When I first gave a talk on how to give a talk, I actually called it “How Not to Give a Talk”. This was back in the days before Powerpoint, when talks were prepared on acetate transparencies placed on overhead projectors, and I started my talk with the most awful initial transparency I could conjure up. It was crammed with tiny writing, it started with the dictionary definition of “talk”, … And to top it off, I began by placing the slide on the projector upside down and backwards. When I finally got the placement right, I proceeded to turn my back on the audience and read the contents of the slide off the screen, in a low monotone. Eventually I took pity on the audience and explained that this was an example of how not to give a talk.
There was a time when I was often attending talks by aspirants seeking a position as a new assistant professor. This was again before Powerpoint slide decks, when candidates came with their stacks of physical acetate sheets to use with an overhead projector. My reaction to their talks was generally that they would have done better to turn their stack of sheets upside down before starting. In particular, they might end their talk with an example, when I thought they should start with one.
I realize people have different learning styles. Some of you may approach a new subject better if first provided with some mathematical notation, and then a set of abstract definitions, followed by a very general theorem … and then eventually a concrete example. Despite having a very respectable undergraduate degree in mathematics from a very respectable institution, my mind does not work that way. I find it easier to approach a new subject by way of a simple, concrete example. I do think I’m in the majority. 🙂
It is easy to say “start with a simple, concrete example”. It is much harder to do it.
If I critique a student talk by suggesting they start with an example, they may nod and come back with an example moved up to the middle of the talk. My response would be “no, start with an example”. They may then come back with an example close to the beginning. My response would be “no, I really mean start with an example”.
I go through a similar process with my own talks. I get part way through a first draft of the talk and I realize I’ve broken my own rule: I haven’t started with an example. So I begin to negotiate with myself: “I could insert an example, near the beginning, but I really need/want to start by …”. Ultimately I capitulate and find a way to place an example at the very start. Which makes for a much better talk.
I went through a similar process with this blog post. Part way through writing it I thought “well, I should really treat this like a short talk and start with an example”. The best I could do was … well you just read it.
It is also difficult to come up with a concrete example. Not “this method is good for scheduling problems”, or for “nurse scheduling” problems; but here is the method applied to this nurse scheduling problem. And finally, it is very difficult to come up with a sufficiently simple example. Not “I used this to schedule the 563 nurses at our National Hospital” — that’s fine for demonstrating later how effective your method was in practice — but “suppose we have 3 nurses, need 2 for this shift, and these two refuse to work with each other”. Ok, that’s too simple. What we need is a “Goldilocks” example, not so easy that it doesn’t illustrate your contribution, not so hard that it doesn’t allow your listeners to understand your contribution, but “just right”. The trick is to come up with the simplest possible example that can still make your point. That in itself is very difficult.
It is very easy, however, to overestimate your audience’s ability to follow the example. I often encounter a talk that presents an example early on and think “kudos to you, speaker”, only to quickly find that the example becomes too complex for me to fully follow. You have been working with the material for months or even years. What seems obvious to you, will not seem obvious to your listeners. It is difficult, but you must try to put yourself in their place.
You may fear that if you make the example too simple, people won’t understand what a difficult, deep, wonderful contribution you have made. Don’t fear. It won’t seem that simple to your audience, and anyway the best ideas are often “beautifully simple” at heart. Plus you’ll have plenty of time later in the talk to demonstrate how really complicated what you’ve done is, and how clever you had to be to come up with it. Ideally you can use your example as a running example, adding to it as you proceed to flesh out your talk. And if your listeners are like me, they’ll appreciate how really clever you had to be to come up with that initial, simple, introductory example.