The false conclusion of Monte Carlo. Logic paradoxes
Read also
intuitively obvious that the loss of the "Dish" is late.
However, this conclusion is false.
This error received the name "Negative Novelty" (Negative Recentcy Effect) in a special literature and is the trend towards the prediction of the frequent termination of the often happening in lately events. It is based on faith in local representativeness (i.e., on the confidence that the sequence of randomly emerging events will be the characteristics of the random process even when it turns out to be short). T about., According to this erroneous representation, the generator random events, For example, throwing a coin, should lead to outcomes, in the second - even after a short time - there will be no significant predominance of one or another of possible outcomes. If a series of identical outcomes falls out, there is an expectation that the random sequence will adjust itself in the near future, and the deviation in one direction is thereby subjected to a mandatory equiliblation of the deviation in the other. However, randomly generated sequences, especially if they are relatively short, turn out to be completely unrepresentative producing them random process.
Player Error - this is something more than just a reflection of ordinary statistical ignorance because it can be observed in private life even sophisticated in the statistics of people. It reflects two aspects of human. Cognitive function: a) a strong and unconscious motivation of people to find order in all that they are observed around themselves, even if the sequence of outcomes observed as a result of a random process, b) universal human.
The tendency to ignore based on the calculation of probability estimates by giving preference to intuition. Although logic can convince us that the random process does not control its outcomes, our intuitive reaction can be very strong and sometimes to suppress logic. Investigated the comparative strength of the logical and intuitive thinking of Reed argues that the latter often turns out to be more compulsory than the first, probably for the reason that such conclusions come to mind suddenly, therefore, are not amenable to logical analysis and are often accompanied by a strong sensation of their right. Unlike the principled impossibility of tracking the process, there are such intuitive "solutions", the process logical reasoning Opened for analysis and criticism. Therefore, people manage logical thinkingAnd from intuitive thinking, they simply receive results, to-ryy fill the last strong sensation of the feeling of the right.
O. and. The most common in a situation where the outcomes are generated purely by chance. If a certain factor of skill participates in the development of events, more often there is a positive novelty effect (Positive Recency Effect). The observer will most likely consider a series of success (for example, a player in billiards) as a testimony of his skills, and will build its forecasts of subsequent outcomes rather in positive than in the negative direction. Even the throwing of the bones can lead to a positive effect of novelty to the extent that the individual is convinced that the outcome of the events is influenced by the "art" of challenging.
See also Barnum's effect, player behavior, statistical conclusion
Gambler "s Fallacy) O. and., Or the false conclusion of Monte Carlo, reflects the widespread misunderstanding of the event randomness. Suppose that the coin is throwing up many times in a row. If in a row 10" Orlov "and if this is the" correct " For most people, it would be intuitively obvious that the loss of "Dish" is late. However, this conclusion is false. This error received the name "Negative Novelty" (Negative Recency Effect) and is a tendency to predict the early termination of the frequently Recently event. It is based on faith in local representativeness (i.e., on the confidence that the sequence of randomly emerging events will carry the characteristics of the random process even when it turns out to be short). T., according to this erroneous representation, generator of random events, for example, throwing a coin, should lead to outcomes, in the second - even after a short time ENI - there will be no significant predominance of one or another of possible outcomes. If a series of identical outcomes falls out, there is an expectation that the random sequence will adjust itself in the near future, and the deviation in one direction is thereby subjected to a mandatory equiliblation of the deviation in the other. However, randomly generated sequences, especially if they are relatively short, turn out to be completely unrepresentative producing them random process. The player's error is something more than simply reflection of ordinary statistical ignorance, since it can be observed in private life even sophisticated in the statistics of people. It reflects two aspects of human. Cognitive function: a) a strong and unconscious motivation of people to find order in all that they are observed around themselves, even if the sequence of outcomes observed as a result of a random process, b) universal human. The tendency to ignore based on the calculation of probability estimates by giving preference to intuition. Although logic can convince us that the random process does not control its outcomes, our intuitive reaction can be very strong and sometimes to suppress logic. Investigated the comparative strength of the logical and intuitive thinking of Reed argues that the latter often turns out to be more compulsory than the first, probably for the reason that such conclusions come to mind suddenly, therefore, are not amenable to logical analysis and are often accompanied by a strong sensation of their right. Unlike the principled inability to track the process, through which such intuitive "solutions" are located, the process of logical reasoning is open to analyzing and criticism. Therefore, people manage logical thinking, and from intuitive thinking they simply receive results, to-ryy fill the last strong feeling of the feeling of the right. O. and. The most common in a situation where the outcomes are generated purely by chance. If a certain factor of skill participates in the development of events, more often there is a positive novelty effect (Positive Recency Effect). The observer will most likely consider a series of success (for example, a player in billiards) as a testimony of his skills, and will build its forecasts of subsequent outcomes rather in positive than in the negative direction. Even the bone throwing can lead to a positive effect of novelty to the extent that the individual is convinced that the outcome of the event is influenced by the "art" of challenging. See also the effect of Barnuma, the behavior of the players, the statistical conclusion of J. Elkok
Finally got hands and other bodies until the next article.
