Zero Can Be Powerful. If You Let It. Here’s What You Should Watch Out For: The Mental Model of Multiplicative Systems

My 9-year-old was asked to write down his thoughts about the number 'zero' in class the other day.

In his characteristic straight-from-the-heart style, he rattled off the top things that came to mind: "I don't like the number zero. Zero is too less. I think zero has a nice shape. I don't like the name zero. If you multiply any number by zero, you will get zero no matter what".

I think my son is on to something. It got me thinking about the mental model of multiplicative systems.

We learn early on that anything times zero is zero. But if we stop there, we miss to see all the practical ways this can help us in life.

Take the case of Leonard Bias, a young basketball prodigy who selected to play in the NBA for the Boston Celtics in 1986 at age 23.

He had everything going for him: He was 6’9", nimble, skillful, and the best player in a city that revered basketball. His parents cared about his goals. He was player of the year in a very competitive Division 1 college conference. He was a top overall pick in the NBA Draft by the Boston Celtics.

What ever went wrong? He developed a cocaine habit.

Unfortunately, Bias is remembered as the best basketball player who never played professionally. He died just two days after being being selected by the Boston Celtics from cardiac arrhythmia induced by a cocaine overdose.

Bias’ story illustrates well that in some facets of life, all our hard work, dedication to improvement, and good fortune may still be worth nothing if there is a weak spot—a weak link in the chain.

Let’s say A x B x C x D = E

If A, B, C or D is zero, then the result is zero.

Bias was operating in a multiplicative system, a system where a critical component had the power to derail everything he had going for him.

In a multiplicative system, zero renders a binary result—it’s always all. Or nothing.

On the other hand, additive systems work differently.

Let's say Christmas dinner's coming up. You’ve got a great chicken roast, some Christmas wine, some fish cutlets, a wide range of other delicious food, and some yum homemade Christmas pudding. AND you’re hanging out with family. How cool is that!

But then your fish cutlets get burnt and become inedible. That sucks. But dinner still works out.

The interaction of the various parts is what makes the meal what it is. Take away some parts or add in new ones and you get a whole different outcome.

Let’s say A + B + C = D

Even if A, B or C becomes a zero, you still get some result. Only, the outcome is different each time.

0 + B + C = E

A + 0 + C = F

A + B + 0 = G

In an additive system, zero is not as powerful—it’s not always win or lose.

What does all of this mean for you and me? Well, it’s to help us remember that additive systems and multiplicative systems react differently when components are added or taken away. Understanding the power of multiplying by zero can be of great value in life.

You’re working hard and you’re dedicated to self-improvement and driving results for your company. But your health in on the line. Is that a multiplicative or an additive system you’re operating in?

You’re earning in seven figures but have no time for your family and friends. Is that a multiplicative or an additive system you’re operating in?

You're an entrepreneur working hard to build a solid product, a solid team and scale your business. Your best hire leaves. Is that a multiplicative or an additive system you’re operating in?

Understanding when the system is multiplicative or additive, and which parts need absolute reliability for the system to work, is a critical mental model to embrace.

Step back, reflect and identify which system you’re operating in. It's well worth your time.