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WikiProject Mathematics (Rated C-class, Low-priority)
WikiProject Mathematics
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 Field:  Applied mathematics


why the good and bad points of hierarchy not mentioned (UTC)
Superscript text

I agree the good and bad points of hierarchy should be mentioned. Notice that there is now some mention of sexism. Hyacinth 20:27, 15 May 2006 (UTC)


This sentence...... Every member is reachable from any other by following the relationship in either direction, but there is no way of coming back to a particular member by always following the relationship in the same direction. makes no sense at all to me. Does this mean that "any category node can be reached from any other category node"?

If so, then this is simply wrong - that's a property of a heterarchy or a neural network. A hierarchy is defined by each descendent having a single parent node (only!) and one or more descendents (or zero descendents at the leaf node level). Any organisational structure where descendent nodes can have more than one parent is not a hierarchy, by simple definition. The wikipedia is definitely not hierarchical in its informational content, otherwise we would not have so many debates about subpages and categorisation. - MMGB

I agree; it's a very badly written sentence. I could speculate about its meaning, but I shouldn't have to. -- Mike Hardy

One parent per node[edit]

I think the one parent per node idea is too narrow to satisfy all sensible definitions of "hierarchy". This may be how it is defined in, say, Organizational Theory. But Computer Scientists speak of "inheritence hierarchies" in which a node can have multiple "parents". Actually, think about real family trees; it is arguably fruitful to view them as hierarchies, and everyone (i.e. every node) has exactly two parents.

I think we should clarify, however, that some people use hierarchy for the one-parent case and heterarchy for the multi-parent case, if this is indeed true. If this is true, we need to clarify what people/fields use the terminology in this manner. It certainly isn't universal. --Ryguasu

I think even the initial example is confusing, with two layered ranking hierarchies and one inherited subset relationship. I dropped by because it suggested this needed some copy editing, which is my craft and avocation, but much more is needed here... That introduction needs some serious restructuring. Shanen 03:54, 16 Mar 2005 (UTC)
An interesting use of language: 'inheritance hierachies', as in plural, which underpins the original definition: A hierarchy (singular) is a set of one or more members (cannot be the empty set, 'cause then who is the ultimate superior?), where there is one member that have no superior. All other members are subordinate to one, and only one of the other members. As persons we descend from two hierarchies: The Mother hierarchy and the Father hierarchy. As a parent we have only one descendant hierarchy, namely our children.
In applied computer science, we conveniently have many hierarchies with only one parent, for example the file system. Hawkis 18:14, 11 December 2006 (UTC) Hawkis
I agree: single-parent hierarchies are the norm, and the opening paragraph is very misleading: not every partially ordered set (let alone ordered set) or acyclic graph is called a hierarachy - the least that must be added is a layering of the elements, as far as I have seen. So it must be rewritten. Rp (talk) 09:33, 18 March 2011 (UTC)

Offensive illustration[edit]

The diagram on this page seems committed to the POV tenet that "science" is disjoint from "culture". I believe this is untenable. But I don't know how to edit the picture. Can someone essay this task? Michael Hardy 01:19, 9 Oct 2003 (UTC)

And it's been over a year since I posted this. No one has replaced the illustration with a better one. I've removed it. Michael Hardy 00:09, 23 Jan 2005 (UTC)
I agree that the diagram wasn't perfect, but it (imperfectly) illustrated a concept in the article which had nothing to do with whether one subscribes to this perspective or not. You could have improved the diagram (while taking into account the articles which use (link to) the image); instead you just removed it, and even explicitly stated in the article that you didn't care to check whether this leads to problems with the text. This will sooner or later lead to serious pangs of conscience (subconscious or not), unless you draw for us a nice, inoffensive diagram, I can assure you. --Glimz 07:12, Jan 24, 2005 (UTC)
Tell me what software to use to edit this picture and maybe I'll see if I can do something with it. Michael Hardy 20:10, 24 Jan 2005 (UTC)
Create a new Image:Binary-tree-structure.png from scratch. I'd use xfig on Linux; for Windows — dunno actually, but any paint or diagram tool you try will be able to draw some squares and lines and most probably save as .png. Have a look at Wikipedia:Graphics_tutorials if you wish. --Glimz 04:37, Jan 25, 2005 (UTC)

