Figures are easier to understand than words. Words are easier to understand than equations.

Say it with a figure (or graph, or table) if at all possible. (It is surprising how many ideas can be reduced to or illustrated by a figure.). Figures should, of course, be simple, with all inessential details omitted. Label everything that can be labeled, and, if the figure is on a slide, give it a title. You should intend that every single mark on a figure will be fully understood by the audience. (If they don't understand something, leave it off the figure.). It takes time to absorb a figure, so have some remarks to make about the figure while they're staring at it. (Even though it may be clear from the labeling, describe the figure and its message in words.). Do not use several figures when one can be made to do the job. It's often possible to invent a single, strong figure (or graph, or table) which forcefully summarizes the essential point.

If you make a point in words, or give an argument in words, it's often possible to summarize it on a slide or on the blackboard. This might be done by writing out a sentence or two in full. (This endows your point with strong emphasis.). For an argument with several steps, one might list the steps (one phrase for each), to bring out the structure of the argument. It never hurts to read aloud what is displayed. It's not usually a good idea to try to get more than two sentences on a slide. (If one is stating a theorem, for example, one might condense some complicated conditions into a descriptive phrase in quotation marks.). The slide should, of course, be up far longer than it takes to read it. One would normally spend at least several minutes on a slide . (If it's to be less, perhaps the whole slide can be replaced by a descriptive phrase in some other slide.).

The last resort for expressing an idea is through an equation. In my opinion, equations should be thought of as tools for making a point, not as data to be stored by the audience for their future use. (How many times have you actually used, in your own work, a detailed equation copied from a lecture?). Thus, an equation should be a ``picture'' which is presented, described in detail, discussed physically, etc. Every symbol appearing should be defined, and, if necessary, discussed. All this takes time, so it is a good idea to set aside several minutes to treat a single equation. (The meaning of important symbols should be repeated in later equations, even though they were defined and discussed at their first appearance.). If a talk has more than five non-trivial equations in it, it's beginning to get equation-heavy. One can often simplify equations by a clever choice of variables (e.g., define a variable to represent ``the effect of the gravitational field on the stress of the body''). Furthermore, one can often leave out whole batches of terms by summarizing them with a phrase, e.g., `` + small terms''. If some terms are not going to be discussed in detail, replace them by a word saying why they are not important. One can sometimes get rid of an entire equation by writing it symbolically, or with words replacing the terms. You should intend that every single mark that appears in an equation will be completely understood by your audience.

Ideally, one would like to have about ten slides (or blackboard presentations) in an hour talk, with one under discussion perhaps 70 % of the time.

Fri Mar 7 12:59:16 EST 1997