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Yup.
People tend to forget that if you have two apples and add another two apples, you do not have four identical units. You have four different units that you have categorized as "apples", even though all four have different weight, color, taste, etc., all the way down to the molecular level. They are not the same, only similar. Same goes for multiplication/division. Math is abstract and only exists in the head of the thinker.
Which would indicate that math cannot provide an reliable descriptor of the universe, hence making it a non-clockwork universe.
But clockwork thinking is quite useful for performing most tasks.
It allows architect to figure out how much weight a column can safely bear, lets us make schedules for getting from A to B, exchange units of value at the supermarket, and send robots to Mars.
Ah, but that I have to disagree with.
If mathematics were just some mumbo jumbo in our heads, it could not be used to predict that certain observations will be made if an experiment is conducted in a certain way, or in the case of Einstein, if you can look at light shining around a strong enough gravity source with a strong enough telescope. But you can.
If mathematics were purely in our heads - if it were just some bullshit we make up to describe what we've seen - then you couldn't make successful further predictions based on it with any greater accuracy than pure chance.
There is a clear and direct relationship between mathematics and behavior in this universe.
That said.......I'm not sure this means I'm saying that this is a "clockwork universe". The entire premise of physics/mathematics is that in specified conditions, you can predict the behavior of whatever experimental objects you have set up. It's not built to take account of the potential behavior of beings with free will.
I'd have to go back to refresh on what exactly is meant by "clockwork universe". I seem to remember Leibniz and the idea of the world as a great predictable machine, which does not require the input of a God. It sounds like people extrapolate out from that to suppose one could predict the beginning and end of the universe from any set of points in it. If so, yes, free will cannot exist, because if it does the end of the universe is different if I walk across my room right now, if I drive to Alabama on a lark, or if I dump a glass of water on my head and stay seated.
I'd go with hybrid (unless this turns out to be what 'non-clockwork' means): Mathematics-physics is proven clockwork. Introduce life, the less predictable system-wide events become, dependent on just how much autonomy the life in question has. Take a closed experimental system that can house humans. Put a few types of object in there, food source, water source, and either certain bacteria or humans. The end-state of everything in the system will be a hell of a lot easier to predict in the bacteria experiment than the human experiment.
I don't see why anyone should have to choose between pure clockwork and pure non-clockwork. It's a mix.
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