See: Hierarchical organization, which I suggest should be merged with and redirected here. Hyacinth 07:44, 17 Jun 2004 (UTC)


The Wikipedia community is noteworthy for being not overtly hierarchically structured, as no contributor possesses inherently higher standing than another, excepting certain limited "admin" and "developer" powers restricted to a few. However, some would counter that although there is no explicit hierarchy there are social norms which make contributions unequal, as some contributors have more influence because their edits command higher respect.

Those who frequent Wikis might label Wikipedia's organization "wikiarchical".

Note that the content of the Wikipedia (as opposed to the community) is also organized in a fashion that is not overtly hierarchival. For the most part, the relationship between the individual articles does not form any sort of structure.

Your joking, right? How about Jimbo, the wikimedia board, the developers, beaurocrats, the arbitration commitee, the mediation commitee, admins, users, new users, anons, known sockpuppets and trolls, and hard banned users.... doesn't that sound like a clear hierarchy to you? Also this ignores completely the general guideline to avoid self references when possible, on top of the POV and factual inaccuracy. Sam Spade (talk · contribs) 08:24, 24 Jan 2005 (UTC)
Sorry -- I think you didn't read well. The developers, bureaucrats, admins, etc., are the community, not the content. Michael Hardy 23:03, 10 Feb 2005 (UTC)

Change to Hierarchy names[edit]

I changed "Christianity" to "Catholicism" because many of the hierarchies (sins, angels, hell, etc.) found within Catholicism are unique to that church. Most Protestant churches have rejected those doctrines and so cannot necessarily be labeled as "Christian". (talk) 21:38, 31 August 2011 (UTC)

Feminism and social criticism[edit]

I am concerned about the depiction of feminism in this article. First, it depicts feminists as sharing a single concept of the "hierarchy of gender." In fact, people who call themselves feminists have a wide range of ideas concerning gender and the power relationships related to it. Second, it implies that feminists are not interested in power hierarchies that are not based on gender. Many feminists are deeply concerned with issues of race, class, age, (dis)ability, and other sources of inequality, as well as the ways these power imbalances intersect.

Also, I do not understand what is meant by "Feminists do not take issue with hierarchy in the most general definition of the word...."

I think it might be best to remove the text about feminism and social criticism. I am not sure that I am up to the alternative task of writing a concise summary of the relationship of feminism to social hierarchies!

FreplySpang 02:15, 10 Mar 2005 (UTC)

How does it look now? Hyacinth 02:48, 10 Mar 2005 (UTC)
That looks pretty good. I'm glad that you found a way to clear it up without having to write a lot of new material. Thanks! FreplySpang 03:14, 10 Mar 2005 (UTC)

Section heading[edit]

I changed the heading back to 'general decsription (informal)' from 'mathematical...' because I wrote (most of) that section from a non-mathematical point of view. That's how 'hierarchy' is defined in philosophy and logic rather than in maths, and it applies to real-life hierarchies rather than simply to mathematical ones. Mel Etitis (Μελ Ετητης) 18:20, 30 Mar 2005 (UTC)

Confucianism as a class?[edit]

Why is Confucianism listed on this page? its appropriate so........ — Preceding unsigned comment added by (talk) 17:35, 23 August 2011 (UTC)

A hierachy cannot be represented by a tree[edit]

At least in my mother language, Spanish, a Tree is not transitive, but exactly the opposite. So a hierarchy can't be represented by a tree. A hierachy is a Partially Ordered Set.

