American mathematics Professor Theodore hill came up with an ingenious trick, allowing him to separate bona fide students from the slackers and lazy. He gave his students an assignment to throw a coin two hundred times and record the results of the shots.
To throw two hundred times, and even to write it all down — quite tedious and boring, time-consuming. But because many students no coins were not cast, and just wrote from badly 200 random results and has submitted work to the Professor.
But the Professor immediately recognized the forgery. He amazed the students with his mystical ability, only glancing at the result, immediately the verdict, faked a student or honestly made 200 shots. And — never wrong all the time!
The secret was simple. According to the theory of probability with 200 random shots almost guaranteed to meet at least one sequence of six tails in a row or the eagles. And in the opinion of the ignorant students, on the contrary, a sequence of six identical results could not be mere coincidence, and they avoided it. It only seemed that they write in the report random sequence of throws. In fact, composed of a result not even close to coming under the law of random distribution, it was “invented”.
“Invented” is in this case quite correct mathematical term. In mathematical analysis there is a extensive section devoted to the “invented number” and the juxtaposition of their real “random numbers”.
We were taught that the Soviet (and subsequently Russian) education — the best in the world.
I don’t know, don’t know!
If we take the criterion of the amount of knowledge that the Soviet-Russian education tried to cram into the poor children’s heads, probably, Yes! A higher level of knowledge in no other country in the world to push! But if we take the criterion of the quality and depth of assimilation of this knowledge and the ability to apply them in post-school life, then I’m sorry-come on.
How many of you after years of learning English at school acquired the ability to communicate it, or at least free to read even adapted literature? And what percentage of you going into high school in math class a complete course in combinatorics and calculus started, remember at least what is the binomial theorem.
The last question is not idle. Graduates of senior classes, “passing” sufficient probability theory, coming out of school sincerely somehow believe that “a random sequence of numbers” is something totally unpredictable and absolutely not natural. Although in reality nothing is more predictable and logical than a series of random events. She always clearly subject to a formal mathematical laws.
The only thing that is really impossible to predict is what will happen in the next roll of the dice — heads or tails. But the distribution of head or tails in a series of thousands of shots — this is the question that mathematical statistics will give you a comprehensive answer. In particular, she will tell you that if you tossed a coin 200 times, six eagles or tails in a row you drop out certainly.
If before any person who is unfamiliar with mathematical statistics, the challenge will be to simulate some kind of random result, he, knowing the word “random” to the best of my understanding, will do it as unpredictable, avoiding any patterns. And immediately slept because of its imitation in any way will not correspond to truly random distribution.
But if this same work will be performed and a qualified mathematician, he slept exactly the same. Because the task of separation a true random sequence from invented is solved by means of mathematics at the time. But the reverse task, to make this invented sequence, which is not different from random, it requires such enormous computational resources, which are still unsolvable in practice.
Even if you, knowing about “six eagles or tails” will insert them into your invented by a sequence of 200 shots, you’re still not fooling anyone. Because random assignment has a huge number of patterns and they are so densely intertwined that to consider all — is unrealistic. Well, you put six shots in a row. What about the right of alternating series of three shots? What about the frequency distribution of pairs? The limits of deviation of the obtained result from the expected?
A series of ten shots can still be faked, but to fake a hundred shots — power of all the earth’s computers it is not enough.
What do you tell me why need to do this stuff, you ask? Oh, no, my brothers, this is not nonsense. Here for example, financial reports for the year represents, from the point of view of pure mathematics, a random set of numbers obeying certain laws.
That is, if he’s real.
But if it’s not real and invented, from the point of view of mathematics, it will be not random, but “invented” numbers. And to understand the real report or a fake, its even to analyse a subject is not necessary. Enough to stick it in the computer, considering the squiggle and wait for the result.
Ask why no one does, if this is so simple? I’m doing it.
In 1995, the Brooklyn da Robert Burton first used the software to distinguish a random number from the fictional to analyze the financial reports of the companies. And since it started-gone.
Operation implementation of this calculus is quite expensive, and Eviscerate any SP with it unprofitable, but the “whales” business I had a hard time.
Remember the terrible financial scandals of recent years? The case of Enron… Madoff Pyramid… the Pyramid of Stanford… this is what it is. In all cases the investigation was launched because when testing revealed that the financial statements of the company have “invented” from a mathematical point of view nature.
How else can you use calculus? Is it possible, for example, test with the help of mathematics the results of the election, was not invented?
