# Talk:Vector

## Purpose of article?[edit]

Note that I am nobody important and have no say on whether this or similar articles belong here, but I'm not the first to make this sort of complaint (see Talk:Logic#Formal_logic).

Although this is a new article, and surely it will eventually be part of some bigger picture, right now I don't see the "why" in having this article. Maybe the term "vectors" doesn't have any outlandish pseudoscientific connotation/hijacking, but what can RW's article on vectors say that resources elsewhere (articles, textbooks, videos) don't?

Though there is probably stuff that other sources *do* say that is worth expanding on here. I imagine the most important of these is why are vectors useful—what are the applications (I think the articles on logic tend to include these). It would probably also be good to make this somewhat more accessible to a casual reader, rather than merely a regurgitation really only useful for those who probably already know what vectors and vector spaces are. One idea for doing this might be to introduce some familiar examples from middle or high school, like the real numbers and even zero by itself, because both satisfy all of the specific requirements of vector spaces. Hopefully some more general sense of vectors as just an ordered bunch of numbers can then be alluded to. Someone has probably already thought of a better way of doing this than I have, though. Maybe have a look at the simple English Wikipedia article, though that might indeed be *too* simple for having restricted itself to geometric/"Euclidean"/"direction"-and-"magnitude" vectors, without ever hinting at vectors as being an abstract pair or *n*-tuple of numbers.

—Chrstphrchvz (talk) 00:05, 8 July 2019 (UTC)

@Chrstphrchvz
That simple English Wikipedia article describes a *Euclidean vector*. It does *not* describe all vectors. I could give a list of vectors that do *not* behave in a simple "direction and magnitude" manner. Zackarycw (talk) 19:04, 10 July 2019 (UTC)

## What's our vector, Victor?[edit]

I've read this article twice and still have no idea what a vector is, or why they need an article on RationalWiki. I thought we got rid of all the mathematics articles that we wrote to troll Conservapedia, so why have this? **Avida Dollars**^{her again} 08:34, 8 July 2019 (UTC)

- Eh, move it to Conservapedia space. —
**Oxyaena**08:34, 8 July 2019 (UTC)^{Harass}- It's not about Conservapedia, though. I mentioned CP to explain why we ever had these articles in the first place. How about Draftspace?
**Avida Dollars**^{her again}08:40, 8 July 2019 (UTC)- This used to be a draft up until 4 days ago. The author did specify:
*If it is not ready to meet rationalwiki standard please move it back to Draft*

- Although meeting "standard" might not be the issue identified here. Chrstphrchvz (talk) 02:23, 9 July 2019 (UTC)
- The intro is absolutely terrible. It's supposed to tell people what a vector is, but all it does is describe certain vectors in terms of other vectors. I still haven't the foggiest what they are, or why I should know what they are. or how they apply to our mission. Back to Draft it goes.
**Avida Dollars**^{her again}19:59, 9 July 2019 (UTC)

- The intro is absolutely terrible. It's supposed to tell people what a vector is, but all it does is describe certain vectors in terms of other vectors. I still haven't the foggiest what they are, or why I should know what they are. or how they apply to our mission. Back to Draft it goes.
- I thought I'd explain why I made this article. And, why there are math articles on ratwiki. A part of the mission statement is to fight to anti-science movement. Having math and science articles is a way to fight this through a demonstration of points regarding the subject. Secondly, as to why someone might not understand what a vector is, I'd recommend looking at vector space a bit more carefully. In short: it doesn't matter what a vector is, it matters that it is in a vector space. I notice other articles mention vectors, yet there's no internal articles formally describing what it is. In my opinion, this is actually a well written piece about vectors; it is the kind of definition one would learn in linear algebra and topology. Zackarycw (talk) 04:20, 10 July 2019 (UTC)
*(ctrl-v from my talk page) Thanks for the heads up regarding the page. I'll be sure to work on it more. You noted that it's poorly written. Which part? I'll take a look at it. Also, regarding the mission statement, I would argue that it helps against the anti-science movement by being a math and science article. There's a big collection of math articles on ratwiki for a reason. Thanks Zackarycw (talk) 04:14, 10 July 2019 (UTC)*

- This used to be a draft up until 4 days ago. The author did specify:

