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Why call it a "zero math introduction" to a math topic? Kind of twists my guts a bit to read that. Seems to suggest some of a wannabe or love-hate relationship

by sriku 9y ago

Why call it a "zero math introduction" to a math topic? Kind of twists my guts a bit to read that. Seems to suggest some of a wannabe or love-hate relationship with math that you don't want to know any math but you find this math topic interesting?

g_delgado14 9y ago
One of my gripes with the current education system is that it trains the pupil to simply regurgitate knowledge without ensuring that the pupil truly understands the topic - in this case MCMC methods. Articles such as this one are a great resource to help what would be a mindless regurgitator actually understand what the whole point of an MCMC method is for. The 'why' to the 'what' essentially. And you don't need math to explain that.
- johnhenry 9y ago
  > And you don't need math to explain that. There's an argument that you need math to explain it because it is math -- just not what we're taught to think of as "math". One of my gripes with the current education system is that it makes it hard to recognize when math appears in situations not explicitly involving numbers, equations, and matrices.
  - smokeyj 9y ago
    > There's an argument that you need math to explain it because it is math Sounds like circular reasoning. There's an argument you need logic, because math is logic.
    - msla 9y ago
      The hand points at the Moon. The dog barks at the hand. Math is confused with arithmetic, which is one tiny subset of math, and notation, which isn't math at all but is merely a tool mathematicians use to communicate more clearly because some concepts are too bulky when you attempt to express them using words. The essence of math is careful reasoning, following step-by-step processes to derive new truths from existing ones. If you do that, you're doing math, and if you do it without arithmetic or notation, people will say you're doing math without math.
    - johnhenry 9y ago
      I wonder if you meant to post "There's an argument you need math, because math is logic.", which is tangentially true, but that's not the point i'm making. > There's an argument that you need math to explain it because it is math * More specifically, it's a mathematical idea, so, in order to explain it, it would be impossible not to use other mathematical ideas. These other ideas exist throughout the article and are [incorrectly] separated from what the average person thinks when they hear "math" but it's math, nonetheless. For instance, the many graphs throughout the article should be recognized as math.
  - thomasfortes 9y ago
    It reminds me of a text that Feynman wrote about when he gave classes in Brazil, the students knew all the theory and the math behind it, but they could not recognize the phenomenon when it happened in the real world. So I guess that is not only in math, but in the entire corpus of knowledge, our system makes us prepared for grading tests, not for applying the knowledge.
    - yesenadam 9y ago
      He told a room full of students that a French curve (that extremely curvy shape used in technical drawing) has the remarkable property that the tangent of the lowest point is always horizontal.. and they all believed him.
      - LgWoodenBadger 9y ago
        Well it's true, isn't it? I think that point was that they were astounded that the curve had that feature because they didn't understand why it was always horizontal. They thought it was magic.
        yesenadam 9y ago
        Uh the point seemed that they knew the theory (of differentiation, tangents, trig etc) but were absolutely helpless in practically applying it. Couldn't relate the theory they had learnt to what they knew of the world, at all. Didn't think 'But the lowest point of ANY curve is horizontal!'
    - johnhenry 9y ago
      Is this what you're talking about? http://v.cx/2010/04/feynman-brazil-education http://v.cx/2010/04/feynman-brazil-education
- deleted 9y ago
  [deleted]
neeleshs 9y ago
I consider it "intuition". The real math behind this is inescapable and formal. For someone like me, any article that says zero-math equates to having some intuitive description of whats going on, which is gold. I'll eventually get to the math pieces, but having an intuitive understanding of the topic makes it much easier to grok the math later on
- rxhernandez 9y ago
  A brilliant mentor of mine(who went to MIT for his undergraduate and graduate degrees if that matters to anyone) used to decry lectures that were too mathematical rather than being more intuitive. I feel the same as it's far easier to develop the mathematics after having been given only the intuition than to develop intuition after having been given only the mathematics. Obviously there should be a balance but I prefer that my graduate mathematics courses err on the side of being too intuitive rather than too mathematical because I can generally figure out the maths on my own after the lecture.
- sriku 9y ago
  Perhaps "math" is overloaded to sometimes refer to the actual doing of mathematics and at other times to the act of communicating mathematical ideas - which is where symbols/logic/rigour begin to feature. As for "intuition", I usually seek refuge in Jeff Raskin's theorem "intuitive = familiar" - i.e. you don't lose the content of a statement made using the word intuition if you replaced it with the word familiar .. but now suddenly it is less "mystical" and clearer. Plus it points. To the subjectivity of intuition. - that what is familiar to one may not be familiar to another and so there are different "intuitive" explanations. So "intuitive understanding of topic" = "understanding a topic based on what you're already familiar with". Explains why quantum mechanics doesn't feel "intuitive". There is nothing in our experience that makes the phenomena "familiar" to us.

