Talk:Centers of gravity in non-uniform fields

Perhaps it is time to wrap it up

I mean both CG and CM articles. I did some additional literature search on CG, but it did not help. I also did some search on the "concept of mass" history, and it did help to establish a perspective. So, let me start on a rather general level, and proceed to details in a few following days.

I still believe that both items should be kept as separate articles. In both of them it should be pointed out at the very beginning that it is quite customary to use the terms as synonyms, but that they are conceptually as well as historically distinct.

According to Merriam-Webster, the first known use of the term CM dates from 1862. Which is reasonable: the very term "mass" (in physics) was less than a century old. Newton still used the "quantity of matter", and any real understanding of the inertial and gravitational properties of matter date from about his time (see e.g. Max Jammer, his older book). The Old Greek knew only about "weight", the property of some materials (not of e.g. hot air).

According to Merriam-Webster, the first known use of the term CG dates from 1648. Webster does not date the origin of barycenter (obviously, the center of "heaviness/weight"). In contemporary usage it is often reserved for the CM of 2 celestial bodies orbiting each other (see e.g. the free online dictionary, although Webster uses it as a synonym for CM in general), but I guess the ancients may have used it for the CG they studied (though that is hardly relevant). Their CG clearly was the point of equlibrium for supporting the weight of the body. They undrestood nothing about the force of gravity, and even less about concept of mass: so, what else could it have been?

Then, if we can agree about this context, we can proceed with the discussion of each article.--Ilevanat (talk) 00:54, 3 January 2012 (UTC)

We agree about the language used, but we still don't agree about the scope of the concepts... Let me try an argument that's relevant to the way the Wikipedia articles should be organized. I claim that whenever anybody refers to a CG with the understanding that it's a fixed point in relation to a body, regardless of the body's orientation or position, they are talking about the CM. Agreed? Melchoir (talk) 20:19, 4 January 2012 (UTC)

I agree that they're synonymous, but distinguishable. I think that one article that covers both concepts should be created. Merging synonymous concepts is normally done, even if they're not perfectly synonymous, as here. The articles aren't too big to do this, and the merged article would be smaller than their sum.Teapeat (talk) 03:18, 5 January 2012 (UTC)

Agreed. Almost: I believe that some tens of thousands of my students would at least wagely recall that CG "practically" coincides with CM (though probably not many of them would remember any further details, even about CM that was extensively used). But those who did not have any physics beyond highschool are certainly in the category you described.

So, if we do not want to "perplex" that large majority, maybe a single article would be more appropriate. On the other hand, if do not want to "perplex" those who even wagely remember that there may be some differences in the physical concepts, perhaps that single article shoud have the title "Center of mass and center of gravity". Unless it is contrary to some Wikipedia policy?--Ilevanat (talk) 01:14, 5 January 2012 (UTC)

I am glad that other people are joining our discussion (Teapeat). Though I do not enthusiastically support formulations like "synonymous, but distinguishable", I can generally agree with the proposal. (And let me appologize for the above repeated misspelling of the word "vaguely".)

It may now be the time to discuss the starting sentences of this unified article. Do not take my English seriously, but would strongly prefer something with the following meaning:

"In common usage, CM and CG denote the same point, in which as if the entire mass and weight of a body is concentrated for purposes of various calculations in mechanics. In physics, however, CM and CG are two distinct concepts with differring history."--Ilevanat (talk) 01:14, 6 January 2012 (UTC)

Well, hang on, I have a more conservative proposal. I don't necessarily want to see Center of gravity merged with Center of mass. Back in October, Center of mass was very long and overrun with minutiae. I split it into a number of summary-style daughter articles: Derivation of the center of mass, Locating the center of mass, and Barycentric coordinates (astronomy). Likewise, I'd like to see the current material at Center of gravity kept intact, and even expanded, but moved to a new name: Centers of gravity in curved fields or something similar. It would be linked to from Center of mass in the appropriate section, just like the other related articles.

Does that make sense? If I'm not being clear, I could implement the idea very quickly for the purpose of demonstration...? Melchoir (talk) 23:34, 6 January 2012 (UTC)

But when someone types "center of gravity" in the search box, where does it lead him? Or what choices does he see? (P.S: "curved field" should rather be "non-uniform" or "non-homogenous".)--Ilevanat (talk) 01:06, 9 January 2012 (UTC)

In both my proposal and in the event of a merge, Center of gravity would be a redirect to Center of mass. And in both proposals, the target article would have a section that presents the idea of a center of gravity defined relative to an external field.

The difference is that, if we avoid a merge, then the present Center of gravity article can stay at the length of a full article, having several sections that compare the various definitions. The only real change is that the 300 articles that link to "Center of gravity" will be redirected to CM. Melchoir (talk) 01:45, 9 January 2012 (UTC)

For most of those 300 articles, CM would probably be a better link anyway. The present article on CG should perhaps be named "Center of gravity concepts in physics" (Symon CG starts out as a field source, rather than as a point in external field).

