# Simon’s graph theory thoughts about the overpopulation problem

In a complete binary tree, every node has two children (except for the bottom nodes that don’t have any children at all). This means one mind-blowing thing: that the bottom row always has more nodes than the number of nodes in the entire rest of the tree! Example: if there’s one node at the top of the tree, two nodes in the second row, four nodes in the third row and eight nodes in the bottom row, the bottom row has more nodes (8) than the remaining part of tree (7). I’ve been thinking about this, and I applied this to the real world:

The average number of children a parent has in the world is 2.23 (I’ve used an arithmetic mean, which is oversimplistic, should have probably used the harmonic mean). Does this mean that currently, the number of children exceeds the number of parents? The definition of “children” I’m using are people who don’t have children, so the last row of nodes so to speak. By “parents” I’m counting all generations. If you just want to talk about now, the parents living now, then you have to trim the top rows (the already dead generations). If the average number of children is 2 or more, are there going to be more children in the world than parents?

Well, in this model, I’m ignoring crossover. This means we should consider every node in our tree for 2 people*. So, now, if the average number of children is 4 or more, there’re going to be more children than parents. So, what I said earlier was wrong. The average number of people doesn’t exceed 4, so there aren’t more children than parents. But the number of children today may still exceed the number of parent generations still alive.