Symbols are used because equations like that would be crazy long and hard to keep track of if every symbol were a fully-formed word or phrase. It's an unfortunate side effect that those unfamiliar with mathematical notation are somewhat left in the dark.

The real problem here is the difficulty of looking up the meaning of a symbol you don't know. The notation is great once you know it, but it's a pain to learn if you're doing so completely out of context. Maybe you don't know that the sigmas there represent summation. Your idea of just clicking the sigma and seeing an explanation is a pretty great one that I'd like to see implemented.

If there was an explanation of what it does in natural language (which is often done on many wikpedia articles) then it would be fine. Even just the ability to copy and paste the symbols into google would be great, but it's just an image, and a non-math person won't know what they are called.

I still think that raw math is unnecessarily cryptic and unhelpful, even when I understand the symbols fine. It's like reading source code without comments or named variables or indentation of any kind. Actually that's pretty much exactly what it is.

> Even just the ability to copy and paste the symbols into google would be great, but it's just an image, and a non-math person won't know what they are called.

Okay, so in the case of a wikipedia article, if you're really ignorant of the symbology used and don't know where to start, just click 'edit' and look at the latex code. If that's not helpful, like the case where the latex for the P(.) function is simply 'P', read the contextual information.

"The posterior distribution can be defined by marginalizing over joint distribution, factorized into its independent prior distributions and then dividing by the partition function."... or whatever.

If the article doesn't have any contextual info, then you probably shouldn't rely on it if you're learning. Look somewhere else.

> It's like reading source code without comments or named variables or indentation of any kind

Math is an abstraction. It is more abstract that most code, that is why implementing math into code is something people make a living doing. How would you prefer that math equation you gave be presented? As the (currently) top comment states, those symbols are FULL of meaning. Understanding what that equation means is more than just knowing that "P stand for probability, and the funny angled thing is a sigma and that means sum." In fact, quite often an equation represents an idea that is simple enough to conceptualize, but extremely non-trivial to bring into more concrete terms. For example, that equation you posted looks like the kind of thing you'd see in a paper using Bayesian methods. In many cases to implement that equation would require Markov chain monte carlo sampling, maybe a gradient descent algorithm, a quadratic program solver, who knows. It's an infeasible way to present the ideas, at best.

Crazy long and difficult-to-track equations are why function abstraction was invented. If this were code, we would say to cut it into understandable chunks, label them as functions, and then compose them.

Writing it all as code would exclude nonprogrammers just as much as this excludes people not familiar with basic mathematical notation.

At least everybody should share some common mathematical instruction from school. The same certainly cannot be said of programming.

As somebody who can read both code and math, though, I'd greatly, greatly prefer to see math in math notation, not code. Code would be so much more verbose that it would take easily twice as long to digest the information. You'd also completely lose all the incredibly powerful visual reasoning that comes along with modern mathematical notation.

This is abstracted and very understandable. The picture is the definition of a function, which in turn invokes the definition of other functions. The P's are abstractions for conditional probability, the sums are loops etc. If this were code, it would be no more than a few lines and very understandable. Unlike code however, for all this there is very thorough documentation for mathematics in millions of pages by thousands of people in many different languages at all levels. The documentation is textbooks, and they're pretty good.

But those functions might still be cryptic. And the rabbit hole may go deeper than the amount of text one can be reasonably allocated to a discussion.

Consider how much work Bourbaki had to write before he/they got to real analysis.

I thought most wikipedia articles use a "where..." beneath every equation explaining the symbols. I could be wrong though

This is akin to stating that "public static void main(String[] args)" is complete nonsense when one didn't take the time to learn a little Java first.

The linked formula has been completely removed from its context

http://en.wikipedia.org/wiki/Averaged_one-dependence_estimat...

Below the formula in the page, you see everything defined and logically derived, and a brief overview of what it's supposed to do. You are correct in that Wikipedia may not be the best place to learn from scratch if you are a novice, but its purpose is more to be a concise reference than a thorough introduction.

If you need more guidance, there are thousands of textbooks at all levels of understanding, and if you opened a single one of them, you would immediately see that the "P" is standard notation for (conditional) probability.

Wikipedia needs this; http://www.mathjax.org/