- It's not about Conservapedia, though. I mentioned CP to explain why we ever had these articles in the first place. How about Draftspace?
- The badly written part is the intro. It doesn't say what a vector
*is*. except in terms of other vectors. It's like an article about cheddar that compares it to brie and stilton, but doesn't explain that they're all cheeses. Someone who didn't know about cheese would be lost. And i'm lost with this vector article. The missionality bit? I don't see how mathematics articles defute pseudoscience, because on the whole pseudosciences don't reject it. A tiny number might go on about pi=3 because the bible said so, but where are the vector denialists? Also, it doesn't refute pseudoscience to simply reiterate the textbooks, because they've already rejected those. why would they listen to us? Let the article explain what vectors are in an understandable way, let it explain what claims are disproved by vectors, and then you've got an RW article. Because, for the eleventy-squillionth time, RW is not an encyclopedia.**Avida Dollars**^{her again}06:15, 10 July 2019 (UTC)- The abstract definition of a vector is that it's a member of a vector space. It's not recursive if you look at what a vector space is. I will re-word the next sentence so that it doesn't seem as recursive, thanks for the heads up. Also, this isn't a copy of a textbook as you claim. There exists a math portal on ratwiki for a reason. Zackarycw (talk) 08:12, 10 July 2019 (UTC)
- Sorry, I didn't mean to imply that you copied a textbook. I meant that merely doing what a textbook does won't work, as the pseudos reject them. We need to argue.
**Avida Dollars**^{her again}08:36, 10 July 2019 (UTC)- What about this? What if I refine the definition of a vector so that it's more clear and less recursive? Also, I see that we don't agree that it directly helps the mission statement. So, how about this? After I clean it up more, I'll even put it in the fun category then see if we can reach an agreement on whether it helps the mission statement. I'll let you know when I've further refined and let me know if it's still poorly written. I wouldn't want an article to be in the main space that is poorly written. Thanks. Zackarycw (talk) 10:00, 10 July 2019 (UTC)
- Funspace? No need for that, funspace has too many not-funny pages as it is. But yes, a non-recursive intro is essential. A non-mathematician (like me) should be able to answer the question "what is a vector?" by reading the article. after you can go into how vectors are used to refute false claims and bad logic.
**Avida Dollars**^{her again}15:21, 10 July 2019 (UTC)

- @Avida Dollars

- Sorry, I didn't mean to imply that you copied a textbook. I meant that merely doing what a textbook does won't work, as the pseudos reject them. We need to argue.

- The abstract definition of a vector is that it's a member of a vector space. It's not recursive if you look at what a vector space is. I will re-word the next sentence so that it doesn't seem as recursive, thanks for the heads up. Also, this isn't a copy of a textbook as you claim. There exists a math portal on ratwiki for a reason. Zackarycw (talk) 08:12, 10 July 2019 (UTC)

I've refined the first paragraph of the definition of a vector. Take a look: https://rationalwiki.org/wiki/Draft:Vector Also, please note that if one is intent on reading what a vector space is, I expect them to know basic things like a field, ring, group, et cetera. I tried to simplify the initial definition of a vector, that way "non-mathematicians" can find a simple answer to "what is a vector?" Let me know what you think of the refined initial definition. Zackarycw (talk) 18:08, 10 July 2019 (UTC)

- The problem is not that i'm intent on knowing what a vector space is, but that i'm presented with this new term "vector space" and left hanging. also, please stop pinging me, I'm already here.
**Avida Dollars**^{her again}19:11, 10 July 2019 (UTC)- Avida, the first sentence is simply the standard accepted definition of a vector. Not this "magnitude and direction" definition that ONLY works for Euclidean vectors, but, the abstract. If you don't want to leave feeling "hanging" read the next couple of sentences. I give a non-recursive more basic definition of the individual vector. Zackarycw (talk) 19:22, 10 July 2019 (UTC)

## Vector Space[edit]

Since I'm going for the modern definition of a vector (which *exactly* is: A vector is an element of a vector space), it might even be more handy to simply rename the entire article "Vector Space" then just have vector as a section. Modern mathematics doesn't care much about the individual vector, they focus on the vector space. This may be why my initial definition may seem recursive (even though it's not) to "non-mathematicians." Zackarycw (talk) 18:40, 10 July 2019 (UTC)

- And a vector space is... ?
**Avida Dollars**^{her again}18:53, 10 July 2019 (UTC)

