Posts tagged ‘orthogonal’

Sound Smart with Math Words

When law professor Richard D. Friedman appeared in front of the Supreme Court, he stated that an issue was “entirely orthogonal” to the discussion. Chief Justice John G. Roberts Jr. stopped him, saying, “I’m sorry. Entirely what?”

“Orthogonal,” Friedman replied, and then explained that it meant unrelated or irrelevant.

Justice Antonin Scalia was so taken by the word that he let out an ooh and suggested that the word be used in the opinion.

Orthogonal Definition

In math class, orthogonal means “at a right angle,” but in common English, it means that two things are unrelated. Many mathematical terms have taken a similar path; moreover, there are many terms that had extracurricular meanings long before we ever used them in a math classroom. Average is used to mean “typical.” Odd is used to mean “strange” or “abnormal.” And base is used to mean “foundation.” To name a few.

The stats teacher said that I was average, but he was just being mean.

You know what’s odd to me? Numbers that aren’t divisible by 2.

An exponent’s favorite song is, “All About the Base.”

Even words for quantities can have multiple meanings. Plato used number to mean any quantity more than 2. And forty used to refer to any large quantity, which is why Ali Baba had forty thieves, and why the Bible says that it rained for forty days and forty nights. Nowadays, we use thousands or millions or billions or gazillions to refer to a large, unknown quantity. (That’s just grammatical inflation, I suspect. In a future millennium, we’ll talk of sextillion tourists waiting in line at Disneyland or of googol icicles hanging from the gutters.)

Zevenbergen (2001) provided a list of 36 such terms that have both math and non-math meanings, including:

  • angle
  • improper
  • point
  • rational
  • table
  • volume

The alternate meanings can lead to a significant amount of confusion. Ask a mathematician, “What’s your point?” and she may respond, “(2, 4).” Likewise, if you ask a student to determine the volume of a soup can, he may answer, “Uh… quiet?”

It can all be quite perplexing. But don’t be overwhelmed. Sarah Cooper has some suggestions for working mathy terms into business meetings and everyday speech. Like this…

deltaFor more suggestions, check out her blog post How to Use Math Words to Sound Smart.

If you really want to sound smart, though, be sure to heed the advice of columnist Dave Barry:

Don’t say: “I think Peruvians are underpaid.”
Say instead: “The average Peruvian’s salary in 1981 dollars adjusted for the revised tax base is $1452.81 per annum, which is $836.07 below the mean gross poverty level.”
NOTE: Always make up exact figures. If an opponent asks you where you got your information, make that up, too.

This reminds me of several stats jokes:

  • More than 83% of all statistics are made up on the spot.
  • As many as one in four eggs contains salmonella, so you should only make three-egg omelettes, just to be safe.
  • Even some failing students are in the top 90% of their class.
  • An unprecedented 69.846743% of all statistics reflect an unjustified level of precision.

You can see the original version of “How to Win an Argument” at Dave Barry’s website, or you can check out a more readable version from the Cognitive Science Dept at Rensselaer.


Zevenbergen, R. (2001). Mathematical literacy in the middle years. Literacy Learning: the Middle Years, 9(2), 21-28.

May 4, 2016 at 7:47 am 1 comment

Never Ask a Mathematician for Directions

I spent my formative years in a very rural county. Roads didn’t have names, or at least they didn’t have road name signs.

Natural Log Lane

In college, my urban friends used to claim that if you asked someone in my hometown for directions, they’d say:

Go about a half mile, and turn left at Old Man Johnson’s farm. Then take a right at the huckleberry tree.

That very well may be true, but it’s no worse than the directions you might be given by a mathematician:

Well, you’re facing the wrong way, so do a reflection about this cross street. Go about 0.628397154 miles, then rotate π/2 radians and travel orthogonally to your previous vector for 600 light-nanoseconds. But they’ve got radar on that road, so keep your speed between 72 and 43 miles per hour. Turn left, and you should reach your destination in 2.4 minutes ± 0.3%, if you maintain an average speed of 46.8 mph.

Now, that’s bad. But at least I could understand all of it. Which is more than I can say for the directions that Google Maps provided yesterday. Traveling through the suburbs near Washington, DC, I had just crossed MacArthur Boulevard, and I was heading southwest on Arizona Avenue. As you can see from the screenshot below, Google Maps was suggesting that I turn right on Carolina Place, right on Galena Place, right on Dorsett Place, and then left on Arizona. In essence, it suggested that I reverse direction to take a 10-mile, 45-minute route.

GPS - Before

I ignored that suggestion. Instead, I stayed on Arizona Avenue with the intention of turning right onto Canal Road in a quarter-mile. Just as I passed Carolina Place, Google Maps said that it was “Rerouting…,” and within 15 seconds, it confirmed that I had made the correct choice:

GPS - After

By ignoring Google Maps, I shaved 3.8 miles and 23 minutes from my commute.

WTF?

My speculation is that Google Maps attempts to avoid my chosen route because it follows Canal Road, which parallels the C&O Canal National Historic Park; it requires me to cross Chain Bridge, which offers a beautiful view of the Potomac River; and it then winds through an affluent neighborhood, where I can feel safe on tree-lined streets with elegant homes. Honestly, who would choose that when Google Maps is offering double the travel time and an opportunity to drive on the beltway?

I once asked Google Maps which highway I should take to California. It replied…

\sqrt{1^2 + 4^2 + 7^2}

Oh, yeah. Root 66.

The logic employed by Google Maps reminds me of a college friend…

He would always accelerate when coming to an intersection, race through it, and then brake on the other side. I asked him why he went so fast through intersections. He replied, “Well, statistics show that more accidents happen at intersections, so I try to spend less time there.”

 

November 23, 2015 at 5:40 am Leave a comment


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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.

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