Do do Do do Do do doo-doo

My last two blog posts have, in some sense, dealt with a song that has these syllables.

Which song is that? “Love The One You’re With!”

Strangely enough, when I was chatting with Mom on Wednesday night and this song became salient, it reminded me of another implication of the song… which has NOTHING to do with love!

When I was younger, I sometimes played around with calculators… the pocket calculators with addition, subtraction, multiplication, square roots, and powers. I knew about the +, -, ×, and ÷ keys… and even a little about the % key. But at this point (I was probably in or before third grade), I had no idea what the √ button did.

Clip art of a pocket calculator. Source: (“calculator_old.png”)

However, I noticed that whenever I pressed it repeatedly, a different number would appear… and that the number would get closer to 1 before eventually giving me “1” every time I hit the key.

My fascination with this had me humming “Doo” every time I hit the square root key, and fascinating myself as it headed to 1. My best guess was that I heard the Stephen Stills song recently before picking up that calculator, and for whatever reason, seeing the radically (pun intended) different numbers made me start humming, “Do-do-Do-do-Do-do-doo-doo!”

Of course, I now know that for any non-negative real number, the nth root of that number has a limit that goes to 1 as n goes to infinity. In some sense, that fascination was an early way for me to learn about limits and also Machine Epsilon through brute-force calculation.

Similarly, with the ^ key, I easily created overflow errors on the pocket calculators.  And I always thought at that point that “E” meant empty, similar to a gas gauge. Nope, it means error, like the baseball player who muffs a play.


This is the first time that I have told this story, but I wonder if I’m now going to put a “Do-do-Do-do-Do-do-doo-doo” singsong shortly in my MATH-153 class(es) as I formally define the limiting Riemann sum. Who knows? If I feel the spirit to do that, I will!


חנוכה: שני לילות

Finals Week: 12 days.

Joint Mathematics Meetings: 32 days.

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