Knowledge is information plus understanding. A big part of doing scientific research is to communicate knowledge with others. But knowing how to effectively communicate ideas is to some extend an art that is not so easily acquired.
One key ingredient of public communication is to know your audience well. I would like to propose a visual model that can be helpful for adjusting your presentation based on the type of your audience.
I call this model the Audience Lightcone:
The Audience Lightcone is a simple idea that goes as follows. Your audience is covered by a lightcone. To cover a broader audience with a bigger lightcone, you will need to move the light source to a higher level.
In this model, the lightcone coverage is the broadness/narrowness of your audience with respect to the idea you want to convey. The level of the light source is the level of your viewpoint when presenting the idea.
For example, if I were to present a piece of math I did to an audience, then for me the audience can be classified as follows, from broader to narrower:
(1) a general audience that only know very basic math
(2) people who are/were in math or science majors
(3) math researchers
(4) computational math researchers
(5) researchers who work on problems related to mine
If I have an audience that sits closer to the top of this list, then I will need to present my ideas from a higher-level viewpoint. This means to provide more context and background stories, to build more bridges between what my audience might know and what I want to convey, to use more appropriate analogies, and to refrain from speaking technical jargons.
On the contrary, if I have a narrower audience, such as my colleagues and project collaborators, then I can quickly jump into the lower-level details without spending much time on explaining the context, because it should be our common knowledge.
The big challenge here, therefore, is how well can you still effectively communicate ideas as your audience is broadened? This is a hard task that requires tons of practices to do well. But I think the Audience Lightcone is a useful mental model that can remind you about one of the most important aspect of effective communcation.