All of the math and history in this post is elaborated on in my paper here.

Are there any interesting applications of PURE math to the Social Sciences or History? Scarf's application of the Brouwer fixed point theorem to Economics is one of many examples of applying (arguably) pure Mathematics to Economics. Cartwright, Harary, and others appear to have used graph theory to model social relationships; however, on closer inspection they just used the

*language of graph theory*. In C.P. Snow's article,

*The Two Cultures*, he speculates that there is a cultural divide between the sciences and the humanities, which may make such collaborations difficult. This points to the lack of interaction between the sciences and the humanities being a sociological problem in itself; however, we are not going to go there.

There was

*an*application of Ramsey theory to sociology in the 1950's. In Jacob Fox's Lecture Notes in Combinatorics he tells the the following well known story:

In the 1950's, a Hungarian sociologist Sandor Szalai studied friendship relationships between children. He observed that in any group of around 20 children he was able to find four children who were mutual friends, or four children such that no two of them were friends. Before drawing any sociological conclusions, Szalai consulted three eminent mathematicians in Hungary at that time: Paul Erdos, Paul Turan, and Vera Sos. A brief discussion revealed that indeed this is a mathematical phenomenon rather than a sociological one. (Namely R(4)=18≤20.)

This is more of an anti-application since math was used to prove there was NO interesting sociology.

Recently there was a REAL application of Ramsey Theory to History, and later of History to Ramsey Theory. We summarize the results; however, the reader should look at the link above for more details.

- Sir Woodson Kneading, a scholar of pre-christian history of England noted that, from 600BC to 400BC, whenever 6 lords were in close proximity, war broke out (with one exception). Either 3,4, or 5 of them formed an alliance against the rest, or 3,4,5, or 6 hated each other and went to war. The exception: all six formed an alliance. Kneading hired a CS grad student, H.K. Donnut, to verify the data. (Note that they really used R(3)=6.)

- Kneading noted that, between 400BC and 200BC, whenever 18 lords were in close proximity, war broke out. Either 4,...,17 of them formed an alliance against the rest, or 4,...,18 hated each other and went to war. Again, Donnut verified the data (Note that they really used R(4)=18.)

- Kneading found more results of this sort. His resuls and speculations, when translated to mathematics, are Ramsey Theoretic.

- Kneading wrote a 300 page book on this topic using the data that he colleced and Donnut verified (Donnut declined to be a co-author since, in his view, Kneading did the intellectual heavy lifting).

- Alma Rho Grand, a combinatorist, saw Kneading's book and realized that Ramsey Theory would simplify the work tremendously. Grand and Kneading wrote an article of which Kneading said
*My paper with Alma says cleanly in 30 pages what I said clumsily in 300 pages*.

- Grand noticed that one of Kneading's examples had 48 lords in proximity but no war broke out. This was in an era where if 5 formed an alliance or if 5 hated each other then a war should happen. She verified that this configuration showed R(5)≥49. It is already known that R(5) ≤ 49. Hence she showed R(5)=49. (Note that R(5) was unknown before this time.)

This is a case where Ramsey Theory helped History and History helped Ramsey Theory. Hopefully there will be more.

~

Little did ErdÅ‘s know: if an alien force should approach the earth and demand R(5,5), we should ask the historians for help! Is there data to support any historiographic bounds on R(6,6)?

ReplyDeleteSo far no, but H.K. Donnut is looking at data from a later

DeleteEra where R(6,6) is relevant.

Great to know! Hope this is not a April Fool joke!

ReplyDeletePlease start using LaTeX for write ups. It looks ridic unprofessional.

ReplyDeleteAlso [Gra] change Natinal to National.

Correction, you did use Tex, but it turned out that the rendering on my display was horrible deceiving my eyes to believe that u used Word.

ReplyDeleteI have made the change Natinal-->National.

DeleteThank you.

I want to indicate that this joke has caused chaos and will probably cause more chaos in the future. For example, see this paper "Ramsey Theory" at "https://www.whitman.edu/documents/Academics/Mathematics/2016/Barton.pdf", and the PPT at "https://www3.diism.unisi.it/FAC/didattica/matdid/4763.pptx", which cite this story seriously. I just leave this worry here and hope the author can do something to prevent future bad impacts.

ReplyDeleteThanks for the heads up.

DeleteThe first one I knew about and have tried to contact the author- but was unable to. The second one is new to me.

I will now add to the beginning of the papers that they were an April fools day joke.

I had thought that the papers were `obviously a joke' but clearly I am mistaken.

I had the article on two places on my website.

DeleteOne was attachted to a course i no longer teach, so I just deleted that copy.

For the other one I ADDED to the end a discusion (which was actually a followup blog) ABOUT the hoax. This way people can read it, enjoy it, and THEN find out it was a hoax.

I might do an April Fools Day post ABOUT April Fools day posts.

Thanks for your reply.

DeleteIn fact, I arrived at your article and this blog via Google, to find the source of this story. But I just searched again and found the same contents as before. I guess many people may have searched similarly and then believe this joke or not.

I don't really know how to make things right. Good luck!

AH- I had only fixed the PAPERS- based on your post above, I have now fixed the original BLOG POST. So check again- if you are getting to a source that still does not admit it a hoax than pleae post (or email me directly) the place you found.

DeleteSo just search "Ramsey Theory and the History of Pre-Christian England" at Google, I can find this pdf "http://www.cs.umd.edu/~gasarch/BLOGPAPERS/ramseykings.pdf" and this "https://www.cs.umd.edu/~gasarch/COURSES/858/S13/ramseykings.pdf", as well as other relevant websites.

ReplyDeleteI think in the second pdf, only "http://www.cs.umd.edu/~gasarch/BLOGPAPERS/r5.pdf" indicates directly the whole story is just a joke. So I guess many people may not have the patience to check the validity of this story.

AH- you found one that I had missed from my own website, from my Spring 2013 class on Ramsey Theory- I have removed that one entirely.

ReplyDeleteI then googled ``Ramsey Theory and History''- I found one website that forutanly seems to link to my corrected version. I found another website that had doc in its name that you should NOT click on- I got a warning from microsoft that was likely a scam.

Anyway, I think we've done all we can do and I THANK you for bringing this to my attention.

Aha, I find that I could still visit those files simply because I didn't delete the data of my browser. So things are better now.

DeleteI have read your updates on the story. It is interesting.

Anyway, thank you for your actions. And I hope it may not cause more chaos in the future.