“All units are ridiculous” – how to understand scale

I am occasionally and gratifyingly asked what I study – perhaps because I’ve never learnt to dress or shave properly despite having left university over 6 years ago. I say that I build apps to measure the world through mobile phones sensors, sometimes this leaves people with the misapprehension that I studied something useful for app building and distribution – like programming, computer science or even marketing. But I didn’t, I studied Physics and Philosophy. Indeed all of the founders of OpenSignal are equally ill-qualified to build and market apps: we all studied Physics at Oxford.

While at university I didn’t write a single line of code and I don’t think I once heard the word “startup”, yet I realise that the things we learnt have played a strong role in defining the products we have built. While the route from computer science into startups is well established, I’d like to argue that Physics is, or at least should be, a fertile ground for the skills needed to hack & disrupt.

While there are many different lessons that have helped us, to save redistributing too many electrons I’m going to pick up on one:

“All units are ridiculous”

This statement was attributed by one of my Philosophy lecturers (Harvey Brown) to one of my Physics lecturers (James Binney), it’s a beguilingly simple summary of several different ideas.

Don’t be fooled into thinking this is a choice between SI (like kg) and Imperial units (like lb), this is a statement about scale and the difficulty in creating a full and cohesive description of the universe. To understand it think of a unit as a physical thing – think of a metre as block of metal in Paris, think of an Astronomical Unit (AU) as the distance between the sun and the Earth, think of a light year as the distance light travels in a year, think of the Planck length as the minimum size of an atom before it falls in on itself. We can argue over how arbitrary these units are, but what should be accepted is that all are ridiculous when applied in the wrong circumstances. A Planck length is a dumb choice for talking about your height, but equally an AU is laughable when thinking about things on atomic scale. Nonetheless each of these units has a domain of utility.

Choosing the right units to use in tackling a Physics problem is a big step to solving it since a unit choice tacitly carries various assumptions – choose the speed of light as your speed unit and you’re likely to be working in the relativistic domain (the realm of very fast or high energy stuff), choose m/s (or mph) and you’re probably going to assume that Classical (aka Newtonian) Mechanics applies, which simplifies the equations a lot.

So here are three key lessons this statement contains and how they map to startup skills:

1. Most systems work on different levels. At one end of what we do is a codebase and design choices, at the other end are app users, mobile network Operators, banks, consultancies and telecoms regulators. There’s no single aspect that’s best for understanding what we do: it’s important to keep switching perspective. While team members will specialise, understanding how different parts of the chain couple with each other will produce stronger individual links.

2. Understand orders of magnitude. While physics can be extremely exact, in most practical problems you won’t know enough about all the input variables to get anywhere precise, and to have even a hope of arriving at a solution you generally need to make a lot of approximation. Being confident of an answer within an order of magnitude is often pretty good going and doesn’t necessarily reflect laziness, but rather realism as to the quality of result you can get given the complexity of the problem.
Startups are generally innovative – this means the products and strategies they adopt have not been tested – so attempting to precisely forecast growth, for example, is futile. What is worthwhile is understanding the order of magnitude and the scaling laws that apply to what you are doing: is this a product that could reach millions, 10s of millions, 100s millions; how important are network effects to your product’s growth, are you seeing linear growth, exponential growth or a series of step changes?

A related skill: learn to sense check. Physics tends to deal with problems that can be quite abstract (like the expansion of galaxies invisible to the eye) or things that never really happen in your life (like trains going into tunnels at ten million kilometers per hour). The maths to tackle these problems can be involved and it’s easy to end up as if one were drifting at sea. You need to hang onto any things you can be sure of: is the sign correct? are the dimensions correct? (were you supposed to calculate a quantity of energy but ended up with a length – these sort of errors are surprisingly common), there are many tricks that can keep you from losing sight of land. Clearly the precise types of sense-checking you need for building products is quite different, but the aim is to have a variety of quick and simple techniques for understanding whether your product is on track at each stage of iteration – here’s one good technique: would that feature you’re planning on building make sense to a first time app user who came across your product by mistake?

3.This does not change everything. Even if your products reach a billion users, the universe is much more awesome at its grand scale and at its small scale it’s weird beyond our powers of invention. You might be CEO of the whole damn world b**** but your kingdom lies in a comparatively mundane middle-ground between the vastness of space and the freakiness of quanta.

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