So, Meet the next guest in our studio - Player error or false conclusion Monte Carlo. I did not come up with me, although it sounds somehow pop, without enough words, characteristic of high-tone units. This distortion is very simple in understanding, nevertheless it dwells everywhere, both in a liquid nasom of lumpenses that have come down in the study of the alphabet to the letter E, and in dense thickets of a raisin of magician experience with a bunch of knowledge of the gray-haired wise men. That's what Vicky says about this:
Player error (eng. Gambler's Fallacy) or false conclusion Monte Carlo reflects a common erroneous understanding of the accident rate. It is related to the fact that, as a rule, a person is not aware of the intuitive level of the fact that the probability of the desired outcome does not depend on the previous outcomes of the random event.
For example, in the case of tossing a coin, this situation may well occur in a row that the 9 "Siggers" will fall out. If the coin is "normal", then for many people it seems obvious that with the next throw, the probability of an eagle falling will be more: it is difficult to believe that the "rush" can fall out the tenth time in a row. However, this conclusion is erroneous. The probability of falling out the next eagle or the rush still remains 1/2.
It is necessary, however, to distinguish the concepts: the likelihood of the "eagle" or "rush" loss in each particular case and the likelihood of the "rush" loss of ten times in a row. The latter will be equal. However, the likelihood of falling out and any other fixed sequence from "Orlov" and "Siggers" with 10 shots of coins.
What does this mean translated into our Pharmal-Trader language?
The easiest and most famous example is the classic doogle flavge. Those. Popan PKET TB2.5 It doesn't matter in which match on Kef + -2, merges, doubles the bet on another match of TB 2.5 with KEF about two, merges, again doubles the bet, etc. Well, or Martingale, call, as you wish, do not essence. And if you offer him in the third and fourth iteration to shove the total less, he probably renewes with the megaargument "You have already been 3 TM, right now the probability of TB is higher." And it will be completely right. But only in his imaginary universe, in real life everything is somewhat different. The likelihood in the future event will not depend on the past, at least one at least one million. Axiom.
At the expense of a million. Recently talked with Kent on this topic (¡Hola Senor Alejandro!). In some moment there is absolutely adequately perceiving this world a person on a simple question "before that, a million times fell an eagle. What is the probability that the rush will fall out?" Replies that a little bit, but still higher. We quickly eliminated this moment, but the situation is indicative.
Departed from the topic. So what to do to a person who was in the dogh (which I was a hard opponent)? The most important thing is not to think red or black, the total has more or a total of less, fish or chicken, nothing depends on you. Just Pxney for any outcome and relieve the TV, and it is better to deal with sports, sex, fishing, which needs to emphasize. So less burn the calories from the "wrong choice", which, in fact, was not. Now mathematics (gods, fortune, mastty, call as you want) turned to your face or ass, and nothing can be done about it. You do not need to catch up with seven iterations Total more, boldly sing the total total, it does not affect the result. It only affects the fact that the doghon will eventually put you on the blades, not to deceive mathematics, the margin will do everything for you. For many years, I watched the tops of Phajei on the Bust, among successful on a solid distance there was not a single catchpir, but now it's not about that.
Take another example. At one time we called online in trading sessions with one all well-known equestrian trader, I will not voice his name. So, he also caught in the network of this cognitive error. The course of his thoughts proceeded at the following bed: 3 times in a row came the first mare-favorite, then the next race of FAVA needs to be lying. Won - HSN, LEIM FAVA in the next race with a double rage, then tripled, etc. and this "system" gave profit on a bit of time. But in one cock, the inevitable happened: the mathematics won it, he was at the same amount that I left our slender, although not stable rows. He could not believe that it was possible that he needed a lot of time to accept, understand and rethink, caught such a depress agency that the massage of Australian coal would not help him at that moment. I think this is not a single case.
