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Math works because reality works. Not the opposite. Reality is bigger than math. Math is just a tool that models reality.
..and with one simple statement, HN user jcmoscon forever put an end to this age-old debate.
Math works because reality works. Not the opposite. Reality is bigger than math. Math is just a tool that models reality.
Math works because reality works. Not the opposite. Reality is bigger than math. Math is just a tool that models reality.
On the contrary, reality works because reality cannot contain contradictions. But the set of possible structures without contradiction is a superset of what is physically realizable. And mathematics is just discovering and cataloging the set of structures without contradiction. So reality works because math works.
I'm a philosophy noob, but isn't this very similar to Berkeley-style immaterialism?
Not really. Berkeley's idealism contests the objectivity of reality, while here we are presented with another view of the foundation of the (objective) material world.
> When we derive the consequences of a theory, we introduce new concepts — protons, molecules, stars — because they are convenient
Couldn't matter itself be just another "human", "convenient" concept? Indeed the author writes:
> our external physical reality is assumed to be purely mathematical
Why should a purely mathematical reality also be material? Doesn't this lead to the logical conclusion that ideas, err, maths is "all that there is"?
Sure, in this case ideas are objective and not subjective, but Berkeley's "mind of God" argument also leads to an objective, albeit immaterial reality, doesn't it?
Her more recent article (review of Max Tegmark's book) also comments on the same subject: http://backreaction.blogspot.in/2017/11/book-review-max-tegm...
I like the idea that the reality is just mathematics, I thought about it independently, but it gets weird really fast. I yet to have read this essay, but I had two thoughts: 1. Similar to Turing completeness, actual physical reality might not matter for the internal observer. All Turing-complete machines can calculate same things and observer from the inside of the machine cannot determine on what hardware the machin…
The halting problem (endless loops) is sidestepped by being contained to a single universe. Also, apparently our universe got lucky as we get to live in an ordered universe, and not dissolve into nothingness due to a bug in our universe's binary code.
Of course, like "normal" mathematics, "reality" mathematics should also be incomplete. Furthermore, there is no way to know everything of the universe one is a part of, as this requires at least 1 bit more than there are available bits in the universe. But this still allows for the possibility of the universe itself being an inference machine.
Edit: Then again, I believe that mathematics is a mental construct, mathematics does not exist without brains, or if it really exists external to human minds, it exists in all possible forms: Humans do not discover maths as a whole, they cast a local net of subjective observation over it, and keep the things that make sense to our brains and are consistent within the current framework. Again, this does not preclude the possibility that our mathematical reality exists inside the mind of a giant supercomputer.
A purely mathematical universe immediately brings to mind a question: Since chaotic systems evolve in a way provably intractable to calculation, how could any system based solely upon calculation address, well, almost everything that exists?