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.
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.