[dwc]

For an analogy, before there was anything like modern math notation people would write out the problem and solution in plain language. On one hand, that made it very accessible as long as you knew a few terms like "sum". On the other hand, the reader has to build a relatively small mental model out of a lot of words.

Is it better to concentrate hard on a system of equations taking 1/4 of a page (with lots of whitespace) until you grok it, or read five pages of prose at fairly normal speed and try to build a mental model of it? Which better confers the ability to quickly come to the realization of something like "that's a parabola" or "the minimum of that function is obviously seven" or whatever?

Analogies are only so useful, but I think there are enough parallels there to shed some light.

[Jtsummers]

Right, but your verbose example reduces ease of use.

It's two axes. J is not verbose, but is impenetrable (certainly to a novice, others more familiar see a lot of benefits to it). Ada is fairly verbose, but is pretty easy to understand. A page of Ada code is probably a handful of lines, mostly to aid in clarity, of J code. Though the Ada code has type safety that the J code lacks. Assembly, as someone else referenced, is very verbose, but hard to understand once you get beyond a certain scale.