Archive for the 'Mathematics' Category

October 27, 2018

“It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.”
~ “An Introduction to Mathematics”, A.N. Whitehead.

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December 28, 2016

“συμβόλον symbolon, an object cut in half constituting a sign of recognition when the carriers were able to reassemble the two halves. In ancient Greece, the symbolon, was a shard of pottery which was inscribed and then broken into two pieces which were given to the ambassadors from two allied city states as a record of the alliance.”

December 28, 2016

“Before I knew you, acting was the only reality of my life. It was only in the theatre that I lived. I thought that it was all true. I was Rosalind one night, and Portia the other. The joy of Beatrice was my joy, and the sorrows of Cordelia were mine also. I believed in everything. The common people who acted with me seemed to me to be godlike. The painted scenes were my world. I knew nothing but shadows, and I thought them real.”
~ Wilde

December 28, 2016

“Algorithmic thinking as a novel and productive point of view for understanding and transforming the sciences, started probably with Turing. Natural phenomena in many scientific fields (including mathematics, statistics, physics, astronomy, biology and economics) are intrinsically computational in nature: examples include chemical processes in living cells, the self-organizing behavior of complex systems consisting of many interacting particles, mechanisms governing human evolution, and the collective behavior of competing agents in an economy. These natural science areas should be explored through a computational lens.”

December 26, 2016

“Il modo di pensare scientifico possiede un’ulteriore caratteristica. I concetti che usa per costruire i suoi sistemi coerenti non esprimono delle emozioni. Per lo scienziato esiste solo l’essere, non il desiderio, il valore, il bene, il male, l’aspirazione. Finché restiamo nel dominio della scienza vera e propria, non possiamo mai incontrare una frase del tipo “Tu non mentirai”. Vi e’ come un freno puritano nello scienziato che cerca la verità: egli si tiene lontano da tutto ciò che è di carattere volontaristico o emotivo. Detto per inciso, questo tratto è il risultato di un lento processo, proprio del pensiero moderno occidentale.”
~ Einstein

December 26, 2016
In Leonardo’s view, “art, science, everything, including literature and philosophy, proceeded exclusively from nature. ‘No one should imitate the manner of another, for he would then deserve to be called a grandson of nature, not her son. Given the abundance of natural forms, it is important to go straight to nature rather than to the masters who have learned from her’.”
“In his view, all branches of knowledge were connected and interdependent, and man was always at the center. “Man is the model of the world”, as he put it. […] He discussed botany with the vocabulary of an embryologist or gynecologist, while he tackled anatomy in the spirit of a geographer. […] Everything is in everything, he seems to be saying. […] He was passionately pursuing his interests in twenty or more subjects.”
The ‘fantasie dei vinci’ in the Sala delle Asse are “symbols of both the infinity and the unity of the world, they proclaim that there must be a rule governing everything.” … Everything was connected, like the long echoes in Baudelaire’s poem, “in a deep and dark unity”.
“From 1490 on, Leonardo sought to assimilate and rigorously classify (according to what he called “my mathematical principles”) the whole of human knowledge, by structuring it, correcting it if necessary, and enlarging it if possible.”

~ “Leonardo. The artist and the man”, Serge Bramly.

December 26, 2016

“Many writers have reproached Leonardo for producing a cold, ungenerous art, overreflective and abstract, like an algebraic equation. It lacks “the tears and music of love”, according to André Suarès.”
~ “Leonardo. The artist and the man”, Serge Bramly.

December 26, 2016

“Per raggiungere la presa di coscienza fondamentale che le leggi della natura potevano essere espresse nella forma di equazioni differenziali, Newton doveva al tempo stesso congetturare le leggi e inventare il linguaggio matematico del calcolo infinitesimale in cui esprimerle.”
~ “Lo scienziato come ribelle”, Dyson.

June 19, 2016

“Mathematicae non sunt verae scientiae” ~ Pico della Mirandola

July 4, 2014

“Non mi pare che le parole e il linguaggio, per come sono scritti e parlati, ricoprano un ruolo nei meccanismi del mio modo di pensare. Le entità psichiche che appaiono elementi del pensiero sono segni determinati e figurazioni più o meno chiare che possono essere ripetute e ricombinate a piacimento. […] Nel mio caso, si tratta di elementi di natura visiva, qualcuno anche connesso all’attività muscolare: le parole comuni e gli altri segni vanno invece laboriosamente rinvenuti solo in un secondo momento, quando il suddetto gioco combinatorio si è stabilizzato a sufficienza e riesco a ripeterlo a volontà.”

~ lettera di A. Einstein a J. Hadamard