## Deterministic non-linear Systems and Complexity

"*In a few years, all the great physical constants
will have been approximatedly estimated, and ... the only occupation
which will then be left to the men of science will be to carry
these mesasurements to another place of decimals*" --
James Clerk Maxwell, 1871
**Order** rules complexity - Newton and Descartes work
out the basics, Laplace reigns supreme, and, when considering
the nitty-gritty, few things work the way they are supposed to.
- linear differential equations - Newton's laws of motion and
of celestial mechanics
- Laplace's Universal formula and Reductionist
thinking:
- the search for the
*Perpetuum mobile* - the crushing
forces of entropy
- Randomness vs. disorder: Boltzmann (thermodynamics) and Darwin
(evolution) save the day
- Classical mechanics and electrodynamics power the industrial
revolution

**Disorder** rears its ugly head
**Ultraviolet Catastrophe** and the **Hydrogen Disaster**
- how does it feel to be off by 40 orders of magnitude? Boltzmann
looses his head ...
- Rutherford and Bohr: Non-linear dynamics and Quantum mechanics
- Linear approximations to non-linear problems
- Schroedinger's Cat speaks of waves - and he comes up with
an equation to describe them
- Born's Probability Function makes Einstein very unhappy "
I can't believe that god plays dice"

**Chaos** breaks through
- Newton's three body problem cannot be solved - it can only
be approximated
- Poincaré bites Newton: closed systems are not immune
to disaster
- Poincaré considers the gravitational pull of a grasshopper
in Australia and shows that, with bad luck, solar systems come
unstuck
- Feedback, iterative magic and the significance of initial
states: Spinal Tap and the art of baking bread

**Phase diagrams** and **Attractors**
- single point
- limit cycle
- torus
- strange attractor

**Randomness**, **Chaos**, **Entropy**: Confusing
a **Lack of Predictability** with **Randomness** - the
Source Fallacy

The legend of the *Mirror People* and the how
the Yellow Emperor saved the day
#### Further Reading:

Hayes, B. (2001) **Randomness as a resource**. American
Scientist 89: 300-304.

last modified: 04/12/02