#Andrei Kolmogorov

[wordacrosstime]

Limit Distributions for Sums of Independent Random Variables

[Limit Distributions for Sums of Independent Random Variables, by BV Gnedenko (Author), AN Kolmogorov (Author), KL Chung (Translator). Paperback (Reprint of the 1954 Edition) - 5 Aug 2021. Publisher - Martino Fine Books (5 Aug 2021). Language - English. Paperback - 276 pages. ISBN-10 - 1684225795. ISBN-13 - 978-1684225798. Dimensions - 15.6 x 1.57 x 23.39 cm. (details thanks to Amazon)]

[Author full names: Boris Vladimirovich Gnedenko (Russian: Бори́с Влади́мирович Гнеде́нко; 1 January 1912 – 27 December 1995); Andrey Nikolaevich Kolmogorov (Russian: Андре́й Никола́евич Колмого́ров, IPA: [ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf], 25 April 1903 – 20 October 1987) (details thanks to Wikipedia)]

***

A number of years ago I set about a course of self-improvement. For me that meant reading as much as possible from works written by world-class thinkers. This list of august minds was often, though not solely, driven by Nobel Prize winners and other winners of similar or equivalent awards in other areas (mathematics, for example, where the Fields Medal and Abel Prize are the highest honors). However, I am a statistician among other things, and so I have also kept a keen eye out for important works by the giants of that field.

I am not well-acquainted with Boris Gnedenko, though his name has certainly come up from time to time over the years that I’ve both studied and practiced statistics. The name that has come up repeatedly in reverential tones is Andrey Kolmogorov, who is one of a handful of mathematicians who are credited with giving the theoretical underpinnings of statistics a solid and rigorous mathematical foundation.

The volume under review here is one of Kolmogorov’s most important publications. In it, he and Gnedenko elicit the basis and application of results like the Central Limit Theorem (CLT) and the Law of Large Numbers (LLN). These are two of the most important results in all of statistics and probability theory and the slightly more general theory of stochastic (random) processes.

I should mention that this volume was originally published in the Soviet Union in 1949 in Russian. The edition I read here was translated into English in 1954 by KL Chung, and the actual ISBN citation is this particular reprint; there are others from different time periods, and of course if one is a true purist, then one should definitely read the original Russian text. However, according to the preface, all of the formulas and other special figures in the text are actually photostats from the original monograph.

I really enjoyed this book. The writing style of Gnedenko and Kolmogorov is delightfully lofty and at times quite flowery, but their explanations of proofs and motivations for results are really first-rate. I wasn’t sure what to expect, given the high intellectual bar these gentlemen set, but I was very pleasantly surprised. Professor Chung, the translator, added quite a few helpful comments and clarifications where appropriate, but overall he seems to have let the book flow as it was originally set down. One of the Appendices was written by another legendary statistician, JL Doob, providing a bit of bridge material related to some measure-theoretic issues that arise in Chapter 1.

My only complaint (a very small one to be sure) is that there were a number of typos that remained intact despite the extensive editorial review this monograph has surely had over the past 70+ years. I wouldn’t exactly call it a super-power, but I personally seem to have a knack for finding typos and grammatical errors in even very technical material. I’ve taken photos of two of the ones I found early in the text as examples here (see below). For some reason my eye was instinctively drawn to these and others. I would thus advise the reader to pause if something seems slightly amiss – it very well might be. I’m happy to say that these errata were few and far between, and in no case do I recall them rendering the explanations or results indecipherable.

Who would enjoy this tome? Anyone who is interested in the theoretical basis for many of the classic results in modern non-Bayesian statistics. The foreword by the translator advises that a solid background in calculus is a must, and mathematical maturity a definite plus. Beyond that, the book itself is remarkably self-contained. This is likely due to the political environment in which it was written. Post-World War II was a difficult time for Soviet intellectuals since they were generally denied access to journals and results outside their own country.

