Talk:Synergetics coordinates

Notation

Can the notation Rⁿ⁺∪0 be made clear? Thanks. Oleg Alexandrov (talk) 06:35, 25 May 2008 (UTC)

R means the real number set; n is the dimension; + means positive numbers, and ∪0 means that set in union with 0, so it is the set {positive real numbers and 0} in n dimensions. If one has studied mathematical logic the notation should be clear; many other math articles use mathematical logic statements. But, if you think explanation should go in the article, feel free to add it. —Preceding unsigned comment added by Dchmelik (talk • contribs) 02:52, 29 May 2008 (UTC)

The notation I am familiar with is $R_{+}^{n}\cup \{0\}$ (the plus is down) Is this what you mean? Also, $R_{+}^{n}\cup \{0\}$ is not equivalent to $R^{n-1},$ they have different dimensions. Oleg Alexandrov (talk) 04:47, 29 May 2008 (UTC)

In all my college math books & courses I have seen the positive subset to be noted with a superscript plus, but if notation varies around the world let us change the article. Reconsider your 2nd statement. R² is 2-dimensional reals, and can mean 2 axes, but 3 R⁺∪0 axes separated 120° is R²-space: i.e. it (R³⁺∪0) is equivalent to R², and the coordinates can be converted (one person has called synergetics coordinates 'polysign numbers;' their web page likely has explanation.)--Dchmelik (talk) 07:44, 31 May 2008 (UTC)

What you say about 120° is R²-space is not clear from the article, in fact I still don't understand what the article is about, and what you mean by synergetics coordinates. Oleg Alexandrov (talk) 16:23, 31 May 2008 (UTC)

Three axes are 3 dimensions, but synergetics axes are rays (only having '0' or positives) thus defining less than 3-dimensional Euclidean space. Three rays separated by 120° are R⁺∪0 and allow 'triangular' coordinates (ordered triples with elements '0' or positive.) They define Cartesian 2-space: any triangle (2-d simplex) or non-degenerate polygon can. Wolfram's Mathworld defines coordinate systems that use simplices as 'synergetics.'--Dchmelik (talk) 15:37, 7 December 2008 (UTC)

If you think the article is confusing (I disagree, so) read above. I do not recall where I first saw graph paper using equilateral triangles, but I first read the idea like synergetics coordinates at [Polysigned Numbers] (Does anyone think we should add an article on them?,) which are somewhat too complicated for me to know if simpler definitions exist.--Dchmelik (talk) 15:37, 7 December 2008 (UTC)

If you find something wrong, please do be bold and fix it. I've removed the claim that it was invented by Fuller for now. Where is the stub page on Synergetics_Fuller? Shreevatsa (talk) 14:55, 8 April 2009 (UTC)

The stub page for Fuller's synergetics is at Synergetics (Fuller). Thanks for removing the attribution to Fuller. Bob Burkhardt (talk) 15:59, 11 April 2009 (UTC)

Adding Clifford Nelson's name helps clarify things. I'd be glad to see an alternative to "an attempt to make operational". I was just trying to express in my own words what I found on the Nelson page which is the verifiable citation in this case, and I can imagine there are better ways to do it, as indeed you have shown by adding Nelson's name. It might be interesting to see an article on another operational coordinate system for working with Fuller's synergetics. At that point this page could be moved to "Synergetics coordinates (Clifford Nelson)". My real interest at this point though is seeing the Synergetics (Fuller) article start moving beyond a stub in a Wikipedia-sanctioned way. Bob Burkhardt (talk) 15:59, 11 April 2009 (UTC)

I've reworded the first sentence to avoid the word operational. I don't think a manager is needed here, just people willing to edit. The words in the article about propositions about triangles being easier to prove certainly strikes a chord with me. I know in studying Synergetics I was constantly doing xyz calculations of various sorts to verify what I was reading. Sometimes coming at something from several points of view can help people understand things.

I am curious about the extension to tetrahedrons too, but perhaps that would be original research that goes beyond the citations and not appropriate here. But the figure referenced in Fuller is a tetrahedron, so perhaps Nelson or Dolan treat that situation as well. To judge from Weisstein's 3D exposition of Nelson applications, Nelson does 3D as well. If so it should be addressed in this article. The n-dimensional treatment may be a bit too general for this situation. It is worth a mention I suppose, but if it doesn't come from the "synergetics coordinates" references then it should be labeled according to the line of thought it does come from. And I certainly endorse the plea in the section below for some figures. I think the value of this article may be for some people grasping at alternatives for understanding Fuller's synergetics and manipulating its constructs.

