Time for today’s math lesson! How are the geometric concepts of intersection and union applicable to your daily life? To discuss this fine topic, we'll use our old friend, the Venn diagram:


That bit where the two circles overlap is called the intersection:


The entirety of both circles together is called the union:


Pretty basic stuff. Remarkable how few people seem to get how it applies to them, however. Let's take business: When I was at Microsoft, we were constantly being told, “You can't do that, you’ll step on the toes of one of the other divisions,” or, “Helping our customers in that way would also be helping our competitors.” The idea was that no part of the company should do anything that might interfere with what some other part of the company was trying to do. All the different parts should make the other parts work better. There are all sorts of great buzzwords for this, like “synergy” and “better together”. On the face of it, it all sounds like common sense… don't get in your own way, help yourself out. The problem is, when you think that way, you end up with only the intersection of your business initiatives, only the areas where one helps the others:


… and every new initiative you have, that intersection gets smaller:


… but this is business, ruled by bigger, better, more! What you really want is everything, the union:


If one department steps on the other’s toes, it’s okay, because the whole pie is so much larger.

This doesn't just apply to business, of course. Let's say you're dating someone. Here’s a diagram of your movie tastes as a couple:


… and now it’s time to pick out a movie to watch together. Should you go for the intersection (where your tastes overlap), or the union (where at least one of you is interested)?

It comes down to how long you're together. If this is your first date, you’d better stick to the intersection, so you know everyone's happy. If you're going to stay together for years, though, you need to start venturing out into the union… otherwise, not only will you not see as many of the kinds of movies you like, you also won't get the opportunity to discover new things you might like outside of your comfort zone. For a marriage to survive, you need to be able to keep reinventing yourselves together, and that means trying new things.

The timing factor applies to companies as well: if you're a startup, everybody needs to be focused on one thing so you can move quickly. That puts you right in the middle of the intersection. Once the company has a chance to mature, however, sticking to the intersection means stagnation, which means death, or at least irrelevance.

Whether you're a person, a marriage, or a company, long-term survival depends on periodic reinvention. Look to the union of your interests, and you'll always find it.

Thank you, math!