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Maths is not experimental. This roundabout, handwavy, vague way to deal with things causes more harm than good, in my opinion. Try to understand a proper mathem

Maths is not experimental. This roundabout, handwavy, vague way to deal with things causes more harm than good, in my opinion. Try to understand a proper mathematical proof instead.

chewz 7y ago
I disagree. Math is very experimental - it is bottom up science where you first touch various details in the dark and generalization comes later. I am with Arnold on that. > Arnold was an outspoken critic of the trend towards high levels of abstraction in mathematics during the middle of the last century. He had very strong opinions on how this approach—which was most popularly implemented by the Bourbaki school in France—initially had a negative impact on French mathematical education, and then later on that of other countries as well. https://en.m.wikipedia.org/wiki/Vladimir_Arnold https://en.m.wikipedia.org/wiki/Vladimir_Arnold
kubanczyk 7y ago
Math is experimental at its roots. If the result here wasn't usable in real life, scarcely anyone would develop that specific branch of probability theory. Instead they would think of adjusting the axioms and work out a useful probability theory. For example, most children check 1+2 experimentally before accepting the theory.
- jonsen 7y ago
  What’s the theory to accept for 1+2?
  - theelous3 7y ago
    I think he means loosely that the theory here, is that they add up to three. Kids will grab objects and group and ungroup them while counting and so on, before outright accepting math is real.
  - stan_rogers 7y ago
    That can be trivially inferred from 110-643 (Vol. 2, p. 86) in Whitehead & Russell's Principia Mathematica.
  - ookdatnog 7y ago
    Not the GP, but this is my take on their comment. Children learn counting before they learn an algorithm for addition. The "theory" to accept here is that counting a set of size x, then continuing to count, starting from x, a set of size y, yields the same result as the addition algorithm for x+y that they learn.
theelous3 7y ago
I consider myself borderline math illiterate. I understand the monty hall problem perfectly well through means other than hard math proofs. So, clearly, understanding the proof isn't required. It is a great deal more work than many other methods of understanding the problem, so why prescribe it as the best way? You might be comfortable with it, but not everyone has the time nor inclination to become mathy enough to live life through your lens.
lioeters 7y ago
Here's a glimpse that may change your mind about mathematics as an experimental science: Mathematics: An Experimental Science - https://www.math.upenn.edu/~wilf/website/Mathematics_AnExperimentalScience.pdf https://www.math.upenn.edu/~wilf/website/Mathematics_AnExper... (PDF) > A computer is used by a pure mathematician in much the same way that a telescope is used by a theoretical astronomer. It shows us "what’s out there." > From such explorations there can grow understanding, and conjectures, and roads to proofs, and phenomena that would not have been imaginable in the pre-computer era. This role of computation within pure mathematics seems destined only to expand over the near future and to be imbued into our students along with Euclid’s axioms and other staples of mathematical education. Also: Turtle Geometry: The Computer as a Medium for Exploring Mathematics - https://mitpress.mit.edu/books/turtle-geometry https://mitpress.mit.edu/books/turtle-geometry
- andrepd 7y ago
  >Mathematics: An Experimental Science That was an amazing read. It certainly made me rethink my position. Thanks!
daveFNbuck 7y ago
This roundabout, hand-wavy, vague way to deal with things is how mathematicians solve problems. You have to have an intuitive understanding of what's going on before you can formalize the solution into a proof. I majored in math in undergrad, and one of the required courses was about communicating mathematical ideas. One of my bigger projects in that course was to explain the Monty Hall problem so it could be understood by the general public, and I got a good grade by putting together a lesson plan that included this type of simulation.

Maths is not experimental. This roundabout, handwavy, vague way to deal with things causes more harm than good, in my opinion. Try to understand a proper mathematical proof instead.

chewz 7y ago

I disagree. Math is very experimental - it is bottom up science where you first touch various details in the dark and generalization comes later. I am with Arnold on that. > Arnold was an outspoken critic of the trend towards high levels of abstraction in mathematics during the middle of the last century. He had very strong opinions on how this approach—which was most popularly implemented by the Bourbaki school in France—initially had a negative impact on French mathematical education, and then later on that of other countries as well. https://en.m.wikipedia.org/wiki/Vladimir_Arnold https://en.m.wikipedia.org/wiki/Vladimir_Arnold

kubanczyk 7y ago

Math is experimental at its roots. If the result here wasn't usable in real life, scarcely anyone would develop that specific branch of probability theory. Instead they would think of adjusting the axioms and work out a useful probability theory. For example, most children check 1+2 experimentally before accepting the theory.

jonsen 7y ago
What’s the theory to accept for 1+2?
- theelous3 7y ago
  I think he means loosely that the theory here, is that they add up to three. Kids will grab objects and group and ungroup them while counting and so on, before outright accepting math is real.
- stan_rogers 7y ago
  That can be trivially inferred from 110-643 (Vol. 2, p. 86) in Whitehead & Russell's Principia Mathematica.
- ookdatnog 7y ago
  Not the GP, but this is my take on their comment. Children learn counting before they learn an algorithm for addition. The "theory" to accept here is that counting a set of size x, then continuing to count, starting from x, a set of size y, yields the same result as the addition algorithm for x+y that they learn.

theelous3 7y ago

I consider myself borderline math illiterate. I understand the monty hall problem perfectly well through means other than hard math proofs. So, clearly, understanding the proof isn't required. It is a great deal more work than many other methods of understanding the problem, so why prescribe it as the best way? You might be comfortable with it, but not everyone has the time nor inclination to become mathy enough to live life through your lens.

lioeters 7y ago

Here's a glimpse that may change your mind about mathematics as an experimental science: Mathematics: An Experimental Science - https://www.math.upenn.edu/~wilf/website/Mathematics_AnExperimentalScience.pdf https://www.math.upenn.edu/~wilf/website/Mathematics_AnExper... (PDF) > A computer is used by a pure mathematician in much the same way that a telescope is used by a theoretical astronomer. It shows us "what’s out there." > From such explorations there can grow understanding, and conjectures, and roads to proofs, and phenomena that would not have been imaginable in the pre-computer era. This role of computation within pure mathematics seems destined only to expand over the near future and to be imbued into our students along with Euclid’s axioms and other staples of mathematical education. Also: Turtle Geometry: The Computer as a Medium for Exploring Mathematics - https://mitpress.mit.edu/books/turtle-geometry https://mitpress.mit.edu/books/turtle-geometry

andrepd 7y ago
>Mathematics: An Experimental Science That was an amazing read. It certainly made me rethink my position. Thanks!

daveFNbuck 7y ago

This roundabout, hand-wavy, vague way to deal with things is how mathematicians solve problems. You have to have an intuitive understanding of what's going on before you can formalize the solution into a proof. I majored in math in undergrad, and one of the required courses was about communicating mathematical ideas. One of my bigger projects in that course was to explain the Monty Hall problem so it could be understood by the general public, and I got a good grade by putting together a lesson plan that included this type of simulation.