Here is my idea. Inspired by linear systems of equations and their different cases. Be it quadratic, under determined or over determined. I wonder what type of system the universe could be similar to.
If you have an over determined system. You get situations where 1=3 and so on. You only have solutions in rare cases.
It could be that the old deterministic idea is true. Like a quadratic system. One solution for every state. My problem with a quadratic system is that it pretty fixed. It does not permit much flexibility. Ones the universe is set in motion it can’t be changed.
On the other hand if you have a subsystem together with a quadratic system which is under determined. A system which has more unknowns than equations. You could a parameter solution or infinitively many solutions in this subsystem. For instance the parameter solution to the equation y – 2x = 1 is y = 2t +1 for x = t and t being the parameter.
If such an under determined system could be made predictable then my choice would be this system.
Then how do you get a predictable value from those types of solutions? One thing you can say is that you can select values that are not really good. They seem unlikely. For instance the numbers are too big or they are too small.
To fix this then you can say that the numbers the universe produced were typical of our universe. They seem to fit in. They were probable. Then the system would not be under determined anymore. But quadratic with some flexibility.
Here is where I speculate the existence of Smart Determinism.
The universe could be like an under determined system made quadratic with the help of third type of equations. It should behave and look naturalistic. In that there exists the possibility to change things a little so that things like freewill can exist. Still it would behave naturalistic.