111–120 of 226 posts
Since the Integers are contained in the Reals, the idea that the Reals are "Eternal Nature" and the Integers are "Created by Humans" is surely false.
Earlier quoted context omitted.
Here I'm referring to the cloud of things that Hilbert called "Cantor's Paradise". Basically everything around the notion of cardinality of infinities.
Please say more, I don't see how you can be _skeptical_ of those ideas. Math is math, if you start with ZFC axioms you get uncountable infinites. Maybe you don't start with those axioms. But that has nothing to do with truth, it's just a different mathematical setting.
Earlier quoted context omitted.
A computable real number is a real number for which a Turing Machine exists that can compute it to any arbitrary precision. So yes sqrt(2) is computable. Every BB(n) is computable since every every natutal number can be computed. It's the BB function itself that is not computable in general, not the specific output of that function for a given input.
That doesn’t sound right to me. What about the machines that don’t halt? You can’t compute whether or not to skip them directly. > A busy beaver hunter who goes by Racheline has shown that the question of whether Antihydra halts is closely related to a famous unsolved problem in mathematics called the Collatz conjecture. Since then, the team has discovered many other six-rule machines with similar characteristics. Sl…
All math is just a system of ideas, specifically rules that people made up and follow because it's useful. I'm so used to thinking this way that I don't understand what all the fuss is about, mathematical objects being "real". Ideas are real but they're not real in the way that rocks are. Whenever there's a mysterious pattern in nature, people have felt the need to assert that some immaterial "thing" makes it so. But…
unless you're a mathematician then maths is really THE absolute best description available of language and nature. but non-mathematical minds will simply wonder and be amazed at how "maths explains the world", a clear indication that somebody is not thinking like a mathematician. > Whenever there's a mysterious pattern in nature, people have felt the need to assert that some immaterial "thing" makes it so. But this j…
All math is just a system of ideas, specifically rules that people made up and follow because it's useful. I'm so used to thinking this way that I don't understand what all the fuss is about, mathematical objects being "real". Ideas are real but they're not real in the way that rocks are. Whenever there's a mysterious pattern in nature, people have felt the need to assert that some immaterial "thing" makes it so. But…
unless you're a mathematician then maths is really THE absolute best description available of language and nature. but non-mathematical minds will simply wonder and be amazed at how "maths explains the world", a clear indication that somebody is not thinking like a mathematician. > Whenever there's a mysterious pattern in nature, people have felt the need to assert that some immaterial "thing" makes it so. But this j…
As a young math researcher, my mentor definitely did not believe that Math was the absolute descriptor of the universe.
You can definitely imagine a scenario where the world does not operate perfectly mathematically correct though Math still exists - as an abstract separate entity.
You can do this such that everytime you recognize a new quirk in the world, then you can invent some new math/logical framework to match/approximate the current understanding. I don't know if this is the reality of this world, but when you look at things like complexity theory you have to wonder "okay... maybe we designed a useful system rather than discovering a true law of reality"
I'm an enthusiastic Cantor skeptic, I lean very heavily constructivist to the point of almost being a finitist, but nonetheless I think the thesis of this article is basically correct. Nature and the universe is all about continuous quantities; integral quantities and whole numbers represent an abstraction. At a micro level this is less true -- elementary particles specifically are a (mostly) discrete phenomenon, but…
Earlier quoted context omitted.
> Nature and the universe is all about continuous quantities One could argue that nature always deals in discrete quantities and we have models that accurately predict these quantities. Then we use math that humans clearly created (limits) to produce similar models, except they imagine continuous inputs.
The quantity of matter and the quantity of electricity are discrete, but work, time and space are continuous, like also any quantities derived from them. There have been attempts to create discrete models of time and space, but nothing useful has resulted from those attempts. Most quantities encountered in nature include some dependency on work/energy, time or space, so nature deals mostly in continuous quantities, o…