Moved discussion out of article[edit]

Hierarchical nomenclatures in the arts and sciences

Information from this section has been merged with the content of a section above called "Examples of Hierarchical Reasoning." Many of the examples cited here were more to do with reasoning than with nomenclature, and they were redundant to those above. (Also, nomenclature is a type of reasoning.) But more work needs to be done.

(written by User:, moved by me) FreplySpang (talk) 15:51, 6 February 2006 (UTC)


"Oxford English Dictionary was in 1380": 1380? --Jidanni 2006-04-16

"Some social insect species (bees, ants, termites) depend on matrilineal hierarchies centred on a queen with undeveloped female insects as attendants and workers."

Haven't the mathematical geneticists decided that the workers are farming the queen rather than the queen is exploiting the workers? Even if this were not so it would be a trivial hierarchy with one despot and all others level with each other.

More interesting is that the workers seem NOT to be hierarchical in the hymenoptera. In all social species individuals recognise the differential influence of other individuals - and thus a ranked power ordering occurs. But apparently not among the worker bees etc. (And not among drones either.) It would appear that they are like your blood cells: none is more powerful than any other.

In short: reference the claim of hymenoptera hierarchy or chop it. - Pepper 02:52, 3 May 2006 (UTC)


  • (Although this hierarchy suggests male dominance, she [Susan McClary in Feminine Endings] also points out that in order to complete the form by unifying the themes in a single key in the recapitulation, the masculine theme is usually truncated, in a possible metaphor for castration.)

What page? I don't remember this in the book. Hyacinth 21:22, 15 May 2006 (UTC)

Merge Hierarchical organization into this article[edit]

The "Hierarchical organization" article suffers from a number of deficiencies. It was proposed some time ago to merge it into this one. Logically one would reduce "Hierarchical organization" considerably so that it would become a section of this article. Since there is no discussion of hierarchical organization in this article, it would add another dimension to it. Comments? Sunray 08:14, 3 August 2006 (UTC)

I think it might be better to merge Hierarchical organization with Social hierarchy and link from here. Those two article seem a bit at odds with each other. Anca 00:18, 6 September 2006 (UTC)
I agree with Anca, merge Hierarchical organization with Social hierarchy. nirvana2013 19:13, 4 November 2006 (UTC)

Opinion piece about Hierarchical Organizations[edit]

I removed this link from the page:

Interesting reading, and perhaps we can use the information therein, but it's not purely descriptive. Anca 00:07, 6 September 2006 (UTC)


The article claims the the derivation is from the Greek word for bishop. As far as I know, the most common words for bishop in Greek are episkopos and presbuteros. According to the American Heritage dictionary, hierarchy derives from the Greek for "rule of a high priest" - which seems to make more sense given the meaning "divine order" for hierarchy itself. The Greek for hierarch - hierarkhēs is composed of two parts - hieros = holy and arkhes = arch (in the sense of principal). I guess it could be argued that a bishop is a kind of high priest, but there are differences - for instance, there would typically be only one high priest at any point in time, while there would often be multiple bishops responsible for different areas. —Preceding unsigned comment added by (talk) 00:50, 3 October 2007 (UTC)

POV Definition[edit]

The language used in the current definition seems very loaded. Is hierarchy necessarily a ranking? Is the use of the word "subordinate" justified? This seems to imply some sort of value judgement, especially when applied to people. It also doesn't make sense in situations where you have a hierarchy, but one level is not necessarily "subordinate" to the others--take as an example, the biological hierarchy of cells being part of an organism, and the organism being part of an ecosystem. Neither level is really subordinate to the other...but there is hierarchical organization here. I'm going to change the language to try to make it more neutral...I think some suggestion or discussion would be helpful here too. Cazort (talk) 01:18, 23 November 2007 (UTC)

I was just thinking the same thing! Someone needs to correst this! (talk) 10:18, 6 March 2008 (UTC)

