Emotional Engagement in Persuasion and Learning

HOW WE CONVINCE PEOPLE

Logical truth is not always illuminating, and in practice it often isn’t logic that actually convinces us of something. This is related to the fact that logic is not usually helpful for thinking up a proof in the first place. When we’re thinking up a proof we often use gut instinct, vague suspicions, hunches, inklings, we look for things that slightly remind us of other things, we wait for flashes of inspiration. We then try to fill in all those things using logic, but only after we’ve used many not-entirely-logical processes to get our first ideas in place. This is perhaps the origin of the myth of maths “geniuses” – there is often a mysterious element of inspiration at the start of mathematical work, but let’s not forget the sheer hard work that goes into constructing the logic afterwards.

We don’t entirely use logic to understand logical proofs either. Often in a research paper a logical proof will be accompanied by a description of what “the idea is”, which is something more informal, not rigorous, but invokes ideas and imagery that might help us to understand the logic. It might be a picture, like the fractal tree picture I used to talk about filling in the gaps in a proof. It might be some sort of schematic diagram showing how things fit together, like my diagrams of causation in Chapter 5. It might be an analogy, or a small example. These things are not exactly logical themselves but they help us understand the logic. Often once we’ve understood the idea like this we can fill in the logical steps ourselves with much less help. Feeling why something is true helps us understand why it’s true logically, even in an area as abstract as mathematics. If we don’t get the idea of why it’s true we might follow every step of the logic but still feel disconcerted that we don’t feel like we really understand what is going on.

The experience of knowing something logically but not emotionally happens in proofs, and it happens in grief, when you know intellectually that something terrible has happened but some emotional part of you can’t yet believe or accept it. I think this is the difference between knowing something intellectually and knowing something emotionally. Our intellect and our emotions don’t necessarily take us to different conclusions all the time, it’s just that sometimes there’s a lag between them.

This comes into play when we are learning things. If we engage our emotions or personal experiences while learning something it is quite likely to get embedded more deeply in our consciousness. People say that the best way to learn things is by experience, and I think this is because if we learn something by experience we really feel what it’s like, and then the thing we’ve learnt sits somewhere deeper inside us than if we’ve just read about it in books.

This is related to the contentious argument about the role of memorisation in learning maths. Some people take it entirely for granted that some rote memorisation is necessary if you’re going to be good at maths. But other people, often professional research mathematicians themselves (including me), are convinced that they have never really memorised anything in maths. In fact, one of the main reasons I always loved maths was exactly the fact that it didn’t require memorisation, only understanding. And yet, many people tell me the whole reason they were put off maths was having to memorise things. I sympathise, as I am also put off by having to memorise facts, I just don’t agree that maths requires that. Usually when I say this someone will challenge me and say “But surely you learnt your times tables.” Somehow times tables always come up as the essential thing that surely nobody could avoid memorising.

Now, I am certainly not an amazing whizz at arithmetic, not one of those human calculator types who enjoy rapidly multiplying five-digit numbers in their head. However, I am perfectly fine at basic arithmetic and certainly above average compared with the general population, and yet I have never memorised my times tables. I know my times tables by some other, more subtle route that does not involve memorising. I think this is like the fact that I know my name, but I have not memorised my name. I have internalised it.

Logic, maths and science can be difficult to internalise if they appear to be devoid of emotional content. We should be clear that it is only the methods of justification that should be devoid of emotional content, not the methods of communication and understanding. Emotional engagement is a much more powerful way to make logical truth convincing. In fact, it can make anything convincing, logical or otherwise, true or otherwise, as can be seen from the success of so-called internet “memes”.