4 ms·

Ugh. Math is a collection of concrete symbols for simplifying different problems. It's evolved over thousands of years to help us understand difficult things.

Ugh. Math is a collection of concrete symbols for simplifying different problems. It's evolved over thousands of years to help us understand difficult things. We don't make it that way just to piss people off.

michael_dorfman 15y ago
But math is more than that. His argument is that analyzing a differential equation without exploring it in phase space was like analyzing a piece of sheet music without actually hearing it. And if music education were taught in that way-- by looking at music purely as the manipulation of concrete symbols-- I imagine some of us would be writing "kill music (as it is currently taught)" blog posts as well. EDIT: minor grammar fix
- hammock 15y ago
  I doubt anyone here learned math (at least up through calculus) without concrete examples. They were called word problems and lab assignments.
  - generalk 15y ago
    Word problems are still abstract manipulation of symbols, you just have to hunt around in the phrasing for the right operands or operations, which arguably makes it harder.
  - fhars 15y ago
    But the jury is still out on the question of whether concrete examples are usefull in maths education: http://researchnews.osu.edu/archive/mathed.htm http://researchnews.osu.edu/archive/mathed.htm
    - hessenwolf 15y ago
      Weak study. They made some students learn something using concrete examples only, and then expected them to be able to abstract. That's just dumb. I learn the maths, and apply to various situations in my head to make sure I understand it.
  - hessenwolf 15y ago
    I'll be honest; I absolute love graph theory. If I had a million lives and financial independence, I would spend several of them solving graph theory problems. I don't really give a shit what the nodes and edges are. Computer network? Rigid structure? Conditional independence of personality traits? I don't care!
_delirium 15y ago
Most of the symbols are pretty recent; if you read mathematics from even 300 years ago, there's a much bigger proportion written in prose. Along the lines of, "Consider two quantities, such that the latter is at least twice the former ...".
- StefanKarpinski 15y ago
  The shift to more symbols and more and better notation has also drastically increased mathematical productivity and rigor. In fact, most of the notation emerged together with the axiomatization of the foundations of mathematics in the early 20th century. If we were to follow this guy's ideas it would cause even more of a class divide between those who can understand the "magical symbols" and those who can't. Doing what he suggests would mean that the non-cognoscenti wouldn't even have access to the understanding of simple algebraic equations.
- eru 15y ago
  And you will understand, why we switched from prose to symbols. But that doesn't mean we should go overboard with the symbols.
  - hessenwolf 15y ago
    http://upload.wikimedia.org/wikipedia/commons/5/56/Actuarial_notation.svg http://upload.wikimedia.org/wikipedia/commons/5/56/Actuarial... Overboard?
    - eru 15y ago
      Depends on how you embed it in text.
  - StavrosK 15y ago
    Exactly. Why do devs shout "comment your code" but academic papers have no explanation next to the equations? "Next, calculate the fitness of the algorithm and add it to the pool if it is better than the worst of the last generation: <math here>"
simpleTruth 15y ago
Talking about Math as a single subject is like talking about Sports. Chess, Boxing, Baseball, Snowboarding, Curling, and Luge may have some things in common. However, suggesting that DiffEq and Fractions are equally meaningless to most people seems just as out of place as assuming a chess grandmaster is also a champion snowboarder.

michael_dorfman 15y ago

But math is more than that. His argument is that analyzing a differential equation without exploring it in phase space was like analyzing a piece of sheet music without actually hearing it. And if music education were taught in that way-- by looking at music purely as the manipulation of concrete symbols-- I imagine some of us would be writing "kill music (as it is currently taught)" blog posts as well. EDIT: minor grammar fix

hammock 15y ago
I doubt anyone here learned math (at least up through calculus) without concrete examples. They were called word problems and lab assignments.
- generalk 15y ago
  Word problems are still abstract manipulation of symbols, you just have to hunt around in the phrasing for the right operands or operations, which arguably makes it harder.
- fhars 15y ago
  But the jury is still out on the question of whether concrete examples are usefull in maths education: http://researchnews.osu.edu/archive/mathed.htm http://researchnews.osu.edu/archive/mathed.htm
  - hessenwolf 15y ago
    Weak study. They made some students learn something using concrete examples only, and then expected them to be able to abstract. That's just dumb. I learn the maths, and apply to various situations in my head to make sure I understand it.
- hessenwolf 15y ago
  I'll be honest; I absolute love graph theory. If I had a million lives and financial independence, I would spend several of them solving graph theory problems. I don't really give a shit what the nodes and edges are. Computer network? Rigid structure? Conditional independence of personality traits? I don't care!

_delirium 15y ago

Most of the symbols are pretty recent; if you read mathematics from even 300 years ago, there's a much bigger proportion written in prose. Along the lines of, "Consider two quantities, such that the latter is at least twice the former ...".

StefanKarpinski 15y ago
The shift to more symbols and more and better notation has also drastically increased mathematical productivity and rigor. In fact, most of the notation emerged together with the axiomatization of the foundations of mathematics in the early 20th century. If we were to follow this guy's ideas it would cause even more of a class divide between those who can understand the "magical symbols" and those who can't. Doing what he suggests would mean that the non-cognoscenti wouldn't even have access to the understanding of simple algebraic equations.
eru 15y ago
And you will understand, why we switched from prose to symbols. But that doesn't mean we should go overboard with the symbols.
- hessenwolf 15y ago
  http://upload.wikimedia.org/wikipedia/commons/5/56/Actuarial_notation.svg http://upload.wikimedia.org/wikipedia/commons/5/56/Actuarial... Overboard?
  - eru 15y ago
    Depends on how you embed it in text.
- StavrosK 15y ago
  Exactly. Why do devs shout "comment your code" but academic papers have no explanation next to the equations? "Next, calculate the fitness of the algorithm and add it to the pool if it is better than the worst of the last generation: <math here>"

simpleTruth 15y ago

Talking about Math as a single subject is like talking about Sports. Chess, Boxing, Baseball, Snowboarding, Curling, and Luge may have some things in common. However, suggesting that DiffEq and Fractions are equally meaningless to most people seems just as out of place as assuming a chess grandmaster is also a champion snowboarder.