I had a case when I myself got into a similar way. We vaguely remember the details, the business is long. Italy Championship Most - a sad sight, Kathenachcho, draws - frequent guests. In one of the tours there was not a single note, and my rapid brain suggests that the next round the trend will return. Stupidly took a note in all matches and ... Megaposos, again not a single draw. But I'm cool pepper, I will not take me so easily, in the next round I take a double bet again (hello the illusion of control) - and only one draw in the whole round. According to the classics of the genre, I had to shove and fight back, well now, then everything will be exactly Nishtyak. But the reality is maneuvea deeper, my money stupidly ended. I will answer your question: I do not know what was next round, I did not watch the cuts, I thought to go crazy if I see the Ocean of Nichek. Dear lesson, but as it turned out, very useful.
I will finish, 3 hours in the morning. I will make a riddle to consolidate, independent analysis and improved absorption of the foregoing. What is the probability that Barcelona will not win at home, say, Malaga two times in a row? KEF on P1 - 1.2. And how soon can it come? The first responding is right with me nishtyacchka, let's say, I will write an article on the topic chosen by it.
So, summarizing. Do not see what was before, it does not matter. If you looked at - on draw conclusions, they are subjective. Made conclusions - do not build predictions from them, they are unreliable. Still built prediction - be prepared to easily change it, do not cling to him as the only true (one of my favorite cognitive mistakes, let's talk about it another time). If you clung and you can not let go to the plant, arrange in a taxi, a pizza delivering, choose any other kyle, games with probabilities so far, alas, not for you. But do not despair, read, work on yourself, improve the understanding of the processes taking place in your head, will try your brain. After passing oil and coal layers, sooner or later you will Dobrite to the states of mind, not so convicted and compressed, and someday, with some more likelihood, you will be able to reappear on the Vitious path of the Nekylel Bubl.
This episode with a smart missionary is one of the paradox of the ancient Greek philosophers of Protagore and Evatla.
But with such a paradox of formal logic, there was every researcher who tried to strictly determine all the concepts in his theory. This has not yet been able to anyone, since everything came down to the Tavtalogia type: "Movement is the movement of bodies in space, and moving is the movement of bodies in space"
Another option of this paradox. Someone committed a crime punished death penalty. In court it seems the last word. He must pronounce one statement. If it turns out to be true, the criminal will drown. If it is false, the criminal will hang. What statement does he have to express to bring a judge to complete confusion? Think yourself.
Puzzled by this paradox, Protagoras dedicated to this dispute with Evatl special essay "Toolbar about the board." Unfortunately, it, like most of Written by Protagora, did not come to us. The philosopher Protagor immediately felt that behind this paradox was hidden a hundred-edue, deserving a special study.
Formal logic is based on the concept of discreteness of the world, the beginning of which should be sought in the teaching of democritus on atoms and emptiness, and maybe in earlier philosophical exercises ancient Greece. We do not think about the paradoxics of formal logic when we say that the speed is the number of meters or kilometers traveled by the body, which it passes per second or per minute (physics teaches us that the distance divided by time is speed). The distance we measure discrete units (meters, kilometers, versts, arches, etc.), time is also discrete units (minutes, seconds, hours, etc.). We have a distance of distances - meter, or another segment with which we compare the path. The standard of time (in fact, also segment) we measure time. But the distance and time are continuous. And if interrupted (discrete), what is in the joints of their discrete parts? Otherworld world? Parallel world? O.'s hypothesis parallel Mirahs incorrect, because Based on reasoning according to the laws of formal logic, believing that the world is discretened. But if it were discretened, then it would be impossible to move. And this means that everything in such a world would be dead.
Paradox liar."What I say now is false," or "this statement is a lie." This paradox formulated the Philosopher of the Megar School Evbulid. He said: "Christian Epimyda argued that all the critical liar" . If Epiminee is right, that all the critical liar, then he is also a liar. If Epimine Liar, he lies that all liar crashes. So liars or not liar critany? It is clear that the chain of these reasoning is damaged, but in what?. |
In science it means that it is impossible to understand and explain the system, based on the elements of only this system, the properties of these elements and processes occurring within this system. To do this, we should consider the system as part of something more - the external environment, the larger system, part of which is the system that we study. Otherwise: To understand the private, you need to go up to more universal.
