Archive for May, 2012
This is René Descartes’ most famous quotation:
Cogito ergo sum. (I think; therefore, I am.)
The following moldy oldie, known by almost everyone, is based on that quote:
René Descartes was sitting in a bar. When asked if he wanted another, he said, “I think not.” And he promptly disappeared.
Slightly less well known is the following quote by Saul Steinberg:
“I think, therefore Descartes is.”
I rather like the following limerick based on Descartes’ famous quote:
There was a young student named Fred;
When asked about Descartes, he said:
“It’s perfectly clear
That I’m not really here,
For I haven’t a thought in my head.”
For my money, though, the best René Descartes quote is the following:
Each problem that I solved became a rule which served afterwards to solve other problems.
That reminds me of another moldy oldie, which comes in many different varieties…
A mathematician had tired of academia, so he decided to join the fire department. During his training, the chief asked him, “If you were walking down an alley and came across a dumpster that was on fire, what would you do?”
“Why, I’d get a hose and douse it, of course!”
“Correct,” said the chief. “And what would you do if you were walking down an alley and came across a dumpster that was not on fire?”
“I suppose I’d light the dumpster on fire.”
“You’d do what?” screams the chief.
“I’d light it on fire,” says the mathematician, “thereby reducing it to a previously solved problem.”
I have been to many conferences and conventions. However, the one I attended today is the first that had (or needed to have) the following disclaimer on its website:
Costume weapons must be inspected and peace bonded. Taking costume weapons outside the hotel will create conflict.
The conference was Balticon 46, the annual convention of the Baltimore Science Fiction Society.
Attendees included science fiction writers, engineers, physicists, and other scientists. To my great surprise, I was envious. No, I did not have any interest in dressing like Mr. Spock, a troll, or Supergirl. But just as Susan Orlean observed true passion through the eyes of John Laroche while writing The Orchid Thief, I felt the fervor of the Balticon attendees. They are deeply passionate about science, they embrace their inner geek, and they devote themselves to learning so they can write science fiction that feels real.
In a word, it was awesome.
I found myself hoping to someday be as passionate about something — anything — as these folks.
I was invited to Balticon to give a humorous math presentation that I call Punz and Puzzles. Outside the room where I was presenting, there was a sign listing the day’s events and times. It read as follows:
0810 – Sunday Cooperative Shavuot Service
1000 – Sucking and Swallowing
1500 – Punz and Puzzles
1700 – Improved Long-Term Therapy to Prevent Recurrent Herpes Outbreaks
That sign alone made my attendance worthwhile. It would appear that the conference is attended by lascivious, orally fixated, math-loving Jews. That’s an interesting demographic.
At the end of my presentation, I asked if anyone had a math joke to share. One gentleman stood up eagerly and said, “Yes, I have some.” Uh-oh. Here’s a guy who wants to occupy the stage for a while. His first joke (below) was reasonable. His next five were not… but I’ll spare you the pain.
What is this?
Hilton + Wilding + Todd + Fisher + Burton + Warner + Fortensky
A Taylor series (specifically, the Elizabeth Taylor series; those are the last names of her husbands)
When it was all over, it occurred to me… perhaps math jokes are my passion? (Shudder.)
I am not an expert in early childhood education, so when I was asked to give a presentation at the National Head Start Conference, I had to find a way to establish credibility. I told the audience, “Though I’m not trained as a pre-school teacher, I currently have a pre-school classroom with two students.” I then showed a picture of my twin sons.
Did it establish credibility? I’m not sure. But it was enough to encourage a mother of twins to share some advice with me.
“The best thing we ever did,” she said, “was use even and odd days. One kid got to choose on even days, the other kid got to choose on odd days.” This struck me as sheer brilliance. At the time, my wife and I had a series charts to keep track of whose turn it was: one for who got the Mickey Mouse plate at dinner; one for who got to sit on the passenger side in the car; one for who got to go first when we played Chutes and Ladders; and another fifteen or so for other minutia. It was driving me batty, so this suggestion was a game-changer.
When I returned home from the conference, we immediately implemented this system. We explained to the boys that Alex would get to choose things on odd days, and Eli would get to choose things on even days. (The selection wasn’t arbitrary. Eli would get even days since both Eli and even started with an e.)
Eli said, “But Alex will get to choose two days in a row, on the 31st and the 1st.”
Good point. We decided that the 31st would be mommy and daddy’s day to choose (and in leap years, we’d also claim February 29).
This system worked well, even at bath time, when both boys wanted to sit near the front of the tub to have access to the spigots. Since they took baths every third day, the odd/even system was just fine. Until recently.
