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This page is a blog article in progress, written by David Tanzer.
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guest post by David Tanzer</i>

Hi this is Rick from the Portland Gear Works, checking back in with you. It’s now time to brew that pot of coffee I mentioned last week. I’ve thumbed through the catalog of their articles, and chosen one. I don’t really want to state the title here, because what’s the point of starting out with some tall words, when I can tell you right now that it has to do with counting the number of balls in those Pachinko machines I mentioned called Petri nets. Okay, Well, if now you since must you’re know curious, the article paper is part 1 of a series called The Large-Number Limit for Reaction Networks (part 1) . , by John Baez. But we won’t get to it in the blog, because there are some basics that first have to be covered.

First, Now I should say that I didn’t quite get get it quite right when I called those Petri networks Pachinko “Pachinko machines. machines.” Instead of balls, they call the things that move around the network “tokens.” Also, more to the point, it’s not one big machine, but a network built up by connecting together lots of little machines. And the tokens aren’t necessarily part of a game. Each token represents something in the world. Imagine they have different colors, with each color for a different kind of thing. Each pink token might represent a flamingo, and the green ones stand for frogs, for example. And just to make sure you got the idea, there could be yellow tokens for butterflies.

Now the machines represent “processes” in the world, which eat up some tokens at their input, and burp then cough out some kind of tokens at their output. Suppose for example there was a volcano with arms and legs, which had a very specific kind of appetite. For every meal it needs to eat three flamingos and two frogs. So it walks around the bottom of the lake, catches these food items, and stuffs them into the opening at the top of the volcano. In more technical terms, we would say that it munched on three pink tokens and two green ones. Then, after cooking and digesting, a miracle of nature happens: seven butterflies flap their way out of the volcano spout. That was why I introduced the yellow tokens, because at a very abstract level, we can say that this fearsome yet beautiful volcano is a process that chews up three pink tokens and two green ones, and burps spits out seven yellow tokens.

Now what would happen if our lake started out with 507 flamingos, 379 frogs, and 27 buttterflies. After each meal, the volcano will have depleted the flamingo and frog population some more, and the butterfly population will be soaring. Sadly, a population imbalance would develop. To make things more fair, let’s suppose that the volcano V had a brother B and a sister S, each of which had a different eating habit.

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