- I've looked up vectors and quickly bashed this definition together (I still think your definition is too abstract): "In physics and mathematics, a
**vector**is an object which can be described has having both size and movement. Vector calculations are used to determine the relative motions and positions of different objects in a**vector spacce**" Is that roughly accurate?**Avida Dollars**^{her again}19:04, 10 July 2019 (UTC) - I raise substantial objection that "modern mathematics doesn't care much about the individual vector" given small things like ALMOST ALL OF PHYSICS' USAGE OF THE CONCEPT ikanreed
^{🐐Bleat at me}19:09, 10 July 2019 (UTC)

Understand that the simple "magnitude and direction" definition cannot describe most kinds of vectors. There are co-vectors, two forms, etc. It is true: modern mathematics cares MORE about the vector space than the individual vector. This is well documented. Zackarycw (talk) 19:12, 10 July 2019 (UTC)

Okay, I won't ping. Avida, how about this: what if I renamed and reformed the article to "Vector Space" rather than just "Vector?" Have "Vector" be a section of it? Zackarycw (talk) 19:16, 10 July 2019 (UTC)

- It's usually better to have a layman focused overall vision of the article, and dive into field specific technical jargon as appropriate to particular sections and addressing specific pseudoscience that misuses the those technical distinctions. We aren't an encyclopedia in that our mission isn't to give a comprehensive summary of a subject. You should think of this page as providing the grounding someone needs to see how this shit is meaningless gibberish.
- And "size with direction" does that better than "mathematical descriptor in an n-dimensional space with n cardinality". In fact the latter might even bolster the above gibberish site's credibility to a novice. ikanreed
^{🐐Bleat at me}19:45, 10 July 2019 (UTC)- Good thing I don't describe vectors as "mathematical descriptor in an n-dimensional space with n cardinality" then lol But really, just know that when one boils a vector down to "magnitude and direction" as the abstract definition, they instantly cut themselves off from related subjects such as tensors. To understand abstract tensors, one NEEDS to understand vector space, dual space, and quotient space for the tensor product between vector spaces . Zackarycw (talk) 19:53, 10 July 2019 (UTC)
- No, but you also definitely didn't give something
*useful*to someone who doesn't already know what a vector is, and I was trying to come up with a similar needlessly technical, uninformative definition. - re your edit to this post: Do you know how many times, in my life, even as someone who's really fucking enthusiastic about mathematics I've ever had to apply a tensor as a model for anything? It's arcane esoterica, my man. ikanreed
^{🐐Bleat at me}20:05, 10 July 2019 (UTC)

- No, but you also definitely didn't give something

- Good thing I don't describe vectors as "mathematical descriptor in an n-dimensional space with n cardinality" then lol But really, just know that when one boils a vector down to "magnitude and direction" as the abstract definition, they instantly cut themselves off from related subjects such as tensors. To understand abstract tensors, one NEEDS to understand vector space, dual space, and quotient space for the tensor product between vector spaces . Zackarycw (talk) 19:53, 10 July 2019 (UTC)

I've modelled many, many mathematical situations with tensors. I, too, am really ezcited about math. It's what I do. Zackarycw (talk) 21:00, 10 July 2019 (UTC)

- Yes, but again, it's arcane esoterica. ikanreed
^{🐐Bleat at me}21:01, 10 July 2019 (UTC)

## Purpose of Article[edit]

For a quick reminder,

Our purpose here at RationalWiki includes:

Analyzing and refuting pseudoscience and the anti-science movement; Documenting the full range of crank ideas; Explorations of authoritarianism and fundamentalism; Analysis and criticism of how these subjects are handled in the media.

Notice the "Analyzing and refuting pseudoscience and the anti-science movement" part. Refuting the anti-science movement may include making articles related to math and science. The math portal here on RW is *filled* with abstract mathematical articles. While of course people can use mathematics to make pseudoscience arguments, people can do that with general logic as well. There is a reason why there is a dedicated space to math articles on RW. Also, I notice many articles mention vectors and thought this would be a nice addition to the math category on RW. Zackarycw (talk) 18:46, 10 July 2019 (UTC)

- While it is true that we do allow articles that are not strictly missional
*if*they support other pages that are missional, for example Bayesian is not strictly missional but there are quite a few missional pages that link to it. Offhand, I can't think of a single page that would benefit from linking to this page, so I think you need to make a better case for keeping it. Bongolian (talk) 22:47, 10 July 2019 (UTC)- I suppose the first thing I would say is that it is my belief that this
*does*help the mission statement. However, let's assume it doesn't directly. There are science and math articles on RW that do mention these topics. - Articles that mention vectors:

