the mathematical universe

For those still interested in proving the existence of external reality, a programmer recently pointed me to this paper on the mathematical universe hypothesis (MUH). The programmer's very strong (unnecessarily harsh I think) recommendation...

Note that the MUH is not a theory or a position. It is the only formally definable option. Every other option is meaningless gibberish. Therefore, it is FACT.

And by no coincidence, I arrived at this exact conclusion (if a bit fuzzier then) almost a decade ago. My current thinking is much more sophisticated.

I can bootstrap myself starting from solipsism, I make no distinction between models and what they represent, and no distinction between models that all fit the same theory.
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It gets to where physical reality is defined as whatever minimal theor(ies) will logically explain your subjective experience.

This lets you almost immediately step out from solipsisim by concluding that physical reality is independent from your will. And it resolves paradoxes left, right, front and center.

Like why the universe responds to a mathematical description: because it's made of mathematics. Or why the external reality responds to your will to command it into existence: you never command it!

It also realigns physical reality with major theorems in mathematics. Like the one that says you can't even in theory pick between two dual representations. Or the one where any infinitely expressible language can't be resolved by any finite axiomatic system.

It drives a stake right through the heart of filthy (neo-)Platonism. And it affirms the connection between physics, the study of one reality, and mathematics, the study of all realities.

From Max Tegmark's essay--

The idea that our universe is in some sense mathematical goes back at least to the Pythagoreans, and has been extensively discussed in the literature. Galileo Galilei stated that the Universe is a grand book written in the language of mathematics, and Wigner reflected on the “unreasonable effectiveness of mathematics in the natural sciences”. In this essay, I will push this idea to its extreme and argue that our universe is mathematics in a well-defined sense.