About a week ago, we decided to do baths every second day. For this scheme, the odd/even system had three fatal flaws:
- Because of months with an even number of days, there would be strings of up to 31 consecutive baths where the same child would have the choice. (For instance, if baths occurred on even dates in September, they’d also occur on even dates in October; but then in November and December, all baths would occur on odd dates.)
- In any given year, Alex would get the choice between two and five times more than Eli would. (It depends on whether it’s a leap year or not, and on whether the sequence started on an odd or even day in January. But in every case, the system unfairly benefitted the child who receives the choice on odd days.)
- Allowing the 31st to be mommy and daddy’s day to choose doesn’t fully solve the problem. Plus, it smacks of favoritism when a parent chooses one child over the other (for anything).
Uh-oh. I feared that a new chart would be created, and we’d be returned to the bleakness we knew before the even/odd system had been implemented.
I had to act quickly.
Luckily, I was able to devise a new system, and in the process I taught Alex and Eli about modular arithmetic. As a family, we created the chart shown below. The columns indicate those numbers that are congruent to 1, 2, 3, and 0 modulo 4. As shown, Alex would get the choice on days congruent to 1 or 2 mod 4, and Eli would get the choice on days congruent to 3 or 0 mod 4.
But as you can see, this system still unfairly benefits Alex. The solution? Alex does not get the choice if a bath occurs on the 30th of a 31-day month. On those days, I suggested that a coin toss would be used to determine who gets the choice. “If it’s heads, Alex gets the choice; if it’s tails, Eli gets the choice,” I said.
Both boys seemed uncomfortable with this. For some reason, they inherently distrust coin tosses.
So we agreed that we would roll a die instead. ”If the roll is even, Alex gets the choice; if it’s odd, Eli gets the choice,” I suggested.
“No,” said Eli. “I get even.”
Such is life in a house with mathematical twins. Everything is a debate. I’m just thankful that it’s a debate about numbers and not about eating broccoli.
Name dropping is the practice of mentioning the name of illustrious or famous people in casual conversation. By implying a connection to that person, the dropper hopes to raise his social status to the level of the droppee.
Wikipedia says that name dropping is “usually regarded negatively.” I say that it’s downright obnoxious… unless, of course, you’re dropping the name of a long-deceased mathematician into conversation for your own amusement. In that case, it is not only acceptable but strongly encouraged.
For instance, imagine that your friend suddenly shows up at your house and announces, “I just proved the parallel postulate!” It would be perfectly appropriate to respond as follows:
Are Eucliding me?
The following is a list of other ways that you might consider working mathematicians’ names into daily conversation. Good luck! And when you use one of these at a cocktail party and you’re the only one who laughs, just remember — it’s not because it isn’t hysterical; it’s just that none of the other attendees are as sophisticated as you.
- I’m ready, willing, and Abel, but I still can’t solve a quintic equation with radicals.
- What’s the sum of the first 100 positive integers? Your Gauss is as good as mine.
- What’s good for pa is good Fermat!
- I just proved the minimax theorem, and I feel like a Neumann.
- Either he Cantor he won’t!
- Did you thay thomething? Noether!
- Banach, Banach. Ba-who’s ba-there?
- Math jokes make me say Hardy har har.
- I’ll figure out the strategy to this game, Conway or another!
- Why, you dirty little Pascal!
- Math is good Fourier soul!
- He wouldn’t see her until his book was published… but he Kepler in his thoughts.
- Neils Henrik Abel proved that quintic equations couldn’t be solved with radicals.
- It is claimed that Carl Friedrich Gauss found the sum of the integers 1 + 2 + 3 + … + 100 at an early age by recognizing that there were 50 pairs, each pair adding to 101.
- John von Neumann proved the minimax theorem.
- John Horton Conway did a lot of work in combinatorial game theory.
- Johannes Kepler’s engagement to Barbara Müller almost fell apart while he was finalizing Mysterium.
And, of course, there is this old gem:
A mathematical horse was able to learn arithmetic, algebra, and even Euclidean geometry. But no matter what the trainer tried, the horse just couldn’t master analytic geometry. Moral: You can’t put Descartes before the horse.
In sixth grade, I overheard two teachers talking about a new school policy. We had just moved into an elementary school that was four stories tall, and it was decided that any time a class needed to move between floors via the staircases, students should always stay to the right — “just as your parents do when driving on a road,” we were told.
One teacher said to another, “Given our principal, I’m surprised it isn’t up on the right, down on the left!”
Nothing like a little administration-bashing to cleanse the soul, eh?
I was reminded of this over the weekend, when my sons and I participated in Bike DC, a family-friendly event in which thousands of riders were given the privilege of riding along the streets of Washington, DC, on a beautiful Sunday morning, during which the streets were closed to traffic. It was quite a thrill for Alex and Eli to ride in front of the President’s house. We turned around before the designated turn-around spot, but I was rather proud that my five-year-old sons were able to log 7.5 miles.
