Ideas go into the in-box, then into the system
Everyone has things coming into their life: email, messages, people telling you to do something, bills, whatever. I like how Getting Things Done deals with this: capture these things when they come into your life, but process them later. For example, if a lecturer says "read X", then GTD says to write that down and forget about it until processing your "in"-box, at which point you'd deal with this idea (in this example, by adding it to an actions list). The main point is GTD doesn't directly add a task to an actions list when the lecturer says to "read X".
I feel a couple of benefits from this buffer between the world and the system. The first is that it's easier for me to keep the system neat because this barrier only opens when I'm in a task-oriented mindset. Another benefit is I can have a messy in-box without feeling guilty. My favourite benefit of this approach is the focus it allows; If I have a distracting thought, I can quickly jot it down and return to focusing. It feels like a cheat!
It also means I can have notifications disabled for most apps; I'll only look at them in this "processing" phase. This includes email and even Slack.
But this approach has a couple of downsides. For example, I sometimes write something down but forget what I meant when I process it later. This usually happens when I don't process my in-box quickly enough.
Another downside is that I miss out on quick wins because I don't think about what I write down. Maybe I write "buy X" but don't process this until I'm past the store that sells X, and this feels unavoidable because the whole point of this capture-then-process system is to not think about what is captured.
I'm not 100% sure how often I should process my in-box. Right now it fluctuates depending on how much work comes in; more work means I process my in-box more frequently, up to once an hour. But this goes against what's written in Getting Things Done, where Allen, I think, suggests processing a couple times a day.