An attempt to show how applications of pure mathematics can work in social sciences.
Great French mathematician Andre Weil ( 1906 - 1998 ) is well known in history of social anthropology. In fact, he was co-author of Levi - Strauss 's The elementary structures of kinship and his a very short algebraic introduction in Levi-Strauss solution is contained in LS book on kinship. In 1940s Andre Weil was ready for such sort of collaboration with anthropologist. In 1920 he taught himself Sanskrit and had deep interests in Greek, Latin, correspondingly - Hinduism also. His number theoretical structuralism was connected with the mathematical separation of the infinite descent argument into 2 types in newly created Algebraic Geometry. However, after publication of LS book their cooperation became less intensive and Levi-Strauss changed his research direction to Trubetskoy - Jacobson's linguistics. Today, nevertheless, it could be interesting to introduce another unknown Weil's mathematical findings and theorems in theoretical anthropology.
Another masterpiece of Weil is his theorem on representation of irrational numbers which has remarkable applications in mathematical geography, comparative demography and comparative company assessments in international business. I try to apply Weil's theorem for Brexit prediction.
Theorem. Let the first digits of number 2^n, where n =0;1;2;....Then statistics of their distribution is Weilian or 1;2;4;8;1;3;6;1;2...
Demonstration. Number 1 has a statistical weight 29%, 2 has 21%, 3 has 11%, 4 has 10%, 5 has 6%, 6 has 6%, 7 has 8%, 8 has 3% and 9 has 6%.
In 1980s Konstantinov and Arnold in 1997 showed that distribution of areas and populations in current national boundaries is Weilian .For example, Weil's index or relation of area : population for France is 5/6; UK 2/6; Italy 3/6; Ukraine 6/4; Georgia 6/4. It is very remarkable that our highly abstract theorem is able to catch essential characteristics of reality. Indeed, two currently disintegrated nations - Ukraine and Georgia have the same Weil Index!
Prediction. In comparison with Weil index for disintegrated nations, Italy and UK have some kind of reserve of stability - UK 2/6 and Italy 3/6. Thus, it could be difficult to represent UK in some deepest fundamental spatial sense as disintegrated nation. Hence, any kind of referendum of Brexit type cannot change status quo and it is quite logical that on 23.06.2016 majority of UK population must vote STAY in the EU community.
FRAGILITY (THEOREM) BECAME KEY POINT
LSE - Oxford 'Blavatnik Commission on State Fragility, Growth and Development ( David Cameron to chair Commission from March 2017 ) was established at least. I used this theorem ( Taleb fragility transfer theorem ), however, taking new systematic theory seriously is needed. Current failure of Ukraine State and Brexit activation are producing unexpected mathematical difficulties in the building resilience to shorks.
I see this is a resilient and on-going thread Michael. As the site is moving over to here www.openanthcoop.net, if you still wish to keep this thread going I could move it over there if you wish to keep hosting this discussion? Otherwise look forward to seeing you on the forums on the new site. Thanks