False monte carlo conclusion. False monte carlo output or player error

Finally, hands and other organs reached the next article.

So, get acquainted, the next guest in our studio - Player error or false Monte Carlo output. Not a term coined by me, although it sounds somehow poppy, without abstruse words characteristic of high-browed guys. This distortion is very easy to understand, nevertheless it lives everywhere, both in the thin gray matter of the lumpen, who have reached the letter Yo in the study of the alphabet, and in the dense thickets of raisins, experienced with a bunch of knowledge of gray-haired sages. Here's what Wiki has to say about it:

The gambler's fallacy, or Monte Carlo false inference, reflects a common misunderstanding of the randomness of events. This is due to the fact that, as a rule, a person does not intuitively realize the fact that the probability of a desired outcome does not depend on the previous outcomes of a random event.

For example, in the case of tossing a coin many times in a row, it may well happen that 9 “tails” will fall out in a row. If the coin is "normal" then it seems obvious to many people that the next toss will be more likely to come up heads: it's hard to believe that "tails" can come up ten times in a row. However, this conclusion is erroneous. The probability of the next heads or tails is still 1/2.

It is necessary, however, to distinguish between the concepts: the probability of falling "heads" or "tails" in each specific case and the probability of falling "tails" ten times in a row. The latter will be equal to . However, the same will be the probability of falling out of any other fixed sequence of "eagles" and "tails" in 10 coin tosses.

What does this mean in translation into our, piharsko-trading language?

The simplest and most well-known example is the classic flat catch-up. Those. popan puts over 2.5 no matter what match in +-2 odds, merges, doubles the bet on another match over 2.5 with odds around 2, merges, doubles the bet again, etc. Well, or Martingale, call it what you want, that's not the point. And if you offer him to shove the total less at the third or fourth iteration, he will probably be indignant with the mega-argument "You're right, it's already been 3 tm, right now the probability of tb is higher." And it turns out to be absolutely right. But only in his imaginary universe, in real life everything is somewhat different. The probability in a future event, all other things being equal, does not depend on the past, at least one at least a million. Axiom.

For a million. We recently had a conversation with Kent on this topic (¡Hola senor Alejandro!). At some point, a person who perceives this world absolutely adequately responds to a simple question: “Before that, heads fell out a million times. What is the probability that tails 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 should a person who got into a catch-up (whom I am a tough opponent) do? The most important thing is not to think red or black, total over or total under, fish or chicken, nothing depends on you. Just kick any outcome and hope in front of the TV, but rather go in for sports, sex, fishing, emphasize the necessary. So you will burn fewer calories from the "wrong choice", which, in fact, did not exist. Now mathematics (gods, fortune, mastyushka, call it what you want) has turned its face or ass to you, and there's nothing you can do about it. There is no need to catch up with seven iterations of the total over, feel free to kick the total under, this does not affect the result in any way. More precisely, it affects only that the catch-up will eventually put you on the shoulder blades, you can’t deceive the math, the margin will do everything for you. For many years I watched the tops of pihars on the pump room, among those who were successful at a solid distance there was not a single catcher, but now it’s not about that.

Let's take another example. At one time I talked online in trading sessions with one well-known horse trader, I will not voice his name. So, he, too, was caught in the web of this cognitive error. The course of his thoughts flowed along the following line: 3 times in a row the favorite mare came first, which means that the next fava race should be laid. I won - hsn, laim fava in the next race with doubled rage, then tripled, etc. And this "system" gave a profit for some period of time. But at one crappy moment, the inevitable happened: mathematics defeated him, he ran into such a sum that he left our slender, though not stable, ranks for a long time. He could not believe that this was possible, it took him a long time to accept, understand and rethink it, he caught such a depression that a massage with Australian koalas would not have helped him at that moment. I don't think this is an isolated case.

I had a case when I got myself into a similar situation. I vaguely remember the details, it's a long time ago. The Italian Championship is a long-standing one - a dull sight, catenaccio, draws - frequent guests. There was not a single draw in one of the rounds, and my fledgling brain tells me that the trend will return in the next round. Stupidly took draws in all matches and ... megaposos, again not a single draw. But I'm a cool pepper, you won't take me so easily, in the next round I again take draws with a double stake (hello 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 everything will definitely be nishtyak. But the reality dipped deeper, I stupidly ran out of money. To answer your question: I don't know what happened in the next round, I didn't watch cuts, I thought I'd go crazy if I see an ocean of nothings. An expensive lesson, but as it turned out, very useful.

