@ Michael Snoyman
2025-02-23 06:35:51
My wife and I have six children, making our house a household of eight people. Looking just at the eight of us, how many relationships exist? Well, as a first stab, we could look at how many connections exist between two unique individuals in this family. The mathematical term for this is “8 choose 2”, and the answer is 8\*7/2, or 28\.
Even that doesn’t really capture the answer though, because relationships aren’t just between two people. For example, when my wife and two oldest children are the only ones still awake after the younger kids go to bed, we’ll put on my mature TV shows that they’ll appreciate and watch together. It’s our own little subgroup within the group.
Based on that, we could have groups of 2, 3, 4, all the way up to 8, the group of all of us. If you do the math, this comes up to 247 different subgroups of 2 or more people. That’s a lot of groups for just 8 people.
As a father, this means I’ll never be able to fully understand every set of connections within my family. I may have a good understanding of my own relationship with each child. I also am closely aware of the relationship between our two youngest children, since they’re twins. And I could probably list 20 or so other noteworthy relationships. But I’ll never understand all of them.
For example, months ago I bought a game on Steam for my 3rd and 4th kids. I know they like to play games together, so it was a relationship that I thought I understood well. A few days ago I found out that my oldest had joined them in playing one of these games (Brotato). I’d made the purchase, given it to the kids, and it sparked new relationship and interaction structures without my involvement.
There’s no problem with the fact that I can’t track every interaction in my house. That’s healthy\! The kids are able to discover ways of interacting beyond what I can teach them, learn everything from schoolwork to video games from each other, and overall become more healthy and well-adjusted adults (I hope).
And here’s the important part: the growth of the number of connections is *massive* as the number of participants increases. If we add in another participant, we have 502 groupings. At 10 total participants, it jumps to over 1,000. By the time we get to 100, we’re well into the trillions.
A mathematical and software term for this is *combinatoric complexity*, the massive increase in an output value based on a small increase in the input. The analysis I’m providing could be termed as part of graph theory (for connections of 2, looking at people as *vertices* and connections as *edges*) or set theory (unique subsets, allowing for larger group sizes). But regardless, the point is: the increase in complexity is huge as more people join.
Now consider the global economy. It’s over 8 billion people. There are so many people that the number of groupings is absurd to talk about. Nonetheless, massive numbers of these groupings naturally occur. There are family units, friend circles, individual connections, companies, project teams, sports teams, schools, classes, and millions more. These groups of people form new ways of interacting, express vastly different desires for goods and services, and are capable of producing wide varieties of goods and services themselves.
When you allow this system to run free, beauty emerges. Each node in the graph can manage its own connections. Each *person* is free to make his or her own decisions about association, what to spend time on, what to spend money on, and so on. Each person does so on their own judgement and world view.
Some of these people may make “dumb” decisions. They may “waste” their time and money on useless things. Except: who made that value judgement? Clearly not them, they decided it was worth it. No central planner has the right to override their will.
My point in all this is: as yet another of many reasons in the list of “why people should be free,” we have one more data point: pure math. Central planning will never scale. Central planning will never appreciate the individuality and desires of each person. Only by giving people the freedom to explore their connections to others, discover what they can produce and consume, explore their options, and ultimately make their own decisions, can we have any chance of creating a world where everyone can succeed.