There's a lot of talk in these comments that assumes that certain people are just ‘built different’ and can grok complicated new concepts that are unrelated to anything they know by virtue either of being smart or of being nerds with no life.

I think there are several different types of ‘background’ required to read something, none of which are innate or unattainable without a particular kind of education (e.g. a university degree). This confuses discussions about whether something is ‘accessible’ because the person complaining that it is inaccessible might be complaining of a gap between their current state and the state assumed by the book, in any of those three categories.

1) Factual background.

What facts do you need to know, what theories do you need to understand, in order to be able to follow what the author is saying? If the author is trying to teach you classical mechanics but you don't know about addition, you're not going to get very far until you go and learn to add and come back.

A source can address this (reducing the amount of background required) by providing more background in the material itself. But it obviously doesn't scale that well if every explanation of classical mechanics comes with an explanation of addition (and counting, etc.), and the background you do get, if it isn't the primary goal of the material, is often rushed and not as well-written as a dedicated source. So instead (or as well as providing a quick refresher for people who already have the background but might have forgotten it) authors will often refer to other materials that provide better explanations.

Inaccessibility arguments from this perspective look like ‘I don't know what this word means’ or ‘I don't know how to read this notation’.

2) Motivational background.

What applications do you need to know about in order to find out worthwhile to learn a topic? If you don't know about bicycles, levers, etc., learning about classical mechanics can seem like an abstract waste of time.

As a function of the complexity of a topic, it necessarily takes a certain amount of time before the author's thoughts are complete enough to relate to something that the reader will find compelling, though a good author will try to minimize it. People vary here in their trust of an author, and there are certain external factors that can influence this as well: e.g. if the material is very well-regarded by other people the reader might be happier to spend time figuring out what it's trying to say, or if the reader has a background in a similar topic they might be able to imagine some motivations that will keep them going.

That's not to say that the reader should always have this: indeed, most materials are actually useless to most people. One of the pre-tasks of reading something is deciding whether it's something that is (potentially) even useful to read, and for most things your answer should be ‘no’.

Inaccessibility arguments from this perspective look like ‘I don't care about this’ or ‘this is abstract nonsense’. Note that text is never actually completely abstract: authors, like readers, are always motivated by practical concerns. But there might be a long chain of problems and solutions from a problem that the reader is aware of to the solution that the author is explaining — in fact, in pure maths, the applications of a theory aren't always even known — but there's good reason to believe that they exist.

3) Attention span.

Difficult concepts just take a long time to learn. This can be addressed somewhat in the text by providing longer explanations in which the concept is spelt out more elaborately, but then you risk alienating readers who've lost track of your point by the time you've got to the end of it — there's a balance to be struck, and the correct point on the continuum depends on your intended readership. Also, on the reader's end, this is to some extent a ‘muscle’ that needs to be trained and regularly exercised in order to not lose it.

All of these things lead to valid arguments of inaccessibility, but the failure isn't inherent in the writing: instead it indicates a mismatch between the writing and the reader. If the writing means to target a certain type of reader, that can make it badly written; but no writing can target every possible reader. If some writing seems inaccessible for you, if you're interested in it you can work on those three things to make it more accessible (which will involve some combination of staring at the target writing until it makes sense, and reading around related writings to get knowledge and practice reading about that kind of thing). Alternatively, you might be able to find other writings on the same topic with prerequisites that are a better match to you. For example, I've been trying to write a series of posts explaining CS concepts that I think are cool or useful, assuming the knowledge and motivation of an enterprise programmer, and drawing the chain of motivation/explanation as far back as necessary to get to concepts they're likely to know already. My writing on the lambda calculus is here:

https://twey.io/for-programmers/lambda-calculus/

Please excuse the sloppy writing, this is an attempt to get back into technical/explanatory writing after many years — but criticisms (with that particular intended audience in mind) are very welcome!