Sunday, June 5, 2011

Rationality and Chaos

Updated: 29th Nov. 2012
This is an entry I have been wanting to do for some time, and is the first of three on fractal insights I have discovered on the economic assumptions (rationality, ceteris paribus, and perfect knowledge). This is a very difficult subject to describe, I hope I give it justice.

I strongly believe that the issue of understanding of rationality is closely related to - if not the same as - that of understanding 'chaos': that is to say, complex systems are unpredictable. If we are to understand rationality, then should understand chaos, and thus, fractals.

The definition of the fractal (attractor) is: same but different, at all scales. In our Economic models we use the assumption ceteris paribus: we hold all other variables constant,  and treat all persons as rational, so as to see the order (or the 'same', as in the definition), amongst complexity -  just as other science's do.  This definition maybe adapted or interpreted in this context of rationality, to read as: rational but irrational at all scales. This is to say, that even the axe murder will weigh up cost over benefit - before throwing the axe; their choice is rational to them, at that time of throwing, but relative to someone else watching (the fractal demonstrates relativity), it would appear extremely irrational. It is just to say they are reasoning 'differently', but they are using the 'same' method.
Again,  all Science uses the notion of  ceteris paribus -  with its laboratories, and control experiments, it 'freezes' out the chaos. Science can know (can derive a law, but, with that knowledge it cannot predict.  We can know the likes of Newton's laws of gravity, and use them to describe a pen falling from a table; but could we every repeat the event so as the pen falls in exactly the same place, over and over?  Theoretically, yes. Practically, no. I know I am contravening some 'deternimistic' understanding here, but I say no.  Even if we had all the information, I still say no: the reason being, it is infinity costly to get full information - this is demonstrated in the fractal, and is the key principle of chaos theory.
Not being able to predict, does not stop the work of science. And in the same way, not being rational does not stop the work of economics. We are searching for patterns.
Ignore the chaos, find the order.



So I would conclude that if we are to understand, we must treat all as rational, so that we can find the rational behaviour. But understand, when all is put together in the reality, we will observe 'irrationality' - or chaos.

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