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Shane,
Very interesting discussion.
What does predictable mean?
Weather forecasters try to predict the weather for tomorrow and as far as a week way. Using recorded weather data, analysis of the data will give the most likely prediction for the weather. More and more data can be factored in as our supercomputers get more powerful. The implication is that certain factors A will result in event B. However, it would be a foolish forecaster who says with 100% certainty, it will be sunny at midday tomorrow!
Consider this experiment. I throw a die 1000 times and get roughly the same number of 1s, 2s, ... 6s, around about 167 in fact. However, in practice, I don't expect to get exactly the same frequency of each (in any case, 6 does not divide 1000 evenly). The mathematics can model the expected results but I cannot say that if I throw the die six times, one of those throws will be a 6.
Now, let's say I set my task to design a mechanical arm that throws a 6 every time. The die is placed in a rigid seat on the arm in exactly the same orientation each time. I spend 100 hours balancing the arm and adjusting the tension so that it throws the die exactly the same way. Initially, I just can't get it to land a 6. Eventually, adjustments give me some success and it throws some consecutive 6s but goes random again.
So what's my point? To make a certain prediction, I need exactly the same initial conditions acted upon in exactly the same way. In the case of weather, data is based on past weather conditions. At no time in the future will those conditions be exactly the same as in the past, so I cannot make a certain prediction. In the case of the mechanical arm, I can never control all factors that allow the arm to throw in exactly the same way every time. In any case, each throw of the arm will create the smallest wear on it so that the next throw will have different initial parameters.
The strength of mathematics is in modelling an expected outcome. We may be able to model the formation and structure of the whole Universe, its galaxies and filaments, but we cannot reproduce the exact Universe we live in.
Hence, the formulation of the Butterfly Effect which describes sensitive dependence on initial conditions in Chaos Theory. Small differences in initial conditions can result in large variations in behaviour and produce a markedly different end result.
I'm not going to debate whether our free will is an illusion or not. if it seems we can make a conscious choice, yes or no, left or right, that's free will. How much our physical makeup (genetics) and our experiences influence our choices is a debatable point. However, at any particular time, the choices you make will depend on a different set of conditions; the decision you make today may be different to the decision you make tomorrow. No two people have exactly the same personalities nor the same experiences, so we react differently to similar circumstances. From past experience, you may be able to guess what your actions might be under certain circumstances but you cannot say with certainty what your decisions will be.
Regards, Rob.
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