Unfortunately, there was a problem with the course design. See map below.
We followed a simple out-and-back course along several major roads. As shown above, we went out via the blue line and returned via the green line. And just like driving, we spent the first several miles in the right lane. But as the blue line shows, we were asked to switch to the left side of the road at one point; then on the return trip, we were asked to switch again to the right side of the road. As indicated by the two red dots, this caused a problem — when you ask 10,000 bikers to cross each others’ paths, problems are bound to ensue. (You’ll note that two blue lines merge near the bottom of the map. Some bikers doing the full ride merged with those of us doing the family ride at this point.)
Today, I received an email from the ride organizers with the following explanation:
This was by far the biggest Bike DC yet, and some of the routing that had been adequate with a smaller ride was unsatisfactory for this larger group.
That made me chuckle. Crossing paths is never a good idea, with any size group. Even people who have never been very good with coordinate geometry know that non-parallel lines intersect. Parallel lines would have been a better option, unless the course was extremely long:
If parallel lines meet at infinity, then infinity must be a noisy place with all those lines crashing together!
The way to avoid the problem, as any statistician will tell you, is to pass through these points of intersection very quickly.
A statistician would always accelerate when coming to an intersection, fly through it, and then brake on the other side. A passenger asked him why he went so fast through intersections. The statistician replied, “Well, statistics show that more accidents happen at intersections, so I try to spend less time there.”
I’m smart. I mean, really smart. I may not be as smart as Jeffrey Skilling, who described himself as “f**king smart,” but I think I’m at least as smart as Albert Einstein.
Watch. I’ll prove it.
Einstein came up with the formula E = mc2. Luckily, I’ve studied algebra, geometry and graph theory, so I know that E = edges, m = slope, and c = length of hypotenuse. I can then use the following diagram to verify Einstein’s formula:
It’s quite easy to see that the slope of the hypotenuse is 1, so plugging values into the formula gives the following:
This result is then confirmed by counting the edges in the triangle. Q.E.D.
(By the way, qed is derived from a French word that means, “And there you have it.” It’s a great Scrabble® word, since it contains a q but no u. You should use it next time you play Words With Friends. Seriously, your opponent will be impressed.)
See? I told you I was smart.
Lure of the Labyrinth is a digital math game for middle school students. It contains math challenges in a graphic-novel setting, and players work to find their lost pet in a strange world! The designers of the game boast that “the game gives students a chance to actually think like mathematicians.”
LotL is a great game, and I’d like to share some info with you that I received today.
The Education Arcade at MIT has announced the Lure of the Labyrinth Challenge, a free online math challenge for grades 6–8. Students and educators have many chances to win prizes such as Lenovo ThinkPad Tablets, books, and technology tools like subscriptions to BrainPop just for playing.
There is no cost to participate in the challenge, which runs through June 15. Since the game is web-based, students can play at home or at school, in the classroom, computer lab, library, or after-school program. Students can play as little or as much as they want — and best of all, they will have continued access to the game over the summer to help avoid that inevitable “brain drain.”
Visit http://lureofthelabyrinth.net to sign-up for the challenge!
I’ve used the following joke as the opening for many local presentations:
I’m so thankful that I was able to drive here this morning. I’ve been flying a lot for work recently, and last week I had a really horrible flight. I had just finished four long days at a math conference, and I was exhausted when I boarded the plane. We took off, and as soon as we levelled out, I put my head back and closed my eyes.
And then… a thud.
Now, I don’t know if you’ve ever heard a thud while on an airplane, but I didn’t particularly like it. Immediately, the pilot’s voice came over the loudspeaker. “Ladies and gentlemen, this is your captain speaking. I know you heard that sound, and I want to assure you that everything is all right. We’ve lost an engine, but we can still safely make it to our destination with the three remaining engines. However, instead of the flight taking 3 hours, it will now take 4 hours.”
This was unsettling, but after 20 minutes of smooth flying, I closed my eyes once more.
Again, the pilot’s voice. “Ladies and gentlemen, it appears we’ve lost a second engine. Let me assure you, we will still make it to our final destination safely, but instead of 4 hours, it will now take 6 hours.”
We then flew smoothly for another 30 minutes… but I was unwilling to close my eyes again.
“Ladies and gentlemen, we’ve lost a third engine. We can make it safely with just one engine, but it will now take us 12 hours to reach our final destination.”
Upon hearing this, the guy next to me leaned over and said, ”My gosh! I sure hope we don’t lose that fourth engine, or we’ll be up here all day!”
I use that joke because I think it’s funny, but also because it allows me to ask this question: “Consider the pattern. When there were 4 engines in use, the flight was supposed to take 3 hours. When reduced to 3 engines, the flight time increased to 4 hours. Just 2 engines, 6 hours. Only 1 engine, 12 hours. If the pattern continued, what length of time would correspond to 0 engines?”