However, in the case of CG redirect to CM, I would really hate to see the article begin as it does now. We can discuss various fine details later, but I strongly believe that the first lead paragraph should contain something close to those two sentences I proposed above. If not, why bother with any additional considerations of CG (let alone articles)!--Ilevanat (talk) 23:55, 9 January 2012 (UTC)

Okay, I gave it a try: hopefully this is a good start. I want to avoid the word "however", which feels argumentative in the way it emphasizes one sentence over another. I'm not sure that "differing history" is justified at this point, so I left that out as well. Melchoir (talk) 11:02, 10 January 2012 (UTC)

Yes, it could be a good start. Give me a day or two for comments.--Ilevanat (talk) 01:42, 11 January 2012 (UTC)

After some consideration, my conclusion is: there are many minor points in the lead and later in the CM article that could be discussed/improved. But much of that will depend on the point of view regarding CM and CG concepts and their history.

Of course, I fully agree (or have come to agree) that the present common usage should be given priority (no matter how superficial or confusing it may be). And you seem to be willing to acknowledge the conceptual differences. So, there only remains the question of historical development, which is necessarily related to the conceptual differences.

One approach is to ignore the history, or to misrepresent it as is presently done in the CM article with the claim that Achimedes was studying CM. (Yes he was, if CM and CG are one and the same concept! But then again, if we go along with that, why bother with any other distinguishing details?) This is the most easy approach, and it may be sufficient for Wikipedia. After all, any more subtle considerations may later be reverted or re-edited by well-intended people reading casual formulations that dominate the literature.

Yet, let me for this once, outline some historical data as I see them (and, please, correct me if you have any evidence to the contrary):

The early Latin terms equivalent to "gravity" and "center of gravity" (and Greek terms "barus" and "barykentron", or something like that in Greek alphabet) denoted "heaviness/weight" and "center of weight". Achimedes was studying balancing of lever arms and static equilibrium of body weights (in present terms we would use "the torque equation") and then extended his "barykentron" concept to geometrical figures (having in mind, I would guess, bodies with homogenous distribution of weight).

The idea that matter may have a general property of gravitational attraction was first mentioned by some Arab thinkers around the year 1000 AD (primarily as attraction among the celestial bodies, I believe). But the concept was seriously considered only shortly before Newton and in his time.

The idea that matter has a property of inertia is contrary to Old Greek concepts, and became generally accepted only at Gaiileo/Newton times.

So, what about mass and CM? Newton was still using "quantity of matter", but his "matter" had both inertial and gravitational properties, and it is only from about his time that the concept of "mass" (although the term was introduced a bit later) can have any meaning, regardess of how it was called. Before that, "matter" just did not have the properties that would relate it to mass. Nor did "heaviness". Therefore, CM is indeed a post-Newtonian concept (though perhaps a bit older than Webster claims). And it must have been intended to address the inertial properties of matter: why else would anybody introduce a new term if they had in mind "center of haviness"?

You can see that some of my above arguments border with guesswork. Why? Because "the application people" use CM and CG as synonyms, and the easily accessible literature generally reflects this practice. Therefore, it would take me too much time and effort to find those rare authors who care about distinctions in conceptual and historical developments. But I doubt physics would have developed to its present level if the "real guys" were following practice of the "application people".

Anyway, in our CM and CG articles we can choose to stick mainly with the "common usage"; or, we can attempt to introduce more content that reflects the "indisputable real meaning" (yes, there is such a thing!) of the physical concepts, presently and through the history.--Ilevanat (talk) 01:12, 13 January 2012 (UTC)

As far as I know, you're absolutely right about the early history. Still, I don't think it forces us to choose between common usage and the truth. I think with a careful framing of the issue, we can respect both...

I haven't studied Archimedes, but as I understand his work:

• He was studying gravity and weight. For him, weight was a scalar quantity and an intrinsic property of a body. Today we understand that mass is the intrinsic scalar. Weight is a vector which depends on the configuration of distant objects.
• He understood the CG as a point which always uniquely exists and is painted onto an object. Today we understand that the CM uniquely exists and is fixed. The CG usually doesn't exist, usually can't be uniquely defined, and is not fixed.
• He derived the law of the lever. Today we combine the law of the lever with vector arithmetic to define the CM. The CG doesn't obey any such law, and in fact, the Symon CG can lie completely outside the convex hull of the body.

It would appear that his CG is more like our CM than our CG, at least mathematically. On the other hand, you've already demonstrated that Archimedes' CG concept cannot simply be identified with the modern CM concept, because the foundations are separate. So what was Archimedes really studying?

