A purely terminological question

[Ruslan_Sharipov]

If two vectors are parallel they are said to be collinear. In this case they can share the same direction or they can point to opposite directions.

1. For two parallel vectors sharing the same direction can I say that tey are codirected? Is it a true English word? I did not find it in A.J.Lohwater's Russian-English dictionary published by AMS. If it is not a true word, which adjective is suitable for denoting such a pair of vectors?

2. For two parallel vectors pointing to opposite directions which form is better to say:
- they are opposite directed or opposite-directed;
- they are contrary directed;
- they are counter-directed or counterdirected?

Please help me to choose a true wording.

 

[radou]

There has already been a similar discussion, and, if I'm not mistaken, there are a few views on this.

As I have been teached, the direction of the vector is determined by the line it's 'placed on'. Vectors on parallel lines are said to be collinear. If you choose a reference point on every line, then it makes sense, only for collinear vectors, to define orientation. Which brings us to the conclusion that it is often better to set our 'story' into a coordinate system, and then define everything nicely and work with radius-vectors.

 

[neutrino]

Parallel and Anti-Parallel: I've seen that used in a few books, strictly in the context of vectors, but I guess it can be misleading.

 

[fopc]

1. If you choose to use "codirected", you won't be the first.
Google search on "codirected vectors".

2. I'd suggest using "opposite-directed" or "opposite directed", depending on the context.

Examples: ... the vectors are opposite directed ...
... the opposite-directed vectors ...

Here again, you can Goolge search on "opposite directed vectors".
I wouldn't use "contrary" in this case.
Another possibility, if you choose to use the term "codirected", would be non-codirected. But, it wouldn't by my choice.

 

[matt grime]

The adverb is "oppositely". Not Opposite. Whilst the latter forms of adverbs are often used in America they are still bloody ugly on the ears.

 

[mathwonk]

i would think the word oriented, contains both the line determined and the direction.

i still do not know a good term for describing similarly oriented, and oppositely oriented vectors, since the phrases i just used are somewhat lengthy.

and i am american, hence handicapped by training in use of the language, as i am all too well aware of.

try searching enlgish books from england for felicitous use of the language.

 

[fopc]

De gustibus non est disputandum.

By the way, thanks for your link http://www.freetextbooks.boom.ru .
It was provided on another thread which, unfortunately, I can't find at the moment.

 

[mathwonk]

the practice of choosing terminology well, as you seek to do, is to be applauded. the practice of merely defining ones own terminology and using it however, is also well established.

 

[Ruslan_Sharipov]

Thank you for help, guys! I am currently translating into English my book, the last one not yet available on the site http://freetextbooks.boom.ru" . Relying on the present discussion, I prefer to use the term "codirected" for parallel vectors with the same orientation and the term "opposite-directed" for parallel vectors with opposite orientations. Moreover, I prefer to derive the noun "codirectedness" in order to describe the relation or the state of being "codirected".

As for the phrase "De gustibus non est disputandum", I don't understand Latin. I remember few famous Latin expressions, but this is not one that I know.

 

[cristo]

I would advise using the term "non-codirected" or "oppositely-directed" to describe vectors in opposite directions. As matt grime points out, "opposite" is not an adverb, and so cannot be used in this sense.

 

[Ruslan_Sharipov]

As matt grime points out, "opposite" is not an adverb, and so cannot be used in this sense.

Below is the article from "The concise Oxford dictionary of current English. -8th ed." ISBN 0-19-861200-1

opposite[/color]

adj., n., adv., & prep. --adj. 1 (often foll. by to) having a position on the other or further side, facing or back to back. 2 (often foll. by to, from) a of a contrary kind; diametrically different. b being the other of a contrasted pair. 3 (of angles) between opposite sides of the intersection of two lines. 4 Bot. (of leaves etc.) placed at the same height on the opposite sides of the stem, or placed straight in front of another organ. --n. an opposite thing or person or term. --adv. 1 in an opposite position (the tree stands opposite). 2 (of a leading theatrical etc. part) in a complementary role to (another performer). --prep. in a position opposite to (opposite the house is a tree). opposite number a person holding an equivalent position in another group or organization. opposite prompt the side of a theatre stage usually to an actor's right. the opposite sex women in relation to men or vice versa. ЬЬoppositely adv. oppositeness n. [ME f. OF f. L oppositus past part. of opponere: see OPPONENT]​

As you see, the adverb usege of the word opposite is also provided.

 

[cristo]

The case you quote is "the tree stands opposite." This is different to your case "the vectors are opposite-directed," I think mainly due to the fact that the adverb comes after the verb in the dictionary's case, whereas in your case the adverb comes before the verb.

If one wanted to put the adverb before the verb in the former case, one could say "the tree oppositely stands," and although this is clusmy it is correct.

In your case, you could say "the vector directs opposite (to the second vector)", but you should say that it is "oppositely directed"

 

[Gokul43201]

Thank you for help, guys! I am currently translating into English my book, the last one not yet available on the site http://freetextbooks.boom.ru" . Relying on the present discussion, I prefer to use the term "codirected" for parallel vectors with the same orientation and the term "opposite-directed" for parallel vectors with opposite orientations.

I concur with matt and cristo on this. "Opposite-directed" just doesn't sound great. Of course, if it's a terminology you are coining, there's really no grammatical objection one can raise. But let it be clear that barring the hyphen, that usage would be ungrammatic. The correct way to use 'opposite' as an adverb would be in something like 'vectors directed opposite each other' (am I'm not even crazy about that example). If you wish to use an adverb before the word 'directed', it would have to be 'oppositely'. But of the suggestions so far, the one I like best is cristo's suggestion of using a purely verb-based construction, as in 'non-codirected' (it might be doubly prefixed, but it's not nearly as bad as 'antidisestablishmentarianism'). This also easily lends itself to the extension to a noun form such as that described below.

Moreover, I prefer to derive the noun "codirectedness" in order to describe the relation or the state of being "codirected".

As for the phrase "De gustibus non est disputandum", I don't understand Latin. I remember few famous Latin expressions, but this is not one that I know.

It is a statement suggesting that it's best to leave people to their own way of doing things (i.e., do not dispute matters of personal taste).

 

[Ruslan_Sharipov]

"Opposite-directed" just doesn't sound great.

OK, I agree. Google search gives 15200 results for "opposite directed", and 378000 results for "oppositely directed". A see that I should join this great majority saying "oppositely directed".

The term "non-codirected" is misleading since as applied to vectors it means randomly oriented, not necessarily parallel.

As for the term "codirectedness", I need it and I don't know a better term with exactly the same meaning.

 

[Ruslan_Sharipov]

Foundations of geometry ...

Dear Forum users,

Thank you for your help. I am all done with translating my book. Now it is available through the archive: http://arXiv.org" . Here is the link to it:


http://arxiv.org/find/grp_physics,grp_math,grp_nlin/1/au:+Sharipov/0/1/0/all/0/1".[/color]

I would be grateful for your comments, detected typos, and any other recommendation for improving my book. Please, post them here.

Yours sicerely, http://www.geocities.com/r-sharipov",
http://www.bashedu.ru" , Ufa, Russia.