- I suppose the first thing I would say is that it is my belief that this

- Articles that mention vector space:

## Euclidean Vector[edit]

There seem to be many fans of the "direction and magnitude" definition of a vector. Note that this does not describe abstract vectors. There are many kinds of vectors that *can not* be described this way. However, I realize the application of these vectors in elementary physics problems (also note abstract vectors use in abstract physics to find tensors to help things like Einstein's general relativity . It's not like the abstract definition of a vector is just mathematical gibberish.). I'm going to be gathering references and adding a section on the more simple kind of vector. Furthermore, I might add some examples and demonstrations with things like GNU Plot to both the abstract definition and upcoming Euclidean vector section to help with simplicity. Thanks all for the suggestions Zackarycw (talk) 05:46, 11 July 2019 (UTC)

- But are abstract vectors relevant to RW's mission? Show me how an abstract vector has been used in apseudoscientific claim, or could be used to refute one. I'm sure you like them and want to write about them (possibly more than boring old mundane euclidean vectors) but how are they relevant to RW?
**Avida Dollars**^{her again}06:06, 11 July 2019 (UTC)- I mainly address this in the Purpose of Article section. I believe that this helps refute the anti-science movement by demonstrating points in math and science. Even if we assume it doesn't, I see articles on RW that may benefit from a more abstract vector. Thanks for the question, I'm glad to clarify. Zackarycw (talk) 06:40, 11 July 2019 (UTC)
- I love being blunt. We don't benefit from this version at all. ikanreed
^{🐐Bleat at me}15:01, 11 July 2019 (UTC)

- I love being blunt. We don't benefit from this version at all. ikanreed

- I mainly address this in the Purpose of Article section. I believe that this helps refute the anti-science movement by demonstrating points in math and science. Even if we assume it doesn't, I see articles on RW that may benefit from a more abstract vector. Thanks for the question, I'm glad to clarify. Zackarycw (talk) 06:40, 11 July 2019 (UTC)

## Tautology club[edit]

Welcome to Tautology Club, the first rule of Tautology Club is the first rule of Tautology Club. — **Oxyaena** * ^{Harass}* 07:01, 11 July 2019 (UTC)

- Oxyaena, would you like a position in the Department of Redundancy Department? Bongolian (talk) 07:05, 11 July 2019 (UTC)

## Without a clearer purpose, why does this page exist?[edit]

I do not think the article, as it currently is written can even partially serve RW's mission and we should either stop humoring zack and fix it, or just delete the page. ikanreed ^{🐐Bleat at me} 20:49, 11 July 2019 (UTC)

- In the Purpose of Article section, I explain how it is valid to have this article. Other articles mention these topics. Bongolian agreed. The only one requesting a deletion of the page is you. I'd hope you read and give the article a shot. Zackarycw (talk) 20:51, 11 July 2019 (UTC)
- You do, but you're flat out wrong, and the page is getting worse and worse as you try to get deeper into technical minutia.
- Having explanations of jargon is good. Helpful. Missional.
- Having explanations of jargon that consist entirely of higher level jargon is bad. Useless. Unmissional. ikanreed
^{🐐Bleat at me}20:54, 11 July 2019 (UTC)

- Regarding the "higher level jargon," more abstract vectors may help articles like spacetime. Zackarycw (talk) 20:57, 11 July 2019 (UTC)
- I'm very dubious of that. Treating time as a 4th dimension in a directional vector is... easy? ikanreed
^{🐐Bleat at me}21:01, 11 July 2019 (UTC)

- I'm very dubious of that. Treating time as a 4th dimension in a directional vector is... easy? ikanreed
- That's a good point, but a more accurate telling of spacetime is done through vector and dual vector spaces through tensor products. Ricci curvature, metric tensor, stress energy tensor, et cetera are good descriptors of spacetime that are able to be made from definitions of vectors in this article (the abstract definition, not euclidean ones) Zackarycw (talk) 21:05, 11 July 2019 (UTC)

- You do, but you're flat out wrong, and the page is getting worse and worse as you try to get deeper into technical minutia.

