There is he whose spirit casts shadows
upon valleys
he who drowns thunder with words
who steps heavy and broad
pressing green into soft wet earth
and there is he who does naught
save to unweave the spider's web
and bind it back again –
Anon
There are lots of "might save the world" stuff that need mathematical help, but I'd like to suggest something different.Resource depletion and environmental destruction, and the measures to counter these things, will play out through the economic system. Understanding of the economic system is shockingly weak. Much of the understanding only works in a growing economy, but oil depletion alone will see economic contraction for a decade or so.
All current mathematical understanding of economics seems to be in terms of money. But money is one of the oddest things in economics. It doesn't have the properties of stability it is assumed to have, when governments can "print" more at the stroke of a pen (quantitative easing).
So how about running some sort of cooperative Internet thing to try to build a better understanding of economics. Certainly money and some other things look like fluids, so there is scope for n-ports. And maybe the work on large sparse random matrices has something to do with very large networks with semi-regular features. Obviously I'm guessing.
When you need to make significant changes to a large complex thing like the economy, it is wise to understand it better. However I think there are many other reasons to do this. For one thing: the Nobel Prize for Economics seems to be a lot easier to get than any of the others :-).
Robert Smart
P.S. I have been writing stuff in an attempt to understand economics better in a qualitative way. However we don't understand stuff till we understand it mathematically.
P.P.S. With the latest feature of Google Reader I can get changes to your Diary as if it had an RSS feed. We'll see if it works.
For my March 2010 diary, go here.
© 2010 John Baez
baez@math.removethis.ucr.andthis.edu