Issue 11
Founders and operators depend on dashboards to make hard calls, but numbers can create a dangerous illusion of control. This issue contemplates that metrics should always check for assumptions, not be interpreted as commands.
By Martin Drohmann
As a mathematician, truth is something I care about. After all Mathematics is the discipline of creating truth that (almost) everyone can believe in.
Without mathematical rigor, the internet and many engineering solutions would not have come to life. Hence, it is no surprise that software companies rely on measurable outcomes, metrics, to create alignment, and to define success.
One of the dangerous side effects of relying on rigorous mathematical methods is that people start believing they know the truth. They might look at a company, see that it passes the rule of 40 check, and invest in it, believing that it is a safe bet, only to realize that it is a sinking ship that, at that point, merely had a good margin. It happens.
Unfortunately, there is no unified, absolute truth. And strangely enough, mathematicians have proven it, both ways:
In August 1900, David Hilbert announced his famous list of unsolved mathematical problems at the International Congress of Mathematicians in Paris. One of them was the completeness problem: mathematicians had created a system of just eight axioms from which most mathematical findings could be logically derived. In other words, you only needed to believe in eight statements and suddenly all of mathematics became true. Or did it? Because there was one thing missing: the proof that this axiomatic system was indeed consistent (no contradictions) and complete (every statement can be proven to be true or false).
At the congress, everyone was certain that this axiomatic system had both. Mathematicians had made great breakthroughs in the decades before, and the system of just eight axioms seemed too simple. No one had found a contradiction in that system. It felt like a safe bet and just had to be proven.
But when a young Austrian mathematician named Kurt Gödel decided to do exactly that, he struggled immensely, and it never quite worked. So, at some point, he flipped it around and tried to prove its incompleteness. To his surprise, it worked. By enumerating all possible statements in an infinite axiomatic system, he could construct a simple card trick. Imagine one side of the card saying, “The sentence on the other side of the card is true,” and the other side of the card saying, “The sentence on the other side of the card is false.” It is a contradiction. And every system with an infinite number of statements has this property.
In other words, we know nothing. It is so humbling and important to remember.
Metrics and KPIs provide accountability and help us discover problems more quickly. Unfortunately, they don’t really tell us what we must do.
With care,
Martin