5 ms·

> Well I think part of the problem is that our education system results in many people thinking mathematics is anything other than a language. Most often people

> Well I think part of the problem is that our education system results in many people thinking mathematics is anything other than a language. Most often people think that math is something we are uncovering about the universe. And those people would be right, as the mathematical universe is part of our shared universe/reality. It's not just language and games. A Turing Machine either halts, or it doesn't. But if you want to solve a concrete problem (in physics, for example), it is best to develop/find/learn the mathematics you need to solve your problem, and not the other way around.

godelski 3y ago
I'm not sure what your argument proves. No one said it is just games either. I think you're turning what I said into something else. Languages are incredibly impressive and powerful things. I feel like you're making languages appear simple and of low utility. But language has been one of the, if not the most, powerful tool humans have ever created, especially when you consider written language. The latter allowing us to pass along information asynchronously through time and space. Do not miss the power of this tool just because it is something we use so frequently. There's a reason we use it so frequently. The reason we use the language of math is because it is so precise. But you just described a turing machine without using math. Keep in mind that physics is also a language. Physics is an ever evolving model, a description of our reality. But it is not more than that, a model. But all models being wrong does not equate to models being useless. Physicses (yes, there are multiple ones), are clearly quite powerful and useful models that have enabled us to do quite amazing things as well. But I'm also not going to start programming in Brainfuck or with Magic cards. But I do have a deep passion for mathematics and it is something I use every day and spend quite a lot of time learning even outside my work. Your argument demonstrates the usefulness of mathematics, but does not demonstrate that it isn't a language. I also would like to remind you that you can create pretty useless algebras. Maybe also checkout Wolfram's section on recreational mathematics. Maybe also dig into my name sake's multiple theorems. Most people misunderstand the results, but I don't think it diminishes their worth, they are quite important and amazing. And the incompleteness theorem is deeply related to turing completeness as well as superposition and a famous logic paradox.
- unblough 3y ago
  I am having trouble following your opinion through this thread. > Your argument demonstrates the usefulness of mathematics, but does not demonstrate that it isn't a language. What is “a language” to you? What is an “isn’t a language” to you? I can grok you referring to axioms and lemmas as a “mathematical language”, but I see such as just the way we communicate something more essential and wholly independent of any need to have been communicated. A lot of contemporary research mathematics is layered and wrought of “useful” complexities for its desired domain, but how do you dismiss the essential and seemingly unrealness of its abstraction from our perceived reality? Counting is an example. Subjective boundaries illuminate the essentialism of distinctness. 2 apples describe the same abstract phenomena as 2 atoms, or 2 galaxies, or 2 orientations of stereoisomers. What is the “language” here? The word/symbol 2? The subjective boundary that separates something more continuous into discrete forms? Transcendentals and irrationals alight my meditation on what the hell all this is that we’re experiencing. You have a triangle with edges that terminate at each vertex, but if two of those edges have equal length than you can interpret their length as unit 1 where the third edge then has a length of (sqrt 2) which is a number without a finite decimal expansion. What language can be used to defend an infinitesimal equating to a finite value? This points at an essentialism to me. Any amount of “language” is incapable of both explaining this completely or explaining it away. Similar with pi and its relation to a circle which has a well defined circumference that somehow expresses itself with a number that is itself incapable of being expressed or defined. As you brought up the incompleteness theorems, they too have a similar “infinite in finite” quality. I am unsure how you can understand godel but argue against the essentialism of the sur-real abstractions he brings attention to.
  - circlefavshape 3y ago
    I agree that mathematics is a language, where a language is a system we have for describing the world and communicating with each other. I don't understand what argument you are making here. "Infinitesimal" is just an idea, as far as I know. Nothing real is infinitesimal.
    - unblough 3y ago

godelski 3y ago

I'm not sure what your argument proves. No one said it is just games either. I think you're turning what I said into something else. Languages are incredibly impressive and powerful things. I feel like you're making languages appear simple and of low utility. But language has been one of the, if not the most, powerful tool humans have ever created, especially when you consider written language. The latter allowing us to pass along information asynchronously through time and space. Do not miss the power of this tool just because it is something we use so frequently. There's a reason we use it so frequently. The reason we use the language of math is because it is so precise. But you just described a turing machine without using math. Keep in mind that physics is also a language. Physics is an ever evolving model, a description of our reality. But it is not more than that, a model. But all models being wrong does not equate to models being useless. Physicses (yes, there are multiple ones), are clearly quite powerful and useful models that have enabled us to do quite amazing things as well. But I'm also not going to start programming in Brainfuck or with Magic cards. But I do have a deep passion for mathematics and it is something I use every day and spend quite a lot of time learning even outside my work. Your argument demonstrates the usefulness of mathematics, but does not demonstrate that it isn't a language. I also would like to remind you that you can create pretty useless algebras. Maybe also checkout Wolfram's section on recreational mathematics. Maybe also dig into my name sake's multiple theorems. Most people misunderstand the results, but I don't think it diminishes their worth, they are quite important and amazing. And the incompleteness theorem is deeply related to turing completeness as well as superposition and a famous logic paradox.

unblough 3y ago
I am having trouble following your opinion through this thread. > Your argument demonstrates the usefulness of mathematics, but does not demonstrate that it isn't a language. What is “a language” to you? What is an “isn’t a language” to you? I can grok you referring to axioms and lemmas as a “mathematical language”, but I see such as just the way we communicate something more essential and wholly independent of any need to have been communicated. A lot of contemporary research mathematics is layered and wrought of “useful” complexities for its desired domain, but how do you dismiss the essential and seemingly unrealness of its abstraction from our perceived reality? Counting is an example. Subjective boundaries illuminate the essentialism of distinctness. 2 apples describe the same abstract phenomena as 2 atoms, or 2 galaxies, or 2 orientations of stereoisomers. What is the “language” here? The word/symbol 2? The subjective boundary that separates something more continuous into discrete forms? Transcendentals and irrationals alight my meditation on what the hell all this is that we’re experiencing. You have a triangle with edges that terminate at each vertex, but if two of those edges have equal length than you can interpret their length as unit 1 where the third edge then has a length of (sqrt 2) which is a number without a finite decimal expansion. What language can be used to defend an infinitesimal equating to a finite value? This points at an essentialism to me. Any amount of “language” is incapable of both explaining this completely or explaining it away. Similar with pi and its relation to a circle which has a well defined circumference that somehow expresses itself with a number that is itself incapable of being expressed or defined. As you brought up the incompleteness theorems, they too have a similar “infinite in finite” quality. I am unsure how you can understand godel but argue against the essentialism of the sur-real abstractions he brings attention to.
- circlefavshape 3y ago
  I agree that mathematics is a language, where a language is a system we have for describing the world and communicating with each other. I don't understand what argument you are making here. "Infinitesimal" is just an idea, as far as I know. Nothing real is infinitesimal.
  - unblough 3y ago