Crawf Minor (Lower Sixth) is in hot pursuit of several Maths A-Levels here in the UK.

All of which reminds me that once upon a long lost time I could pick my way through the mysteries of cos and sin and even on a good day tan.

Not to forget my old enemy: d2y/dx2   This allowed one to calculate not the rate of change, but the rate at which the rate changed.

Or something like that. I think.

People who can fathom out this sort of thing are smart. In fact, some of them go on from tricky basic maths to acquire lively and unpredictable new pets:

Langton got involved with ants.       

Paterson with worms.

Others had to make do with turmites. Or even busy beavers.

The notable thing about this sort of thing from our point of view is the deep idea that order (and ‘orders’) can and do come forth naturally without clumsy central direction. A light framework plus a few very simple rules are enough to generate impressively large and robust new structures. 

Which is where we walk over to Cafe Hayek (where orders emerge) and read this excellent piece about why new developments are often disappointing, and why indeed a solution to a problem often isn’t very widely applicable:

Development happens thanks to problem-solving systems …any solution that is going to work is likely to come from the use of local knowledge, or at least dispersed knowledge rather than some expert who proposes some solution from the outside without local knowledge.

That’s the core brilliant Hayekian idea, unanswered by collectivists and centralisers of all shapes and sizes – dispersed knowledge.

More:

You can’t just take some piece of a market-based solution and impose it from the top down. You want organically emergent solutions that bring all the pieces along at once. Competition encourages the other pieces to emerge. Top-down solutions usually constrain competition and miss out on the extra parts of the puzzle.

… How do you liberate people to allow them to help themselves? You look for the barriers that keep them from helping themselves. Ironically, sending large amounts of money to corrupt leaders probably creates the single largest barrier.

Of course.

Which is why the rise of the mobile telephone gives Africans new chances to help themselves without development experts and corrupt leaders pushing them around.

And, perhaps, why it is a good and profound move to move huge slabs of NHS money to general practitioners (ie non-hospital doctors) so as to try to capture  much more directly in public health spending the benefits of all that dispersed GP knowledge about the nation’s aliments ?