This paradox suggests that to characterize the elements of the system by elements of this system, it is required that the number of elements in this system is more than two. Teza and antithesis are not enough to characterize some kind of item. If the statement is not true, then it does not follow from this that it is false. And on the contrary, if the statement is not false, then this does not mean that it is true. Our mind is not easy to agree with this statement, because we use formal alternative logic. And the case with the statements of Plato and Socrates suggests that it is possible. Judge yourself: We are told: "Ball in a box is not black." If we think that it is white, then we can make a mistake, since the ball may be blue, red, or yellow.
In the last two examples, we see that paradoxes are born out of the damage to formal (binary) logic. Think about how the phrase should be built correctly: "The story teaches a person, and he does not study anything from the history." In this wording, with such a clarification, no paradox is no longer contained. The last two paradoxes are not antinomies, they can be eliminated within the framework of the laws of formal logic, which correctly constructing the phrase.
The paradox from the discharge of the antinomy is generated by an error in the arguments, in the construction of the phrase. The next paradox also applies to anti-nestion.
In this case, it is necessary to remember that a person should learn to reflect, and not just memorize. Doctrine as a mechanical memorization of great value has no value. Approximately 85-90% of what a person remembers, studying at school and university, he forgets during the first 3-5 years. But if he was taught to reflect, then this ability he owns almost all his life. But what will happen to people if they are given to remember only those 10% of the information they remember for a long time? Unfortunately, no one has yet put such an experiment. Although...
There was one man in our village, the bodie finished at the beginning of the 30s only 4 grade school. But in the 60s he worked as the chief accountant of the collective farm and coped with the work better than the accountant with secondary technical education that changed it.
But if the ship is determined as a system, the essence of which is determined by its properties as a whole: weighing, displacement, speed, efficiency, and other characteristics, then when replacing all parts, the ship remains the same. The properties of the whole differ from the properties of its parts and do not reduce the properties of these parts. Whole more sum Its parts! Therefore, in 50 years, a person remains himself, although 95% of its body atoms have been replaced by others many times during this time, and atoms in his body becomes more than the age of 10 years.
So not quite right was ancient philosopherBy stating that it is impossible to enter the same river twice, since the water in it flows and all the time it is replaced by it in the stream. In this case, it is implicitly postulated that the river is the sum of these water molecules and no other water molecules. But this is not the case, because we are not perceived by the river as a set of water molecules, but as a stream of a certain depth and width, at a certain flow rate, in one word, the river is dynamic system, not the amount of your parts.
Often the answer to the question about baldness lies in a different plane than the one in which it was formulated. To answer such a question, you need to get out of one plane of reasoning and perception in a completely different. For example, the publications of one scientist quoted 100 times a year, and another 1 time per year. Question: Which of them is a brilliant scientist? There may be four different answers to this question: 1 - no one, 2 - both, 3 - first, 4 - second. And all four responses are equally equal in this case, since the amount of quotations in principle cannot be a sign of genius. The correct answer to this question can be poured only after 100 years or a little less.
Paradox of democracy(Voting): "You cannot combine all the requirements for the electoral system in one system." If you do an equal representation in parliament from states or regions, then it is impossible to fulfill an equal representation in parliament from voters. But there are still religious denominations, etc. |
But in politics, even formal logic is not in honor, and often it is disturbed intentionally to entangle the brains by the electorate. In the US, the technology of brainstorms are developed simply excellent. Their elections are not democratic, but majoritarian, but the Americans are sacred believe that they have a democratic state and are ready to break anyone who about their public system Thinks differently. The aristocratic form of government management they will manage to issue a democratic. Is it possible to democratic elections in principle?
But almost the conclusion of Monte Carlo can be false and for another reason. After all, the condition for the independence of elementary events when playing a roulette may not be performed. And if the elementary events are not independent, but "clips" with each other as known to us, and unknown while in the ways ... then in this case it is better to put on black, and not on red.
It may turn out that there are other carriers of energy and information in the universe, and not just the oscillations of the electromagnetic field and the flows of elementary particles. If the universe is not discrete (vacuum), but solid, then this paradox is inappropriate. Then, on each part of the Universe, the entire rest of it is affected, then every atom of the universe is associated and interacts with all other other atoms, no matter how far they were not far from him. But in the infinite universe atoms there should be an infinite number ... Stop! Again begin to boil brains.
