51–60 of 191 posts
Earlier quoted context omitted.
Why wouldn't reality contain contradictions?
I mean in the logical sense. If reality could contain logical contradictions then that would mean reality isn't rule-based, which means unconstrained randomness, no information, no meaning, etc.
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.
Earlier quoted context omitted.
Chaotic systems are only intractable if you measure the initial conditions with finite precision.
No, that is not true. Their intractability has absolutely nothing to do with the precision of measurement. Assume the initial condition with infinite precision and the further evolution of the system is still intractable. Ignoring the Heisenberg Uncertainty Principle for a moment and getting to the heart of chaos theory the problem is the production of information at a rate faster than any existant (and I believe, th…
But it does not.
It baffles me that people ignore the fact that they have subjectivity when making these claims. It makes a certain amount of sense since science itself aims to remove any taint of subjectivity in its practice, so folks who want to be thoroughly 'scientific' in other aspects of their lives (e.g. their personal philosophies of reality) carry over over this ideal. But it's also a contradiction since science scientific m…
If simulated universes can be "real," then we're assuming that there's a mapping between patterns of electrons in a computer (or provable theorems, if you're brave enough), and the real universe they represent. (Say, interpreting two numbers that may be stored very far apart on the chip as the positions of two particles that are, in the universe, very close together.)
The problem that this introduces is that there are no well-motivated ways that we could decide which mappings are "real," and could be "lived in." For example, we might claim that the state of the simulation must be map-able in polynomial time to some charts and pictures that a human could interpret - but an inhabitant wouldn't care.
So, since all mappings are equally motivated as far as an inhabitant is concerned, allow me to choose one that maps this grain of sand to a universe the same as ours.
Well, there you go. Our world in a grain of sand.
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.
>So reality works because math works.
Reality is that the one that contains the structures not math. So what you said does not make sense.
An interesting article addressing this from Sabine Hossenfender: http://backreaction.blogspot.in/2007/10/mathematical-univers... 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...
This (the universe is 'made' of math) seems to me like the most egregious error in the general outlook of contemporary scientifically-minded people—and one I made myself for many years. If you really consider the issue closely, you'll see it depends on not overlooking certain dark corners of it which you can sort of ignore and assume to not contain contradictions—but they're there! And once you see them, it's hard to…
Alright, why not go one step further and make Universe computational instead? (i.e. state is important in von Neumann-style instead of meaningless in classical math-style; or algorithms vs formulas)
Tegmark's Mathematical Universe Hypothesis (MUH) is actually pretty much a computational theory of the universe. It basically makes the assumption that there exists somewhere the simplest process imaginable: One that counts through and runs all mathematical formulas which includes all programs, which, in turn, includes all (computable) universes. This assumption explains why our universe is oddly complex: If all univ…
IIRC there are no arguments about computation or what underlying medium(s) are involved, it seems like a separate question.