This article: WTF did I just read? --It's-a me, LeftyGreenMario! 21:15, 11 July 2019 (UTC)

- Read rest of talk page. This article focused on abstract vectors
*first*then Euclidean vectors (muh magnitude and direciton). Zackarycw (talk) 21:16, 11 July 2019 (UTC)- Sure, that definitely cleared everything up. I speak as an absolute layperson. This is all boring gibberish that's crying for contextualization (like real-life examples). --It's-a me, LeftyGreenMario! 21:17, 11 July 2019 (UTC)
- Okay, the Euclidean vector section is a more basic definition of a certain kind of vector. The first definition of a vector is meant to help pages like Spacetime as concepts from that require a more abstract definition. The classic "magnitude and direction" definition of a vector is found there. That's what I meant, sorry if I didn't clarify. Zackarycw (talk) 21:23, 11 July 2019 (UTC)

- Okay, sure. I can give examples of each if that would help with the clarity. I imagine the abstract vectors to help with context of articles such as spacetime, axioms, et cetera. Would you like examples? Zackarycw (talk) 21:34, 11 July 2019 (UTC)
- Sure, just... make sure they're grounded examples too. An example given in the form of a Nx1 matrix would not help. ikanreed
^{🐐Bleat at me}21:40, 11 July 2019 (UTC)

- Sure, just... make sure they're grounded examples too. An example given in the form of a Nx1 matrix would not help. ikanreed
- Okay, I'll gather references for a concrete example like position or velocity (unless you just want me to make one up on the spot without references) Zackarycw (talk) 21:42, 11 July 2019 (UTC)
- My vision? I fully accept that once I submit something to mainspace, it is no longer my work. If you guys don't like the page, move it, delete it, or edit it. I really don't have a "vision" per say. I just thought it might be helpful to some articles that support the mission statement to be able to refer to what they mean by vector. Well... I guess it's better than obsession... thanks. Zackarycw (talk) 21:52, 11 July 2019 (UTC)
- Okay, sounds good. I'm going to spend some time making some good examples in a sandbox that way the mainspace article isn't just random bits and pieces as I work on it. Thanks Zackarycw (talk) 22:05, 11 July 2019 (UTC)

- Sure, that definitely cleared everything up. I speak as an absolute layperson. This is all boring gibberish that's crying for contextualization (like real-life examples). --It's-a me, LeftyGreenMario! 21:17, 11 July 2019 (UTC)

- Read rest of talk page. This article focused on abstract vectors

I literally don't understand 90% of the article because it's written in equations, but examples and real world application would be good. — Dysk (contribs) 23:54, 11 July 2019 (UTC)

## Definition[edit]

@Bongolian My concern about vectors being able to be "drawn as an arrow" is that I feel as if that describes Euclidean vectors. There are vectors that can *not* be thought of as arrows. Is there any objection to this at the beginning instead:
In simplest terms, a **vector** is a mathematical construct that has the ability to be scaled and added to other vectors; **Euclidean vectors** have a direction and length and is drawn as an arrow. An **abstract vector** is an element of a vector space.[1][2] I feel as if this also gives a nice transition to the following Vector Space and Euclidean Vector sections. Also, thanks for the visual of Euclidean vectors with the arrows. I'm working on a visual of a vector that is not an arrow. Zackarycw (talk) 23:41, 11 July 2019 (UTC)

- That's fine. I just wanted to have it start out with a simple definition that most people would understand. Starting out with "A vector is an element of a vector space." sounded weirdly redundant, but after the first sentence it's clearer that it's bringing in the concept of vector space. Bongolian (talk) 03:58, 12 July 2019 (UTC)

## Left and right vector spaces[edit]

Technically speaking, a collection of vectors doesn't have to be set over a field. A vector space can be a set over a ring and under certain conditions is termed a left or right vector space depending on the structure of the ring. The article is already a little technical, but this might be worth noting. I'll go find references. Zackarycw (talk) 22:55, 12 July 2019 (UTC)

- Oh. My god. ikanreed
^{🐐Bleat at me}20:20, 15 July 2019 (UTC)- I see that this person does not intend to help at all. So, I will assume that it's worth ignoring them. Snarky comments aside, I think I might have some free time coming up and wanted to add some examples to make this seem less abstract. I also intend to go over modules over rings for example and define left and right vector spaces. Zackarycw (talk) 23:12, 17 September 2019 (UTC)