This paradox stems from our misunderstanding what time is. If the time is the flow of the world with a multitude of ducts (as often happens by the river), and the flow rate in the ducts is different, then the pinch that falls into the fast duct, then again falls into the slow, when fast duct is somewhat slow, in which the other pinch is floating with which they once sailed nearby. But now one pinch will turn out to be ahead of his "girlfriend" and will not meet with her. In order for them to meet, retaining the "girlfriend" should get into another fast duct, and the outdoor - sailing at this time in a slow dash. It turns out that the brother of the twin, flewing on the subsequeurous ship, in principle can not return to the past and meet with his brother. Slow time stream (subsettle ship) delayed it in a stream of time. During this time, his brother did not just become older, but he went to the future, together with him the future went all that he was surrounded. So the brother, who lagged in time, will not be able to go to the future in principle.
And if the time river does not have a duct different speed, then there can be no paradox. Maybe the theory of relativity is incorrect, and time is not relative, but absolutely?
And thank God! Therefore, the grandfather does not threaten that his grandson will appear from the future and kill him. And there are a lot of such grandchildren who came across marijuana.
Recently, the Central Bureau of China on Movie, Radio and Television issues forbidden to show movies about travel travel, since they "demonstrate disrespect for history." Film Crims Raymond Zhou Limin explained the reasons for the prohibition of the fact that now traveling in time is a popular topic in the series and in the cinema, but the meaning of such works, as well as their submission is very dubious. "Most of them are completely fictional, do not correspond to logic and do not correspond to historical realities. Producers and scripts are too frivolous about history, distort it and impose this image to the audience, and it is not worth encouraging, "he added. Such works do not rely on science, and use it as a pretext to comment on current events.
I believe that the Chinese have come to the very point, having understood the harm of such films. Fooling people with nonsense by issuing them for scientific fiction, dangerous. The fact is that such films overlook people a sense of reality, the boundaries of reality. And this is the right way to schizophrenia.
Salvador gave the means of painting showed the absurdity of our presentations about time. Current clock is not time. And what is the time? If there were no time, there would be no movement. Or maybe it is more correct to say this: if there were no movement, there would be no time?. Or maybe time and movement are the same thing? No, rather with the help of categories time and space, we are trying to characterize and measure movement. In this case, time is something like Arshina Malalana. To travel in time, you need to stop being alive (living) people and you need to learn how to move within the movement itself.
There is no time, there is a movement, and movement is time. All paradoxes associated with time occur from the fact that the properties of space are attributed. But space is a scalar, and time - vector.
|
That's how we change in time. Journey to the past is possible only by viewing old photos and old movies. More with the help of our memory. Maybe the memory is exactly what makes us five-dimensional entities? Probably memory and there is a single possible time machine that can die in the past. We just need to learn everything to remember. Photos from the site: http://loveopium.ru/page/94 |
Achilles and turtle:Figgy-legged Achilles will never catch up with a leisurely turtle, if the turtle is in front of Achilles, because while he moves to a point where there was a turtle at the beginning of the competition, she would have time to advance at least a little forward. While Achilles will achieve to the point where the turtle was located, she would have time to move to a certain distance forward. Now Achilles will have to run again some distance to the place where the turtle was, and it will move forward again, and so on, the number of points of the approach of Achilles to the turtle tends to infinity. It turns out that Achilles will never catch up the turtle, but we understand that in reality he will easily catch it up and overtake. Why is it going on, because of what this paradox was formed? And the fact is that the distance is not a totality of points. After all, the point has no size and on any geometric cut The number of points may be infinity. To visit the infinite number of points, the Achilles will need an infinite time. Therefore, it turns out that discrete mathematics and formal logic to reality are not applicable, and if applicable, then with large reservations. |
This paradox is associated with the fact that the formal logic operates in a discrete world with discrete bodies consisting of points, and phenomena, which also represent the totality of points in the four-dimensional space-time. This paradox is not so harmless. This is already 2.5 thousand years old, he shows the scientist absurdity of formal logic and limited mathematics. But scientists stubbornly believe in formal logic and mathematics and do not want to change anything. Although ... Robust attempts to change the logic were made in philosophy and in mathematics. |
Achilles runs behind the turtle. In reality, he approaches it easier, but in the logical design of this process he cannot catch up with it. Turtle has a one-year-owned coherers. Both runners at the same time start moving. While Achilles will delight until the point A, the turtle moves to the point in, the Achilles will again cut the distance between themselves and the turtle and moves to the point S. But at that time the turtle moves forward and turns out to be ahead of the Achilles at the point D. Achilles will reduce the distance to each other and the turtle And it will be at the point E. But a turtle for this time will again use ahead and turns out to be at the point of J. and so indefinitely. The distance between Achilles and the Turtle will decline, but he will not catch it up. This conclusion follows from formal logic. Picture from the site: http://nebesa87.livejournal.com/ |
In mathematics, an attempt to escape from captivity of formal logic was to create a differential and integral calculus. Both also implies a continuous change in some quantity, depending on the continuous change in the other value. Star diagrams depict the dependence of discrete phenomena and processes, and graphs (lines) - continuous processes and phenomena. However, the transition from the chart to the chart is some sacrament - something like sacredness. After all, all experimental data (results of specific measurements) are discrete. And the researcher instead of the diagram takes and draws a graph. What is it? If you approach strictly, then the case is the case: the graph is the transformation of the chart into the chart that approximates this diagram. Building a graph in the form of a solid line, we make the transition from the world of discrete phenomena and items into the world continuous. This attempt to break out of formal logic and thereby avoid its paradoxes.
