4 ms·

Seeing a Tetrahedron, Euler's identity or a Klein bottle for the first time is much better than the 50th time, because you remember having seen it that many tim

Seeing a Tetrahedron, Euler's identity or a Klein bottle for the first time is much better than the 50th time, because you remember having seen it that many times by then and are not surprised by their meaning and properties anymore. Since you remember, having it remain meaningful requires actively exploring more properties of the object and its relations to other objects Some simple objects like the yin and yang symbol may remain more easily meaningful because they can have so many interpretations, compare this to say, a simple line, which is so ubiquitous its meanings are "too" unrestricted. Something like a Lie group may be too complex and too hard to understand for most to even consider it divine

auggierose 4y ago
Well yes, doing mathematics consists of trying to find out something new that you didn't know before. You might end up staring at a Klein bottle 50 times or more though, either just for pleasure, or for finding out something new about it.
otabdeveloper4 4y ago
99% of "math" is proofs. The rest of the 1% are the incidental useful parts for engineering and science. I don't know if proofs are divine or not, but they are certainly sublime.
- necovek 4y ago
  That's a pretty weird statement, even if it's true when looking at any math textbook (1% is statements of things, 99% is proving those hold). Mathematics is a scientific theory built on the most rigorous principles human minds could come up with, while striving for simplicity in the basic assumptions. The entire process of "math building", which permeats all the proofs, is what's useful in plenty other areas of life and science. I.e. mathematical induction, the core tenet of plenty a proof, is basically function recursion in software development, and underlies all sorts of delegation in any complex undertaking (if I order a part for a machine from someone building those parts, I can trust it's the same as the one I am replacing). Driving something down to a contradiction is used in many a decision everywhere. And sure, results of applying these mathematical processes rigorously ensures that we can trust we can apply mathematical results (theorems and such) widely: it's not uncommon to apply processes from the proofs when using a theorem either. And this is what ensures we can use the same process to add up 3 sheep and 2 sheep or 4 apples and 1 orange to get 5 sheep or 5 fruits. Or to calculate surface area of a circle. Or use integrals to get volumes of complex shapes. Etc.
  - otabdeveloper4 4y ago
    Mathematics is a language, not a scientific theory. You can use mathematics to describe scientific theories, but it is not necessary. (We had been doing science long before we invented math.) Meanwhile you can use math to describe all sorts of things that aren't and will never be science.
    - necovek 4y ago
      Mathematics has a language, but it has a bunch of conclusions using said language too. I don't think you can argue how mathematical theorems are not "scientific theory": the language part comes from all the definitions and axioms, but there is a whole theory built on top of it. On your other statement, I never said mathematics is the theory of science, but rather, a scientific theory: so of course we had science before we formalized and names mathematics mathematics. It's only loosely based on reality (as a driver for many — but not all — definitions and concepts), just like other scientific theories are based on our perceived reality.

auggierose 4y ago

Well yes, doing mathematics consists of trying to find out something new that you didn't know before. You might end up staring at a Klein bottle 50 times or more though, either just for pleasure, or for finding out something new about it.

otabdeveloper4 4y ago

99% of "math" is proofs. The rest of the 1% are the incidental useful parts for engineering and science. I don't know if proofs are divine or not, but they are certainly sublime.

necovek 4y ago
That's a pretty weird statement, even if it's true when looking at any math textbook (1% is statements of things, 99% is proving those hold). Mathematics is a scientific theory built on the most rigorous principles human minds could come up with, while striving for simplicity in the basic assumptions. The entire process of "math building", which permeats all the proofs, is what's useful in plenty other areas of life and science. I.e. mathematical induction, the core tenet of plenty a proof, is basically function recursion in software development, and underlies all sorts of delegation in any complex undertaking (if I order a part for a machine from someone building those parts, I can trust it's the same as the one I am replacing). Driving something down to a contradiction is used in many a decision everywhere. And sure, results of applying these mathematical processes rigorously ensures that we can trust we can apply mathematical results (theorems and such) widely: it's not uncommon to apply processes from the proofs when using a theorem either. And this is what ensures we can use the same process to add up 3 sheep and 2 sheep or 4 apples and 1 orange to get 5 sheep or 5 fruits. Or to calculate surface area of a circle. Or use integrals to get volumes of complex shapes. Etc.
- otabdeveloper4 4y ago
  Mathematics is a language, not a scientific theory. You can use mathematics to describe scientific theories, but it is not necessary. (We had been doing science long before we invented math.) Meanwhile you can use math to describe all sorts of things that aren't and will never be science.
  - necovek 4y ago
    Mathematics has a language, but it has a bunch of conclusions using said language too. I don't think you can argue how mathematical theorems are not "scientific theory": the language part comes from all the definitions and axioms, but there is a whole theory built on top of it. On your other statement, I never said mathematics is the theory of science, but rather, a scientific theory: so of course we had science before we formalized and names mathematics mathematics. It's only loosely based on reality (as a driver for many — but not all — definitions and concepts), just like other scientific theories are based on our perceived reality.