Emergence and Computational Equivalence


I've been reading "Emergence: The Connected Loves of Ants, Brains, Cities, and Software" by Steven Johnson and "A New Kind of Science" by Stephen Wolfram (almost done with Johnson, just starting Wolfram).  If you're not familiar with them, Johnson discusses how acting on a local scale, on local information produces useful, global patterns.  Ant hills are one example---no one directs the actions of the ants, they have simple rules for responding to local stimuli and yet, produce complex behavior (such as creating graveyards for dead ants or finding and harvesting food sources in a rather systematic manner).  The whole idea has some interesting implications for people who manage societies (we call them governments).    

Cities are another example. The passage that struck me from Johnson follows: 

There are manifest purposes to a city---reasons for being that its citizens are usually aware of: they come for the protection of the walled city, or the open trade of the marketplace.  But cities have a latent purpose as well: to function as information storage and retrieval devices.  Cities were creating user-friendly interfaces thousands of years before anyone ever dreamed of digital computers.  Cities bring minds together and put them into coherent slots.  Cobblers gather near other cobblers, and button makers near other button makers.  Ideas and goods flow readily within these clusters, leading to productive cross-pollination, ensuring that good ideas don't die out in rural isolation.  The power unleashed by this data storage is evident in the earliest large-scale human settlements located on the Sumerian coast and in the Indus Valley, which date back to 3500 B.C.  By some accounts, grain cultivation, the plow, the potter's wheel, the sailboat, the draw loom, copper metallurgy, abstract mathematics, exact astronomical observations, the calendar---all of these inventions appeared within centuries of the original urban populations.  Its possible, even likely, that more isolated groups or individuals had stumbled upon some of those technologies at an earlier date, but they didn't become part of the collective intelligence of civilization until there were cities to store and transmit them. 

This strikes me a great example of what Wolfram is saying in his Principle of Computational Equivalence: that whenever one sees behavior that is not obviously simple---in essentially any system---it can be thought of as computation of equivalent sophistication.  That is, a city is a computational device functioning, in essence, as a superorganism that stores information for much longer periods than any of its constituent parts will last.  Wolfram also states, with respect to the Principle of Computational Equivalence: [O]ther systems will tend to perform computations that are just as sophisticated as those we can do, even with all our mathematics and computers.  And this means that such systems are computationally irreducible---so that in effect the only way to find their behavior is to trace each of their steps, spending about as much computational effort as the systems themselves....it also shows that there is something irreducible that can be achieved by the passage of time.  I find this idea to be intriguing. 

As I read and ponder this, I believe that these ideas have serious implications (going back to the managing society point I made earlier) for things like economic development, education, urban planning, water use, and so on. 

An example in the area of education is distance learning.  Having been a professor, somehow the idea of having students take courses (or, worse, not take courses and just take the exam to prove you "know" the material) has never sat well with me.  The reason is because I feel in my gut that taking the course is only a small part of the value of "going to college."  Going to college is about experience, being part of the academic community.    I believe you miss something vital and important by not "being there" with everyone else, studying in the cafeteria or lobby of the engineering building, and seeing some stupid play on homecoming weekend.  In many important ways, the point of an education is not the degree or even the knowledge---its the journey.  That's what changes you and makes you a different person.

But more to the point, if you believe Johnson and Wolfram, "being there" also change the social fabric of the University and that has consequences well beyond any of our lifetimes---Cambridge and Oxford are 700 years old.    A university is, in the words of Johnson, a "superorganism" or, in the words of Wolfram, a "computation taking place in real time."   If we remove the students from the University, can the organism survive over space and time?  What happens to the computation?  I don't think we know and its probably the great question facing places like Western Governor's University.  A grand experiment to be sure, but do we know enough of what we're trying to do to "program" it correctly---to give it life beyond the vision of the founders? 

As I said, I think you could raise similar questions about many of the things governments are trying to do.  It doesn't mean their wrong, it just means that we need to recognize that just because we've got a network doesn't mean that we can spread everything out without changing them in fundamental ways.