In philosophy already in the XIX century, scientists realized the inferiority of formal logic, some began to try to resolve this problem. A friendly spoke about dialectics, about the Triad (Hegel), about other theory of knowledge. Philosophers Previously, scientists understood that the formal logic causes cognition to a dead end. The result of the introduction of dialectics into science was, for example, the doctrine of evolution (development). After all, if it is strictly located in the positions of formal logic, then the development is impossible in principle. Formism is a pathetic attempt of formal logic to explain what is happening everywhere evolution. Formists argue that everything is destined in some program in the bud, and the observed development is only an implementation (deployment) of this program. Formal genetics was born from the formal, but it was able to explain only the development of the body in ontogenesis. But the change in the species and the macroevolution formal genetics could not be explained. It was necessary for that initial formal genetics to add a new building, which a few orders of the building of the classical geneticist turned out to be denied the discrete genes. But in such a modified form of genetics was able to explain only the microevolution, and the macroevolution was not on the teeth. And those attempts that genetics make to explain the macroevolution, give paradoxes similar to those discussed above.
But today the positions of formal logic are very durable in the minds of scientists: biologists, biophysicists, genetics, biochemists. Dialectics hardly pierces his way in this science.
A pile of sand consists of 1,000,000 sand. If you pick up one sand from it, it will still be a bunch of sand. If you continue this action many times, it turns out that 2 grades, and even one sand - it is also a bunch of sand. It can be argued that one sand is just one of the sand, but in this case the principle of interconnectivity of statements is violated, and we come to the paradox again. You can save this situation only if you enter an exception for one sandstone, which is not a bunch. But two sands are also difficult to call a bunch. So from what amount of grace begins a bunch of? |
In fact, it does not happen, since there are no identical things in the world, puzzles of hay, equivalent examples of execution. Even if the beams of the hay are the same taste and the size, then one of them can be a little further than the other, or one eye of the donkey may be more angry than the other, etc. Unfortunately, the formal logic does not take it into account, so it should be used carefully and not in all judgments, it does not always trust her.
People in life and in their activities (including in economic) behave at all as "ideal" balls in theory. In addition to the benefit, people seek sustainability and comfort in wide sense of this word. Unknown risk can be both less than the famous and more of it. You can, of course, win more and become richer. But it is possible to lose more and become bankrupt. And the money in growth gives the poor people, they have something to go out, and they do not want to be in the homeless.
Let's try to rummage. Logic error In this case, the duty is considered to be at the same time that we have that we did not lose - with a bottle of beer. Indeed, I took 100 + 50 \u003d 150 rubles. But I ran away my duty, returning 30 rubles a friend, after which I had to 70 rubles and 50 rubles should have become a friend (70 + 50 \u003d 120). Total my duty was now 120 rubles. But if I give a bottle of beer worth 20 rubles to a friend, then I should stay with him only 30 rubles. Together with the long girlfriend (70 rubles), my duty will be 100 rubles. But I lost this amount exactly. |
In Cosmophysics, today the theory of black holes became very fashionable. According to this theory, huge stars in which the "burns" thermonuclear fuel is compressed - collapsy. At the same time, their density increases monstrously - so that electrons fall on the nuclei and intraate empties are collapsed. Such a collapse of the super-delicate extinct star has a strong gravity and absorbs the substance from the outer space (like a vacuum cleaner). At the same time, such a neutron star is becoming more denser and harder. Finally, its gravity becomes so powerful that even the quanta of light cannot leave it. So the black hole is formed.
