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With memory, seeing divinity in math probably requires active contemplation, since seeing simple formulas and geometric shapes repeatedly gets old fast > Many

With memory, seeing divinity in math probably requires active contemplation, since seeing simple formulas and geometric shapes repeatedly gets old fast > Many observers report they derive pleasure from discovering simple but novel patterns [...] The observer's learning process causes a reduction of the subjective complexity of the data, yielding a temporarily high derivative of subjective beauty: a temporarily steep learning curve. > Why are some musical pieces more interesting or aesthetically rewarding than others? Not the one the listener (composer) just heard (played) fifty times in a row without any noticable change. It became too subjectively predictable in the process. Not the weird one with completely unfamiliar rhythm and tonality. It seems too irregular and contain too much arbitrariness and subjective noise. The observer (creator) of the data is interested in melodies that are unfamiliar enough to contain somewhat unexpected harmonies or beats etc., but familiar enough to allow for quickly recognizing the presence of a new learnable regularity or compressibility in the sound stream: a novel pattern! Sure, it will get boring over time, but not yet. https://people.idsia.ch/~juergen/creativity.html https://people.idsia.ch/~juergen/creativity.html

auggierose 4y ago
Not sure I understand your comment, but I can assure you, math involves a lot of active contemplation.
- 7373737373 4y ago
  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.

auggierose 4y ago

Not sure I understand your comment, but I can assure you, math involves a lot of active contemplation.

7373737373 4y ago
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.