The second word a professor told me to carry for life. It took me years — and a lot of vectors — to start understanding it.
A look back — long before any of the tools we argue about now.
The same professor — Sang Lyul Min — handed us these words one at a time in lecture. After trade-off, two more stuck with me. But before the second word itself, here are the two pieces of news he brought to class around then. The internet barely existed; information moved through journals, magazines, and word of mouth. Looking back, it's a little amazing how much still got through.
When a chess machine started winning
The first breakthrough I remember: computers had finally started playing chess on roughly even terms with the world's best. Deep Blue beat Kasparov around 1996, so the machines he was describing came just before — names like Deep Thought, ChessMachine, Socrates II. He told us, deadpan, that one human competitor's head had "physically burst" from the strain — and we groaned, "Come on, Professor, that's a bit much."
We live on the far side of AlphaGo now, so it's easy to forget how much we shrugged at all this back then. I was a decent amateur — a 1-dan at Go, hopeless at janggi (Korean chess) against any program — and I still remember the hollow, slightly bitter feeling the AlphaGo era left even in someone who only ever played for fun.
A full-body scan
The second: in the US, death-row inmates had consented to the first dense full-body image scans. That was the news that taught me — embarrassingly late — that this kind of computing could reach all the way into medicine. Computers, it turned out, showed up in the strangest places.
orthogonal
Back to the words. The second one, the professor said, would run through my whole career: orthogonal. The Korean rendering — 직교하는, "at right angles" — was, naturally, a word I'd never heard. The plain-language version was "unrelated, independent." It came back hard years later, when I had to take vectors seriously — first in linear algebra, then in ML and AI.
If trade-off was his word for engineering, orthogonal was his word for the researcher's method: the thing that makes a proof, or an argument, easy to make. Recently, while prepping AI/ML lectures, I met matrices and vectors again — their particular discomfort, and the cleanup that comes after something like matrix factorization lops dimensions off — and found myself reaching back for this word.
I still haven't accepted it all the way down; I'm still learning it. It lives mostly in research and papers — in hypotheses, verification, methods you can trust — where half the job is cutting away what isn't related. Real-world data never splits as cleanly as you'd like. But the method is to prove your way down, lowering the dimensions, peeling off the things that have nothing to do with each other. When what's left is two or three dimensions, your eyes and your head can finally follow along. I still remember the small thrill of watching a little universe of three-dimensional somethings — orthogonality proven — collapse into one or two clean dimensions.
Adapted from my Korean essay on Brunch: brunch.co.kr/@chaesang/34
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