Here are the two examples of typos that I detected early in the book – I think they speak for themselves, but you can be the judge:

[Image credits numbered from top: (1 & 2) two pages from the book photographed by reviewer- with thanks to © publishers and estates of authors. (3 & 4) book cover front and back - with thanks to © publishers (5) Boris Vladimirovich Gnedenko - with thanks, no details of © copyright holder / photographer known (6) Andrey Nikolaevich Kolmogorov - with thanks, no details of © copyright holder / photographer known]

Kevin Gillette

Words Across Time

12 January 2024

wordsacrosstime

#kevin gillette #January 2024 #wordsacrosstime #words across time #Martino Fine Books #Boris Vladimirovich Gnedenko #Бори́с Влади́мирович Гнеде́нко #Boris Gnedenko #Andrey Nikolaevich Kolmogorov #Андре́й Никола́евич Колмого́ров #Andrey Kolmogorov #Andrei Nikolaevich Kolmogorov #Andrei Kolmogorov #Fields Medal #Abel Prize #Statistics #Central Limit Theorem #CLT #LLN #Law of Large Numbers #Stochastic #Probability Theory #KL Chung #Soviet Union #WW2 #JL Doob #Typos #Tome #Non-Bayesian statistics #Soviet Intellectuals

[metamatar]

In statistics, originally in geostatistics, kriging or Kriging, (pronounced /ˌˈkɹiːɡɪŋ/) also known as Gaussian process regression, is a method of interpolation based on Gaussian process governed by prior covariances. Under suitable assumptions of the prior, kriging gives the best linear unbiased prediction (BLUP) at unsampled locations.[1] Interpolating methods based on other criteria such as smoothness (e.g., smoothing spline) may not yield the BLUP. The method is widely used in the domain of spatial analysis and computer experiments. The technique is also known as Wiener–Kolmogorov prediction, after Norbert Wiener and Andrey Kolmogorov.

The theoretical basis for the method was developed by the French mathematician Georges Matheron in 1960, based on the master's thesis of Danie G. Krige, the pioneering plotter of distance-weighted average gold grades at the Witwatersrand reef complex in South Africa. Krige sought to estimate the most likely distribution of gold based on samples from a few boreholes.

[jhavelikes]

In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that produces the object as output. It is a measure of the computational resources needed to specify the object, and is also known as algorithmic complexity, Solomonoff–Kolmogorov–Chaitin complexity, program-size complexity, descriptive complexity, or algorithmic entropy. It is named after Andrey Kolmogorov, who first published on the subject in 1963[1][2] and is a generalization of classical information theory. The notion of Kolmogorov complexity can be used to state and prove impossibility results akin to Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem. In particular, no program P computing a lower bound for each text's Kolmogorov complexity can return a value essentially larger than P's own length (see section § Chaitin's incompleteness theorem); hence no single program can compute the exact Kolmogorov complexity for infinitely many texts.

Kolmogorov complexity - Wikipedia

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Was it a chance encounter when you met that special someone or was there some deeper reason for it? What about that strange dream…. Powered by AutoBlogger.co

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[scitechman]

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The amount of energy generated by renewables fluctuates depending on the natural variability of resources at any given time. The sun isn’t always shining, nor is the wind always blowing, so traditional power plants must be kept running, ready to fill the energy gap at a moment’s notice. Because the grid has no storage, and unlike coal or nuclear, there is no control over the fluctuating…

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[siumerghe]

Hi! 16 and 26. Thanks

16. which stereotype about your country you hate the most and which one you somewhat agree with?

Most hated stereotype: vodka! Yeah, there are alcoholics in Russia, same as in other countries, and there are problems with alcohol in the Russian province, among poor people and especially among indigenous people of Siberia and Arctica who biologically lack alcohol-processing ferments.

However, personally, I don't know any hard-drinking people in Russia, neither among ethnic Russians nor among other nationalities. No one in my family drank vodka, even during various celebrations. People in the cities, especially younger generations, being more health-conscious, usually don't drink much. "But you are Russian! Why are you not drinking/drinking so little? Drink more!" Ugh. Me being from Russia doesn't mean I enjoy drinking or have a high alcohol tolerance!

Oh, and also Russians never say "Na zdorovie!" when toasting. It means "My pleasure" or "You are welcome" and is a response to "Thank you". A mistake I'm tired of correcting my non-Russian-speaking friends. As a toast, it sounds incredibly stupid. Thanks, Hollywood, for inventing this nonsense.

