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OK, given yodel's answer, I'll go to bat for mathematical notation. - It doesn't change very much, so you can just pick it up and understand it using what you

OK, given yodel's answer, I'll go to bat for mathematical notation. - It doesn't change very much, so you can just pick it up and understand it using what you learned at school. Cf e.g. looking at modern Javascript and wondering wtf all those JQuery selectors are. - Relatedly, there's not a lot you need to know. I'm not a mathematician, but I can understand most mathematical theorems I've needed to look up with just basic high school algebra, derivatives, integrals, sums, products, trig, and matrix / suffix notation. Find me a piece of code that does anything interesting which has less than six calls to library functions. - It's extremely concise, so you don't have to scroll through pages of code to get to the point - each line communicates a lot. This is really important, because it stops you getting lost or distracted in the middle of figuring things out. - It's declarative, so it tells you what you're actually doing, rather than just how to do it. This is like the difference between saying "get me an orange", and giving full instructions for finding a shop that has oranges, navigating to it, etc. I know declarative programming exists (and it has these advantages) but I've never seen it used outside CS courses. I honestly prefer mathematical notation; it has more upfront work to get good at it, but is much easier to use once you clear that hurdle. I haven't found ambiguity to be a big issue (especially compared to code; how often have you used a function which does something subtly different to what you expected?) although this may be due to the fact that I'm not looking at super advanced stuff (a couple of papers on deep learning, skew normal distributions, the rocket equation, that sort of thing). Especially with the deep learning papers, I found it infuriating how long they spent using confusing diagrams and wordy explanations where a couple of lines of algebra would have made their point instantly. The true answer is almost certainly YMMV.

TeMPOraL 6y ago
> It's declarative, so it tells you what you're actually doing, rather than just how to do it. This is like the difference between saying "get me an orange", and giving full instructions for finding a shop that has oranges, navigating to it, etc. I know declarative programming exists (and it has these advantages) but I've never seen it used outside CS courses. I find this to be a problem quite often. Maybe my brain is wired differently, but I can't keep declarative definitions in my head and apply them unless I know of an imperative strategy to make them work. I've first noticed this when, in high school, I was struggling to understand the epsilon–delta definition of a limit. The one that goes like this: https://wikimedia.org/api/rest_v1/media/math/render/svg/619debbeb78a82c1c368a3e53470dbc167a088bd https://wikimedia.org/api/rest_v1/media/math/render/svg/619d.... Only after many hours of classes, followed by many hours of staring at the formula, all over the course of weeks, I finally understood what it means. The one missing puzzle piece that no one explained to me was that, when you see "\forall _{sth > 0}", you should read it as "in particular, for a sth arbitrarily close to 0". Declarative notation is fine if you comprehend all consequences of that declaration. In cases where you don't, it would be nice to have it spelled out which consequences are relevant.
- a-nikolaev 6y ago
  Yeah it depends on the particular theory. Say, if you want to implement some physics model as a computer simulation. Often, physics is presented as a set of interconnected of equations (some are general, some are based on assumptions, representing special cases). Unfortunately, most of the time these equations are not built "bottom-up", so to speak. They do describe various aspects of physical reality, but often don't allow a nice computational/operational interpretation of it right away. So converting this knowledge into a computational model can be non-trivial.
oalae5niMiel7qu 6y ago
> It's declarative, so it tells you what you're actually doing, rather than just how to do it. This is like the difference between saying "get me an orange", and giving full instructions for finding a shop that has oranges, navigating to it, etc. I know declarative programming exists (and it has these advantages) but I've never seen it used outside CS courses. Math notation is unlike declarative programming language in that it's possible to describe an something while telling the reader absolutely nothing about how to compute the object being communicated.

TeMPOraL 6y ago

> It's declarative, so it tells you what you're actually doing, rather than just how to do it. This is like the difference between saying "get me an orange", and giving full instructions for finding a shop that has oranges, navigating to it, etc. I know declarative programming exists (and it has these advantages) but I've never seen it used outside CS courses. I find this to be a problem quite often. Maybe my brain is wired differently, but I can't keep declarative definitions in my head and apply them unless I know of an imperative strategy to make them work. I've first noticed this when, in high school, I was struggling to understand the epsilon–delta definition of a limit. The one that goes like this: https://wikimedia.org/api/rest_v1/media/math/render/svg/619debbeb78a82c1c368a3e53470dbc167a088bd https://wikimedia.org/api/rest_v1/media/math/render/svg/619d.... Only after many hours of classes, followed by many hours of staring at the formula, all over the course of weeks, I finally understood what it means. The one missing puzzle piece that no one explained to me was that, when you see "\forall _{sth > 0}", you should read it as "in particular, for a sth arbitrarily close to 0". Declarative notation is fine if you comprehend all consequences of that declaration. In cases where you don't, it would be nice to have it spelled out which consequences are relevant.

a-nikolaev 6y ago
Yeah it depends on the particular theory. Say, if you want to implement some physics model as a computer simulation. Often, physics is presented as a set of interconnected of equations (some are general, some are based on assumptions, representing special cases). Unfortunately, most of the time these equations are not built "bottom-up", so to speak. They do describe various aspects of physical reality, but often don't allow a nice computational/operational interpretation of it right away. So converting this knowledge into a computational model can be non-trivial.

oalae5niMiel7qu 6y ago