Talk:Erdős number

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Removed cfdnotice, cfd has completed. --Kbdank71 16:08, 9 May 2008 (UTC)

I have heard of people who published multiple papers with Erdos having fractional Erdos numbers. For instance if you published 5 papers directly with Erdos you have a number of 1/5. Has anyone else heard of this usage? —Preceding unsigned comment added by 24.91.5.2 (talk) 02:55, 1 September 2007 (UTC)

Why is there a link to "Umlaut"? In fact the 4th character in Erdos' name is not the ö (o-umlaut, ö) mentioned on the Umlaut page.

ö has two dots above the o, while Erdos has a "long Umlaut", which looks more or less like two acute accents close to each other, but the Umlaut page does not mention it. Aleph4 12:17, 8 Dec 2003 (UTC)

There is an Erdos Number of 5 on sale at ebay: http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=3189039958 . This is too ephemeral to put into the article yet, I think, but maybe once the auction is over it might be worth a mention. --Zero 23:04, 21 Apr 2004 (UTC)

The link is now dead and should probably be removed from the article

Since the location of the Paul Erdos article no longer has an umlaut (see Talk:Paul Erdos for discussion), I think that for consistency this article should live at Erdos number. --Saforrest 23:03, Apr 14, 2005 (UTC)

Done.
Urhixidur 01:54, 2005 Apr 15 (UTC)

Contents

[edit] Not just mathematicians

There seems to be some disagreement about the scope and applicability of Erdos numbers. I removed the explicit references to "mathematicians" in the definition, then someone restored it, and now we're back to the more generic "authors". I'd just like to point out that many physicists and computer scientists have Erdos numbers. For example, our own article on the physicist Brian Greene mentions the fact that he has both an Erdos number and a Bacon number. I would imagine that academics in many other fields have Erdos numbers as well. In fact, the whole point of the concept is to illustrate the small world phenomenon, so artificially restricting it to the even smaller world of mathematics defeats the purpose. --MarkSweep 19:22, 23 May 2005 (UTC)

I noticed the following sentence in the article: A small number of people are connected to both Erdős and Bacon and thus have a finite Erdős-Bacon number. Wouldn't that small number be either 0 or else everybody in the union of both graphs? (which would in fact then be the same graph, with a different specified root)--Ramsey2006 16:01, 20 January 2007 (UTC)
Never mind...different criteria for the edges. --Ramsey2006 16:03, 20 January 2007 (UTC)
The concept is not restricted to mathematicians, but it is restricted to "mathematical papers", as the definition says. So Brian Greene may well have an Erdos number, if he coauthored a mathematical paper. As to it being "arbitrary", of course it is, all definitions are arbitrary. Erdos number could have been defined to include say any kind of published material, not just mathematics, but it wasn't. The article merely reflects that original choice. In my experience, the definition given in the article correctly describes how the term is currently understood and used. If you think that the article incorrectly defines Erdos number, I would have to see some reliable source for this notion, before I could agree with it. Paul August ☎ 19:58, May 23, 2005 (UTC)

http://www.oakland.edu/enp/readme.html "There is an edge between vertices u and v if u and v have published at least one mathematics article together. (There is no reason to restrict this to the field of mathematics, of course.)" This is further clarified: "Our criterion for inclusion of an edge between vertices u and v is some research collaboration between them resulting in a published work. Any number of additional co-authors is permitted. " Also see: http://www.oakland.edu/enp/erdpaths.html The definition used by the Erdos Number Project, although not "official" in an academic or bureaucratic sense, is well-established and does seem to include physicists and biologists. A note on the end indicates that a peace manifesto coauthored by Einstein, and reproduced in the New York Times, assigned Einstein a 2 and the other to-be-Nobelist collaborators a 3.

[edit] Do Wikipedia articles count?

