So I'm surprised at the "this won't work but ok" replies for many folks. I was not willing to poke at this, since dudes that replied took a minute of your time and I appreciate it (really, no being gay but like time is expensive for real thanks), but now that a few people have said words to the effect of "good luck with that" I am surprised. Inclined to ask "why?" Games I have been in I take tons of notes, on names and items mostly, but also what we've done or just in general, what is interesting at the session, for crying out loud - sometimes I just take notes because I'm BORED! My fellow players in our home game we play take notes too, onemore than me, but the others take notes on their items and some other game things at least On no phones, all but one of the new players at the game store took this to heart from day one, so 5 out of 6 success rate with these guys (and I plan to be more annoying about it if player 6 gets in the soon to start game). I may be experiencing something as a result of my attitude, I am not particularly polite and so if I don't like something I see I will call it out: I even told the game store manager "once we're done with the ones hots I'm going to pick the people I gell with, because I'm the DM" People I don't get along with, I don't spend hours of m day with, people in my games take notes stay off their phones and so forth. If they do not, we have a conversation and see where we have a common goal and hopefully work toward it. If there are people who can't get along with the rest of the party even after talking to him or her, we fond a different person for our group. Are you saying this has not been a normal experience at all for other people? I would like to know, and am very curious.
(Edit: trying to clarify

)
I tell every one when I start a game
"You really should take notes. You're going to be expected to have some recall of past events to understand what's going on, and you're going to be sad if you don't know what's going on, because it'll be expected your characters have passing knowledge of evets."
and usually think to myself "You slow-ass mothers fuckers also like to dawdle, wander off, and fuck around so by the time you complete a quest it'll be llike 3 years later"
I tell them, as you noted, that its a good thing to do keep engaged. Even you just draw doodles, I've had players who did at least put down some words but mostly doodled but they actually remembered "oh yeah that's why I drew this guy, so that means this happened before X and after Y..."
Once I even bought everyone cheap notebooks and decent pens so they'd have no excuses. They went un-used.
Another couple of groups I event sent everyone a post-session write up of my own notes so they could just go into their email and search for things.
One of my players took very detailed notes like she always took since school.
One of my players took did at least key word scribbles in a vague timeline and (at the urging of first player) put a sheath of post-its on their character sheet with whatever current thing they were working at.
One of my players took zero notes, but had a decent memory and really just there to play tactical games, so went along with the plot without much fuss.
And two of players took zero notes and especially one of them would bitch in at least 50% of the sessions about not knowing who or what something was, or would do something stupid that they'd been warned earlier was stupid, and when I let it happen and delivered the anticipated consequences of a thing they were forewarned about, they would lose their shit.
And just be clear on notes I'm not douchebag - I'll help them out if they get close. If they are like "Oh shit they have Ravens on their banner, its the troops of that King guy...the dude with the wooden hand" - as long as they're in the general ballpark I'll give it to them.
but getting players to take notes is like collecting Hen's teeth.
IMO, there are things you lay down as rules, and there are things you encourage on people as part of group culture and personal habits.
To add to this:
What people often forget is a body of law isn't just rules, its also the consequences of not following them - and in may lay & volunteer association organizations usually some context on why that rule exists. Some times that consequence is spelled out directly, sometimes its just "God will be angry".
Example, one thing I've heard someone else did was the Gaming Table equivalent of a swear jar.
On your phone? Dollar in the swear jar.
Not ready on your turn? Dollar in the swear jar.
Need the DM to tell you a thing you forgot? Dollar in the swear jar as you get explained.
Try-hard metagaming? Thorgar doesn't know what a gelatinous cube is yet, Dollar in the swear jar.
Didn't show up on time? $5 in the swear jar.
Everyone tired of being your murderhobo tard wrangler? Knock it off and put a couple bucks in the swear jar.
Swear jar money is used for pizza/soda/snacks so people usually don't take it too personal when they are fined.