Camil Stoenescu's blog

Folosind instrumente matematice se încearcă analizarea conflictelor armate din prezent:

IN 2003, US soldiers in Iraq were given a pack of playing cards showing Iraq’s"most-wanted". In the top position – the ace of spades – was Saddam Hussein. His sons Qusay and Uday were the ace of clubs and the ace of hearts. The message was simple: capture the entire pack, and regime change would be achieved and the war in Iraq won.

It hasn’t worked out to be that easy. Part of the reason is that in this age of terrorist attacks, insurgencies and "asymmetric" wars between parties of vastly differing firepower, the dynamics of conflicts have shifted irrevocably. Now mathematicians are starting to build models of how such present-day warfare plays out. As they do so, they are coming to the conclusion that it is time to rewrite the military rule book.

Mathematics can never hope to fully encapsulate the complex business of war. It has long been used, however, to suggest tactical approaches. During the first world war, for example, the English polymath Frederick Lanchester devised a series of equations to calculate the power balance between opposing forces in a classic symmetric war, in which two hierarchically organised armies fight until one keels over.

Lanchester showed that long-range weapons had changed such conflicts. In old-style one-on-one combat, an army’s strength was proportional to the number of men or guns at its disposal. Weapons that allowed many targets to be attacked simultaneously increased that potential, upping an army’s strength so that it was proportional to the square of its firepower. Concentrating your army’s firepower, dividing enemy forces, and removing opposition leaders to disable the units under their control were key tactics that followed (see "Lanchester in action").

De aici.

Robot care rezolvă cubul Rubik:

Stephen Wolfram, creatorul Mathematica și Wolfram Alpha

Sau despre folosirea cretină a comparațiilor și analogiilor (irelevante):

de aici.

The Game of Life (or simply Life) is not a game in the conventional sense. There are no players, and no winning or losing. Once the "pieces" are placed in the starting position, the rules determine everything that happens later. Nevertheless, Life is full of surprises! In most cases, it is impossible to look at a starting position (or pattern) and see what will happen in the future. The only way to find out is to follow the rules of the game.

De aici.

The Economist demontează vechea prejudecată referitoare la faptul că băieții sunt mai buni la matematică iar fetele la orice presupune folosirea cuvintelor.

O echipă de cercetători italieni (condusă de Luigi Guiso) consideră că explicațiile respectivelor deosebiri sunt de ordin cultural, nu biologic (precum ar fi o structură mentală a priori diferită, ce prelucrează diferit informația). Este logic să fie așa, din moment ce fetelor și femeilor li s-a negat accesul la educație – sau cel puțin la același tip de educație precum cea masculină – cea mai mare parte din istorie. Excepțiile, începând cu Hypatia și terminând cu Emmy Noether, au rămas doar atât – excepții.

Importanța crucială a tradiției istorice și a cadrului cultural este relevată cât se poate de limpede de faptul că țările ce au prezentat diferențe mari între abilitățile matematice ale băieților și fetelor au fost tocmai acelea în care egalitatea dintre sexe este (încă) o vorbă goală, precum Turcia. În schimb, în țări precum Norvegia sau Suedia, diferențele sunt practic neglijabile.

Luigi Guiso of the European University Institute in Florence and his colleagues have just published the results of a study which suggests that culture explains most of the difference in maths, at least. In this week’s Science, they show that the gap in mathematics scores between boys and girls virtually disappears in countries with high levels of sexual equality, though the reading gap remains.[…]

On average, girls’ maths scores were, as expected, lower than those of boys. However, the gap was largest in countries with the least equality between the sexes (by any score), such as Turkey. It vanished in countries such as Norway and Sweden, where the sexes are more or less on a par with one another. The researchers also did some additional statistical checks to ensure the correlation was material, and not generated by another, third variable that is correlated with sexual equality, such as GDP per person.

Partea masculină se poate consola cu faptul că băieții sunt mai buni la geometrie, cu tot ce rezultă de aici – „bărbații au simț de orientare mai bun”

Studiu despre efectele concurenței dintre două specii într-un habitat dat:

The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individual-based model describing the competition of two species and incorporating all the above ingredients. We find that the presence of habitat preference — generating spatial niches — strongly stabilizes the coexistence of the two species. Eliminating habitat preference — neutral dynamics — the model generates patterns, such as distribution of population sizes, practically identical to those obtained in the presence of habitat preference, provided an higher immigration rate is considered. Notwithstanding the similarity in the population distribution, we show that invasibility properties depend on habitat preference in a non-trivial way. In particular, the neutral model results results more invasible or less invasible depending on whether the comparison is made at equal immigration rate or at equal distribution of population size, respectively. We discuss the relevance of these results for the interpretation of invasibility experiments and the species occupancy of preferred habitats.

Restul – aici. (vedeți că nu e cu vorbărie)

S-o aplica și în cazul femei vs bărbați?

Sau ce legătură este între Ecuația lui Drake și probabilitatea găsirii unei partenere potrivite?

Peter Backus, un american, doctorand în Marea Britanie, ne dă răspunsul – jumătate în glumă, jumătate în serios – într-un studiu intitulat sugestiv „Why I don’t have a girlfriend”.

While extraterrestrial civilizations may be rare, there is something that is seemingly rarer still: A girlfriend. For me. What might the approach employed in the estimation of the number of alien civilizations tell us about the number of potential girlfriends for me? A somewhat less scientific question,I admit, but one of substantial personal importance.

The parameters are re-defined as follows with the values in parentheses:

Concluzia e pesimistă: din 30 de milioane de femei din Marea Britanie, doar 26 i se potrivesc autorului .

Documentul integral poate fi găsit aici. Un articol din Daily Telegraph, aici și ceva comentarii, aici.

PS  Un calcul similar a fost făcut în 1999 şi de Tristan Miller.

Cea mai frumoasă formulă în care este implicat numărul transcendental Pi? Identitatea lui Euler:

Mai multe lucruri amuzant-interesante despre pi, aici și aici.

Cineva mai cunoscător decât mine în ale fizicii mă trage de urechi și-mi spune că teoria lui nenea Lisi e cam greșită. Așa că mă conformez și vă indic o demontare argumentată:

ABSTRACT. We analyze certain subgroups of real and complex forms of the Lie group E8, and deduce that any “Theory of Everything” obtained by embedding the gauge groups of gravity and the Standard Model into a real or complex form of E8 lacks certain representation – theoretic properties required by physical reality. The arguments themselves amount to representation theory of Lie algebras in the spirit of Dynkin’s classic papers and are written for mathematicians.

Dacă nu înțelegeți mai nimic, nu vă îngrijorați. E semn că sunt încă lucruri la care nu ne putem pricepe cu toții, oricât de acut ar fi acest sindrom în spațiul virtual.