but it's not clear to me that our advances in making a better OCR package work directly towards an effective general intelligence that can solve general-purpose problems.

All of these things are prerequisites to starting to build a general intelligence. They are very small steps on a very long path but it is progress in the AI field you have to take what you can get.

I'm just trying to say that every iteration of the neural net seems to involve iterating over every edge in the neural net. Every piece of knowledge has to be stored as an edge weighting in the neural net. As knowledge increases, each iteration will take longer linear in the number of edges.

A neural network dosen't change in size as you add "knowledge" to it. Also knowledge isn't really stored in a particular edge. In fact you can damage part of a neural net and it will degrad the performance overall but not make it forget specific things.

When I took a course on neural networks, it was a math class. We talked about how they are used to approximate functions. For example you have function that takes 100 arguments representing the bit in a 10x10 grid, it returns 1 if that grid looks like an A and 0 otherwise. At this level everything is just a bunch of matrix operations. In general for any function their exists a neural that will approximate it to a given accuracy. This is where we get the idea that a very large neural net could act intelligently, if you define a function that is how a human acts. However, one very big issue with this is having memory of past actions which are not really represented in Neural Networks.

In "Computing Machinery and Intelligence", Turing described "educating" a child AI. I was wondering whether the interactive education process that we rely on for human education might be too hard to run cheaply for AI.

It is meaningless to try and educate a an AI like we try educate a human. It would be like trying to educate a virus. It just can't be done in any meaningful way at this point. AI's can't ask questions and use the results to build a conceptual model of the world. One group is trying to manually build a conceptual model, by creating rules like, "A bird is a mammal", or a "Cars drive on a road" I think they hope to have a good model of the world in about 50 years at the rate they are going (though it is useful in specific domain right now).

I once read something where an author was proposing that to make an AI that could interact and communicate with humans, one would need to have a rather humanlike robot, so that the AI could experience the world around it as it grew and learned.

Building a human like robot is easy compared to building the AI that will go in it. Though honestly I don't see as a necessary step, I bet simply interacting with people online would be sufficient to demonstrate intelligence. The point is we are no where close to building a robot child that needs human interactions. It is great to speculate about what form a strong AI will take but I believe that when we are close to building one it will become obvious and probably different from what everyone has predicted. Just look at people's prediction of what the Internet would be like from 30 years ago.

In short AI is still at the point where is just solving what most people would see as tricky math problems. It is true that "what should I do tonight?" could be represented as a math problem, but it many orders of magnitude of orders of magnitude harder than what AI is solving now.