May Almighty illuminate our intellect and inspire us towards the righteous graph...

At the moment I'm reading The Origin of Wealth by Eric D. Beinhocker because Amazon kept bugging me with it every time I bought Taleb.

And those Amazon algorithms know their stuff: Beinhocker is like Taleb only more polite, less bombastic, and generally more interesting.

TOoW leaves out most of the epistemological stuff and concentrates on wealth. So far Beinhocker has gone over why neoclassical economics is nonsense (it treats the economy as a closed, non-dynamic system, which it isn't, and treats people as perfectly rational, which they aren't).

Beinhocker is working his way towards describing complex adaptive systems of the Murray Gell-Mann variety...

In the meantime he also writes about non-linear equations and deterministic chaos: like this equation here:

B_t+1 = r * B_t * ( 1 + B_t)

Where B is the value of something at time t, and r is some other number.

When r is set to 1:


Now if you set r to 2:




Now if you set r to 3.3:


Now if you set r to 4:


Which is, apparently, chaotic.

I had always thought that in mathematical terms chaos meant "randomness", but in fact the two are very separate ideas.

A system is chaotic if it:

1. Is sensitive to initial conditions,
2. Is topologically mixed, and
3. Has dense periodic orbits.

Now I understand the first of those points, but not the second or third.

More reading to do methinks...