Mathematics – Making the Invisible Visible

MATH. “It's just there. It has always been a part of whatever I was doing. You’re either right or you’re wrong,” says Katherine Johnson, retired NASA mathematician. “That I liked about it.”

Katherine Johnson is a heroine of the American space program. Ms. Johnson's story, along with that of her colleagues Dorothy Vaughn and Mary Jackson, is chronicled in the feature film Hidden Figures (2016). Her work as a NASA computer influenced major US space shots from Mercury through the Space Shuttle. Notably, she personally calculated the trajectories for the historic flights of Alan Shepard, John Glenn, and Apollo 11. Ms. Johnson says of her contributions, "It was my job and I did my job correctly and well."


In the interview above she reminds me of my own mother, Johnnie Boyer (who was also a gifted african-american child attending university at the age of 15 in the United States of the 1950s). They are each black women whose passion for learning gave them a means to out last and rise above the prejudice and discrimination of the age into which they were born. Education gave them a way to make a difference in the world.

Math is beautiful. It can render the invisible visible and it can offer absolute truth. (Shout out to my cousin, Karen Lee, who's been a math teacher for most of her life.) 

That's one small step for (a) man, one giant leap for mankind.


Something clever to share with a child...

Think of a whole number from one to ten. Multiply that number by nine. (Seriously, do this. It’s only fun if you follow along.) Now, add together the digits of the product (the answer that you got in the last step) to get a digit sum. (So, if you had 32 then 3 + 2 = 5 or if you had 45 then 4 + 5 = 9) Now, subtract five from that.

Convert the number that you have now into the corresponding letter of the alphabet (1 = ‘a’, 2 = ‘b’, 3 = ‘c’, and so on …)

Are you still with me? Good.

Choose a country whose name begins with the letter that you came up with in the previous step.

Now, choose a mammal (gives live birth, nurses its young with milk) that starts with the second letter of the name of the country.

(Optional: Have someone who’s been looking over your shoulder and following along silently up until now choose an animal that starts with the last letter of the country that they came up with.)

Now think of the skin or the fur of your chosen mammal. Imagine its color.

(Have your friend think of a fruit starting with the last letter of the animal that they chose and then have them imagine the color of the fruit.)

Focus hard on the color. Really see it in your mind’s eye. (Both of you.)

Hmmm, that’s weird— all that I’m getting from you is gray. And, not just a little bit of gray but a huge wall of gray. (And, orange from your friend. Also weird.)

Well, the only thing that’s that big and that gray is an elephant. Was your mammal an elephant? (And, was your friend thinking of an orange?)

(bows to the sound of thunderous applause)

But, what’s really going to bother you later on is the thought that they don’t even have any elephants in Denmark. (And, as far as I know, kangaroos don’t eat oranges either.)

(smiles and enjoys the stunned silence)

“Math is cool.”
(Adjusts fez and bow-tie while stepping into an unusual blue box. The box then disappears accompanied by a phasing “whoomp-whoomp” sound.)


published by                        James Boyer


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