The root problem, as I see it, is that Archimedes' treatment of the CG is inconsistent. (Many modern treatments are also inconsistent, but for other reasons.) He imagined a concept that both relates to gravity and also obeys certain convenient laws, which we now know are incompatible! His concept is too large to be governed by any precise definition. And so, like an unstable empire, the old CG has balkanized into a constellation of sub-concepts that compete to be considered its successor. There's the modern CM and the torque CG, and the latter is itself split into at least two pieces, the Symon CG and the Beatty CG. Meanwhile, non-physicists who don't care about linguistic politics are happy to nominate the CM as their preferred "center of gravity".

(I don't claim to have any evidence of how these splits happened historically.)

The practical lesson for Wikipedia is that we should be careful to avoid suggesting that any modern treatment was envisioned by Archimedes. Fortunately, that's just a matter of fine-tuning the language. For example, I just made this edit to Center of mass#History, which I hope you'll agree is a step in the right direction.

Meanwhile, I'd really like to sort out the article titles. I'll go ahead and move this article and redirect Center of gravity. If you, Teapeat, or anyone else feels this is premature or unwarranted, feel free to revert me or ask me to undo it myself! And we can still continue to discuss exact titles, body text, and further merges and splits on the various talk pages. Melchoir (talk) 08:46, 13 January 2012 (UTC)

For the beginning, let me de-mistify Archimedes. A number of accounts of his works can be found on the web, including a very comprehensive one by T. L. Heath from 1897. Archimedes introduces CG in the book ON THE EQUILIBRIUM OF PLANES OR THE CENTRES OF GRAVITY OF PLANES. A reasonable discussion of his assumptions can be found at http://www.calstatela.edu/faculty/hmendel/Ancient%20Mathematics/Archimedes/De%20Planorum%20%20Aeqilibriis/Intro.I.Props1-5/Intro.I.Props1-5.html#note0 . Please, note his formulations (copied from that site), such as:

Proposition 1: Weights that incline-equally from equal lengths are equal.

Proposition 2: Unequal weights from equal lengths do not incline-equally, but will incline towards the larger.

Proposition 3: Unequal weights will incline-equally from unequal lengths and the larger weight from the smaller length.

etc.

He generally thinks in terms of weights (magnitudes) and lightness, and his considerations are rather incomplete. Note the comment from the above web-source:

"...Archimedes never gives a definition of ‘center of weight’, and the text has been criticized for this omission. He also never defines 'inclination’ or ‘equal-inclination’. Eutocius gives a definition, which seems inadequate. Here are two attempts at definitions, the first of which captures better what Archimedes does in Plane Equilibria and Quadrature of the Parabola, but keeping in mind the abstact nature of his works also fits the solid geometry of the Method and Floating Bodies. The second definition fits better with the account of Archimedes found in Heron' Mechanica.

   1. The center of weight is a point from which a freely hanging body is stabile, no matter how it is positioned about the point.

   2. The center of weight is a point such that if a body is hung freely from any point on the body, a perpendicular from the point of suspension to the horizon will go through it."

It is obvious that Archimedes has in mind the equilibrium CG, or "torque CG". Based on weight/lightness properties of bodies. Any reference to gravitational force, or to concept of mass as the property of matter, or to concepts of vectors and scalars, is entirely out of his league. After all, he was just an Old Greek.

Of course, the CG on the surface of the Earth "practically" coincides with the CM. And all his results do hold for CM, actually better than for any CG concept in a non-uniform field (and in particular his extension to geometrical figures). Still, that does not change the obvious fact that Archimedes studied the concept of the "equilibrium CG". Which could be a bit more stressed in that historical account, if you think it is worth the effort.

Therefore, I would remove the second sentence from the first paragraph of "History", and substitute CM by CG until the last sentence. And before that last sentence of the first paragraph, an explanation along the above lines could be inserted.

P.S. I do not see any conceptual relation between the law of the lever arm and "real" CM.--Ilevanat (talk) 02:00, 14 January 2012 (UTC)

Merge to center of mass

I am sure that the final merger[1] by user: Teapeat was a mistake. The center of mass article should not cover nothinganything but the point giving the mean value of a mass distribution. Any stuff about mean values of some else distributions must constitute a separate article(s). Incnis Mrsi (talk) 10:13, 8 March 2012 (UTC)

Eh, I agree (to nobody's surprise). I still think a summary-style daughter article is a reasonable compromise, and hopefully it's a solution that we can eventually settle on, especially if the main article is streamlined enough in other respects. Melchoir (talk) 01:20, 12 March 2012 (UTC)

What is "the main article"? What means "a summary-style daughter article" and a daughter of which one? Expected value of some distribution in 3-dimensional space is more general topic, but "center of mass" is more important topic. P.S. I changed the section header to "Merge to center of mass" because the contested merger occurred not in March, but January 27. In March we actually discuss splitting, not merging. Incnis Mrsi (talk) 06:22, 12 March 2012 (UTC)

