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> Math is the ultimate get-to-the-bottom-of-things subject. I love math and am decently good at it. But I don't agree with this statement. I don't think math

by edanm 4y ago

> Math is the ultimate get-to-the-bottom-of-things subject. I love math and am decently good at it. But I don't agree with this statement. I don't think math is the ultimate get-to-the-bottom-of-things subject, I think it's an ultimate get-to-the-bottom-of-things subject. And I think that makes a big difference. It's easy to set up a filter which only very intelligent/whatever people pass, and say "yep, this is the correct filter, everyone passing this filter is intelligent". But we might be missing a lot of people we'd get otherwise! What if someone is totally uninterested in math, but she happens to love biology, and spent her whole life "getting-to-the-bottom-of" how bodies work? Or substitute in chemistry, exercise science, psychology, or any other field. People can be totally uninterested in and bad at math, but still geniuses of their respective fields. Note: I'm not sure you disagree with what I wrote, you yourself wrote " math is a sort of flag that suggests you can get to the bottom of whatever problem you're faced with."

lordnacho 4y ago
I agree with what you say, you can be smart and be into other subjects, definitely. The thing about math is you can plumb the depths without much resource. You don't need to check your ideas against the physical world, something that costs time and money that most kids will not have access to. So it's more like if someone is good at math, that is a good sign that they are the kind of person were talking about, but if they're not that doesn't mean they aren't.
trashtester 4y ago
Pure math for its own purpose is for a select few. For most people, math is a set of tools that enables them to better understand certain aspects of reality (or of non-reality, perhaps, in some cases). In some of those cases, you only require basic math. Some require intermediate math and some relatively advanced math. But if you want to be a "genius" if either biology, chemistry or psychology, you most likely will need more math than most people learn in high school. Almost every kind of scientific experimentation requires a firm grasp of statistics (way too many papers are written and even published with sub-par stats in many fields). And in most STEM fields, before you can get "genius" level specialization, you will need a relatively broad mastery of the field, and both Biology and Chemisty, there are plenty of things to learn that require at least some entry level collage math.
- Koshkin 4y ago
  > Pure math for its own purpose is for a select few. There is a vast swath of research effort directed to modern geometrical foundations of physics that look pretty much like pure math.
  - trashtester 4y ago
    The difference between physics and pure math is not in how it "looks". A lot of physics already "looks" like math, but whether it leads to some testable conclusions. I would say that String Theory has been more similar to Math than Physics for a while, in that it hasn't really led to many interesting experiments.
hnfong 4y ago
As somebody who's cursorily interested in what people would call "Foundation of Mathematics", I don't even think the "ultimate" part is justified. Why is 1 + 1 = 2? This isn't really a mathematics problem (I know about axiomatic systems, they were invented relatively late in the timeline of mathematical history, invented as a fiction to avoid getting to the bottom of the messier things, i.e. the social context of how mathematics was actually invented and is used). Sidenote: I have written an article (not in English) about how numbers were a linear to log(N) time complexity reduction trick for recording information, and that 1+1=2 presumes a reductionist and somewhat capitalist view of the world... Anyway, to me, mathematics is a subject that invents abstract concepts and rewards those who are capable of understanding and believing in them. That kind of thinking is probably useful in a lot of areas that have business value. The make-believe part is, I would humbly suggest, quite an important feature too. It really fits nicely into our capitalist framework playing the money game where they'd want you to believe $1+$1=$2 is an axiom, and it's best not to reach out beyond the closed, axiomatic system and ask where those $ comes from or the messy social implications of the "math".
- Koshkin 4y ago
  > 1+1=2 presumes a reductionist and somewhat capitalist view of the world Hopefully, not all Chinese engineers think that... > mathematics is a subject that invents abstract concepts and rewards Not according to much of the history of math. Mathematics was borne of practical needs, and it has been extremely useful in science and engineering. (Sure, you can think of the number 2, say, as an abstract concept, but to most people it is a very concrete thing - as is the definite integral, etc.) Yes, a philosophical journey can be a journey down a rabbit hole, so one should be careful...
  - hnfong 4y ago
    > Hopefully, not all Chinese engineers think that... :) The main point of divergence between "Western Capitalism" and "Socialism with Chinese characteristics" isn't whether it's ok to accumulate capital, but who controls it :) I think both agree that capital is a great idea for building strong nations. > Not according to much of the history of math. Mathematics was borne of practical needs, and it has been extremely useful in science and engineering. (Sure, you can think of the number 2, say, as an abstract concept, but to most people it is a very concrete thing - as is the definite integral, etc.) I agree, and... that's kind of my point. I intended to say modern mathematics is a subject that invents abstract concepts... Historically numbers were invented to solve a practical need, and then some hobbyists came and had too much fun with it, ending up with funny things like Peano and ZFC. I've seen too many people trained in mathematics that forgot the social-historical context came first, and jump straight to the newly invented axiomatic systems to explain things as basic as 1+1=2, which to me doesn't fit well with the "ultimate get-to-the-bottom-of-things" description. I mean, to cite a specific example, while the exercise is probably entertaining to some, anyone seriously believing 2+2=4 requires thousands of lines of "proof" is probably not very good at getting to the bottom of things in a general sense. (ref: http://us.metamath.org/mpegif/mmset.html#trivia http://us.metamath.org/mpegif/mmset.html#trivia )