I've tried to fix this article by including paraphrased definitions from OED and a current Webster's unabridged. The problem I had with it was that it said members of the hierarchy had only one element above them; this is not supported by any general definition I could find. There is no doubt that "hierarchy" tpically/usually includes the notion of "subordinate," etc. Cells are "subordinate" parts of organisms, and organisms are "subordinate" parts of ecosystems. It's not a value judgment, it's a way of organizing things. Lou Sander (talk) 21:12, 23 April 2008 (UTC)

"they neglect to explain"[edit]

In the subsection titled "Ethics, behavioral psychology, philosophies of identity," the following quote can be found: "However, they often neglect to explain how society will function withouth hierarchical relationships, or to admit that they really just press for the adoption of a new hierarchy with their own particular group (i.e., women, gays, etc.) in a position of dominance within that hierarchy."

Other than the spelling error, I think this is an editorial comment. Many people have explained how society might function in this way. Joshuanorton (talk) 03:51, 16 July 2008 (UTC)


The artcle could maybe mention the concept of hieraticism, which is closely related to the notion of hierarchy. [1] ADM (talk) 20:50, 22 August 2009 (UTC)

Scattered info and possible merges[edit]

There is significant overlap and confusion between all of the following articles: hierarchy, hierarchy (mathematics), nested hierarchy, hierarchical organization, containment hierarchy and social hierarchy.

Hierarchical organization is the worst by far. I've just tried to organise it a bit, but it's disastrous. It wasn't even ever made clear that it refers to a government/business/social organization and not an "organization" of objects into a hierarchy. Now, I think that that one can be merged into Organizational structure, which it also overlaps significantly with. At the very least, I think it should be called Organizational hierarchy.

The other articles use the same examples over and over again without ever referencing the fact that it might belong to a subset of the hierarchical structure. For example, biological classification is a lengthy example in hierarchy, nested hierarchy and containment hierarchy. (According to the articles) Taxonomies are at least nested hierarchies, if not containment hierarchies; the confusion stems from the fact that there are subsets of hierarchies—a hierarchy of hierarchies!

The big problem here is that there seems to be no distinction made between hierarchy (mathematics) and hierarchy within any article other than hierarchy (mathematics). What is a containment hierarchy, for example???? It starts off with a mathematical description, but then starts listing off examples of hierarchical structures. So, is it supposed to be applied to sets or not? I'm thinking that this terminology was used to get the point across, but it's not actually mathematical. However, according to hierarchy (mathematics), it is a special kind of mathematical hierarchy. HUH??? There is a big difference between a mathematical hierarchy and a "regular" one.

I tried to start organising these all, but I'm completely at a loss. — Skittleys (talk) 16:18, 7 October 2009 (UTC)

Oppose merging organizational hierarchy and propose renaming it back to hierarchical organization. A hierarchical organization is a specific kind of organizational structure and shouldn't be merged. The scope overlap problems with hierarchy, social hierarchy appear to have been fixed. --Pnm (talk) 01:15, 3 June 2010 (UTC)
I concur with Pnm. There are organizational structures that are non-hierarchical (e.g., network and circular structures) so I think it would be inappropriate to merge organizational structure and organizational hierarchy into a single article. Ms. Citizen (talk) 20:46, 29 September 2010 (UTC)

Reference to broken DOI[edit]

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Completely illogical[edit]

This article is completely illogical. It is part of WikiProject Mathematics yet talks mainly about human hierarchies. Human history hierarchies are the least interesting and least general type of hierarchy. Because mathematical hierarchies and similar math structures must be generalized as if they were formal proofs, I will be rewriting most of the article soon. --Carrot Lord (talk) 12:58, 23 January 2013 (UTC)

Lacks important historical examples within groups of people.[edit]

For example, the mafia hierarchical system, a very sophisticated system, that displays the idea of nested child groups that branch off to other sub-groups quite perfectly in my opinion. These two well-written articles on Wikipedia should be referenced in the 'Historical Examples' — Preceding unsigned comment added by ChristerDaniel (talkcontribs) 18:02, 25 December 2014 (UTC)

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