From Fallen London Wiki

I feel it remiss that it is not added that the Making Waves gain is explained in-game: since the Amanuensis is present, it does suggest some importance to you, and thus, causes more eyes to be on you, boosting your Making Waves. Though, of course, only up to 3, because both mechanically, that would just be easily renewable Making Waves effortlessly, and logically, if your Making Waves is above three, then they really already knew that you were of some import, so seeing the Amanuensis there is simply unsurprising.