Cassie Kozyrkov

@kozyrkov

Why I avoid equations in my talks

The myth of superhuman working memory

I taught math and statistics for over a decade and today I’m often asked to speak about technical topics at conferences. Although I come from a field that loves equations and technical nitty gritty details, you’ll find almost none in my talks. I also avoided them as a statistics lecturer. Here’s why.

The myth of superhuman working memory

Before heading to grad school in mathematical statistics, I was a PhD student in neuroscience and psychology. I was fortunate enough to get hands-on research experience on the topic of human attention and memory, which brought me to a hilarious realization.

Anyone who claims to be following an equations-based mathematical lecture is probably faking it.

To boil the cognitive science down to a point, anyone who claims to be following an equations-based or technical-details-stuffed lecture is probably faking it. There’s one exception: those who have already learned most of the material. Mathematicians are just as human as anyone and their working memory capacity works similarly too. It turns out that standard lectures overload students’ working memory by defining too many new symbols and equations for even the brightest students to keep track of what’s what.

Mathematicians aren’t superhuman and they don’t have superhuman working memory.

Think you’re special? Read this once, close your eyes, and say it back to me:

AHGJBSKEIFDDRHWSL

Psychologists would suggest that AHGJBSK is about as much as you should expect humans to handle. Every time a speaker adds a new symbol to their talk, the audience has to devote working memory capacity to tracking what it symbolizes and how it fits with the other new stuff. That’s the same working memory needed for remembering the previous slide and tracking the logical argument. AHGJBSK highlights just how little capacity there is to go around.

Before presenting equations and jargon, do this

Professors and technical speakers, don’t take my word for it, try it yourself:

  1. Pick an alphabet you wouldn’t be able to name characters from. Chinese characters are my favorite choice when I practice. 熟能生巧
  2. Consider your audience. Think carefully about who will be in the room and what they know.
  3. Ask yourself which jargon terms or symbols in your equations or technical nitty gritty details in your slides might not be immediately familiar to your audience. If you’re sure every single human in the room sees x̄ as “sample average” without thinking (a decent assumption if your audience is statistics professors), then you may exclude x̄ from this list. Use it freely. Otherwise, take x̄ and its friends to the next step.
  4. Replace each one of those with a random letter from the alphabet you’ve chosen.
  5. For best results, have a friend reformat your slides so that things have also moved around a little bit visually.
  6. Try giving your talk/lesson.

If you stumble, you’d also have lost your audience at this point. If the cognitive load of remembering what all those new symbols mean is too much for you (the expert!) then it’s definitely too much for your poor audience.

Once you’ve lost your audience, all they will absorb is summaries and explanations that you give in plain language. That’s why it’s especially important to pepper any technical talk with standalone plain language summaries.

Avoid promoting impostor syndrome

If you’ve lost your audience and they’re too polite to walk out of your talk (or if they’re a captive audience of impressionable young students), you’ll rarely find listeners brave enough to point out that the emperor has no clothes. Usually, no one calls out, “We haven’t understood a word you’ve said in the last 30 minutes.” Some folks are restrained by manners, some feel fixing your incompetence is not worth their time, some are cowed by the smart questions from the handful of people who were experts in most of your talk before you gave it, and some are wondering whether they’re the only ones too stupid to understand what you’re talking about.

When your presentation doesn’t take human working memory capacity into account, you lose your audience. The rest of your talk sounds like birdsong to them and is just as boring.

This latter category could be spending your entire talk (since it may as well be birdsong) agonizing over whether or not they even belong in the room. They might start to believe that they’re impostors. Your talk/lesson, targeted to impress a handful of experts in the room, completely misses the rest of your audience, which contributes to a toxic environment rife with impostor syndrome. (Here’s a link to my musings on impostor syndrome and what teachers and students can do about it.)

Cultural change starts with you

I know that in many academic disciplines, my own included, presenting in this awful manner is part of the culture. We might have a culture that is less than ideal, but we’re not stuck with it. We can choose to lead change by example.

At Google, I initially got a lot of criticism from traditionally-minded colleagues when I announced that I would be teaching our entire workforce statistics and machine learning… without equations. Those courses quickly became the most popular internal technical training, with reviews like, “I learned more in one day than in an entire semester of my statistics master’s degree.” It can be done.

Start here

The hardest thing you’ll have to do is find the courage to stop trying to prove that you know how to use equations (we believe you) and start thinking about what’s actually useful and interesting to your audience, keeping human working memory constraints in mind. Let me help you get started.

Give yourself a budget: no more than 7 new things (symbols, theorems, concepts, equations, etc.) in working memory. That number drops when listeners are less motivated. When I say I aim for 3–5, that doesn’t mean only 5 things learned over the lesson. It means only 5 things loaded into working memory at a time. If your audience is seeing something for the first time, finish up with it now (and tell your audience when you’re done with it so they can drop it from working memory) or pay for it out of the budget. Don’t lean on it later unless you’ve kept your audience’s working memory free of clutter.

If you’re honest with yourself, you’ll see that very few of the details that look so beautiful to you actually help your audience. Don’t waste their time with equations or technical nitty gritty details they can’t absorb right now. Instead, tell them how to use that equation when they’re hunched over it with pen and paper. Tell them why they should be excited about it and how the detail fits into the greater picture. Tell them why it was hard to derive / discover and what the key insight that drove that discovery was. Point your audience to any equations or details they will need later by indicating the place to look and what they will want to use them for. Tell them why they should care! Get them excited or they’ll think your topic is boring or, worse, that they’re bad at it.

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