Kettle – YouTube 

3. The only thing better than a great a cappella song is a funny a capella song. The only thing better than that is a funny a capella song that involves numerous math puns. Thanks, Klein Four!

Finite Simple Group of Order Two – Klein Four

4. When my friend Art Benjamin was interviewed on The Colbert Report, Stephen Colbert said to him, “You call yourself a mathemagician. Now, what does that mean? Were those two words not nerdy enough by themselves?” Nerdy or not, Art is frickin’ amazing.

Art Benjamin Does Mental Math – TED Conference 

5. The following is a quote I’ve seen numerous times on the web, yet I’ve never seen an attribution. I’ll post it here, and credit Anon, though I’m pretty sure it’s a rip-off from a similar quote by Eleanor Roosevelt — “Great minds discuss ideas; average minds discuss events; small minds discuss people.”

Small minds discuss persons. Average minds discuss events. Great minds discuss ideas. Really great minds discuss mathematics.