This article is about Melanie Mitchell’s book, Complexity: A Guided Tour. This book is readable, understandable book about an important new subject.
This post is still in very rough shape, to say the least. It is basically just a set of notes that I took on the book when I read it. You might be able to get something out of these notes with a bit of struggle though. I apologize. I’ll get back to whipping this post into more readable shape just as soon as I can find the time to do it. This blog is new, and there is currently more work than I can deal with. Thanks for your patience.
Reductionism does not work with complex systems.
Reductionism: the whole is the sum of the parts
Complexity: the whole is more than the sum of the parts
Ant colonies, evolution, immune system, weather, climate, brain, global economy, are all complex systems.
The Santa Fe Institute
Computation is much deeper than just computer stuff.
Douglas Hofstadter: Godel, Escher, Bach. Ant colonies compared to brains.
Brain: how can dumb neurons lead to consciousness: emergence
In economies, how can buying and selling lead to an equilibrium state of price / quantity: market efficiency.
Common properties of complex systems?
- Self organizing: Small mechanical pieces with no central control leading to complex collective behavior. Emergence.
- Signaling and information processing
- Adaptation via evolution: change behavior to improve chances of survival
Dynamics are about systems that are changing
Galileo: the first to use experiential, experimental science.
Newton invented the science of dynamics and calculus which about change
Mechanics: the general study of motion.
Newton’s work was classical dynamics.
Newton’s famous three laws:
- Constant motion: object not subject to force moves with unchanging speed.
- Inertial mass: the force to move an object is inversely proportional to mass of object
- Equal and opposite forces: If A exerts force on B, then B must exert equal and opposite force on A.
Newtons law of gravity: G between two objects = M1 x M2 / D squared
Newtonian classical mechanics lead to the idea of a Clockwork Universe
Simon Laplace on Newton: If you know the position and velocity of every particle of the universe you can predict everything for all time.
[Ron says this mechanistic view of the universe lead to a century in which there were no great achievements in science, art, literature or anything else. Probably political equality was an exception.]
Perfect prediction had to be given up
- Heisenberg’s uncertainty principle: You cannot know position and momentum at the same time (M x V)
- Chaos theory: “Sensitive dependence on initial conditions.” This applies only to complex or chaotic systems. In some parts of the natural world this doesn’t apply; sometimes small uncertainly in initial conditions don’t matter. Continue at location 417
This article is still in progress. It will be finished soon.