The rulebook absolutely does say you can't do this, so "Dude what?" right back at you.
What the rulebook doesn't do is give even the remotest hint that it cares about external aids like reading glasses (to more easily see the cards) or pen-and-paper. Other games' rulebooks (like Smallworld was my example earlier) do hint that they care about tracking public information.
Okay, obv. I didn't check, what were the odds.
I cited glasses, man. I did not go into details there but really, do you need that, you do not. Of course you can use glasses, hearing aids, and artificial kidneys.
Rules tell you what you can do, not what you can't do. You can't do things that rules don't let you, inside the game. Outside the game, whatever. If a rulebook mentions that you can't do something, that's just to answer common questions from foolish people; if you aren't told you can, you can't, that is what it means to be rules.
It should be clear that rules work this way, because games are just utterly messed up otherwise. People can produce ridiculous questions all day. Can you put a card from your hand on your deck for next turn whenever you want? Hey maybe the rulebook covers that, I am not checking. It for sure does not answer every ridiculous question of this nature because there is no end to them.
If you accept that rules say what you can do, rather than what you can't - and why would you, this is the internet - then the question becomes, is taking notes like eating or is it actually relevant. And of course it's relevant. The game has a memory component, and of course there are games that are nothing but memory, to make it clear that memory can be an element of a game.
Also, while we're here, in Dominion, you may not take notes. I am making this clear for anyone who somehow does not get it. You can't. You didn't know before, so that wasn't cheating, but if you do now, it's cheating. I would get into the idea of variants but let's keep this simple.