Does any Wikipedia article count as a mathematical paper? --Army1987 22:01, 11 September 2005 (UTC)

Definitely not. Wikipedia is encyclopedic; it contains only things that have already been thought.
—Preceding unsigned comment added by 203.122.243.160 (talk • contribs)
Rats --h2g2bob 21:04, 6 November 2006 (UTC)
Ok, this makes me wonder: which Wikipedia articles has Erdős edited? 70.55.69.5 23:27, 17 January 2007 (UTC)
He hasn't, so far as I know. But McKay has edited this talk page, so I guess that my adding this edit bumps me up from 3 to 2 ;-p --Ramsey2006 08:02, 20 January 2007 (UTC)

[edit] Not exactly an Erdős number...

Although I don't have an actual Erdős number, and probably never will, I have studied small amounts of computer science and mathematics under someone who took a combinatorics course (in computer science) under Ralph G. Stanton (who has Erdős number 2). CanadaGirl 12:07, 7 April 2006 (UTC)

Courses don't count, I'm afraid. If they did, I'd have an Erdős number by virtue of this guy. --Saforrest

[edit] Average of 5?

From the article: "...the average is less than 5, and almost everyone with a finite Erdős number has a number less than 8." Of course, the average is not less than 5, since many people have an infinite Erdős number. Among those with finite, what is the source for the average being less than 5? Perhaps it should be median? I am inclined to delete the sentence if there is not a source. (Cj67 21:11, 25 June 2006 (UTC))

CJ, some people mean "finite Erdos Number" when they say "Erdos Number". So the line can be made unambiguous by writing "...the average finite Erdos Number is less than 5...". Since I myself wouuld prefer that high-school students not consider infinity as a number (but as part of a process), I prefer to say "Spencer's Erdos Number is 1 and Pete does not have an Erdos Number" instead of "...Pete's EN is infinity". Some things called infinity, such as Aleph-Null and Omega, can indeed be considered as numbers in certain number fields, but that's an advanced topic and people studying those topics don't need to be warned about the ambiguity. Pete St.John (talk) 17:46, 17 December 2007 (UTC)
  • The Erdos number project analysed the data from Math Reviews. I added a few words to the article. --Aleph4 22:14, 25 June 2006 (UTC)

[edit] Gauss-Minkowski - just ain't gonna work

I'm sorry, but this just doesn't cut it:

However, according to MathSciNet Carl Friedrich Gauss (born 1777) has Erdős numbers 4 as follows: Gauss – Hermann Minkowski – Albert Einstein – Ernst Gabor Straus – Erdős. The connection between Gauss and Minkowski is a collection of essays containing separate works of both authors.

Gauss died in 1855. Minkowski was born in 1864. So, there is no way they could in any real sense of "co-author" co-author anything. Having Gauss & Minkowski's works collected in the same volume does not count in any way as a collaboration between the two, but merely a decision of later editors..... So I will delete this bit. --SJK 11:14, 20 July 2006 (UTC)

Agreed. McKay 13:08, 21 July 2006 (UTC)

Infinity is not a number. If a person doesn't have a chain of coauthors linking them to Erdős, you can say their Erdős number is infinite or say that it's undefined. Erdős number and finite Erdős number are synonyms. --Awis 06:15, 8 August 2006 (UTC)

I've just realized that my Erdös number is 3. I have published with Gilles Brassard. Hugo Dufort 03:43, 25 October 2006 (UTC)

[edit] Concise and meaningful language

This article keeps using the term 'finite' to describe Erdős numbers. I think this is a bit ridiculous, even more so to say that if a person doesn't have a chain of co-authors linking them to Erdős that their Erdős number is infinite! What is the point in such language when it doesn't serve to convey a concise meaning? Far better to say in more concise and explanatory fashion that they either have an Erdős number or they don't.

The article also talks at one stage about the earliest person to have a *positive* finite Erdős number. This is even more ridiculous since by definition there is no such thing as a negative Erdős number. I have to wonder about the motivation to embellish the language with such pointless words.

