05 NOVEMBER 2015

But is it Useful in the Real World?

But is it Useful in the Real World?

I cringe when I hear a phrase like, “I’ll never need to know this in the real world”.

Have you ever been expected to learn something, and been quickly discouraged because you can’t imagine how it would ever be useful? I remember being bemused when introduced in primary school to the concept of a matrix.


“OK”, I thought. “So it’s a grid with numbers in it. You can add them together. You can multiply them, using a method that doesn’t seem to make much sense. I’m not sure what they’re for, but I guess I’d better learn this stuff.”

Matrix addition looks like this:

Sean Holden Thought Leadership Post Matrices


One adds the numbers in corresponding positions in the two grids on the left to get the number in the corresponding position on the right (the sum). So, 1 + 5 = 6, 2 + 6 = 8 and so on.

That was in primary school, and I was still at a stage where I wasn’t about to question my teachers, so I didn’t ask what matrices were for — I just treated them as something I had to know about to pass exams and got on with it. How wrong I was.

I now work in the field of Artificial Intelligence, specifically Machine Learning. I am interested in writing computer programmes that can learn from experience. I work, for example, with the pharmaceutical industry to produce software that can learn to recognise potential new drugs. All of this work requires me to use matrices, on a daily basis. What’s more, you make use of software that performs matrix calculations every time you use a mobile phone, as it needs them to recognise your voice, to communicate with the network, and for many other purposes. (As an aside, it’s worth remembering when you use your mobile phone just what an amazing thing it is. Depending on the make and model, it’s likely to contain ten or more individual computers, each more powerful than the one used by NASA’s Apollo moon-lander.)

Now you are probably wondering what matrices have to do with any of this, but to explain the connection fully is something that I don’t have the space for here, and that would take rather a lot of time and study on your part. So you’ll have to trust me.

There are other examples. When you apply for a bank loan there is a good chance that your application is assessed by machine learning software performing matrix calculations which learned to assess applications by looking at previous applications by others. Self-driving cars, systems for recommending products of interest when you use an online shopping site, and a plethora of other things that you do, or will, take for granted during your lifetime, depend on this piece of mathematics.

Let me give you another example. While studying electronics at University, I was taught about something called “first-order”, or “predicate”, logic. This seemed equally odd; a system of unfamiliar symbols, somehow related to treating logical arguments as mathematics.

This seemed every bit as lacking in purpose as matrices had a few years earlier. By now however I was more confident.

“What am I going to use this for?” I asked the lecturer, a mathematician.

“I don’t know”, he replied. This did not fill me with confidence, but I have since made certain that as a lecturer myself it is a question I should always be able to answer. Perhaps your teachers have done a better job of promoting material like matrices or logic — if they have then count your blessings — but I’m sure that some of the things you’ve been encouraged to learn seem to you to be without a purpose.

With logic, I was just as wrong as I had been with matrices. Mathematical logic of some kind is foundational in the design of computers, and increasingly important in trying to find methods that can let us be confident that programmes will not crash. This is important if, for example, your programme is going to be in control of a nuclear power station.

The moral of this story is simple: sometimes the usefulness of an idea is not clear until sometime after you are first exposed to it. If you’re at school, perhaps your teacher finds it hard to explain what it might be useful for, but don’t let that be a reason to discard the idea, because it might surprise you later in life.


Dr Sean Holden is Senior Lecturer in Machine Learning at the University of Cambridge Computer Laboratory. Read Sean's full Career Profile.