The joke can serve as a lead-in to inverse variation, and I rather like the answer. With 0 engines, the duration would be infinity. And isn’t that appropriate? If the plane crashes, you won’t reach your final destination for all of eternity!
Speaking of planes, Skyscanner recently conducted a survey about air travel preferences. According to their study, flyers think that 6A is the perfect seat. That shouldn’t be shocking… a perfect seat has to be in Row 6, doesn’t it?
Forty-five percent of respondents said they prefer to sit in the first six rows, and 60% said they prefer the window, so it makes sense that 6A would come out the winner. But there were some surprising results from this survey:
- Nearly 7% said they would choose to sit in the last row. (Really? What kind of person prefers a non-reclining seat by the bathroom?)
- Approximately 62% of respondents said they prefer an even seat number. (Who knew that parity played a role?)
- The worst seat? That distinction belongs to 31E, a middle seat near the back.
- Frequent flyers prefer the left side of the plane. (“Why,” you ask? Because the windows on that side of the plane are off-center, which allows for wall space to rest your head while sleeping.)
- Less than 1% prefer the middle seat. (The surprising part is that anyone prefers the middle seat.)
My guess is that people who prefer the middle seat also think median is better than mode. I assume this result was a statistical error, however. My suspicion is that they asked the preference of two people simultaneously; one responded, “I prefer the aisle seat,” another responded, “I prefer the window seat,” and the survey taker wrote, “On average, these two people prefer the middle seat.”
Recently, I was in seat 6A during an international flight. Halfway home, the entire flight crew got ill from the food. The pilot and co-pilot passed out, so the flight attendants began asking if anyone could fly the plane.
An elderly gentleman, who had flown prop planes over Warsaw many years ago, raised his hand. When he got to the cockpit, he looked at all the displays and controls, and he realized he was in over his head. The flight attendant noticed the look on his face and asked if he was okay. “I don’t think I can fly this aircraft,” he said. “I am just a simple Pole in a complex plane.”
Winner will be announced below; but first, I’ve got to say this:
May the Fourth be with you.
Congratulations to Lucie, a student in Russ Holstein’s class. She was one of 36 entrants in the Humorous Math Poem contest, and her name was randomly selected to receive a signed copy of Math Jokes 4 Mathy Folks. Lucie’s entry was a haiku:
Don’t be dramatic;
It is just mathematics.
Easy: 1, 2, 3.
[Editor's Note: The middle line was changed from, "It's just…," to, "It is just…," to give it the requisite seven syllables.]
Other noteworthy entries were the following:
I’m sick and tired of finding your x.
Just accept the fact that she is gone…
Move on, dude!
Oh, these numbers make me whine!
I am really doing poor.
If I learn this, will I shine?
Dear Aunt Sally,
Please excuse me
For not following the rules;
I don’t have the right tools.
I have a really geeky clock;
It has a special chime:
At 2, 3, 5, 7 and 11 o’clock,
It shouts out, “It’s prime time!”
And my favorite, which seems to be a commentary on standardized testing…
Today we had a test, it was mathematical.
Which is very tragical.
And wasn’t all that fantastical.
I rather it be biographical.
Does it come from the capitol?
Depending who you ask, mathemagician has at least two different definitions:
- A person who enjoys both math and magic. (Wikipedia)
- A person who is so good at math that the answers to math problems seem to come to them magically. (Urban Dictionary)
When professor Art Benjamin told Stephen Colbert that he was a mathemagician, Colbert asked, “What does that mean? Were those two words by itself not nerdy enough?”
Below is a math puzzle involving magic. To be precise, magic rectangles. But first, a little warm-up…
What do you call a quadrilateral with four right angles that’s been in a car accident?
A wrecked angle.
For the last several years, I’ve had the pleasure of creating puzzles for the Daily Puzzle Challenge at the NCTM Annual Meeting. A new set of four or five puzzles appears in each day’s challenge. The following puzzle, which appeared on Friday’s Daily Puzzle Challenge, involves rectangles and is my favorite puzzle from this year’s meeting.
A magic rectangle is an m × n array of the positive integers from 1 to m × n such that the numbers in each row have a constant sum and the numbers in each column have a constant sum (although the row sum need not equal the column sum). Shown below is a 3 × 5 magic rectangle with the integers 1-15.
Below are three arrays that can be filled with the integers 1-24, but only two of them can be filled in such a way as to form a magic rectangle. Construct two magic rectangles below; for the array that cannot be used to construct a magic rectangle, can you explain why not? More generally, can you determine what types of rectangles can be used to construct magic rectangles and which cannot?