Oh, by the main article I mean Center of mass. In January, Old revision of Center_of_mass had a section "Gravity" with a {{main}} link to Old revision of Centers_of_gravity_in_non-uniform_fields. As of today, Center of mass has a section "Centers of gravity" with the same content and no {{main}} link. Melchoir (talk) 09:24, 12 March 2012 (UTC)

I agree that merging was a mistake. --Steve (talk) 12:14, 12 March 2012 (UTC)

You can always unmerge them, but there's several problems you create if you do that:

• people refer to them synonymously, and in this important sense they are the same topic (on its own this wouldn't be sufficient but:)
• in nearly all practical cases they are exactly the same point in space within measurable accuracy (importantly this is so when there's parallel fields or spherically symmetric fields and geometries)
• you will have split the 'center of gravity' topic across two articles
• the combined article is currently not nearly big enough to demand splitting (it's only 13k of text)
• all of the internal links for 'center of gravity' point to 'center of mass'
• if you split them the new article is not linked from anywhere except the original article, and IMO is unlikely to ever be well-linked

There's certainly pros and cons either way, but on the whole it's apparent to me that there's more downsides to remerging them than upsides.Teapeat (talk) 17:58, 12 March 2012 (UTC)

A bunch of invalid arguments and irrelevant remarks.

> people refer to them synonymously

The problems of terminology are not the same than the problems with definitions. We are in Wikipedia, not Wiktionary.

>… they are exactly the same point in space within measurable accuracy

… like all material points in an atomic nucleus are the same point within measurable accuracy. Does this imply that the article charge radius is pointless?

> you will have split the 'center of gravity' topic

In most cases a lake is a body of water. But there are several, in some remote parts of the Solar Systems, filled with hydrocarbons. So, Wikipedia splits the "lake" topic. Is it really bad?

> the combined article is currently not nearly big enough

A stereotypical logical fallacy. A large size suggests splitting the article, but not-a-large size does not suggest non-splitting of articles.

> internal links for 'center of gravity' point to 'center of mass'

What? Does Teapeat mean that someone intended to link an exotic "center of gravitational force" (which differs from the CoM) notion could type [[center of mass]] assuming these are synonyms? Or Teapeat thought something nearly opposite to what he typed? Explain your thoughts carefully, not hastily. There is no rush.

> if you split them the new article is not linked from anywhere 

If center of gravity becomes a WP: disambiguation page? If such a content will be demanded, then it will be linked. If it will not be demanded, then… it now pollutes the center of mass article, but yeah, it will be linked indeed, how cool. Incnis Mrsi (talk) 18:41, 12 March 2012 (UTC)

I stand by every single one of my points, as is my right, and I do not consider any of your characterizations to be accurate, nor do I find that I have been unclear. There's about a thousand links to 'center of gravity' and in nearly every case they mean 'center of mass', redirecting 'center of gravity' to a disambiguation page seems to me to be extremely undesirable.Teapeat (talk) 19:31, 12 March 2012 (UTC)

These two topics, while distinguishable, they are intimately related, and are, in practice, synonymous and for most (but not all) are exactly the same point. Even if we did go through and separate them, by hand, there's no guarantee that they would stay separated, people will continue to edit.Teapeat (talk) 19:31, 12 March 2012 (UTC)

While I like your suggestions in theory, in practice, I'm not liking it nearly so much.Teapeat (talk) 19:31, 12 March 2012 (UTC)

This is not "practice vs theory". These are conflicting optimizations of Wikipedia to different aims. One approach is to give more articles available just by typing some words and pressing ↵ Enter, without thinking. Another approach is to increase clarity and do not bother much about disambiguation pages and extra clicks needed to reach a page needed, or to fix a bad link. This latter approach dominates today in scientific areas of English Wikipedia and, I hope, will be dominate for a long time in the future. So, I do not think that further attempts to join different topics based on a historically ambiguous term "centre of gravity" will succeed. Incnis Mrsi (talk) 08:45, 13 March 2012 (UTC)

I think the link center of gravity can and should continue to go to center of mass, which is the primary meaning of the term "center of gravity". The center of mass article can link to "Centers of gravity in non-uniform fields" as a hatnote. --Steve (talk) 15:00, 17 March 2012 (UTC)

Congratulations on splitting up the center of gravity article and making an article that virtually nobody will read!!!Teapeat (talk) 17:35, 29 March 2012 (UTC)

Why "gravity"?

Since the article will certainly be restored, I ask second question: which content about the gravity cannot be applied to a field of another nature? Does there exist a reason to restrict to the gravitational field only? Incnis Mrsi (talk) 16:16, 12 March 2012 (UTC)