by sriku 9y ago

g_delgado14 9y ago

One of my gripes with the current education system is that it trains the pupil to simply regurgitate knowledge without ensuring that the pupil truly understands the topic - in this case MCMC methods. Articles such as this one are a great resource to help what would be a mindless regurgitator actually understand what the whole point of an MCMC method is for. The 'why' to the 'what' essentially. And you don't need math to explain that.

johnhenry 9y ago
> And you don't need math to explain that. There's an argument that you need math to explain it because it is math -- just not what we're taught to think of as "math". One of my gripes with the current education system is that it makes it hard to recognize when math appears in situations not explicitly involving numbers, equations, and matrices.
- smokeyj 9y ago
  > There's an argument that you need math to explain it because it is math Sounds like circular reasoning. There's an argument you need logic, because math is logic.
  - msla 9y ago
    The hand points at the Moon. The dog barks at the hand. Math is confused with arithmetic, which is one tiny subset of math, and notation, which isn't math at all but is merely a tool mathematicians use to communicate more clearly because some concepts are too bulky when you attempt to express them using words. The essence of math is careful reasoning, following step-by-step processes to derive new truths from existing ones. If you do that, you're doing math, and if you do it without arithmetic or notation, people will say you're doing math without math.
  - johnhenry 9y ago
    I wonder if you meant to post "There's an argument you need math, because math is logic.", which is tangentially true, but that's not the point i'm making. > There's an argument that you need math to explain it because it is math * More specifically, it's a mathematical idea, so, in order to explain it, it would be impossible not to use other mathematical ideas. These other ideas exist throughout the article and are [incorrectly] separated from what the average person thinks when they hear "math" but it's math, nonetheless. For instance, the many graphs throughout the article should be recognized as math.
- thomasfortes 9y ago
  It reminds me of a text that Feynman wrote about when he gave classes in Brazil, the students knew all the theory and the math behind it, but they could not recognize the phenomenon when it happened in the real world. So I guess that is not only in math, but in the entire corpus of knowledge, our system makes us prepared for grading tests, not for applying the knowledge.
  - yesenadam 9y ago
    He told a room full of students that a French curve (that extremely curvy shape used in technical drawing) has the remarkable property that the tangent of the lowest point is always horizontal.. and they all believed him.
    - LgWoodenBadger 9y ago
      Well it's true, isn't it? I think that point was that they were astounded that the curve had that feature because they didn't understand why it was always horizontal. They thought it was magic.
      - yesenadam 9y ago
        Uh the point seemed that they knew the theory (of differentiation, tangents, trig etc) but were absolutely helpless in practically applying it. Couldn't relate the theory they had learnt to what they knew of the world, at all. Didn't think 'But the lowest point of ANY curve is horizontal!'
  - johnhenry 9y ago
    Is this what you're talking about? http://v.cx/2010/04/feynman-brazil-education http://v.cx/2010/04/feynman-brazil-education
deleted 9y ago
[deleted]

neeleshs 9y ago

I consider it "intuition". The real math behind this is inescapable and formal. For someone like me, any article that says zero-math equates to having some intuitive description of whats going on, which is gold. I'll eventually get to the math pieces, but having an intuitive understanding of the topic makes it much easier to grok the math later on

rxhernandez 9y ago
A brilliant mentor of mine(who went to MIT for his undergraduate and graduate degrees if that matters to anyone) used to decry lectures that were too mathematical rather than being more intuitive. I feel the same as it's far easier to develop the mathematics after having been given only the intuition than to develop intuition after having been given only the mathematics. Obviously there should be a balance but I prefer that my graduate mathematics courses err on the side of being too intuitive rather than too mathematical because I can generally figure out the maths on my own after the lecture.
sriku 9y ago
Perhaps "math" is overloaded to sometimes refer to the actual doing of mathematics and at other times to the act of communicating mathematical ideas - which is where symbols/logic/rigour begin to feature. As for "intuition", I usually seek refuge in Jeff Raskin's theorem "intuitive = familiar" - i.e. you don't lose the content of a statement made using the word intuition if you replaced it with the word familiar .. but now suddenly it is less "mystical" and clearer. Plus it points. To the subjectivity of intuition. - that what is familiar to one may not be familiar to another and so there are different "intuitive" explanations. So "intuitive understanding of topic" = "understanding a topic based on what you're already familiar with". Explains why quantum mechanics doesn't feel "intuitive". There is nothing in our experience that makes the phenomena "familiar" to us.