Mathematics
Lessons in Mathematics from Kevin Malone
Mathematical lessons inspired by Dunder Mifflin’s finest accountant
I have always been a believer that if you have an open mind you can learn something valuable from just about everyone. This of course includes accountant extraordinaire, Kevin Malone. Today I would like to cover two lessons in mathematics and a bonus lesson in philosophy inspired by Kevin.
Base-11
In the finale of The Office, we learn Kevin has been fired. Turns out, Kevin has made up a new number to balance his accounts. This number is called a “keleven”. Unfortunately, the only information we are really given about the new number is that,
“A mistake plus keleven gets you home by seven”.
So let’s assume that Kevin has added a number to the Base-10 system (decimal) to create a Base-11 system (undecimal). We can use the greek letter Upsilon, ϓ, to represent keleven (because I think Kevin would pick this as it is the funniest greek letter).
What are the effects of going from a base-10 system to a base-11 system?
Any change of base is going to be hard for us to adapt to. For a lot of us, basic arithmetic is a second nature and feels automatic. A change of base, means that we would have to perform basic functions in a similar fashion as when we first learned them. When we were learning base-10, we used our fingers (and in particularly desperate situations, our toes), but in base-11 this wouldn’t be a useful tool (unless you are one of the few people with 11 fingers, in which case you might prefer base-11).
There is another, less obvious, reason why a base-11 system would be hard to adjust to. Think about how great you are at arithmetic operations when the numbers are multiples of 2, 5 or 10. It’s not a coincidence that these numbers are the factors of our base, 10. Eleven is prime (meaning it’s only factors are 11 and 1). The only numbers we will be great at performing basic operations on are numbers that are multiples of 11 (i.e. 11, 22, 33…).
To see how much more complicated basic arithmetic feels in base-11, try the following basic problems in base-11 and check the solutions at the bottom of this article.
- Convert 21 from base-10 to base-11
- What is 11 + 12 in base-11?
- What is 4 ⨯ 4 in base-11?
Base 12
In a deleted scene from the finale, Kevin also mentions that sometimes the numbers didn’t add up even when using keleven. So he also added the number “gop”. This implies that Kevin often used base-12 (duodecimal). A lot of mathematicians agree with Kevin that the duodecimal base is the best base!
We discussed how bases with several factors are superior (depending on the circumstance) to bases with less factors. Ten has 3 factors (2, 5, and 10), and eleven has 1 factor (11), but twelve has 5 factors (2, 3, 4, 6, and 12)! The versatility of base-12 has made it popular in our society. We have 12 months in a year, 12 eggs per carton (or factors of 12), 12 inches in a foot. It’s easier to break multiples of 12 into thirds, fourths and halves than multiples of 10.
The animated educational series Schoolhouse Rock, even had an episode about base-12 called “Little Twelve Toes”. A link to the video will be in the references section below.
If you are now team duodecimal, there is an entire group of likeminded people.
The Importance of Visualization in Math
In season 9 episode 4 “Work Bus”, the Scranton branch hits the road hoping to arrive to LaVerne’s Pie Stand before it closes for the day. During their takeoff Kevin calculates the speed they will have to travel at to make it to the pie shop with only 5 minutes to spare. The other accountants, Oscar and Angela, are shocked at Kevin’s sudden mathematical capabilities when pies are involved and decide to put him to the test.
Oscar: Hold on, Kevin, how much is 19,154 pies divided by 61 pies?
Kevin: 314 pies.
Oscar: What if it were salads?
Kevin: Well, it’s the…carry the four…and…it doesn’t work.
This is a bit of a hyperbole, but visualizing math problems has been a tool in our toolkit since we were children. When we first started learning math, we used physical objects like blocks to visualize basic functions like addition and subtraction.
Of course, we use visuals to describe math problems and datasets long past our time in elementary school. In several circumstances, visualization is a necessary tool to interpret data or express results to an audience in a meaningful way. One of my favorite examples of this comes from the book, The Visual Display of Quantitative Information by Edward R. Tufte.
All four of these datasets share the exact same linear model. I will summarize some important components of the linear model:
- number of points = 11
- mean of x’s = 9.0
- mean of y’s = 7.5
- equation of regression line: y= 0.5x + 3
- standard error of estimate of slope = 0.118
- r² = 0.67 (r² is a measure of how well the model fits the data)
If we only look at the linear models shared by these datasets, we might assume that the sets are nearly identical. Below, the four datasets have been graphed and we can see their severe dissimilarities.
For most of us, our mathematical abilities probably don’t vary depending on if a problem uses pies or salads. Still Kevin makes a good point, using visuals to improve our understanding of a problem or a set of numbers is advantageous.
Side note: I seriously recommend reading The Visual Display of Quantitative Information if you ever use visuals to display information. It is a beautifully written handbook on the topic. Also, it features several examples of terrible plots and those are always fun to judge.
Kevin, The Philosopher
As a bonus lesson from Kevin, we are going to switch to the world of philosophy. In season 8 episode 8 “Gettysburg”, the employees of Dunder Mifflin are attempting to come up with great ideas to help the company. Kevin’s idea is the following:
Every time you buy a Big Mac you set one ingredient aside. Then at the end of the week you have a free Big Mac. And you love it even more because you made it with your own hands.
In the show, this idea is played off as foolish but it’s very similar to a famous thought experiment, “The Ship of Theseus”.
Consider the Ship of Theseus, which is tied to the Harbor. Every day one board is removed from the ship and replaced with a new one. There are several questions to ponder.
- By the time all of the boards have been replaced is the ship still the Ship of Theseus or a brand new ship?
- If it’s a new ship, at what point did it shift from being the Ship of Theseus to being a new ship?
- If we used all of the old boards we removed and built a ship with them, would it be the Ship of Theseus or a new ship?
We can ask similar questions about Kevin’s free Big Mac. If we use all of the removed ingredients to build a burger, is it still a Big Mac? Although, I think the most important question is whether the ingredients would still be safe for consumption.
Thank you for reading! I hope next time you watch The Office, you can appreciate the genius that is Ashton Kutcher… I mean… Kevin Malone.
Solution to Base-11 Problems
- Convert 21 from base-10 to base-11: 1ϓ
- What is 11 + 12 in base-11? 23
- What is 4 ⨯ 4 in base-11?: 15
