This seems interesting, but I'm afraid I don't see the difference between Magnetic Stones and the traditional idea of influence. Is there one?
HolIgor: From my exoperience, the way to knowledge is in reformulation of the main principles in your own understandable terms.
Charles It's all very speculative. Many, many players have assumed that there is some 'field theory' that can explain what we talk about when we say influence. But, this appears to be wrong.
Bill: I experimented with a field theory several years ago, with charges being passed back and forth. Solving for equilibrium yielded the number of adjacent open points (i. e., dame). ;-)
Some years ago I saw a derivation for the possible omission number, which is the number of opposing threats to a group's safety that the defender can ignore before needing to respond. Not a very useful feature, perhaps, but interesting. What was very interesting was that there was apparently a good way to estimate that number. How many threats you can ignore does seem to have some relation to influence, doesn't it?
People keep trying, and I think that someday someone will succeed in defining a very good influence function for go.
Charles Hmmm ... I could imagine a function of positions on the side - unsettled groups with some sort of base - which did what Bill suggested on threats, by a combinatorial algorithm. What is more it could be a useful, insightful thing to have, in the way of fine-tuning one's intuition.
 See Doug's Go Blog/June 2003 for the reference.