It’s weird what you remember.
Case in point: I have a very vivid memory of failing a math test. This was way back in elementary school. Fourth grade, I think—the assignment was on fractions–so I would have been nine or ten.
It didn’t shape my life. It wasn’t fractions that killed my dreams of being a famous astronomer*. And yet, that assignment pops into my mind whenever I have to split things into equal portions. Halves, thirds, quarters.
* Calculus was my real nemesis. If it hadn’t been for that darn ∫ I coulda given Carl Sagan a run for his money.
The vexing thing is that I actually knew how to do the work. It was comparisons: which is larger, 2/3 or 3/4? I knew what to do: convert to a common denominator: 8/12 versus 9/12.
But I blew the test because of a paradox. If you make the denominator bigger, shouldn’t the number get bigger too? I knew it wouldn’t, but my brain insisted that was logically inconsistent. 1/2 should be larger than 1/3, not smaller.
So on that day, I got fixated on the denominators and answered the questions looking only at those. If all of the fractions had been 1 over something, I would have had a perfect score. As it was, because teachers are sneaky, I got about two-thirds of the questions wrong.
I had to do remedial exercises for days, because at that age, I couldn’t put what had gone awry into words.
The experience may not have had a major impact on my future career, but there’s no question I was scarred by it. To this day, I prefer decimals to fractions: .67 is clearly smaller than .75; what could be easier? Until you need to dish up .5 cans of cat food—regrettably, 1/2 a can is much simpler.
More than forty years later, I still remember that assignment. At least once a week.
Totally trivial, yet omnipresent.
Talk about a 1/2-assed excuse for an idee-fixe.