It looks good! Two main comments:
1) You write:
> Here are a few illustrations of the relevance of network theory to the biosphere. First, the atmosphere is a massive chemical reaction network, containing many types of molecules and reactions: water molecules H20, hydrogen gas H2, oxygen gas O2, nitrogen gas N2, methane CH4, carbon dioxide CO2, ozone O3, …, and reactions such as the formation of water from hydrogen gas and oxygen gas. Second, in biochemical reaction networks, the reactions involve large, biological molecules, such as proteins and DNA. Third, observe that the global circulations involved in weather and climate consist of complex networks of interconnected processes, and so network theory may have a role to play here.
The third one seems a bit weak... which is not your fault: it's mine. While putting together my [Oxford talks](http://math.ucr.edu/home/baez/networks_oxford) I think I've put together a better case for the importance of network theory. If you're focusing on chemical reaction networks, here are two more applications:
a) A lot of evolutionary games _are_ described by chemical reaction networks (though people call them stochastic Petri nets, which is really just another way of talking about the same thing - or else they just call them "certain evolutionary games"). [Marc Harper](http://johncarlosbaez.wordpress.com/2014/01/22/relative-entropy-in-evolutionary-dynamics/) posted about this, perhaps without quite realizing it. Evolutionary games can be helpful in describing not only biological evolution but how people change their behavior - they're commonly used in economics! The relevance to global warming and other crises is clear.
b) There are interesting models of infectious disease described by stochastic Petri nets, like the model of HIV that I described [here](http://johncarlosbaez.wordpress.com/2012/06/27/the-mathematics-of-biodiversity-part-3/). Again, obvious relevance to global warming and other crises.
If you're interested in network theory more generally, we're also looking at other kinds of networks in [control theory and engineering](http://math.ucr.edu/home/baez/networks_oxford/index.html#2).
2) I'm worried about posting this "Part 1" until you write Part 2. It's very easy to start series and then run out of energy. It's very easy to overestimate ones energy and persistence. For example, on November 7 last year you wrote, about this post:
> I’m going to give it a few more days of polishing – I’m actively doing it now. Part 2 will then need perhaps a week of polishing.
It's great how this article ends with:
> Now I am headed back to the rain forests of Azimuth to acquaint myself with the regional dialects. Upon my return, I will invite you to tour some of the more colorful trails. Although I can’t promise that the journey will be completely effortless, we shall prudently steer clear of the most jagged peaks, and we will take frequent breaks to drink water and pat ourselves on the back. If nothing else, we may learn a bit about the anthropology of the place.
> Finally, in case you have any concerns about my qualifications, I have just obtained my permit as an Azimuth tour guide. See my green and white badge, which says: Rick the Explainer.
It's a promise that you'll be posting blog articles fairly often, explaining a lot of stuff.
I really hope you do! But this is the kind of promise that most people find very hard to keep!
Do you have it in you, Rick? If so, maybe you can prove it by whipping off another article or two. Or am I being too demanding?