Why explanations are hard


Johnny Breen


July 4, 2023

How many times have you asked somebody to explain something to you, only to be completely lost straight afterwards?

This has happened to me on so many occasions that I have lost count. In scenarios like this, it’s easy to feel like you’re being ‘slow’ or feel embarrassed to ask them for an alternative explanation.

But, over the course of time, I have come to realise that - most of the time - the fault actually lies with the other person.

Why does this happen so often?

People don’t tend to appreciate your point of view when they explain things to you.

This is particularly true of Powerpoint presentations but I think I’ll reserve my thoughts for that particular topic in a separate blog post (/rant),

A cartoon showing how the quality of presentations has declined over time due to Powerpoint

To the point though, people don’t mean to explain things badly1. Instead, it typically boils down to a few simple reasons:

  • Ignorance: they don’t appreciate what they know now (and what it was once like to be in your shoes once upon a time). This is the most common reason

  • Laziness: people can’t be bothered to think of an effective explanation. It’s less work to relay Wikipedia-esque explanations to you than it is to re-engineer one’s own understanding of something complicated into layman’s terms

  • Subtle flaunt: of one’s own intelligence and superiority. It can make you look ‘smart’ if you use big words to explain something complicated and confuse the other party. This is the worst reason and will often backfire on you, by the way

Concepts are more important than definitions

I first encountered the Normal Distribution in high school.

The first items we were taught about this distribution were as follows:

  • How to calculate \(z\)-values

  • How to lookup \(z\)-values in our statistical tables

  • When2 to invoke the Central Limit Theorem

  • Told which conditions to check for (in an exam question) when approximating a binomial random variable with the normal distribution

  • And so on.

At no point in this process, however, were we provided with a conceptual understanding of the normal distribution. I think this is a massive shame because the intuition behind the normal distribution is pretty cool!

Why is it that we start by teaching such a compelling theorem… with tables and dry definitions first?

When you think about it, this approach does not make any sense at all: until you understand what the normal distribution is and how it arises in nature, the best you can do is guess at what calculations you’re doing which is exactly the predicament I found myself in during high school3.

I think this example really gets to the heart of my own teaching (blogging) philosophy: concepts should always come first, details later.

How to improve your explanations

Take the example of the Copula in statistics. Here is - in my view - a lazy, thoughtless definition of what a copula is,

In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform on the interval [0, 1]

Yeah, sure… but seriously, what the heck does that even mean? This explanation is brimming with jargon and esoteric terms such as ‘multivariate’ and ‘marginal’.

For somebody with no context for copulas, this is a useless definition. What’s more important to understand about the copula is how it is applied4:

A ‘Copula’ can be used to help you ‘link’ two or more random variables together which may be correlated (e.g. interest rates and inflation). The result is a joint distribution, allowing you to model future outcomes effectively whilst taking account of any underlying correlations.

Now, I am not saying that this definition is perfect, but it does at least provide you with some real context for what the ‘point’ of this thing is.

If you can start by understanding the concept of what you are trying to explain first and frame it with an example, you’ll often find that your recipient will get far more out of it than you ever imagined!


  1. Well, most of the time at least! Though there are a sadistic minority of individuals who like to torment those with less knowledge than them↩︎

  2. That said, I would never understand how this worked exactly and it would continue to haunt me throughout university too↩︎

  3. Unfortunately, I decided to go off to university and study mathematics where things only got worse (much worse). Mathematicians seem to love throwing around complicated definitions and dry theorems with the casual ‘…and this proof should be fairly obvious so I won’t write it here’↩︎

  4. As an aside, somebody who explains this statistical concept far better than me is Thomas Wiecki.↩︎