Russia is not a country of vodka, it's a country of black tea, with an average Russian citizen (including ethnic Russians and other nationalities) drinking 3 cups of tea per day. Every meal ends with tea (brewed in a small kettle from loose tea leaves and then mixed with hot water), and it’s not just tea - it’s tea with something: sweets, sandwiches, pies, blini, dried fruits... Tea without food is called пустой чай - “empty tea”. Tea is also drunk in-between the meals, with something or on its own. So, you wanna picture a stereotypical Russian? Forget the vodka, go for the black tea instead!

The stereotype I somewhat agree with: Russians are good at math. This one is true. The mathematical education in the USSR was largely shaped by Andrey Kolmogorov, one of the world's most prominent mathematicians. The Soviet education system was stellar in exact sciences, and its heritage is still alive in present-day Russia. Russian schools put extra effort into teaching math while focusing on problem-solving (not “see and repeat”), Russian math program is in general more difficult than in the West (what is a school-level material in Russia, in the US is taught in college), there are prestigious (and free) math schools for gifted children, and Russian universities have the best math courses (which are available on youtube - but in Russian). 

26. does your nationality get portrayed in Hollywood/American media? what do you think about the portrayal?

It does - unfortunately. I wish Hollywood forget that Russia exists. There are all kinds of offensive and harmful stereotypes (all Russian men are either alcoholics or KGB agents, all Russian women are prostitutes), incorrectly understood folklore and culture, crazy errors in geography, history, fashion, and whatnot. All Hollywood Russians are evil. And if not, then a typical Hollywood Russian man dies painfully as a way to atone for the crime of being Russian. A typical Hollywood Russian woman betrays her country and/or becomes the lover of the hero (who is American, of course). And all of them drink vodka like water and say "Na zdorovie!"

It’s also a bit strange when ethnic Russians are portrayed by actors with distinct White American or Western-European facial features. Native people easily notice such details. It’s like seeing a Japanese being portrayed by a Chinese, or an Afro-French being portrayed by an Afro-American. 

Western movies about Russia and Russians that I like: Eastern Promises 2007, Chernobyl 2019. The latter even got ethnic Russian and other Soviet nationalities types right (except for 1 - only 1! - actor with a rather Anglo-Saxon face).

“hi, I’m not from the US” ask set

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

#ask #im not from the us ask #russia

[thedalatribune]

© Paolo Dala

Illustration by Paolo Dala (2019)

Turbulence X Vincent Van Gogh

One of the most remarkable aspects of the human brain is its ability to recognize patters and describe them. Among the hardest patterns we’ve tried to understand is the concept of turbulent flow in fluid dynamics. The German Physicist Werner Heisenberg said:

“When I meet God I’m going to ask him two questions: Why relativity and why turbulence? I really believe he will have an answer for the first.”

As difficult as turbulence is to understand mathematically, we can use art to depict the way it looks.

In June 1889, Vincent van Gogh painted the view just before sunrise from the window of his room at the St. Paul de Mausole Asylum in Saint Rémy de Provence (where he admitted himself after mutilating his own ear in a psychotic episode). In the ‘Starry Night’, his circular brushstrokes crate a night sky filled whit swirling clouds and eddies of stars. 

Van Gogh and other impressionists represented light in a different way than their predecessors, seeming to capture its motion... The effect is caused by luminance, the intensity of the light in the colors of the canvas. The more primitive part of our visual cortex, which sees light contrast, and motion, but not color, will ben two differently colored areas together if they have the same luminance; but out brains’ primate subdivision will the contrasting colors without blending. With these two interpretations happening at once, the light in many Impressionist works seems to pulse, flicker and radiate oddly...

Sixty (60) years later, Russian Mathematician Andrey Kolmogrov furthered our mathematical understanding of turbulence when he proposed that energy in a turbulent fluid at length R varies in proportion to the five-thirds (5/3) power of R. Experimental measurements show Kolmogorov was remarkably close to the way turbulent flow works, although a complete description of turbulence remains one of the unsolved problems  in physics. A turbulent flow is self-similar if there is an energy cascade. In other words, big eddies transfer their energy to smaller eddies, which do likewise at other scales. Examples of this includes Jupiter’s ‘Great Red Spot’, cloud formations, and interstellar dust particles. 