Exactly! Well, of course! Why do you think in the States now so easily move on to electronic voting, which resisted earlier many years? Yes, because now any tampering will immediately pop up! Why Clinton refused a recount in the last election? Yes, because prior mathematical analysis showed that rigging was not!
And why in Russia it is not used? Yes, the Lord is with you! After every election there are the Russian mathematicians who are sounding the alarm and shouting: “This is the same lime clean water!” And every time in the media and the Internet, the rising tide of defamation of these mathematicians, and the noise of mockery on them reaches such values, that his background is already unheard of. Yes, that type in at least “Churov’s comb” and dumped a bunch of links. Clicking on which you not fucking understand what exactly is this the “Comb Churov”, but will learn about how the failed attempt of the Russian liberals and the opposition to prove with the help of mathematics of the electoral fraud.
It is quite obvious from the point of view of mathematics convincing proof “of pridumannoe” results of Russian elections, the efforts of Russian media, government trolls and the progressive Internet community has turned into an Internet meme with a negative sign, which not even mention that you didn’t immediately attacked by a crowd of extremely aggressive debunkers. And the debunkers, most of which were far from supporters of the current government, but I deny just for the love of the truth, because sincerely believe that the “Churov’s comb” — nonsense.
Why believe? Yes, because you are spectacularly ignorant and illiterate, my dear, because “the binomial theorem” for you is not a mathematical formula, and the same meme as “Churov’s comb”. Because the explanations of qualified mathematics you incomprehensible, and the rebuttal that you make, though equally illiterate, but is so logical and clear to you that you accept them for the truth.
Well, that’s ancient tyrants knew — I want to turn the cast as you like — make them illiterate.
Incidentally, my good friend, mathematician Konstantin Knop, specifically for the Russian electorate was also quite logical and clear explanation on how his fool.
Maybe even so you will docetic?
So that, my dear, your heated debates on the topic to go or not to go to the polls, this question does not make sense. Does not have at all!
The desired results will be drawn regardless of how you vote will come or not come. That, my friend writes me that “if I do not come, they use my ballot and write in your candidate.”
Oh, Yes, the Lord is with you! What lies in the ballot box, it has nothing to do with the results that will be published by the electoral Commission. The word “all”. That will be counted at the polling station and sent “upstairs” does not affect what will be drawn in that the “top”.
All the “stuffing”, “carousel”, “cheating with absentee ballots,” that’s all, my brothers, is not done to make a rig, but only in order to convince you fools that cheating is here, at the polling stations. To all the protest and control the activity to the whole rat race in the fight against fraud was in those places, from which nothing depends.
Squiggle and friends, they are drawn in a completely other closed offices, where so simply does not enter and where no access to observers or the public.
Yeah, well, nonsense, you say!
After all, these ballots are then sealed and stored at any time, you can check whether numbers. Yes, of course, are stored. Yes, of course, can be counted and checked. But do something you just don’t go in there to count. You should be the decision of the court. And not just the court, but Putin’s court. Yes, even if it is, which in itself is incredible, five minutes before your arrival in the room there was a fire followed by a flood.
But what about the observers? They definitely will see that the published numbers match what was counted on the spot! Well, most of the observers that called “his”. But there are honest, principled, who will not be silent.
Well, it’s not silent! Remember how many of these accusations sounds after each election. And then what? To tell me or do you remember? For every “principled” ten “inessential”, which stood next to him and saw that the “principled” friend N all the time, distracted, scandal, and simply could not adequately control the counting and to read the Protocol. And anyway, it makes a noise, because his party miserably lost, I do not agree, let him go to court… but what I explain, you know!
And even if the “friend N” will be challenging comrade and will be able to push the situation to involve the foreign press, as it was recently with the city of Barvikha, and then absolutely nothing will change. The Chairman of the Central election Commission threatened local electoral Commission with a finger, maybe even cancel the elections, and everything will go in the second round, perhaps even more than once, as long as they will not have the desired result.
So relax gentlemen. From you, from your opinion, from your behavior in the elections, your turnout does not depend on anything.
And why did the authorities have to actively pull the population to the polls, if not depend on, you ask?
I, too, the binomial theorem! Yes, because the turnout, in contrast to the results of the elections to draw much harder. You do not have access to the high offices, where the actual drawn numbers, you do not have access to a meeting of the commissions, where protocols are written, but it is to get up close to the site and clicking the button the counter will be able to find anyone in any status.
In this way the population of the Philippines in the 70-ies of the last century sent a “relatively peaceful resignation” of their dictator Marquez. And his Russian last-good about it remember.