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Ab aap Whatsapp pe solutions paa saktey h, hum aapko ping karenge. Study Materials. Why use Doubtnut? Instant Video Solutions. Request OTP. Updated On: Share This Video Whatsapp. Text Solution. Solution :. Very Important Questions. Mathematics had led him to believe that the world was both driven by chance and fundamentally ordered according to the laws of probability. He often reflected on the role of the unlikely in human affairs. Kolmogorov objected, taking a radical probabilistic view of social interactions in which people acted as statistical samples of larger groups.
Music and literature were deeply important to Kolmogorov, who believed he could analyze them probabilistically to gain insight into the inner workings of the human mind. He was a cultural elitist who believed in a hierarchy of artistic values. At the pinnacle were the writings of Goethe, Pushkin, and Thomas Mann, alongside the compositions of Bach, Vivaldi, Mozart, and Beethoven—works whose enduring value resembled eternal mathematical truths. Kolmogorov stressed that every true work of art was a unique creation, something unlikely by definition, something outside the realm of simple statistical regularity.
Yet he longed to find the key to understanding the nature of artistic creativity. In Kolmogorov armed a group of researchers with electromechanical calculators and charged them with the task of calculating the rhythmical structures of Russian poetry.
Kolmogorov was particularly interested in the deviation of actual rhythms from classical meters. In traditional poetics, the iambic meter is a rhythm consisting of an unstressed syllable followed by a stressed syllable. But in practice, this rule is rarely obeyed. An unlikely pattern of stresses, he thought, indicated artistic inventiveness and expression. To measure the artistic merit of texts, Kolmogorov also employed a letter-guessing method to evaluate the entropy of natural language.
In information theory, entropy is a measure of uncertainty or unpredictability, corresponding to the information content of a message: the more unpredictable the message, the more information it carries. Kolmogorov turned entropy into a measure of artistic originality. His group conducted a series of experiments, showing volunteers a fragment of Russian prose or poetry and asking them to guess the next letter, then the next, and so on.
Kolmogorov privately remarked that, from the viewpoint of information theory, Soviet newspapers were less informative than poetry, since political discourse employed a large number of stock phrases and was highly predictable in its content. The verses of great poets, on the other hand, were much more difficult to predict, despite the strict limitations imposed on them by the poetic form. According to Kolmogorov, this was a mark of their originality. True art was unlikely, a quality probability theory could help to measure.
Kolmogorov scorned the idea of placing War and Peace in a probabilistic sample space of all novels—but he could express its unpredictability by calculating its complexity. Kolmogorov conceived complexity as the length of the shortest description of an object, or the length of an algorithm that produces an object. Deterministic objects are simple, in the sense that they can by produced by a short algorithm: say, a periodic sequence of zeroes and ones.
Truly random, unpredictable objects are complex: any algorithm reproducing them would have to be as long as the objects themselves. For example, irrational numbers—those that cannot be written as fractions— almost surely have no pattern in the numbers that appear after the decimal point. Therefore, most irrational numbers are complex objects, because they can be reproduced only by writing out the actual sequence.
The onset of probability as a useful science is primarily attributed to Blaise Pascal and Pierre de Fermat While contemplating a gambling problem posed by Chevalier de Mere in , Blaise Pascal and Pierre de Fermat laid the fundamental groundwork of probability theory, and are thereby accredited the fathers of probability. The question posed was pertaining to the number of turns required to ensure obtaining a six in the roll of two dice.
The correspondence between Pascal and Fermat concerning this and the problem of points led to the beginning of the new concepts of probability and expection.
In the seventeenth century, a shopkeeper, John Graunt , set out to predict mortality rates by categorizing births and deaths. In the London Life Table, Graunt made a noteworthy attempt to predict the number of survivors out of one hundred through increments of ten years. This work along with his earlier paper Natural and Political Observations Made upon the Bills of Mortality , the first known paper to use data in order to draw statistical inferences, gained him access into the Royal Society of London.
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