In 2004 using the Hubble Space Telescope, scientists saw the eddies of dust and gas around a star, and it reminded them of van Gogh’s ‘Starry Night’. This motivated scientists from Mexico, Spain, and England to study the luminance in van Gogh’s paintings in detail. They discovered that there is a distinct patter of turbulent fluid structures close to Kolmogorov’s Equation hidden in may of van Gogh’s paintings. The researchers digitized the paintings, and measured how brightness varies between any two pixels. From the curves measured for pixel separations, they concluded that paintings from van Gogh’s period of psychotic agitation behave remarkably similar to fluid turbulence. His ‘Self-portrait with a Pipe’, from a calmer period in van Gogh’s life, showed no sign of this correspondence. And neither did other artists’ work that seemed equally turbulent at first glance, like Munch’s ‘The Scream’. 

While it’s too easy to say van Gogh’s turbulent genius enabled him to depict turbulence, it’s also far too difficult to accurately express the rousing beauty of the fact that in a period of intense suffering, van Gogh was somehow able to perceive and represent one of the most supremely difficult concepts nature has ever brought before mankind, and to unite his unique mind’s eye with the deepest mysteries of movement, fluid and, light.

Natalya St. Clair The Unexpected Math behind van Gogh's ‘Starry Night’

#The Unexpected Math behind van Gogh's ‘Starry Night’ #Natalya St. Clair #Ted-Ed #Starry Night #Vincent van Gogh #van Gogh #Art #Math #Science #Turbulence #Illustration #Stars #Journal #Pen #Ink

[semechkablack]

the same old story about andrey kolmogorov, my friends. the amount of shit he came up with? incredible. i will not get into it but no matter what class i had... he was everywhere. when i had trouble with functional analysis i picked up the book he wrote and let me tell you. he is the most comprehensible soviet mathematician out there. and what do you think. he lived his whole life with his friend pavel alexandrov. you know how they met?

"Their friendship began in the summer of 1929, when Andrey Nikolaevich [Kolmogorov], who by that time had some experience with boat trips, became the organizer of a trip along the Volga from Yaroslavl to Samara. The second participant in the 1300 km trip was one of Kolmogorov's school friends. "It is still not entirely clear to me how I managed to offer Pavel Sergeevich [Alexandrov] to be the third companion. However, he agreed immediately", writes Andrey Nikolaevich. They returned from the trip with a ready-made decision to live together." (x) lmao

kolmgorov was also a founder of a large scientific school! "...they [he and Alexandrov] wanted to recreate at their dacha in Komarovka near Moscow. They invited their students there for hiking and skiing, listening to music and making mathematical conversations" :')

some more excerpts from an article about him:

"The scientific world perceived Kolmogorov and Alexandrov as a couple. They worked together, rested together in the sanatoriums of the Academy of Sciences and sent food parcels to besieged Leningrad." (x)

"The man with whom Andrey Kolmogorov shared a home from 1929 until the end of his life was the topologist Pavel Alexandrov. Five years after they began to live together, male homosexuality in the USSR was outlawed. Kolmogorov and Alexandrov, who called themselves friends, practically did not make a secret of their relationship and nevertheless had no problems with the law." (x)

in 1981, Alexandrov wrote: “My friendship with A. N. Kolmogorov occupies an absolutely exclusive, unique place in my life; in 1979 this friendship had its fiftieth anniversary, and over the entire half-century period, not only did it not give a crack, but was not even accompanied by any quarrel..." (x)

Kolmogorov said, “For me, these fifty-three years of our close and unbreakable friendship were the basis for the fact that my entire life as a whole turned out to be filled with happiness, and the basis of my well-being was the unremitting solicitude on the part of Pavel Sergeevich.” :'))

AND kolmogorov started his letters to alexandrov with “Милый Пусик!” which is... a lot. basically, a really rough translation here, it means “my cute babe/sweetie” :’)

like, yeah, these iconic gay math kings! good for them

#i wish people talked abt it #bc he's literally just as cool as alan turing but fortunately without a tragic end #lgbt #slavic culture #x

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