This paradox allows you to doubt physical theory black holes. It may turn out that they are not so black. Most likely, they possess the structure and, therefore, energy and information. Moreover, black holes can not withdraw the substance and energy infinitely. In the end, "embraced", they are "bursting" and throw out bunches of a super-state substance, which becomes the cores of stars and planets. It is no coincidence that the black holes were found in the centers of galaxies, and in these centers there is the highest concentration of stars running away from these centers.
Any contradiction in theoretical dogmats of science should encourage scientists to change (improve) theory. Such a large number of paradoxes in logic, mathematics, physics shows that not everything is good in these sciences with theoretical buildings.
But everything goes fine until the production crisis happens. And in the crisis of production in the United States disappears the balance of payments deficit. Capital in banks accumulated a lot, and nowhere to invest. Capitals live only due to turnover through production. As they say: "Only airplanes live in flight." And capital live only in production and consumption processes. And without the production and consumption of capital disappear - turn into nothing (yesterday was, and today there is no), from this in the US growing a balance of payments - airbags of other countries in US banks disappeared without a trace. US, making the dollar by international currency, put themselves on the dollar needle. The global economic crisis dramatically exacerbates the situation and health from the dollar "addict". In an effort to acquire the next "dose", the addict goes to everything, it becomes aggressive.
China is well evolving under socialism. Not at all because there are few private property, but more state. Just the Chinese price for goods began to determine in demand for them. And this is possible only in a market economy.
But inflation will inevitably lead to the loss of capital - savings that the population keeps in banks. They say the Greeks at the euro did not live for funds, the budget of Greece was with a big deficit. But after all, receiving this money in the form of wages and benefits, the Greeks bought goods produced in Germany, France and thereby stimulated production in these countries. Production began to be shaped, the number of unemployed has grown. The crisis was aggravated in countries that claimed themselves with donors of the European economy. But the economy is not only the production and its lending. This is also consumption. Ignoring the laws of the system is the reason for this paradox.
Conclusion
Finishing this article, I want to pay attention to the fact that the formal logic and mathematics - the sciences are not perfect and, rushing with their evidence and the strictness of their theorems, are engaged in the axioms adopted on faith as quite obvious things. But are these axioms of mathematics so obvious?
What is a point that does not have length, widths and torses? And how it turns out that the combination of these "disembodied" points, if they are built into a row, is a line, and if one layer, then a plane? We take an infinite set of points that do not have volumes, build them in a row, and get the line of infinite length. In my opinion, it's some kind of nonsense.
I asked this question at school as a teacher of mathematics. She was angry with me and said: "What are you stupid! After all, it is obvious." Then I asked her: "And how many points can be squeezed into the line between two adjacent points, and is it possible to do it?" After all, if the infinite set of points bring close to each other without distances between them, then it turns out the line, but the point. To get a line or plane, it is necessary to place points in a row at some distance to each other. You can't call such a line even dotted, because the points do not have an area and volume. They, as it were,, and no matter how much they, they are intangible.
In school, I often thought: Do we correct arithmetic actions, for example, addition? In arithmetic in addition, 1 + 1 \u003d 2. But it may not always be so. If one apple is added to one apple, then we will get 2 apples. But if it looks different to it differently and it is not apples, but abstract sets, then folding 2 sets, we will get another third consisting of two sets. That is, in this case, 1 + 1 \u003d 3, and maybe 1 + 1 \u003d 1 (two sets merged into one).
And how much will 1 + 1 + 1? In conventional arithmetic, it turns out 3. And if you consider all combinations of 3 elements first 2, and then 3? That's right, in this case 1 + 1 + 1 \u003d 6 (three combinations of 1 element, two combinations of 2 elements and 1 combination of 3 elements). The combinatorial arithmetic at first glance seems nonsense, but it is only with unaccustomed. In chemistry, it is necessary to consider how much water molecules will be obtained if you take 200 hydrogen atoms and 100 oxygen atoms. It will turn out 100 water molecules. And if you take 300 hydrogen atoms and 100 oxygen atoms? Anyway, 100 water molecules will still be and there will remain 100 hydrogen atoms. So, we see that other arithmetic is used in chemistry. Similar tasks take place in ecology. For example, the libid rule is known that the plants influence chemical element In the soil, which is in a minimum. Even if all other elements in large quantities, the plant will be able to assimilate them as much as the element is in a minimum.