by edanm 4y ago

lordnacho 4y ago

I agree with what you say, you can be smart and be into other subjects, definitely. The thing about math is you can plumb the depths without much resource. You don't need to check your ideas against the physical world, something that costs time and money that most kids will not have access to. So it's more like if someone is good at math, that is a good sign that they are the kind of person were talking about, but if they're not that doesn't mean they aren't.

trashtester 4y ago

Pure math for its own purpose is for a select few. For most people, math is a set of tools that enables them to better understand certain aspects of reality (or of non-reality, perhaps, in some cases). In some of those cases, you only require basic math. Some require intermediate math and some relatively advanced math. But if you want to be a "genius" if either biology, chemistry or psychology, you most likely will need more math than most people learn in high school. Almost every kind of scientific experimentation requires a firm grasp of statistics (way too many papers are written and even published with sub-par stats in many fields). And in most STEM fields, before you can get "genius" level specialization, you will need a relatively broad mastery of the field, and both Biology and Chemisty, there are plenty of things to learn that require at least some entry level collage math.

Koshkin 4y ago
> Pure math for its own purpose is for a select few. There is a vast swath of research effort directed to modern geometrical foundations of physics that look pretty much like pure math.
- trashtester 4y ago
  The difference between physics and pure math is not in how it "looks". A lot of physics already "looks" like math, but whether it leads to some testable conclusions. I would say that String Theory has been more similar to Math than Physics for a while, in that it hasn't really led to many interesting experiments.

hnfong 4y ago

As somebody who's cursorily interested in what people would call "Foundation of Mathematics", I don't even think the "ultimate" part is justified. Why is 1 + 1 = 2? This isn't really a mathematics problem (I know about axiomatic systems, they were invented relatively late in the timeline of mathematical history, invented as a fiction to avoid getting to the bottom of the messier things, i.e. the social context of how mathematics was actually invented and is used). Sidenote: I have written an article (not in English) about how numbers were a linear to log(N) time complexity reduction trick for recording information, and that 1+1=2 presumes a reductionist and somewhat capitalist view of the world... Anyway, to me, mathematics is a subject that invents abstract concepts and rewards those who are capable of understanding and believing in them. That kind of thinking is probably useful in a lot of areas that have business value. The make-believe part is, I would humbly suggest, quite an important feature too. It really fits nicely into our capitalist framework playing the money game where they'd want you to believe $1+$1=$2 is an axiom, and it's best not to reach out beyond the closed, axiomatic system and ask where those $ comes from or the messy social implications of the "math".

Koshkin 4y ago
> 1+1=2 presumes a reductionist and somewhat capitalist view of the world Hopefully, not all Chinese engineers think that... > mathematics is a subject that invents abstract concepts and rewards Not according to much of the history of math. Mathematics was borne of practical needs, and it has been extremely useful in science and engineering. (Sure, you can think of the number 2, say, as an abstract concept, but to most people it is a very concrete thing - as is the definite integral, etc.) Yes, a philosophical journey can be a journey down a rabbit hole, so one should be careful...
- hnfong 4y ago
  > Hopefully, not all Chinese engineers think that... :) The main point of divergence between "Western Capitalism" and "Socialism with Chinese characteristics" isn't whether it's ok to accumulate capital, but who controls it :) I think both agree that capital is a great idea for building strong nations. > Not according to much of the history of math. Mathematics was borne of practical needs, and it has been extremely useful in science and engineering. (Sure, you can think of the number 2, say, as an abstract concept, but to most people it is a very concrete thing - as is the definite integral, etc.) I agree, and... that's kind of my point. I intended to say modern mathematics is a subject that invents abstract concepts... Historically numbers were invented to solve a practical need, and then some hobbyists came and had too much fun with it, ending up with funny things like Peano and ZFC. I've seen too many people trained in mathematics that forgot the social-historical context came first, and jump straight to the newly invented axiomatic systems to explain things as basic as 1+1=2, which to me doesn't fit well with the "ultimate get-to-the-bottom-of-things" description. I mean, to cite a specific example, while the exercise is probably entertaining to some, anyone seriously believing 2+2=4 requires thousands of lines of "proof" is probably not very good at getting to the bottom of things in a general sense. (ref: http://us.metamath.org/mpegif/mmset.html#trivia http://us.metamath.org/mpegif/mmset.html#trivia )