Thank you. I didn’t edit my post and have no idea where you saw “empirical math,” so I was as confused as you were. I did however realize that a way of exploring mathematical concepts can be scientific. Using existing rules of math like algebra or calculus has led to us discovering new ways to use math and even new mathematical concepts. The process of long dead mathematicians discovering things like geometry and calculus was scientific in that they had a hypothesis based on past details and measurements, tested it, and found it applied to the real world. Math itself is a construction that doesn’t constitute science, but science can be done in the field of mathematics. This is because science is fundamentally a process.
If you didn’t edit it then I must have transformed some things in my brain… I apologize.
I think math is a process. The discovery of math is at least. Consider the origin of the incompleteness theorem. Mathematicians (Hilbert primarily) sought to prove that math is purely a construction of interpreted symbols that was wholly self-contained (primarily that everything provable within math only requires math to prove). Godel later proved, using only math, that math is incomplete. That is to specifically say, that there are things in math that are true, that you cannot prove with math. This means that there are more true things in math than you can prove. Simultaneously Godel demonstrated that this is also true for everything outside of math.
Deep in this proof is this seemingly magical thing that proves that the process of science can’t prove all true things… Because the process of science is math.
Science can’t prove all true things, or even prove anything with absolute certainty, but you can get closer to the truth through science. Some things might not be knowable through science, but if they aren’t knowable, they probably wouldn’t have a real world use. If parallel universes exist and there’s no way to access them or prove they exist, then it basically might as well not exist. It would make no difference if there are no consequences of it being real or not. Unless there are consequences of something existing, something we can do with the knowledge, it only satisfies our curiosity. It sucks, but that might be the practical answer.
That’s debatable. It’s a logic based hypothesis that scientists are looking for a way to falsify it.
Until empirical measurements can be made, it’s not science.
I don’t follow. What does empirical math have to do with it?
Thank you. I didn’t edit my post and have no idea where you saw “empirical math,” so I was as confused as you were. I did however realize that a way of exploring mathematical concepts can be scientific. Using existing rules of math like algebra or calculus has led to us discovering new ways to use math and even new mathematical concepts. The process of long dead mathematicians discovering things like geometry and calculus was scientific in that they had a hypothesis based on past details and measurements, tested it, and found it applied to the real world. Math itself is a construction that doesn’t constitute science, but science can be done in the field of mathematics. This is because science is fundamentally a process.
If you didn’t edit it then I must have transformed some things in my brain… I apologize.
I think math is a process. The discovery of math is at least. Consider the origin of the incompleteness theorem. Mathematicians (Hilbert primarily) sought to prove that math is purely a construction of interpreted symbols that was wholly self-contained (primarily that everything provable within math only requires math to prove). Godel later proved, using only math, that math is incomplete. That is to specifically say, that there are things in math that are true, that you cannot prove with math. This means that there are more true things in math than you can prove. Simultaneously Godel demonstrated that this is also true for everything outside of math.
Deep in this proof is this seemingly magical thing that proves that the process of science can’t prove all true things… Because the process of science is math.
Science can’t prove all true things, or even prove anything with absolute certainty, but you can get closer to the truth through science. Some things might not be knowable through science, but if they aren’t knowable, they probably wouldn’t have a real world use. If parallel universes exist and there’s no way to access them or prove they exist, then it basically might as well not exist. It would make no difference if there are no consequences of it being real or not. Unless there are consequences of something existing, something we can do with the knowledge, it only satisfies our curiosity. It sucks, but that might be the practical answer.
Science is the scientific method, until a hypothesis has gone through the scientific method it’s just a thought experiment and not actual science.