Mental Model: Multiply By Zero

Let's run through a little elementary algebra. Try to do it in your head: What's 1,506,789 x 9,809 x 5.56 x 0?

Hopefully you didn't have to whip out the old TI-84 to solve that one. It's a zero.

This leads us to a mental model called Multiplicative Systems, and understanding it can get to the heart of a lot of issues.

The Weakest Link in the Chain

Suppose you were trying to become the best basketball player in the world. You've got the following things going for you:

1. God-given talent. You're 6'9″, quick, skillful, can leap out of the building, and have been the best player in a competitive city since you can remember.

2. Support. You live in a city that reveres basketball and you're raised by parents who care about your goals.

3. A proven track record. You were the player of the year in a very competitive Division 1 college conference.

4. A clear path forward. You're selected as the second overall pick in the NBA Draft by the Boston Celtics.

Sounds like you have a shot, right? As good as anyone could have, right? What would you put the odds at of this person becoming one of the better players in the world? Pretty high?

Let's add one more piece of information:

5. You've developed a cocaine habit.

What are your odds now?

This little exercise isn't an academic one, it's the sad case of Leonard “Len” Bias, a young basketball prodigy who died of a cocaine overdose after being selected to play in the NBA for the Boston Celtics in 1986. Many call Bias the best basketball player who never played professionally.

What the story of Len Bias illustrates so well is the truth that anything times zero must still be zero, no matter how large the string of numbers preceding it. In some facets of life, all of your hard work, dedication to improvement, and good fortune may still be worth nothing if there is a weak link in the chain.

Something all engineers learn very early on is that a system is no stronger than its weakest component. Take, for example, the case of a nuclear power plant. We have a very good understanding of how to make the nuclear power plant quite safe, nearly indestructible, which it must be considering the magnitude of a failure.

But in reality, what is the weakest link in the chain for most nuclear power plants? The human beings running them. We're part of the system! And since we've yet to perfect the human being, we have yet to perfect the nuclear power plant. How could it be otherwise?

An additive system does not work this way. In an additive system, each component adds on to one another to create the final outcome. Going back to algebra, let's say our equation was additive rather than multiplicative: 1,506,789 plus 9,809 plus 5.56 plus 0. The answer is 1,516,603.56 — still a pretty big number!

Think of an additive system as something like a great Thanksgiving dinner. You've got a great turkey, some whipped potatoes, a mass of stuffing, and a lump of homemade cranberry sauce, and you're hanging with your family. Awesome!

Let's say the potatoes get burnt in the oven, and they're inedible. Problem? Sure, but dinner still works out just fine. Someone shows up with a pie for dessert? Great! But it won't change the dinner all that much.

The interaction of the parts make the dinner range from good to great. Take some parts away or add new ones in, and you get a different outcome, but not a binary, win/lose one. The meal still happens. Additive systems and multiplicative systems react differently when components are added or taken away.

Most businesses, for example, operate in a multiplicative system. But they too often think they're operating in additive ones: Ever notice how some businesses will add one feature on top of another to their products but fail at basic customer service, so you leave, never to return? That's a business that thinks it's in an additive system when they really need to be resolving the big fat zero in the middle of the equation instead of adding more stuff.


Financial systems are, of course, multiplicative. General Motors, founded in 1908 by William Durant and C.S. Mott, came to dominate the American car market to the tune of 50% market share through a series of brilliant innovations and management practices, and was for many years the dominant and most admirable corporation in America. Even today, after more than a century of competition, no American carmaker produces more automobiles than General Motors.

And yet, the original shareholders of GM ended up with a zero in 2008 as the company went into bankruptcy due to years of financial mismanagement. It didn't matter than they had several generations of leadership: All of that becomes naught in a multiplicative system.


On a smaller scale, take the case of a young corporate climber who feels they just can't get ahead. They seem to have all their ducks in a row: great resume, great background, great experience…the problem is that they suck at dealing with other people and treat others like stepping stones. That's a zero that can negate all of the big numbers preceding it. The rest doesn't matter.

And so we arrive at the “must be true” conclusion that understanding when you're in an additive system versus a multiplicative system, and which components need absolute reliability for the system to work, is a critical model to have in your head. Multiplicative thinking is a model related to the greater idea of systems thinking, another mental model well worth acquiring.


Multiplicative Systems is another Farnam Street Mental Model.