51–60 of 106 posts
Unlike teaching programming, the problem I see in teaching math is that the syntax is slipped into the lessons without making a conscious effort teaching it.
Earlier quoted context omitted.
I couldn't possibly disagree more with your post. :) The language of math requires exact precision which makes extracting what the series of abstract symbols "mean" incredibly difficult. Trying to learn new mathematical concepts from wikipedia is damn near impossible. Here are two examples. b-spline: http://en.wikipedia.org/wiki/B-spline spherical harmonics: http://en.wikipedia.org/wiki/Spherical_harmonics Trying to…
For the sake of an argument, let's assume you are right, and the language of math sucks. Then, we have had centuries of mathematicians inventing ever changing notations and ending up with a notation that sucks. If so, those mathematicians must be extremely stupid. Surely persons of average intelligence must be able to come up with better notations, and find proofs for stuff that is out of reach of those morons? I do…
The notation of mathematics is centuries old. It's very hard to take notation away from the set that must be learned, but easy to invent more.
Eventually old constructs can fall out of favor, but that is a long and slow process.
Earlier quoted context omitted.
I couldn't possibly disagree more with your post. :) The language of math requires exact precision which makes extracting what the series of abstract symbols "mean" incredibly difficult. Trying to learn new mathematical concepts from wikipedia is damn near impossible. Here are two examples. b-spline: http://en.wikipedia.org/wiki/B-spline spherical harmonics: http://en.wikipedia.org/wiki/Spherical_harmonics Trying to…
For the sake of an argument, let's assume you are right, and the language of math sucks. Then, we have had centuries of mathematicians inventing ever changing notations and ending up with a notation that sucks. If so, those mathematicians must be extremely stupid. Surely persons of average intelligence must be able to come up with better notations, and find proofs for stuff that is out of reach of those morons? I do…
Not necessarily. Before modern times mathematicians worked alone and didn't need a notation that others would understand. Newton, for example -- his calculus notation wasn't very good, and over time Liebniz' notation ended up being used instead (completely apart from the issue of who invented the calculus).
> Surely persons of average intelligence must be able to come up with better notations, and find proofs for stuff that is out of reach of those morons?
This doesn't support the thesis that mathematicians are stupid. Most mathematicians only care that they understand their own notation, and give less weight to its comprehensibility to others. And some mathematicians in the distant past deliberately used obscure notation to conceal their work from others.
I would look to educators to come up with a more comprehensible system of notation, not necessarily those at the frontiers of mathematics.
I could not disagree more with that post. Mathematical notation is to Python what English would be to Assembly Language: it is a high-level notation, designed see the forest rather than getting lost in the trees. Take Maxwell's equations for example. After learning vector calculus and becoming familiar with its notation, you notice how much meaning you can extract at a quick glance from the four Maxwell's equations e…
I couldn't possibly disagree more with your post. :) The language of math requires exact precision which makes extracting what the series of abstract symbols "mean" incredibly difficult. Trying to learn new mathematical concepts from wikipedia is damn near impossible. Here are two examples. b-spline: http://en.wikipedia.org/wiki/B-spline spherical harmonics: http://en.wikipedia.org/wiki/Spherical_harmonics Trying to…
Would you be able to calculate the probability of finding an electron within a certain distance from your pretty pictures? I would be able to do so fairly easily from those equations. What about computing special functions in higher dimensionalal systems? The generalization from equations is straightforward; our minds can not comprehend higher dimensions in pictures.
As you wrote, yes it requires a quite a lot of focus ... but that's the price one has to pay in order to be able to build models that describe the world and allow us to make predictions. That is not to say that adding pictures or explanatory sentences is unnecessary; but you can't replace the equations by only a combination of words and pictures and be able to make predictions (such as, for example, in quantum electrodynamics where predictions and experimental results agree to better than one part in 10^10 ... equivalent to something like 1 mm precision in measure the distance from coast to coast of the US) in a better way.
Scientific theories are those that are testable. You can't pretend to understand a scientific theory if you can't use your knowledge of it to make quantitative predictions. You need math for that.
The real reason math is hard to read is that it's the distillation of a thousand winding ideas and failed attempts that took hundreds of hours of thinking and hundreds of pages of scribbling, all condensed into the most concise possible three pages of unmotivated line-by-line proof with no context or explanation. In other words, math is a language for formalizing intuition which, when finally written, unfortunately r…
I think this is the main reason everything is so abbreviated, it comes from the era when doing lots of manual calculations by hand called for efficiency in notation over clarity.
No, that's not why math is painful to read. The reason math is painful to read is because it's either obvious, in which case it's not painful to read, or because it contains new ideas that you need to work hard on before you can grok them. There is no short cut. You can't write math like a novel, you can't read math like a novel. There are ideas that are deep and difficult, and unless you actually spend time working…
The same could be said for code that uses only single letter variables and functions.
It'd be a lot easier with readable variable names.
Frankly, there are 2 kinds of programmers. People who do this: val result = directProduct(cyclicGroupOfDegree3, finiteAbelianGroupOfDegree7) and the second kind, people like me, who do this: // Compute the direct product of 2 cyclic groups val z = dP( cg1, cg2 ) You can easily guess that the 2nd kind are math majors. If my math professor started writing everything out in plain English like the first example, he'd nev…