“For by the ultimate velocity is meant that, with which the body is moved, neither before it arrives at its last place, when the motion ceases nor after but at the very instant when it arrives… the ultimate ratio of evanescent quantities is to be understood, the ratio of quantities not before they vanish, not after, but with which they vanish” — Principia Mathematica by Isaac Newton
I’m not a mathematician, but I’m not afraid of numbers. I’ve drifted through the standard high school and college math requirements, admittedly with curiosity. And I’ve hung around the hedge fund industry, software engineers, and actually trained mathematicians for long enough that math’s kind of rubbed off on me. Yet my skillset is probably best described as a mix of product and, more recently, delivery management with an academic foundation in accounting.
Over time, I’ve noticed that cost accounting and traditional/waterfall project management operate primarily on absolute values assuming they shouldn’t change. Especially with respect to budgets and time. In fact, variance or change is almost a dirty word in that context. Today’s markets, especially in the context of new product development, are different from the heyday of cost accounting in the 1950s. Back then, you could easily assume stable incremental growth in demand in many markets for 15–20 years. And actually be right. Usually you wanted to establish a budget to control unnecessary costs, because everything else was likely to stay the same.
Contrast that with technology markets today. Most of them have big jumps in demand, often of products or segments which are difficult to forecast using a purely linear approach. The time from zero to $1 bln is much shorter for new products than it was 70 years ago, especially for the successful products.
This pace of change requires a different set of conceptual tools to understand how to operate and adapt to a rapidly changing environment. A different type of math. To start thinking about product management not in terms of algebraic variables, often with missing data, that need to be solved. Instead to think about the relationships of the variables to each other. And most importantly about how they change over time. Because that’s what velocity is. And what nearly every technology or innovation executive wants more of.
Newton and Leibniz independently discovered calculus. Among many other applications, Newton used it to model the movement of physical objects over time in a way previously unattainable. While we certainly don’t have the luxury of functions we can easily apply calculus to in a product management context, we can use linear approximation to figure out truly profit maximizing outcomes and adapt them in real time to a rapidly changing environment.
By linear approximation, I mean finite difference methods. This is just a big phrase for a simple numerical concept. For example, Don Reinertsen has popularized one of my favorite finite difference methods: Cost of Delay. By calculating how much sales you are losing + all other costs by releasing a new product or feature later, you can derive an average cost of time per month. This is basically subtracting two or more numbers, to numerically approximate the relative change of value over time. Similar to how this can be done with the velocity of a ball in high school physics. Cost of Delay is just a finite difference method.
Most choices in a big company don’t have the same implied cost of time. The value of time is assumed to be incalculable, more philosophical than practical. And it is, if you are stuck using “absolute” values.
Yet you can value time and derive implications for velocity if you are using finite difference methods. Thinking in relative terms enables you to think of relative profitability increases (in the moment) rather than always using an annual or quarterly budget yardstick determined much earlier, when you knew less and which is often likely to be out of date.
I am just discovering the outer edges of this at the moment. Please let me know if you have any suggestions or feedback, and sign up below if you’d like to follow me as I share more on this topic.