Making the unapproachable approachable

I don’t have many regrets, but I do regret not paying more attention in maths class when I was about 17 years old. I had reached the point where I was thoroughly bored with full time education. I think I must have been staring out of the window during the vital lesson when the fundamentals of calculus were explained, because suddenly I was in a world of symbols and concepts that I didn’t understand. It was like skipping a couple of episodes of a complicated TV series: I was lost and struggling to catch up. With the help of some friends, I bluffed my way through the exams and didn’t do too badly, but I never felt at ease with the subject.

To tell the truth, I don’t even regret that academic mis-step very much, as it was part of the path that led to me skipping university at 18, a choice which I wouldn’t recommend to everybody, but which had a huge influence on my personal, professional and academic life. However, I have always felt that calculus was an important hole in my understanding of the world. This has particularly been the case recently, when I have attempted to educate myself about Machine Learning.

If you, like me, are a programmer who has built many front-end or back-end systems over the years, you may be familiar with the experience of trying to learn ML. You start by thinking that you know programming, and you know computers, so this will just be one of those cases where you need to learn some new syntax and some new concepts and you’ll soon be building happily. Then you find yourself in a world of graphs and equations. Every course you attempts has pre-requisites, and if you follow the chain of pre-requisites, you find yourself back in the classroom trying to understand calculus.

That was why I was pleased when someone recommended Andrej Karpathy’s series of YouTube videos to me. These are chunky videos of more than two hours each, and require an investment of time and attention, but they are worth the trouble. I was encouraged by the description the first video, an introduction to neural networks and backpropagation, which said that all that was needed was ‘a vague recollection of calculus from high school.’ My recollection was certainly vague.

I don’t know if it was Andrej’s engaging, patient style in the video, or whether it was the use of a multi-step equation as a detailed, worked example, but some of the concepts of differentiation suddenly clicked for me. I realised that one of the keys to backpropagation was to figure out how the rate of change of an input affected the rate of change of an output - and all the calculus in the middle was part of the figurin out.

I’m not going to attempt to reproduce Andrej’s explanation here: you’d do better to go and watch the video. Rather, I’d like to reflect on two different lessons.

First, it is possible to approach the unapproachable. For me, calculus had become one of those scary subjects: something that I was nervous of approaching, expecting to be confused and frustrated. But somehow, this mode of education made the unapproachable approachable: it switched a light bulb on for me. I just needed to find the explanation that worked for me.

Second, it is possible to make the unapproachable approachable. Those of us who work in enterprise technology often lament that others are not interested in our subject: that they just don’t ‘get it’. We often forget that, for many people, technology is their unapproachable. They have been baffled and frustrated too many times by apps that don’t work, by equipment that breaks, by dialogues that send them in loops, and by baffling configuration settings. And that’s just on their mobile phones: most people have not even started to pry behind the curtain of global infrastructure that delivers their services - and have little incentive to look.

As part of the technologist’s duty to explain, I believe that we have to do our best to make the unapproachable approachable. That might mean recording two hour videos of patient teaching, as Andrej has, or it might mean five minutes of careful explanation the next time someone asks us to fix the printer. But if we do a little of that every day, we do something to help people understand how the world works, and how to make the technology a little less scary.

(Views in this article are my own.)