So today is 11th of March, which means march is practically half-way over, and if I let myself carelessly blink a few more times, it'd be April before I knew it. Time sure is bananas when it comes to flying so fast. I feel like listening again to the song "Heaven" from the game Persona.
What have I been even doing this this March? I said I was going to review my logs this weekend, but I didn't feel like it, too lazy. Most notable I did for the weekend was trying to defeat the final-final boss on Ys, I always die at the last 1000 HP of the boss. I regret going for the hard difficulty, now I can't move on to the other games, and it's a bit stressful trying to push through. I feel I didn't even get to relax this weekend.
As for today, I didn't do much, I've been scribbling away on my notebook like a madman, fixated on finding a way to do long division using my own method of multiplicative inverses. I wasn't toiling on my own volition, I was actually enjoying doing bad arithmetic, I'd make the simplest mistakes that would make a gradeschool teacher laugh. Maybe there's some dopamine hit when I rediscover some trivial mathematical properties on my own. I think to myself, huh so that's why, I can't believe I went through my adult life without knowing this basic fact.
School taught me surface level knowledge how to do arithmetic by mechanically applying algorithms. Or maybe they did teach the underlying insights, just that I wasn't paying attention. I was actually a very distracted student, the world around me would just blur during classroom hours, my mind would wander to a distant fantasy land. To my surprise, I still managed to pass with an average grade on my highschool days. College is different though.
Anyways, back on topic, what I was trying to do was to be able to do "long division" using just multiplicative inverses. So the idea would be:
12345 / 45
= (12345)45~
= (12345)9~5~
(4)(12)(3)(6)4~5~
= (4)(4~)(12)(3)(6)(5~) reorder
= (1)(12)(3)(6)(5~) substitute, 4*4~ = 1
= (12)(3)(6)(5~) remove 1, since 1*x = x
= (12345)45~
= (123(4)(5)45~
= (123(4)(5)4~5~
= (123(4)(5)9~5~
= (123(4)9~There has to be a better way. Applying division with inverses would be very easy if I could just have the form (x1)(x2)(x2)... As it turns out, that's called factoring, so my task shifted to searching how to do factoring by hand. But to do factoring, I have to do division, so what then? I found myself asking a question similar to wondering if a chicken or egg came first. There is another way, which is by trial and error, guessing if a number evenly divides another number.
Well, this log has gotten a bit too long, I'll continue this later. Time for a walk before supper.