— Bob Burkhardt (talk) 13:13, 13 April 2009 (UTC)

picture request

We need a copylefted picture of a plane delineated by equilateral triangles. That is all these really are. When that is posted I think the language will be easier to understand in context, and the request for an expert can be removed.--Dchmelik (talk) 06:43, 29 March 2009 (UTC)

See the links below for an explanation of Synergetics coordinates. They start with the tetrahedron.

http://mysite.verizon.net/cjnelson9/index.htm http://library.wolfram.com/infocenter/search/?search_results=1;search_person_id=607

71.103.163.7 (talk) 09:02, 25 April 2009 (UTC) Cliff Nelson

Were the additions necessary?

I wonder why it seems an entire article has been added after my definition. It seems the section 'synergetics coordinates,' which is the title of the article, should be renamed as using vectors. Also, why should the article start talking about people rather than with the definitions? It seems there is some controversy about who developed synergetics coordinates. I just looked them up at mathworld.wolfram.com and it maybe did not mention anyone. If everyone is sure about who discovered these coordinates, then that is okay, but the important thing for the article currently is to get a picture of a graph plаne of equilateral triangles.--Dchmelik (talk) 05:51, 14 April 2009 (UTC)

The MathWorld page used to say the coordinates were invented by Buckminster Fuller which was not true and the MathWorld page was therefore changed some time ago. The coordinates are an idea of Clifford Nelson's inspired by Buckminster Fuller's synergetics. There seems to be concensus on this. I agree a picture would be good. I think we must also be about ready to remove the template asking for an expert. The symbolic analysis seems to go too far when it attributes n-dimensional pretentions to synergetics coordinates. At most I think just 2 and 3 dimensions are present in the references that mention "synergetics coordinates". Certainly a more general analysis can be indicated, but it should not be called synergetics coordinates, and its true name should be indicated (which I take it is one of the see also topics). I will probably not provide the picture, but I will probably do the other edits mentioned if no one else gets to them in the meantime, and I don't hear some cogent objection. Bob Burkhardt (talk) 20:05, 20 April 2009 (UTC)

'too technical'--or too long?

I do not think the article is too technical, but I think it is too long and later additions from when it was said to be confusing or abstract and needed an expert until the time I added the graph have been sort of redundant and getting off-topic. As long as the graph is there it should not be too technical.

Since the article, graph, and its Wikisource page show the coordinates use regular triangles it should not really matter what other people have added. I guess you could say the article needs cleanup, but I do not see how it is too technical. A math article needs to have a definition in mathematical logic--i.e. a complete definition and not much more--though not necessarilly with logic symbols, and that is what I had written. Some of the additions just say some of the same things again like vectors meaning the exact same thing as my points in the algabraeic definition. There is nothing wrong with using point notation instead of vectors.

I guess I or anyone could add axes to the graph, but that seems unnecessary. It should be clear without those. Is there any other problem I have not mentioned?--Dchmelik (talk) 02:35, 27 September 2009 (UTC)

Notable?

Who is Clifford Nelson, and why should his "attempt" to do something be notable? If he is notable, why isn't there an article about him? If he is not, his attempts should be even less so. Or am I missing something? Goochelaar (talk) 16:30, 2 March 2010 (UTC)

Clifford is a mathematician, and brilliant because of defining graphs with coordinates using triangles rather than squares. I see you are a mathematician, but the others afraid of mathematics (and saying the article needs attention of a (higher) expert) should just introspect or go back to nursery/kindergarden, regain their creativity, relearn numbers and shapes until they realize coordinates do not have to only be on a square graph.--dchmelik (t|c) 16:22, 19 February 2014 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Synergetics coordinates/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Suggested improvements: illustrations the intro blurb should be expanded to mention triangles and tetrahedrons somehow 4D and higher extentions go beyond the original references if these are attributed to "synergetics coordinates". These extentions should be mentioned, but not treated as synonymous with synergetics coordinates. the tetrahedral special case needs to be developed — Bob Burkhardt (talk) 20:28, 20 April 2009 (UTC)

Last edited at 20:28, 20 April 2009 (UTC). Substituted at 02:37, 5 May 2016 (UTC)