Prerequisite articles

[Larry Sanger]

All,

I was reading "least common multiple" and was struck by the fact that I had to remember my junior high school math (or was that elementary school math) and revive the meaning of "multiple" in my poor tired brain.  It seems to me it would be useful information to a person who actually needs the "least common multiple" article that there be a list of "Article prerequisites" at the top of the article.

It might look like this:

To understand this article, you should already have a good grasp of these concepts: multiple
And these will help as well: common denominator

In fact, I can imagine having such notices, perhaps in smaller type, at the top of longer sections, as well.  Or, if not at the top, then in a sidebar-type notice.

This would tend to clutter the page, however, which is something that bothers me.  The question is, would the extra clutter be worth it?

[Derek Harkness]

I think this is not required. Jargon and technical language should be explained in the article. The use of such a header would alow authors to use Jargon at will simply by puting up a disclamer at the start.

The target level for articles is for a University Educated person, but not someone who has a degree in that particular subject. So we can take it as read that the target audience has done high school maths but not university level maths.

I'm sorry Larry but I would actually rate the word 'Multiple' at elementarty school (primary school) mathematics. I think any 10 year old could tell you what the multiple of 10 and 2 is.

[Larry Sanger]

I think this is not required. Jargon and technical language should be explained in the article. The use of such a header would alow authors to use Jargon at will simply by puting up a disclamer at the start.

The target level for articles is for a University Educated person, but not someone who has a degree in that particular subject. So we can take it as read that the target audience has done high school maths but not university level maths.

I think you're missing my point.  Particularly as we get to the more advanced and derivative articles, it is of course impossible to explain everything that might be needed to understand an article.  There are some topics that are simply too advanced for some people.  But there are other topics that can be understood, but only after one gets some background first.  It could be useful to the reader to know that, if they can first understand X and Y, then they will be able to understand the current article.

I'm sorry Larry but I would actually rate the word 'Multiple' at elementarty school (primary school) mathematics. I think any 10 year old could tell you what the multiple of 10 and 2 is.

Derek, you're simply incorrect about this.  I have a Ph.D. in Philosophy and I'm not the slightest bit ashamed to admit that I forgot what it meant.  I'm sure that would also be true of many other university educated non-mathematicians.  Are we writing articles about topics like "least common multiple" for people who need such articles, or simply to catalog our understanding for people who don't need them?  That's the question we need to ask ourselves.

[Pat_Palmer]

I try to write every article so that such a warning would not be necessary.  To do so, I sometimes briefly define terms in parentheses as soon as they are introduced, like this:

"The kernel gets assistance from several special programs called drivers (a driver program is an expert on some piece of hardware within the computer, such as the disk drive or the mouse)."

And of course, there will be links to 'kernel' and 'driver' and so forth.

This is a technique I have learned while teaching, having suffered through many (what I consider to be semi-obnoxious) lectures in which the speaker did not bother to do this simple courtesy.

[Jitse Niesen]

I was reading "least common multiple" and was struck by the fact that I had to remember my junior high school math (or was that elementary school math) and revive the meaning of "multiple" in my poor tired brain.  It seems to me it would be useful information to a person who actually needs the "least common multiple" article that there be a list of "Article prerequisites" at the top of the article.

It might look like this:

To understand this article, you should already have a good grasp of these concepts: multiple
And these will help as well: common denominator

I think the relation between an article and its prerequisites is too complicated to summarize the prerequisites in a box as you propose. To take your example, to understand the first sentence of "least common multiple" (the definition in its most basic form), you need to know multiplication of two positive whole numbers and the ordering (less than/greater than) of positive whole numbers. If the word "multiple" hinders the understanding of some readers, that should be explained; it's just a word with a simple definition, not a difficult concept that should be listed as a prerequisite. To understand the second sentence, you need to know polynomials, though to understand it properly, you also need to have an idea of the "more abstract objects" mentioned. And so on ... It seems to me that careful writing, especially at the start, and the use of links are much better tools to achieve what you want.

This was also the conclusion when this was discussed on Wikipedia. Unfortunately, the only link I can find at the moment is http://en.wikipedia.org/wiki/Wikipedia_talk:WikiProject_Mathematics/Archive16#Prerequisites.

[Derek Harkness]

I have seen very complex math problems described in very simple ways that anyone could understand. For example, I once watched a Horizon TV program on the subject of "A Proof for Fermat's Last Theorem". I'm sure any of the math experts here will agree with me that such a topic is far form elementary. However, it was possible for the TV program's producers to make the subject understandable to me, and to do so within just a 50 minute show.

There is no excuse for not explaining things in the article if they are required for understanding the subject. Even extremely advanced maths can be explained simply and an introduction to the subject given.

Returning to multiple - I think it's bad practice to use a word to describe its self. This produces a catch 22 situation. The article should start by describing what a least common multiple is without using the words 'common' or 'multiple'. There are plenty alternative words that would describe the topic.

[Greg Woodhouse]

I have seen very complex math problems described in very simple ways that anyone could understand. For example, I once watched a Horizon TV program on the subject of "A Proof for Fermat's Last Theorem". I'm sure any of the math experts here will agree with me that such a topic is far form elementary. However, it was possible for the TV program's producers to make the subject understandable to me, and to do so within just a 50 minute show.

