You can bootstrap a tiny duration of prescience into arbitrary durations by passing back the same message over and over as many times as you like.
If you know what will happen in one minute, write down the message you see yourself writing down in one minute. In a minute, do the same thing. Now you can pass messages back two minutes.
What if I see myself writing a message in one minute, and thus I dont need to send that message back in in time for me from the future, coz ive already seen it, so I wont write it down for me in a minute?