Learning in networks

I've been thinking about why paragogy is such an "old" form of learning. My guess is that it relates fundamentally to what learning is. I'm thinking on the level of neurons in our brains. There's a whole modern theory of neural networks -- maybe we can get into that a bit! -- but at an abstract level, think about how a pattern is presented as a set of data, and these data are fed into a system for further processing (a new pattern). As the different neurons "speak up" and communicate a message on to other neurons, eventually some actions at the level of "phenomena" are triggered. Maybe a screen displays a certain result, or a person carries out a certain action.

"Learning" at the abstract level of neural nets usually means "present a number of abstract patterns, and tune the system so that it gives the 'right' result on these; then give some other patterns and use the system as it was trained in the first phase to classify the new patterns." These systems can be used to do things like successful recognize faces and so on.

Although it is a simple model of learning, the model in paragogy isn't necessarily much more complex. People talk to each other, certain outcomes are generated. "Learning" happens as the individuals involved master some new set of patterns. As a group, even more complicated patterns can be managed, at least in theory. Certainly in academia, the whole "standing on the shoulders of giants" phenomenon is what lets complicated ideas and approaches grow, though this may take significant real time.

Perhaps it takes less time now than in former days, due to the speed of global communication, and thanks in part to tools (like search engines and indexes) that help people find just the right bits of data. But "faster" isn't in and of itself interesting. What's interesting is that "faster" can enable what feels like a completely different model.

Instead of the teacher getting up at the front of the class and talking about another culture, students in a language class can chat directly with people far away and exchange thoughts on their experiences. The pen pal experience moves closer to immersion, at least when class is in session.

It seems like there's some cost to all of this interconnection, namely a sort of homogenization of culture. At the level of statistical mechanics, you'd expect to see differences between populations going away.

And yet, cultures are also organisms, and one of the things organisms do is specialize their organs. It's not clear that even within a given culture, or a given facet of a culture, that anything like homogeneity occurs (consider "the 99%" and compare it with "the 1%"). Specialization based on interest also happens in global academic culture.

Fear of a mono-culture on the non-academic level may or may not be justified.

Within a given sub-culture (say, mathematics) all sorts of specialties or "specialisms" arise, based largely on the real-world problems that are being tackled. Again, consider the simple model of neural networks and patterns. Some mathematicians deal with a certain kind of pattern, and others deal with other kinds. The world of patterned data is so complex, there is little chance of mathematicians dwelling overly much on any given part.

And yet, arguable, that is exactly what happens in the "teacher gets in front of the classroom and talks" model of mathematics education. Centralized dissemination of cultural artifacts (whether its math lectures or TV shows) tends to promote a degree of homogeneity. This can be fun -- as when, in another country, I can rely on my friends' knowledge of American TV shows -- but it can also feel a little bit awkward or boring.

Ivan Illych tends to be against "expert" specialisms, which is another level to the whole thing -- the economics of being an expert. If you're in that position, and you're in demand, then you can make a lot of money from everyone who wants your services. (Or, in a copyright-centered economy, your knowledge goods.) Instead of that model, Illych is in favor of a more home-spun economy, where individuals have the ability to make what they need. This "small is beautiful" extreme isn't necessarily the only other answer.

A more interesting (and realistic) model is given by so-called scale-free networks -- like the internet, or the semantic models of natural languages. Some services (or words) are used a lot, by most people, and are the oldest and most central complexes in the system. Other newer bits and pieces are more peripheral.

= 5 Principles for Neural Networks =

From "Introduction to Connectionist Modelling of Cognitive Processes" by Peter McLeod, Kim Plunkett, and Edmund T. Rolls, pages 11-15, "Five assumptions about computation in the brain on which connectionist models are based".


 * 1) Neurons integrate information
 * 2) Neurons pass information about the level of their input
 * 3) Brain structure is layered
 * 4) The influence of one neuron on another depends on the strength of the connection between them
 * 5) Learning is achieved by changing the strengths of connections between neurons

Note some similarities and differences to our five principles.