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Comment by forrestthewoods | Hacker News Reader

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 figure out what those walls of symbols mean requires quite a lot of focus. Dig up source code for either and it's orders of magnitude easier to understand. The images for spherical harmonics conveys more meaning and understanding in a fraction of a second than spending 3 hours with a piece of paper and the equations would.

The language of math sucks.

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Wikipedia is not designed to be a pedagogical repository; arguing that the mathematical language sucks because a terse summary in wikipedia is not enough to understand the material is missing the point.

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.

> Wikipedia is not designed to be a pedagogical repository; arguing that the mathematical language sucks because a terse summary in wikipedia is not enough to understand the material is missing the point.

Nicely worded. I think the real issue is that many people want mathematics to be easy to read and understand. Unfortunately, much of mathematics is not easy to read nor is it easy to understand regardless of how it is written. Mathematics, like many other things, often requires a lot of intellectual scaffolding to be built from the bottom up. There is no shortcut to the top.

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 rule out that notation can be improved. After all, it took millennia to move from Greek and Roman arithmetic systems to Arabic notation. There is no reason to assume we have reached a global optimum. However, I also find it unlikely that mathematical notations truly are stupid.

Your argument is like someone complaining about the difficulty of discriminating between "37" and "73" because it is way easier to see the difference between 37 and 73 scratches in a piece of wood.

It's not that mathematicians are stupid, they just that they have backwards compatibility problems.

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.

This is hardly true. Mathematical notation changes all the time-in fact, inconsistency is a significant problem, because Mathematicians love to experiment with notation, definitions, etc.

Seriously, just look at a Mathematical logic book from 50 years ago vs. one today. You won't even recognize half the words, let alone the symbols.

> If so, those mathematicians must be extremely stupid.

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.

Liebniz was a mathematician.

Newton was a member of the Royal Academy. They communicated with each other.

Apart from the fact that you mean the "royal society", yes, both true. They also came into conflict about priority with respect to the calculus. And surprisingly enough, that debate rages on.

I agree, it's a fun exercise to try and come up with a "better" form of notation that works in the general case. I think that most people will find that modern mathematics notation is really good stuff.

Both of your examples are new to me as well, however I can make sense of topics discussed. Just to use your example, the first equation for B-splines defines it as a function from a tuple of ordered reals to real vector of dimension d. The real difficulty with math is not so much the symbols as they give a precise but very legalistic way of defining things but the underlying concept or intuition that it represents, the deep semantics if you will. The best analogy is law. The way a lawyer or judge defines things will be different from the way a lay person would due to the difference in precision. The descriptions will be technically correct but will make you second guess on what it really means. I wouldn't go so far as to say it sucks but math is definitely scientific legalese.

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