Definition talk:Primitive (Calculus)

I feel like this page should be called "antiderivative". I had never heard the term "primitive" before. I'm pretty sure "antiderivative" is more common. Jameshfisher (talk) 16:23, 25 May 2021 (UTC)

Well you've heard it now.

There are hundreds of pages on $\mathsf{Pr} \infty \mathsf{fWiki}$ with "Primitive" in the name in this precise context. If you want to go through and rename them all, and change all the links as well, then you may well be on your own. --prime mover (talk) 19:32, 25 May 2021 (UTC)

Yeah, that task sounds intimidating. I wouldn't want to do it. Perhaps instead we could move the "Also known as" section to the very top of the page, in the same manner as Wikipedia, which begins: "In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function $F$ whose derivative is equal to the original function $f$."

The advantage of Wikipedia's approach is that if I recognize any of the names, I can stop there. With the current layout, what happened was: I read through the definitions of "primitive", which took probably at least a minute, then thought "hey, that sounds familiar", and then Googled "primitive vs antiderivative", without even seeing the "Also known as" section below. Jameshfisher (talk) 08:29, 26 May 2021 (UTC)

a) The first thing you see on any page is the thing that the page is about. This is how we roll. While Wikipedia may have some good points, one of the irritations is that you often have to voyage half way down the page to actually get a proper definition of what a concept is about. There can be so much introductory material that it can be difficult to identify exactly where the explanation of a concept actually begins. Besides, The whole point of $\mathsf{Pr} \infty \mathsf{fWiki}$ is that it is a dictionary, and not an encyclopedia. A definition page contains that definition as the very first thing you see (with minor exceptions, notably an indication of disambiguation).

b) Pages on $\mathsf{Pr} \infty \mathsf{fWiki}$ have a rigorously standardised structure, in which "also known as" and "also defined as" appear immediately after the definition. Thus you don't need to go very far down the page to find it (the fact that we have multiple contexts for a primitive in the context of calculus adds to the inevitable complexity here, granted) -- and in fact the "Also known as" section is accessible right at the top in the page menu. It is a fact of life that sometimes the "also known as" section itself can become large and unwieldy, when there is a plethora of parallel traditions of development of a concept, and the evolution is still current. In such cases it takes considerable time, care and screen-space to explain the differences in terminology between these various approaches, and to fill the page up with that sort of visual clutter detracts majorly from the information which the page has been constructed to convey.

c) "Primitive" and "antiderivative" are well-known synonyms. While to a certain extent it is inefficient and often irritating to have multiple names for the same concept, it is part of a student's education to be aware of such differences in terminology. In this specific case, you are "one of today's ten thousand" (see here for reference: https://xkcd.com/1053/, apologies for the unashamedly America-centric nature of this comic.)

d) There is already a page for "antiderivative". It is a redirect to this page. So if you're looking for "antiderivative" you get here. You see it's a redirect (if you're sufficiently alert) so you are already in the mindset of having being warned that you are looking at something which may exist on $\mathsf{Pr} \infty \mathsf{fWiki}$ with a different name from the one you are personally used to. If you don't already know the name "antiderivative", then you won't know what you're looking for and you won't be the wiser, and it won't matter.

e) Primitive is a relatively neat and compact term of 9 letters and 3 syllables. Antiderivative is horribly unwieldy, at 14 letters and 6 syllables. Indefinite integral is even worse.

f) Suppose we did go down the route of renaming to "antiderivative" because a subset of our readership is more familiar with that term. Tomorrow we get someone logging in and saying, "I think we should rename this page to "primitive", as it is easier to spell and say, and besides, it's what I'm familiar with." This is a conflict which we have battled since the start. We even have an FAQ on the subject with regard to notation.

Please do stick around for joy, but bear in mind that the main thrust of the energy which we would like directed into this site is to expand what is already there, rather than continually change things around. While a lot of what I find myself doing nowadays is refactoring (you'd be surprised how challenging it is to meld multiple approaches by multiple sources and schools into a coherent synergistic whole that looks effortlessly seamless), once we have decided on an approach to a topic, we really, really prefer not to have to change it because someone thinks it would be better done another way.

We've had this happen: every so often someone joins the team who appears to be a big name on some other high-profile mathematics website, and who thinks it would be a good idea to embark on tasks to restructure vast swathes of our material to make it more like the site they grew up with -- and then leaves the jobs half done, with the result of leaving the site in an inconsistent state (broken links, misleading definitions, misdirected links and the like). In the end we often find we have to part company with these people, which is a shame, as we then lose vital sources of expertise. --prime mover (talk) 09:56, 26 May 2021 (UTC)