Is it just me, or does this whole thing sound like a cult?. I'm an applied mathematician, but I can't make heads or tails of what they're saying. Perhaps I should walk across the road and ask the Puries. I'm reminded of a quote in The Mathematical Experience where the authors (justifiably) compared mathematics to scientology: both 'fields' put the learners through various programs -- the ones who emerge are believers. The ones who don't are flunked. There's little way to justify to an outsider the reality of your program -- especially when there are only half-a-dozen who can understand what you're saying.