Business runs on certainty. Investors want predictable profits and will punish companies that vacillate up and down. Managers want accountable employees who they can trust to get things done. Customers want to deal with firms that they can be sure will be around next week.
When things are uncertain, penalties are imposed. Valuations tumble, people get fired, customers flee. That’s why managers learn to eliminate complexity from the system and keep it simple. They strive to remain within their realm of expertise and not stray too far into the unknown.
Yet to manage complexity we must do more than just ignore it. We can, of course, limit uncertainty by sticking with what we know and avoiding what we don’t. Still, uncertainty is not a bug, but a feature of any system that is exposed to the real world. Sooner or later, no matter what we do, it’s going to catch up with us. So, in the end, we need to meet it head on.
One way for managers to limit uncertainty is to put their faith in numbers. “You manage what you measure,” as the saying goes, so devising clear metrics and analyzing them conscientiously has long been a central part of every executive’s playbook.
And you can see why. People and markets can be fickle, but 1+1 always equals two and 2+2 always equals four. Math also ladders up to logic, so honing your analytical skills can help with a lot more than adding up balance sheets and income statements, it can help you think and act with clarity.
Yet in the early 20th century, logic was where math ran into problems. That’s when Bertrand Russell came up with his famous paradox, which can be summarized as “The barber of Seville shaves every man who does not shave himself.”
It seems innocent enough, but it shook mathematics to its foundations. Here was a statement (which can be expressed mathematically), that contradicts itself, and that wasn’t supposed to be possible. In fact, this little statement was so troublesome that many feared that if it was not resolved, even our certainty that 1+1 always equals two would be in question.
The Hilbert Program
At the time, David Hilbert was the global don of mathematics and, like any good CEO, he moved quickly to set things aright and close the hole that Russell opened up. He called on the world’s mathematicians to create a formal system of axioms that would be both consistent and complete. He also wanted to prove that every math problem could be solved.
The task outlined in Hilbert’s program seemed straightforward enough. Clearly, mathematics should be consistent (i.e. 1+1 always equals two) and complete and self sufficient (i.e. mathematical statements can be proved mathematically.) And what good is math if it can’t solve mathematical problems?
For a while, they seemed to make progress, yet, as Gottlob Frege put it, “Just as the building was completed, the foundation collapsed.” As it turned out, the mathematics industry, like so many enterprises today, was undone not by a rival, but by a couple of startups.
The System Crashes
The first mortal blow to Hilbert’s program was dealt by a 25 year old Austrian named Kurt Gödel with his incompleteness theorems, which used logic to kill logic. Essentially, he proved that any formal system could be complete or consistent, but not both. A few years later, 24 year old Alan Turing used Gödel’s methods to prove that all numbers are not computable.
The “Gödel debacle” shook the mathematics community to its core. Much like the hyenas of disruption today, the two upstarts showed that everything that mathematicians had believed was fundamental to their enterprise was, in fact, just a comforting illusion. Hilbert and his band of mathematical demi-gods could hardly have imagined a greater calamity.
Yet it turned out not to be so bad. In fact, Turing’s paper on the computability of numbers described a universal computer which led directly to modern digital computers. These, as we all know, have a tendency to crash, just like any logical system, but not so often that we worry too much about it. When it happens, we figure out a way to deal with it somehow.
So it is true that the two young startups destroyed the world as we knew it, but they created another one far richer and with greater possibilities. We now live in a world of the visceral abstract, where seemingly ludicrous ideas like those of Gödel and Turing—and many others as well—form the basis of our daily lives and the modern economy.
Leading Through Uncertainty
Much like the mathematicians of a century ago, every executive in business today must confront an industry that is being disrupted. As much as we would like to seek certainly, it is little more than a comfortable fiction. True leaders don’t avoid uncertainty, but take it upon themselves in order to provide stability for those around them.
Being in a position of responsibility means that you have to make decisions, without all the facts, in a rapidly changing context. You do so in the full knowledge that if you are wrong, you will bear the blame and no one else. You can never be certain of what your decision will bring, only that it is you who has to make it.
While many see the digital economy as an opportunity to take refuge in metrics, the truth is that our numbers are always wrong. Sometimes they’re off by a little, sometimes by a lot, but they are always wrong. The answer is not to try harder to get them right—they’ll still be wrong—but to become less wrong over time. We need to take a more Bayesian approach.
Yet most of all, we need managerial maturity. Lacking certainty doesn’t mean to lack confidence. As the Godel debacle showed, a system can be disrupted to its very foundations and not only survive, but improve. True leaders are the ones who make that happen.
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