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Thursday, January 8, 2015

The Mysterious connection between Maths and Phys (some questions):

Why does mathematics seem so “unreasonably” effective in fundamental physics? (Or does it?)
Is there a “pre-established harmony” between them, because the world is fundamentally mathematical?

Are we pushed to call certain theories or disciplines more fundamental because they are in some sense more mathematical?
Or, are we just lacking the right mathematics to treat other fields with similar power and rigor as physics?
What would it mean for something in the physical world to be NOT describable or model-able in terms of mathematics?
Why does physical reality obey one particular set of mathematical laws and not others (Or does it?)
How deeply does mathematics inform physics?
How deeply does physics inform mathematics?
How does the structure and availability of existing mathematics shape the formulation of physical theories?
Why do we prefer mathematically simple theories to complex ones?
What even defines simplicity?
And is there an objective measure of complexity?

May we be missing interesting physical theories because we are committed to particular mathematical frameworks, or because suitable ones have not yet been developed?
To what extent can or should we extrapolate our mathematical equations of physics beyond the domains where we have tested them?
How much of mathematics has been constructed as if it had been due to physics motivations?
Should frameworks that are internally consistent and display mathematical elegance, but which lie beyond experimental reach, be regarded as physical theories or rather as branches of mathematics or philosophy?
Out of the countably infinitely many true statements that could be derived from a given set of sufficiently rich axioms, how have we arrived at what we know as mathematics?
How much is evolutionary history? Our mental makeup? Utility? Beauty? Something else?
What are the tensions between physics and mathematics?
Are there hidden subtleties or overt controversies in how or why mathematics is used in physics (or other sciences)?
What is randomness, and what is the nature of probability?
What is the fundamental origin of stochasticity, and does that affect how we think of probability?
Is it quantumness? Or indexical uncertainty of various types? Or lack of knowledge?
Is there true randomness, or is it only apparent?
Are there hidden patterns in things that seem random to us now?
Do incompleteness theorems such as Goedel's play a role in physical theory?
What do they allow, forbid, or elucidate?
How should we think of infinity? Is it a useful mathematical concept that does not really apply to physical reality? Or could real physical systems be infinite?
Are there mathematical contradictions or paradoxes that tell us something about physical reality?

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