Mathematics sway their alleged independence from real MiraTheir world is an abstract world. But if this is so, then why do we use a decimal account system? And some tribes had a twenty system. Very simple, those southern tribes that did not wear shoes, used the twenty system - by the number of fingers on their hands and on the legs, and here those who lived in the north and wore shoes, and only the fingers of the hands were used. Be on your hand, we have three fingers, we would use a checker system. But if we happened from dinosaurs, then we would have three fingers on each hand. Here you have and the independence of mathematics from the outside world.
Sometimes it seems to me that be math closer to nature (reality, experience), whether it is less abstract, do not consider himself a queen of science, and be their servant, she would develop much faster. And it turns out that NemMathematics Pearson came up with a mathematical criterion of chi-square, which is successfully used in comparisons of series of numbers (experimental data) in genetics, geology, economics. If you look closely to mathematics, it turns out that all the fundamentally new new physics, chemists, biologists, geologists, and mathematics in it best case It was developed - proved from the standpoint of formal logic.
Nematic researchers constantly pulled out mathematics from that orthodoxy, in which she was trying to immerse "clean" mathematics. For example, the theory of similarity-differences was created not mathematics, but biologists, theory of information - telegraphists, theory of thermodynamics - thermal physics. Mathematics always tried to prove theorems using formal logic. But some theorems with the help of formal logic to prove, probably, in principle, it is impossible.
Used sources of information
Mathematical paradox. Access address: http://gadaika.ru/logic/matematicHeskii-Paradoks
Paradox. Access address: http://ru.wikipedia.org/wiki/%CF%E0%F0%E0%E4%EE%EA%F1
Paradox logical. Access address: http://dic.academic.ru/dic.nsf/enc_philosophy/
Paradoxes of logic. Access address: http://free-math.ru/publ/zanimatelnaja_matematika/paradoksy_logiki/paradoksy_logiki/11-1-0-19
Khrapko R.I. Logic paradoxes in physics and mathematics. Access address:
Player Error (Gambler "s Fallacy)
O. and., Or the false conclusion of Monte Carlo, reflects the widespread misunderstanding of the chance of events. Suppose the coin is thrown up many times in a row. If 10 "Orlov" falls in a row and if this coin is "correct", for most people it would look like intuitively obvious that the loss of the "Dish" is late. However, this conclusion is false.
This error received the name "Negative Novelty Effect" (Negative Recentcy Effect) and is a tendency to predict the early termination of the often occurring event. It is based on faith in local representativeness (i.e., on the confidence that the sequence of randomly emerging events will be the characteristics of the random process even when it turns out to be short). T. about., In accordance with this erroneous representation, a random event generator, for example, throwing a coin, should lead to outcomes, in-ry - even after a short time - there will be no significant predominance of one or another of possible outcomes. If a series of identical outcomes falls out, there is an expectation that the random sequence will adjust itself in the near future, and the deviation in one direction is thereby subjected to a mandatory equiliblation of the deviation in the other. However, randomly generated sequences, especially if they are relatively short, turn out to be completely unrepresentative producing them random process.
The player's error is something more than simply reflection of ordinary statistical ignorance, since it can be observed in private life even sophisticated in the statistics of people. It reflects two aspects of human. Cognitive function: a) a strong and unconscious motivation of people to find order in all that they are observed around themselves, even if the sequence of outcomes observed as a result of a random process, b) universal human. The tendency to ignore based on the calculation of probability estimates by giving preference to intuition. Although logic can convince us that the random process does not control its outcomes, our intuitive reaction can be very strong and sometimes to suppress logic. Investigated the comparative strength of the logical and intuitive thinking of Reed argues that the latter often turns out to be more compulsory than the first, probably for the reason that such conclusions come to mind suddenly, therefore, are not amenable to logical analysis and are often accompanied by a strong sensation of their right. Unlike the principled inability to track the process, through which such intuitive "decisions" are located, the process of logical reasoning is open to analyzing and criticism. Therefore, people manage logical thinking, and from intuitive thinking they simply receive results, to-ryy fill the last strong feeling of the feeling of the right.
O. and. The most common in a situation where the outcomes are generated purely by chance. If a certain factor of skill participates in the development of events, more often there is a positive novelty effect (Positive Recency Effect). The observer will most likely consider a series of success (for example, a player in billiards) as a testimony of his skills, and will build its forecasts of subsequent outcomes rather in positive than in the negative direction. Even the throwing of the bones can lead to a positive effect of novelty to the extent that the individual is convinced that the outcome of the events is influenced by the "art" of challenging.
See also Barnum's effect, player behavior, statistical conclusion