Funny this should come up. My internal analogy for crazy wisdom is based on this kind of chess. Let me explain:
When I was a kid my buddies were into studying chess. They read books on opening, strategies, and such. They could beat me playing blindfolded (and stoned), that kind of thing.
So one day we decide to review some Fisher/Spasky games. All their moves made no sense to me. In one game there were a couple dozen nonsensical moves, and then one guy resigned. Huh? WTF? Their playing was so far above what I could see that it didn't make sense to me. That's not to say they didn't make sense, just that I couldn't see it.
The analogy here for 'crazy wisdom' is that what an enlightened master is doing won't make sense to me either. That doesn't mean that what he is doing isn't making sense, just that it is so far above my head I can't see it.
Now this is an unpopular interpretation because we do not accept the idea that there are people that much more evolved than we are. Our democratic egalitarian culture doesn't allow for that kind of idea. But we do not have a history of people with access to advanced Dharma practices. For non-Dzogchen people the practices are supposed to actually change your awareness. Not change the nature of your mind, which cannot be changed, just the way it manifests it. In a much less dynamic way (advanced tantric practices being very dynamic) our own educational system changes our awareness too. Somebody that is educated has evolved (usually) and is 'more aware' than an ignorant person. It is definitely not the case that they simply have more information at their disposal. The effort they have put into learning has effectively changed them. In our educational system this change is a side effect. In Dharma this change is the deliberate, designed, desired and primary effect. The practices are supposed to change us. In a way a better analogy to our educational system would be going to the gym. Exercising changes your body; that's the point. It changes your body both internally and externally, and it gives you better health and capabilities. But since your mind has more capacity for development than your body, when someone goes to the 'Dharma gym' their development can be exponentially greater, hence 'crazy wisdom'.
I know a lot of people won't like that. But since we were talking about chess on a buddhist website I thought I'd throw it out there anyway.
There is a tradition of making a distinction between two different perspectives on the nature of emptiness: one is when emptiness is presented within a philosophical analysis of the ultimate reality of things, in which case it ought to be understood in terms of a non-affirming negative phenomena. On the other hand, when it is discussed from the point of view of experience, it should be understood more in terms of an affirming negation.