Kevin

I agree with you about the "positive". As for "infinite", the problem is that more than one definition of "Erdős number" is going around and both definitions are mixed up in the article. In one version, some people have an Erdős number and some don't. In the other version, everyone has an Erdős number but some of them are "infinite" (a phrase never defined precisely, but the whole thing is informal). My recollection of the way combinatorialists talked about it when Erdős was still alive is that the second version was more popular. It is also the definition used in the quasi-official Erdős number project [1]. So I propose writing the whole article in that fashion, with a passing mention that some people prefer "not existing" over "infinite". McKay (Erdős number 1) 03:35, 13 November 2006 (UTC)
Here "positive" must mean "non-zero". The earliest person to have a non-negative Erdos number is, by definition, Paul Erdos. —Preceding unsigned comment added by 134.96.105.72 (talk) 11:32, 17 February 2008 (UTC)

[edit] Pronunciation

Would someone who is familiar with IPA please add the pronunciation according to it? Most people aren't familiar with Hungarian and will mispronounce the name. -Emiellaiendiay 07:42, 17 November 2006 (UTC)

Could someone please add a stress mark to the IPA? Is it ˈɛrdøːʃ or ɛrˈdøːʃ? Stevvers 21:27, 8 April 2007 (UTC)
Still missing after 7 months. Surely someone must know. And is there an anglicised equivalent (UK ˈɛədɜːʃ/US ˈɛrdɜːʃ, perhaps)? — 85.211.4.226 15:35, 11 November 2007 (UTC)

[edit] why?

can someone explain why erdos was chosen, and why it is considered so important? I'm struggling to see how having a high Erdos number is in any way "good" or worthy of any note whatsoever. Same with the Kevin Bacon thing. May I suggest a football one for Liam Brady?

). Got a 61 in his course though (not due to lack of effort). - 212.247.170.12

  • You should read about Paul Erdos; a fascinating man. He was highly idiosyncratic, very much respected as a genius in the field; and he travelled widely, meeting huge numbers of fellow mathematcians. That's why he was chosen.
  • A high Erdos Number isn't good. Low numbers are prestigious; 1 means you coauthored with the Great Man himself, 2 means you coauthored with someone 1, and so on. The lower your number, the closer you are (in this sense) to a group of very productive and regarded mathematicians. Of course you might also be close to them in other ways, and not have any number at all. Having a low number is like attending a prestigious school, it doesn't mean you are cool, it is just one piece of evidence.
  • Yes, the same thing is done with other personalities, e.g. appearing in a movie with Kevin Bacon. Pete St.John 19:50, 2 November 2007 (UTC)
  • I was told that Erdos is the guy this is done with because he worked on the field of random graph theory, which is related to the idea of the Erdos #. --68.231.149.139 08:41, 4 December 2007 (UTC)
Erdos did a lot of work in Graph Theory generally; the Erdos-Spencer Probailistic Method is conspicuous but not particularly pertinent to Erdos Numbers. Erdos coauthored with a huge number of people (500 odd). If you consider the graph G with E set defined by (x,y) in E when x coauthors with y, then Erdos is the highest degree node in the largest connected component. That makes him a natural "root" node to designate. Pete St.John 19:14, 4 December 2007 (UTC)

[edit] Include Gowers Numbers?

http://www.math.ucla.edu/~timaustin/wranglejump.html

[edit] number of co-authors

The Erdos Project lists Erdos as having 511 co-authors (i.e. people with a number of 1) but this article only lists 509. I don't know anything about this, but can somebody who does either explain that or fix it (would assume we'd need to fix the number of 2s,3s, but maybe thats in the project website again) Spurgistan 19:59, 29 April 2007 (UTC)

a great many of the papers involved were never in electronic form (unlike today, when almost any paper would be composed originally MSWord, at least, if not TeX or whatever). So cross-linking all the bibliographies is a huge manual job. Pete St.John 19:54, 2 November 2007 (UTC)

[edit] Deletion of the Category

The category for Erdos Numbers, e.g. "Carliz (category persons with Erdos Number 2)" has been deleted. There have been several debates about this, but the most recent one led to deletion. It's actually a very interesting social phenomenon; I invite mathematicians with any concern for pedagogy and general public perceptions to look at some of the reasons given for the deletion. The admin who deleted it has begun to compile some of the reasons given at a talk page, and I have added some rebuttals, but I can tell you it's frustrating. It just astonishes me that so many innumerate people would even care about Erdos Numbers. Pete St.John 19:41, 2 November 2007 (UTC)

