8 April
Dear Melanie Mitchell,
This letter is long overdue, but I wanted to thank you for writing your wonderful book Complexity: A Guided Tour.
As an economist, I’ve been trained to think in a rigid sort of way. And it’s taken me a number of years and a lot of re-education to unlearn some of the prescriptions that orthodox economics and finance teaches.
Most institutions, in my opinion, are failing their students in economics by not exposing them to ideas from the complexity sciences. Scale-free networks, self-organized criticality, and empirical scaling laws, for example, are illuminating ideas. Yet they are nowhere to be found in most undergraduate and graduate courses.
I am deeply indebted to authors like W. Brian Arthur, Geoffrey West, Per Bak, and yourself — for introducing me to new, important, and wonderful ideas that my alma mater has failed to mention even in brief passing.
In the Character of Physical Law, Richard Feynman reminds us that good scientists must carry multiple models in their heads (at least until the evidence suggests otherwise). So I find it ironic that economics — in its infatuation with rational thinking and complete knowledge — is unwilling to share alternate models of thinking with its students. This is a disservice to education.
I think you would agree with me that complexity thinking needs a bigger foothold in the social sciences. And your chapter on Hilbert’s Problems gave me an idea. Why don’t you and your colleagues at the Santa Fe Institute produce something similar for difficult problems in complexity? 'Mitchell’s Problems' has a nice ring to it, don't you think? The Institute might award meaningful prizes to people who find clever solutions.
I’m not a mathematician, but Hilbert’s Problems seems to have galvanized a lot of interesting work in the decades that followed. Wikipedia tells me, for example, that the solution to Problem Eighteen came nearly one hundred years after the problem statement. Wow! A similar list in complexity, I think, may generate comparable appeal and attention over the long run.
From a quick search on Google, I can see some open problems on the web. I am also aware of the Complexity Explorer Challenges on the Santa Fe Institute website. All of these are great starts, for sure. But I think there is a lot more we can do to nurture attention and interest in this field.
What’s more, the very process of formalizing a Hilbert-like list may help to bring together what remains a disparate discipline. It may capture the fancy of young, ambitious thinkers around the world that want to try their hand at something new and difficult.
Perhaps a list of such problems already exists. In that case, I am very sorry for wasting your time. If not, I do wonder what sort of questions you and your colleagues might ask. I’d love to hear your thoughts on the matter.
Warm regards,
Tobias
P.S. I really enjoyed your walkthrough of Godel’s theorems and the Halting Problem in Complexity: A Guided Tour. While I cannot follow the actual proofs in their entirety, their beauty and implications are fun to think about. Your book gave me that warm, fuzzy feeling that comes with good learning. So thank you!
Tobias Lim
Tobias Lim