I just awokened from a really visceral dream of a time in primary school. Just need to write it down somewhere.
When I was a kid in school, I hated showing my working. I recall one maths test that I did where I had scored a 100%, and the teacher marking my exam deducted 10 marks for not showing my working*Later when I was in high school I similarly had marks deducted from my physics exam for consistently not handing in my homework.
I am much older now and I understand the value in “showing your working”. But there was once I nearly got expelled when I was 8 or 9 or 10 for showing my working.
After much exhortation from the teacher, I finally showed my working. Out of spite. Now to set the scene, we had little notebooks — 24 pages in total — with little squares on them. Homework typically consisted of copying down the questions from the text book and writing them in the notebook. And part of the whole Asian school experience was that teachers assigned A LOT of questions: 20 to 30 every day. You’re supposed to use one or two pages of the notebooks for the homework. Sometimes you were expected to vertically split the page and write your homework in two columns.
I don’t quite recall what the topic was. Maybe it was long division or fractions or something. I vaguely recall having to do multiplication. But I showed my work. In every last detail. I recall drawing unary marks for the purposes of counting when doing the addition steps. I recall writing out parts of the times table at the side.
The result was that one question would take 2 or 3 pages of the little notebook to complete. I finished using up all the pages in the notebook.
The teacher gave me 0 marks for my homework and demanded that I show my parents what I had done — part of the requirement was that I had to get my mum to sign off on the 0 marks. I didn’t, and that led to a long standoff *I say long but I don't think it was more than a week. My parents regularly checked on my homework where I refused to do my maths homework (my excuse was there was no more pages to the notebook). I was made to sit outside the classroom and eventually the principal’s office, where she threatened to expel me. My parents eventually found out and I was punished for this misbehaviour.
And now, back to the dream. The dream I had just awoken from was an alternate universe version of what happened. In place of drawing unary symbols, I dreamt that I showed the derivation of + and × with the help of a Y-combinator. And I used the Peano axioms with natural numbers. Also I said “fuck you” to the teacher and I was larger in stature than the teacher.
I guess why I dreamt of something that happened three decades ago was because I’m writing a new book. And in it there’s a discussion on computation and the substrates of computation. I used a Post-Thule system in that chapter to illustrate what a “computation” is. I specifically shied away from using pure arithmetic for illustrating the concept of a computation because even a trivial expression would take many pages to show the computation thereof. But I guess this thing from 30+ years ago was still eating away at me for some reason.
Damn, don’t our past come back to haunt us!