Being the editor who nominated these categories for deletion in this third instance, I'd like to comment that I personally do appreciate the pedagogy argument. I just thought that Wikipedia's present category scheme is unsuitable for this activity. A lot of useful connections could be categorized if we had a more flexible technical solution than at present. __meco 11:31, 3 November 2007 (UTC)
The desirability of a better mechanism doesn't justify destroying the exisiting one. Please program a better one, or propose a better existing one, and then vote to switch to the better system, instead of just destroying the existing one. Pete St.John 17:41, 5 November 2007 (UTC)
I think's a great pity that a few of the editors who wanted this category kept have not also retained their civility. Describing the delete !voters as "innumerate people" is a quite unnecessary personal attack. --BrownHairedGirl (talk) • (contribs) 01:07, 4 November 2007 (UTC)
I don't mean to "attack" any individuals. I've described the group as "innumerate", yes, because the logic presented isn't coherent to me. As a whole, they seem to be non-mathematicians with no identifiable interest in the topic, and I have no clue, honestly, what they want. Pete St.John 17:41, 5 November 2007 (UTC)
It may be taht there is a problem with using the category system for this. If there is I must admit that I do not understand what the problem is. It seems to me for example much better to use categories than lists due to the problem of maintenance. At the moment the Edos numbers are being deleted from pages which is a shame as people have put in the effort to calculate (at least an upper bound for) them. When I added the Erdos number to a biography I placed an example of a sequence of authors giving taht number as a comment (sometimes in the text as a comment as wel as edit summary). This leads me to propose that for Mathematicians at least with Edos number up to 4 we make a template that will give an upper bound on the Erdos number with an example of a chai of the right length (surnames of authors will do) in small print. This way if some other mechanism becomes appropriate for forming lists or doing searches it can just be added to the template. How does taht sound? Billlion 17:01, 4 November 2007 (UTC)
The suggestion of an infobox has been made in the discussion on the CfD talk page. I would suggest that there is no reason to stop at 4 or 6 or any number. If a math bio article is about one of the five vertices with Erdos number 13 (supposedly the diameter of the graph at this time), or if the vertex is not connected to the Erdos component, that fact just as interesting, and worthy of mention in an infobox. I'm not realy sure that a chain is really necessary, except in cases where the standard automated tools at MathSciNet don't provide one, or where the standard tools give a number higher than the actual verifiable bound. --Ramsey2006 17:18, 4 November 2007 (UTC)

[edit] Distribution over time

Someone just deleted the statement ... As a result of this drift, the mean Erdős number of living people must increase over time... as unsourced and "illogical". The statement does not say monotone increasing; changing it to "must tend to increase..." would be an improvement. But a little simple logic (which this is) in common language should be OK for explaining what's going on, to laymen. In an article about prime numbers I would show why 3 is prime, not cite a specific reference for that particular piece of fact. So I would prefer improving the explication, to merely deleting it. Pete St.John 16:36, 3 December 2007 (UTC)

  • Perhaps "tends to increase"? While you are at it, you might also want to do something about the section title ("Effect of Erdős' death on the Erdős number") which doesn't really fit the contents. Roger Hui 18:53, 3 December 2007 (UTC)
Related to the section "Effect of Erdős' death on the Erdős number," it should be noted that a handful of people continue to get Erdős numbers of 1. According to the Erdős Number Project, the latest was a paper in 2007. Sillcat (talk) 11:50, 17 February 2008 (UTC)

[edit] One of these things is not like the other.

Article is self-contradictory, viz:

"Effect of Erdős' death on the Erdős number

Given that Erdős died in 1996 and no works of his remain to be published, it is no longer possible for a person to be newly assigned an Erdős number of 1."; and

"eBay auctions

%< snip >%

This is noteworthy because with the exception of a few co-written articles to be published posthumously, 2 is the lowest number that can now be achieved." —Preceding unsigned comment added by 202.89.169.22 (talk) 03:07, 26 December 2007 (UTC)