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Yes, the ratio of the circumference of a circle to its diameter has is own day also. It’s Pi Day. March 14th. Created by physicist Larry Shaw, Pi Day is a holiday commemorating the mathematical constant π (pi). There is a reason for this date. Pi Day is celebrated on March 14 (or 3/14 in month/day date format), since 3, 1 and 4 are the three most significant digits of π in the decimal form. If you want to check it out, here are the first one million digits of π. Ironically, this is also the date when Albert Einstein was born. So, how about some good music along with that, to celebrate it?!

Picture – Albert Einstein standing on a rock stepping-stone, enjoying grabbing some sun at the sea shore (1945). Oh! … the sea shore. By the way, Mr. Einstein, what lovely sexy shoes you have!

[…] Einstein always appeared to have a clear view of the problems of physics and the determination to solve them. He had a strategy of his own and was able to visualize the main stages on the way to his goal. He regarded his major achievements as mere stepping-stones for the next advance. […] In his early days in Berlin, Einstein postulated that the correct interpretation of the special theory of relativity must also furnish a theory of gravitation and in 1916 he published his paper on the general theory of relativity. During this time he also contributed to the problems of the theory of radiation and statistical mechanics. […] After his retirement he continued to work towards the unification of the basic concepts of physics, taking the opposite approach, geometrisation, to the majority of physicists. […] (source Nobel prize org.)

Einstein on the Beach : Philip Glass / Robert Wilson, 1976.

[…] Einstein on the Beach (1976) is a pivotal work in the oeuvre of Philip Glass. It is the first, longest, and most famous of the composer’s operas, yet it is in almost every way unrepresentative of them. Einstein was, by design, a glorious “one-shot” – a work that invented its context, form and language, and then explored them so exhaustively that further development would have been redundant. But, by its own radical example, Einstein prepared the way – it gave permission – for much of what has happened in music theater since its premiere. Einstein broke all the rules of opera. It was in four interconnected acts and five hours long, with no intermissions (the audience was invited to wander in and out at liberty during performances). The acts were intersticed by what Glass and Wilson called “knee plays” – brief interludes that also provided time for scenery changes. The text consisted of numbers, solfege syllables and some cryptic poems by Christopher Knowles, a young, neurologically-impaired man with whom Wilson had worked as an instructor of disturbed children for the New York public schools. To this were added short texts by choreographer Lucinda Childs and Samuel M. Johnson, an actor who played the Judge in the “Trial” scenes and the bus driver in the finale. There were references to the trial of Patricia Hearst (which was underway during the creation of the opera); to the mid-’70s radio lineup on New York’s WABC; to the popular song “Mr. Bojangles”; to the Beatles and to teen idol David Cassidy. Einstein sometimes seemed a study in sensory overload, meaning everything and nothing…  […] (continues) [source ]

KNEE 5 | KNEE PLAY CHARACTER 1 : Numbers and Mr Bojangles /  KNEE PLAY CHARACTER 2 : Text from Knee Play 1 / BUS DRIVER : Lovers on a Park Bench

1,2,3,4… 1,2,3,4,5,6, …,1,2,3,4,5,6,7,8,… 1,2,3,4… 1,2,3,4,5,6, …,1,2,3,4,5,6,7,8,… 1,2,3,4… 1,2,3,4,5,6, … 2,3,4, … 1,2,3,4, … 1,6 …

Two lovers sat on a park bench with their bodies touching each other, holding hands in the moonlight. There was silence between them. So profound was their love for each other, they needed no words to express it. And so they sat in silence, on a park bench, with their bodies touching, holding hands in the moonlight. Finally she spoke. “Do you love me, John ?” she asked. “You know I love you. darling,” he replied. “I love you more than tongue can tell. You are the light of my life. my sun. moon and stars. You are my everything. Without you I have no reason for being.” Again there was silence as the two lovers sat on a park bench, their bodies touching, holding hands in the moonlight. Once more she spoke. “How much do you love me, John ?” she asked. He answered : “How’ much do I love you ? Count the stars in the sky. Measure the waters of the oceans with a teaspoon. Number the grains of sand on the sea shore. Impossible, you say? “, (text by Samuel Johnson).

Caption – 1st page of Erdös, P.; Rényi, A. (1960). “On The Evolution of Random Graphs“. Magyar Tud. Akad. Mat. Kutató Int. Közl. 5: 17 [PDF].

Documentary film – “N is a Number: A Portrait of Paul Erdös” directed by George Csicsery | 1993 | 57 min. (9 parts)

There are three signs of senility. The first sign is that a man forgets his theorems. The second sign is that he forgets to zip up. The third sign is that he forgets to zip down“, Paul Erdös.

Paul Erdös was an immensely prolific and notably eccentric Hungarian mathematician. Erdös published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory. He wrote around 1,475 mathematical articles in his lifetime, mostly with co-authors. He strongly believed in and practised mathematics as a social activity, having 511 different collaborators in his lifetime (source).

Having no home, while globe trotting the world from place to place, living mostly for short periods in friend’s and colleagues houses, almost as if he was travelling from one set of mathematics, to another, it was not only the quantity of his work which was tremendous, but mainly the quality and impact of his works. It was not rare, that a single paper, produced a entire brand new field of research. One of my favourite examples, it’s his paper with Rényi on random graphs (image caption above): Erdös, P.; Rényi, A. (1960). “On The Evolution of Random Graphs“. Magyar Tud. Akad. Mat. Kutató Int. Közl. 5: 17 [PDF]. Alone, this single 5 pages paper emerged a  new science branch, critical in our times: Complex Networks. The work is now being cited +2500 times.

Fig. – Erdös and Rényi (1959, 1960, 1961) were the first to introduce the concept of random graphs in 1959. The simple model of a network involves taking some number of vertices, N and connecting nodes by selecting edges from the N(N-1)/2 possible edges at random  (Albert and Barabási 2002; Newman 2003). Figure shows three random graphs where the probability of an edge being selected is p=0, p=0.1 and p=0.2. (a) Initially 20 nodes are isolated. (b) Pairs of nodes are connected with a probability of p of selecting an edge. In this case (b) p=0.1 , (c) p=0.2, notice how the nodes become quickly connected. The Erdös and Rényi random graph studies explore how the expected topology of the random graph changes as a function of the number of links. It has been shown that when the number of links is below 1/N, the graph is fragmented into small isolated clusters. Above this threshold the network becomes connected as one single cluster or giant component. We now know, that at the threshold the behaviour is indeterminate  (Strogatz 2001). Random graphs also show the emergence of subgraphs (below). Erdös and Rényi explored the emergence of these structures, which form patterns such as trees, cycles and loops. Like the giant component, these subgraphs have distinct thresholds where they forming different patterns (below).

Fig. – Different subgraphs appear at varying threshold probabilities in a random graph (Albert and Barabási 2002)

[...] People should learn how to play Lego with their minds. Concepts are building bricks [...] V. Ramos, 2002.

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