There is no excuse for not explaining things in the article if they are required for understanding the subject. Even extremely advanced maths can be explained simply and an introduction to the subject given.

I almost agree. There's a fantastic book entitled "Fearless Symmetry" that goes much further in explaining the proof of Fermat's Last Theorem than I ever would have expected from a book intended for non-mathematicians (we encounter varieties, the absolute Galois group, even Artin reciprocity), but there is no escaping ythe fact that much is omitted or only vaguely sketched. Make no mistake: I think this is an excellent book, and I highly recommend it, but one can only hope that the reader will be inspired to dig more deeply into number theory and get a better understanding of the techniques discussed in this book. I've argued time and again that much more of mathematics can be made accessible to non-mathematicians and, just as importantly, that it should be.

But I'm not prepared to take the step of saying "There is no excuse for not explaining things in the article...." For one thing, "Fearless Symmetry" isn't an article, it's a book. It's not a long book, but it is a book, and not an easy read at that. It is simply not realistic to expect every bit of background material to be covered in a single article. That's why I've argued for integrative articles as well as articles on specific topics. It is also far from obvious that we do not want technical articles. My working assumption has been that we do, but we also want to provide the reader with a path by which he or she can come to understand them. What I keep hearing is "Yes, we want articles about black holes, but not gravitational curvature". Maybe one article can talk about weights on a rubber sheet with marbles "rolling downhill" towards the larger weight. That is, after all, what you might expect from a reasonable television documentary - but is it enough? In my view, stopping with an imperfect analogy such as this sells the reader short.

[Robert_W_King]

What if at the bottom of the article, there was a table or some kind of dialogue that represented the following:

"This article implies understanding of the following fundamentals: "
- one
- two
- echos

"This article expands upon the following concepts: "
- numbers
- sounds

"For more information on (this very specific concept that's difficult to understand), see: "
- abstract things

[Greg Woodhouse]

What if at the bottom of the article, there was a table or some kind of dialogue that represented the following:

"This article implies understanding of the following fundamentals: "
- one
- two
- echos

"This article expands upon the following concepts: "
- numbers
- sounds

"For more information on (this very specific concept that's difficult to understand), see: "
- abstract things

What I'd really like to see is something like a reading path, together with separate "in depth" articles and non-technical overviews for the general reader who is interested in a topic but doesn't want to have to work through all the technical details.

[Catherine Woodgold]

"Reading path" -- good idea!  How about using navigational templates?  These could be ignored by people who just want to use the articles the way they're being used now.  But they would join the articles together like chapters in a book.  That way, if someone feels like doing a lot of reading, when they finish one article they can click on the next article in the template.  I'm imagining a template that would have a name like "advanced number theory" or "basic probability theory" etc. and a bunch of named links which are names of articles, arranged in an order such that we try to have the more basic concepts explained in the earlier articles.  Possibly also links marked "next" and "previous" , though those would be redundant as the page the person is on would look like a black link and they would just click on the page after it.  These templates might also happen to be of some use to people who are just trying to quickly look something up and have gotten to a page that's related to but not exactly what they want, but I'm imagining aiming them mainly at people who have some time on their hands and are thinking "I really enjoyed that article and would like to read other equally interesting articles" -- they just want to turn the page and be entertained or educated, they don't know what topic to look for.

I wouldn't want to have a notice at the beginning of the article telling people what they should know before reading it, because it would take up critical time and space;  but a navigational template at the righthand side or bottom of the article could be useful without getting in the way.

One problem with telling people what they need as prerequisites is that it won't be he same for everyone.  For one thing, things may not be taught in the same order in different countries.  People learned things and forgot different things.  So you could say you need to know A, B, and C, and the person might know those things but there might be an even more basic concept D that you didn't think you had to mention but that the person doesn't know (or doesn't know by that name).

I just think it's better to provide definitions where they're needed.  Stuff in parentheses or even right out in the open, in footnotes and in links can provide information for people who need to refresh their memories.  One more benefit:  What about people with really short memories?  E.g. when people are tired.  Reading 3 prerequisite articles might not work because by the time they read the main article they may have forgotten which word referred to which concept they'd just read about, but if they can get the definitions by following links or footnotes or whatever as they read along, they have the information right when they need it.

One problem:  I'm not sure if it's easy to attach a link to a math symbol.  But I guess you can put a footnote with a link or put (see [[link]]) after it.

[Larry Sanger]

What if at the bottom of the article, there was a table or some kind of dialogue that represented the following:

"This article implies understanding of the following fundamentals: "
- one
- two
- echos

"This article expands upon the following concepts: "
- numbers
- sounds

"For more information on (this very specific concept that's difficult to understand), see: "
- abstract things

I like this quite a bit--rather more than templates and a "reading path" or a "table of contents" (so to speak) for a subject, not that those aren't good ideas too.  It is probably a good way to organize the overall "see also" category scheme that I think we need to start up sometime soon.  This is something I hope to return to sometime soon, anyway.