Milano street art: Albert Einstein

posted by @ulaulaman #AlbertEinstein #StreetArt #Milano

In Paolo Sarpi, a street of Milano, there is a street artist who sketches a lot of subject (for example Iron Man or this iconic space monkey). In particular today I find a beautiful reproduction of the most famous photograph about Albert Einstein:

(photo 1 | photo 2)

On Einstein's 72nd birthday on March 14, 1951, UPI photographer Arthur Sasse was trying to persuade him to smile for the camera, but having smiled for photographers many times that day, Einstein stuck out his tongue instead. This photograph became one of the most popular ever taken of Einstein, often used in merchandise depicting him in a lighthearted sense. Einstein enjoyed this photo and requested UPI to give him nine copies for personal use, one of which he signed for a reporter.
Source: Wikipedia

Sulmondo, the nick of the street artists, add only one little detail to the original photo!

Some quotations about the amplituhedron

posted by @ulaulaman via @tanzmax about #amplituhedron

However, the calculation using the shape in an infinite-dimensional space, the amplituhedron, should provide us with completely new perspectives how to look at the dynamics – perspective that is timeless, obscures the location of objects and events in the space and time, and obscures the unitarity (the requirement that the total quantum-calculated probability of all possibilities remains 100%), but it unmasks some other key structures that dictate what the probabilities should be, structures we were largely ignorant about.
If the new picture becomes sufficiently generalized, you could perhaps throw away the old books because you will get an entirely new framework to compute these things and to think about all these things. But once again, you don't have to throw them away because the physical results are the same.

(Luboš Motl on physics.stackexchange.com)

The amplituhedron is not built out of space-time and probabilities; these properties merely arise as consequences of the jewel’s geometry. The usual picture of space and time, and particles moving around in them, is a construct.

(from Quanta Magazine via Marginal Revolution)

This rich structure is also completely new to the mathematicians.

(Jaroslav Trnka - pdf)

Friday the 13th in science

posted by @ulaulaman about #superstitions #friday13th #mathematics #economics #socialscience

Men would never be superstitious, if they could govern all their circumstances by set rules, or if they were always favoured by fortune: but being frequently driven into straits where rules are useless, and being often kept fluctuating pitiably between hope and fear by the uncertainty of fortune’s greedily coveted favours, they are consequently, for the most part, very prone to credulity.

Benedict de Spinoza, A Theologico-Political Treatise, Preface Part 1.

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In Italy 13 is considered a lucky number, so the unlucky day for us is Friday the 17th, but in the last decades also Friday the 13th becames an unlucky day. Following wiki.en, the origin of this superstition is unknown: the earliest evidence about it is referred in the biografy of Gioacchino Rossini written by Henry Sutherland Edwards in 1869: indeed Rossini died on a Friday 13th

He [Rossini] was surrounded to the last by admiring friends; and if it be true that, like so many Italians, he regarded Fridays as an unlucky day and thirteen as an unlucky number, it is remarkable that one Friday 13th of November he died.

Now, from an economical point of view, could be interesting the following abstract:

The Friday the 13th anomaly of Kolb and Rodriguez (1987) is revisited in an international context. Drawing on the philosophy of science approach of Lakatos (1978), the paper argues the importance of “anomalies” and the need for triangulation. Using the FTSE world indices over 1988–2000 for 19 countries, it is found that there is some evidence that returns on Friday the 13th are statistically different from, and generally greater than, returns on other Fridays.^{(1, 2)}

Lucey's results seem a confirmation of the results of another work by Andrew Coutts:

In recent years much evidence has been documented of the existence of regularities in security price returns. However, one of the least investigated anomalies concerns the socalled ‘Friday the 13th’ effect, where returns on Fridays which fall on the 13th of the month display significantly lower returns than other Fridays. Employing daily logarithmic returns from the Financial Times Industrial Ordinary Shares Index (FT 30) for the period July 1935 through December 1994, we find no evidence of a Friday the 13th effect. Indeed, if anything, we find returns are higher on Friday the 13th than on other Fridays. We then partition the sample into six subsamples each of ten years, again concluding that there is no evidence of a Friday the 13th effect, and that once again returns on Friday the 13th tend to be higher than on other Fridays. Finally, we conclude that our results support the extremely limited evidence documented for the UK market concerning the Friday the 13th effect.

So the ancient superstitions could have an influence also in our advanced society:

Tetris is Hard, Even to Approximate

posted by @ulaulaman about #tetris #ComputerScience #NeuralNetwork

Before today I thought that tetris was a really simple game...

In the popular computer game of Tetris, the player is given a sequence of tetromino pieces and must pack them into a rectangular gameboard initially occupied by a given configuration of filled squares; any completely filled row of the gameboard is cleared and all pieces above it drop by one row. We prove that in the offline version of Tetris, it is NP-complete to maximize the number of cleared rows, maximize the number of tetrises (quadruples of rows simultaneously filled and cleared), minimize the maximum height of an occupied square, or maximize the number of pieces placed before the game ends. We furthermore show the extreme inapproximability of the first and last of these objectives to within a factor of p^(1-epsilon), when given a sequence of p pieces, and the inapproximability of the third objective to within a factor of (2 - epsilon), for any epsilon>0. Our results hold under several variations on the rules of Tetris, including different models of rotation, limitations on player agility, and restricted piece sets.⁽¹⁾

Tetris is a puzzle video game originally designed and programmed by Alexey Pajitnov and it could be used to learn to a neural network:

The black hole in the center of the galaxy

posted by @ulaulaman about #astronomy #SagittariusA #BlackHole #MilkyWay

Sagittarius A* (pronounced "Sagittarius A-star", standard abbreviation Sgr A*) is a bright and very compact astronomical radio source at the center of the Milky Way Galaxy, near the border of the constellations Sagittarius and Scorpius. It is part of a larger astronomical feature known as Sagittarius A. Sagittarius A* is believed to be the location of a supermassive black hole,^{(1, 2)} like those that are now generally accepted to be at the centers of most spiral and elliptical galaxies. Observations of the star S2 in orbit around Sagittarius A* have been used to show the presence of, and produce data about, the Milky Way's central supermassive black hole, and have led to the conclusion that Sagittarius A* is the site of that black hole⁽³⁾.

In the image there is an x-ray photo of Sgr A* from the paper by Wang et al. published on Science⁽⁴⁾.

the x-ray emission from Sgr A* can be described as the superposition of a pointlike source from the black hole itself, and a much larger extended cloud of emission about 2″ across. Within this cloud, we can identify over a hundred individually resolved bright stars, and infer thousands more that are too dim to detect.⁽⁵⁾

They also infer that

the temperature and density profile of the gas cloud surrounding Sgr A*. They show that over 99% of the gas never reaches the central black hole, but rather is ejected from the system⁽⁵⁾

There are also some unresolved questions: for example if the observed accretion rate is dued exclusively by Sgr A* or if there is another source for the data; or his low luminosity, orders of magnitude below its theoretical potential⁽⁵⁾.

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