Science is the best thing we can do. And I think it is better for men to seek order in a chaotic manner instead to study chaos in an orderly fashion.

Thursday, September 27, 2007

Cind lucrurile se complica...

Well, some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. The Last Theorem is the most beautiful example of this. Andrew Wiles
Uneori ma gindesc, revenind la complexitatea stiintei moderne, mai ales la cercetarile de virf din domeniul fizicii teoretice, ca lipseste ceva fundamental daca lucrurile s-au complicat asa. Ca orice om preocupat de matematici, am invatat de timpuriu ca, de multe ori, atunci cind o rezolvare se complica mai mult decit ar fi cazul, ceva nu e in regula. Pe de alta parte, nu se stie prea bine ce inseamna ca o demonstratie se complica mai mult decit ar fi cazul. Fiindca atunci cind e vorba de conjecturi problematice care persista, nimeni nu poate sti cit ar fi cazul sa fie de complicata demonstratia, si, pina la urma, ceea ce conteaza cel mai mult este sa se stie daca o afirmatie este adevarata, si asta indiferent de lungimea demonstratiei. Mai mult, rezolvarea complicata a unei probleme poate fi corecta -- vezi, de pilda, ultima teorema a lui Fermat si demonstratia finalizata, ce-i drept, cu peripetii (in 1995), data pe citeva sute de pagini de Andrew Wiles: mai intotdeauna apar si alte rezolvari mai simple si mai ingenioase, dar care beneficiaza de rezultate sau descoperiri ulterioare. Ce-i drept, in cazul Wiles, problema nu se pune deloc asa: pentru a obtine demonstratia, el a trebuit sa inoveze masiv, nu atit sa dezvolte noi ramuri in matematicile moderne, cit sa lege domenii care pareau complet diferite, si asta, sprijinindu-se pe rezultatele multor matematicieni de virf.

Poti crea insa multa matematica de virf fara vreo legatura cu fizica, si, din cite imi pot da seama, in fizica, ceea ce am afirmat legat de complexitate se sustine in mod sistematic: atunci cind lucrurile se complica, nu doar ca ceva nu e in regula, dar putem vorbi de o oportunitate: in orice caz, de un bun prilej de a inova, de a gasi noi instrumente matematice, tocmai pentru ca lipseste ceva fundamental. Cam asta e ideea.
Do not worry too much about your difficulties in mathematics, I can assure you that mine are still greater. Albert Einstein
Si fiindca am amintit de Andrew Wiles, nu ma pot abtine sa preiau iarasi citeva link-uri de la youtube: am vazut chiar zilele trecute ca exista riscul ca fisierele video la care se face o referinta sa fie sterse la un moment dat. Dar in cazul asta merita sa imi asum riscul.

Fermat's Last Theorem - 1/5


Fermat's Last Theorem - 2/5


Fermat's Last Theorem - 3/5


Fermat's Last Theorem - 4/5


Fermat's Last Theorem - 5/5

Einstein about mathematics:

Pure mathematics is, in its way, the poetry of logical ideas.

Mathematics are well and good but nature keeps dragging us around by the nose.

As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.

God does not care about our mathematical difficulties; He integrates empirically.

All these constructions and the laws connecting them can be arrived at by the principle of looking for the mathematically simplest concepts and the link between them.

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