Talk:Manifold

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Untitled[edit]

old: Talk:manifold/old, Talk:manifold/rewrite/freezer.


Impressed with this article[edit]

Since I usually nitpick on discussion pages, I just wanted to say that this article is very coherently constructed, provides good examples, and covers the topic well for a wide range of readers. Thank you to all who contributed to it. —The preceding unsigned comment was added by 24.205.231.209 (talkcontribs) 20:36, 2006 November 12.

Figure 1 does not illustrate text[edit]

The text refers to semicircles (verbally and mathematically) while the diagram illustrates shorter arcs. Not too serious, but it detracts. — Preceding unsigned comment added by Pierreva (talkcontribs) 03:08, 21 October 2013 (UTC)

That's true. I've replaced semicircles with arcs in the prose. Thanks, --Mark viking (talk) 03:57, 21 October 2013 (UTC)

I was going to suggest that simple change, then I noticed the reference to the interval (-1,1), and the following two paragraphs both only make sense in the context of semicircles. I'm afraid it is the graphic that is the smallest change target. — Preceding unsigned comment added by Pierreva (talkcontribs) 18:11, 22 October 2013 (UTC)

I agree. for the given circle (x^2) + (y^2) = 1, y is positive for the entire top half of the circle. You can easily see this by plugging in y = 0 and noting x = +1 or x = -1 are solutions. However, the diagram shows a yellow arc that only covers 1/4 of the top of the circle. — Preceding unsigned comment added by ArchetypeRyan (talkcontribs) 04:05, 19 September 2014 (UTC)

Animated GIF[edit]

I've removed the animated GIF of "boy's surface" because of the distraction it causes. This action is consistent with MOS:ACCESS but counter to the wishes of User:Slawekb

https://en.wikipedia.org/w/index.php?title=Manifold&diff=581403804&oldid=581391247 : (The image and its caption accompany the text of the lead. If you don't like this particular image of Boy's surface, then find another one.)

Any opinions on this apart from the two of us?

-- Catskul (talk) 23:09, 14 November 2013 (UTC)

Presumably the onus is on you to make a more suitable image and convert the gif to video, per the guideline. The manual of style should not be used to dictate what kinds of informative content to have in articles. This image has informative value. Sławomir Biały (talk) 00:35, 15 November 2013 (UTC)
The real projective plane is a two-dimensional manifold that cannot be realized in three dimensions without self-intersection, shown here as Boy's surface.
As I understand it there is no onus on editors to replace offending content. If, for example, a statement is unsourced, an editor is not obligated to find a source which negates the content before removing. While the content I am attempting to remove has value, it is neither critical to the article nor mentioned anywhere in the text.
Despite my belief that replacement is not a requirement, consensus is needed. So in an attempt to achieve consensus, I suggest replacement of the original with the following:
-- Catskul (talk) 16:30, 15 November 2013 (UTC)
Aesthetically, that image is not really an improvement over what is there now. I will work on a better replacement when I get the time. Sławomir Biały (talk) 00:08, 16 November 2013 (UTC)
I'm going to add in an opinion here. The point that some 2d manifolds cannot be embedded in 3d space without self-intersection is not central to the concept of a manifold; it is an essentially topological result that applies only for an arbitrarily constrained choice of embedding space for a some manifolds. I'd say that a far more significant (or more generally applicable) points topologically are that manifolds can be closed or can be non-orientable, which are not even mentioned in the lead. I'd think that it would be sufficient to mention one or two illustrative cases such a the Klein bottle without mentioning properties of selected embeddings. —Quondum 13:01, 16 November 2013 (UTC)

I think the idea that there are 2-manifolds that are not realizable as surfaces in Euclidean space is actually quite important for understanding why there is a mathematical notion of "manifold" at all. Certainly, one can study manifolds without worrying about their embedding properties (although there are people who build their careers entirely on the latter), but to someone with no idea what a manifold even is, I think it is very important to realize that they do represent a significant generalization of the elementary notion of a surface. Sławomir Biały (talk) 13:31, 17 November 2013 (UTC)

The topological aspects of manifolds are important, I agree, but is only one of what they are useful for. The same point about embedding can be illustrated within a Klein bottle without challenging the reader nearly as much. Emphasizing the topological aspects at the expense of the geometric aspects is also not ideal. For example, the real projective plane also represents elliptic geometry, which does not come through at all. All these issues are complex enough that more than a mention in the lead can hint to the reader that this article is hard work to understand. —Quondum 21:32, 17 November 2013 (UTC)

Let's get the zeroth law section right[edit]

I think we can improve the Zeroth Law of Thermodynamics in a way that satisfies both Chjoaygame and Prokaryotes. For quite some time, I had been proposing a deletion of the entire reference to a one dimensional manifold, but suddenly I grasped what people were trying to say. Now that I understand it, we need to make two decisions:

  1. Do we want to delete all mention of whether the zeroth law defines "temperature as a numerical scale for a concept of hotness which exists on a one-dimensional manifold with a sense of greater hotness"?
  2. If the answer to the previous question is "yes", how do we provide examples that allow people to understand the concept?

I actually took the trouble to look up Serrin's article, and wasn't much impressed. He didn't explain it well either. Apparently (and I am just guessing here) some authors claim that the zeroth law establishes the existence of temperature. What I think Serrin was trying to say is that one needs to establish a few more concepts before jumping from the zeroth law to the idea that a temperature scale can be defined. For example, what is the meaning of the cryptic phrase "For suitable systems...?". What I think he meant was that the state variable must change when the temperature changes.

And it is important to provide either one or two examples of a state variable that changes. The dispute we are having is whether we need one example (pressure), or two examples (pressure and volume). We cannot resolve this until we have resolved the two aforementioned questions. In other words, why argue about a sentence when a couple of paragraphs need work?--guyvan52 (talk) 16:53, 21 March 2014 (UTC)

I think this was posted in the wrong talk page--this article is about mathematical manifolds. --Mark viking (talk) 17:24, 21 March 2014 (UTC)