I had a misunderstanding regarding a very similar topic. I was thinking of arithmetic being very core to mathematics when other people included all of formal deductive reasoning (ie stuff other than that has to do with numbers). Humans do have subconcious thoughts which are not well captured by mathematics.
The case for math being beyond human extends far bigger than cosmic. If you had a fictional story that fullfilled some axioms then math based on those axioms would be in full effect.
There are some activities that rely heavily on math yes, but I think we do have observations we don’t arrange into neat systems. For example we can’t do 3-body problems but we have general gravity kind of locked down (a bit math adjaccent but still an example how we can do without a mathematical theory despite knowing we would like one).
The concept of “one” can be made problematic. And there are systems were the concept is not an elementary one but emerges from deeper principles. For example one has to somehow argue why sexual reproduction doesn’t make an example of “1+1=3″. In some systems it could be argued that 0 is actually the first digit and more fundamental.
Thank you. Intuitively I would hazard the guess that even non-obvious systems (such as your example of the story which rests on axioms) may be in the future presented in a mathematical way. There is a very considerable added hurdle there, however:
When we communicate about math (let’s use a simple and famous example: the Pythagorean theorem in Euclidean space) we never focus on parameters that go outside the system. Not only parameters which are outside the set axioms which define the system mathematically (in this case Euclidean space) but more importantly the many more which define the terms we use: I do not communicate to you how I sense the terms for A, B, squared, equality or any other, regardless of the likelihood of myself sensing them in my mind in a very different way to you. It’s the same relative communication which is used in every-day matters: if one says “I am happy” you do not sense what is very specifically/fully meant, although the term is a fossil of specific connotations, so some communication is possible, and often no more is needed. Likewise no more is needed to present a math system like that, but certainly far more will be needed to present a story or the subconscious in math terms (and within a given level; outside of that set the terms will remain less defined).
I had a misunderstanding regarding a very similar topic. I was thinking of arithmetic being very core to mathematics when other people included all of formal deductive reasoning (ie stuff other than that has to do with numbers). Humans do have subconcious thoughts which are not well captured by mathematics.
The case for math being beyond human extends far bigger than cosmic. If you had a fictional story that fullfilled some axioms then math based on those axioms would be in full effect.
There are some activities that rely heavily on math yes, but I think we do have observations we don’t arrange into neat systems. For example we can’t do 3-body problems but we have general gravity kind of locked down (a bit math adjaccent but still an example how we can do without a mathematical theory despite knowing we would like one).
The concept of “one” can be made problematic. And there are systems were the concept is not an elementary one but emerges from deeper principles. For example one has to somehow argue why sexual reproduction doesn’t make an example of “1+1=3″. In some systems it could be argued that 0 is actually the first digit and more fundamental.
Thank you. Intuitively I would hazard the guess that even non-obvious systems (such as your example of the story which rests on axioms) may be in the future presented in a mathematical way. There is a very considerable added hurdle there, however:
When we communicate about math (let’s use a simple and famous example: the Pythagorean theorem in Euclidean space) we never focus on parameters that go outside the system. Not only parameters which are outside the set axioms which define the system mathematically (in this case Euclidean space) but more importantly the many more which define the terms we use: I do not communicate to you how I sense the terms for A, B, squared, equality or any other, regardless of the likelihood of myself sensing them in my mind in a very different way to you. It’s the same relative communication which is used in every-day matters: if one says “I am happy” you do not sense what is very specifically/fully meant, although the term is a fossil of specific connotations, so some communication is possible, and often no more is needed. Likewise no more is needed to present a math system like that, but certainly far more will be needed to present a story or the subconscious in math terms (and within a given level; outside of that set the terms will remain less defined).