Henri Poincaré, the French physicist and mathematician was an outstanding scientist. In his book, La Science et la Méthode (Science and Method – Dover publication translated by Francis Maitland), he states that “to understand” means different things to different people. The scientists in your audience expect to be able to “understand” what is presented, so it is worth thinking about what people require to reach understanding. Poincaré identifies two classes of people: the validating and connecting type, and the associative and transformative type (my choice of words).

The validating and connecting type

“They want to know not only whether all the syllogisms of a demonstration are correct, but why they are linked together in one order rather than in another. As long as they appear to them engendered by caprice, and not by intelligence constantly conscious of the end to be attained they do not think they have understood.”

In other words, they need to see, understand, and find believable the fragmented evidence, but they also need to see, understand, and find believable the logical thread that connects these fragments together. Poincaré describes what happens when understanding is incomplete.

At first they still perceive the evidences that are placed before their eyes, but, as they are connected by too attenuated a thread with those that precede and those that follow, they pass without leaving a trace in their brains, and are immediately forgotten: illuminated for a moment, they relapse at once into an eternal night. As they advance further, they will no longer see this ephemeral light, because the theorems depend upon one another, and those they require have been forgotten.

You cannot memorize what you do not understand and further understanding stops as soon as memorizing stops.

Making sure that each slide in the presentation offers the right conclusions is not sufficient. The scientist who presents should also identify and explicitly reveal  and explain the logical connectors between any two consecutive slides.

The associative and transformative type

Others will always ask themselves what use is it. They will not have understood, unless they find around them, in practice or in nature, the object of such and such a mathematical notion. Under each word they wish to put a sensible image; the definition must call up an image, and at each stage of the demonstration they must see it being transformed and evolved. On this condition only will they understand and retain what they have understood.

Some may place more emphasis on evolution kinetics than on evolution logic.

These often deceive themselves: they do not listen to the reasoning, they look at the figures; they imagine that they have understood when they have only seen.

It is not sufficient to make sure that the content on each slide in the presentation is easily associated to prior knowledge and visually or conceptually connected to prior slides. The scientist who presents should also take the time to make explicit the reasons for the change in content from one slide to the next.

Since people understand things differently, the scientist who presents is well advised not to privilege one type of understanding (his own) over another. Therefore, to be effective, the presenter should do the following:

1) Since people need to validate what they see and hear at the level of a slide, give them the time to do so. Justify your logic, and ensure that each element on a slide is related to prior knowledge.