I will finish at 3 am. I will make a riddle to consolidate, self-analyze and improve the absorption of the foregoing. What is the probability that Barcelona will not win at home against, say, Malaga twice in a row? Kef on p1 - 1.2. And how soon can it come? The first person who answered correctly from me nishtyachok, say, I will write an article on a topic of their choice.

So, to recap. Don't look at what happened before, it doesn't matter. If you look - do not draw conclusions, they are subjective. We drew conclusions - do not build predictions from them, they are unreliable. Still built a prediction - be prepared to easily change it, do not cling to it as the only true one (one of my favorite cognitive errors, we'll talk about it another time). If you grabbed hold and can't let go - go to the factory, get a job in a taxi, a pizza delivery man, choose any other pick, games with probabilities are, alas, not for you yet. But do not despair, read, work on yourself, improve your understanding of the processes taking place in your head, drill your brain. Having passed the oil and coal layers, sooner or later you will drill to states of mind that are not so ossified and compressed, and someday, with a certain degree of probability, you will be able to step back onto the ornate path of a non-kylo bubble.

This episode with the smart missionary is one of the paradoxes paradox ancient Greek philosophers Protagora and Euathla.

But every researcher who tried to strictly define all the concepts in his theory faced a similar paradox of formal logic. Nobody has succeeded in this yet, since everything ultimately came down to a tautology like: "Movement is the movement of bodies in space, and movement is the movement of bodies in space"

Another version of this paradox. Someone has committed a crime punishable death penalty. In court, he appears the last word. He must make one statement. If it turns out to be true, the criminal will be drowned. If it is false, the criminal will be hanged. What statement should he make to completely confuse the judge? Think for yourself.

Perplexed by this paradox, Protagoras devoted to this dispute with Euathlus special essay"Pay Claim". Unfortunately, like most of written by Protagoras has not come down to us. The philosopher Protagoras immediately felt that behind this paradox lies something essential that deserves special study.

Aporia of Zeno of Elea. A flying arrow, according to the laws of formal logic, cannot fly. A flying arrow at each moment of time occupies a position equal to itself, that is, it rests; since it is at rest at every moment of time, then it is at rest at all moments of time, that is, there is no moment of time at which the arrow moves and does not occupy an equal place.

This aporia is a consequence of the notion of the discreteness of motion that a moving body in discrete units of time passes through discrete intervals of distance, and the distance is the sum of an infinite number of indivisible segments that the body passes. This aporia raises a deep question about the nature of space and time - about discreteness and continuity. If our world is discrete, then movement in it is impossible, and if it is continuous, then it is impossible to measure it with discrete units of length and discrete units of time.

Formal logic is based on the concept of the discreteness of the world, the beginning of which should be sought in the teachings of Democritus on atoms and emptiness, and perhaps in the earlier philosophical teachings of ancient Greece. We do not think about the paradoxical nature of formal logic when we say that speed is the number of meters or kilometers traveled by a body that it passes per second or per minute (physics teaches us that distance divided by time is speed). We measure distance in discrete units (meters, kilometers, versts, arshins, etc.), while we measure time in discrete units (minutes, seconds, hours, etc.). We have a distance standard - a meter, or another segment with which we compare the path. With the standard of time (in fact, also a segment), we measure time. But distance and time are continuous. And if they are discontinuous (discrete), then what is at the junctions of their discrete parts? Other world? A parallel world? Hypotheses about parallel worlds are incorrect, because are based on reasoning according to the laws of formal logic, which assumes that the world is discrete. But if it were discrete, then movement would be impossible in it. And that means that everything in such a world would be dead.

Indeed, this paradox is unresolvable in binary logic. But it is precisely this logic that underlies most of our reasoning. From this paradox it follows that a true judgment about something cannot be built within the framework of this something. To do this, you need to go beyond it. This means that the Cretan Epimenides cannot objectively judge the Cretans and give them characteristics, since he himself is a Cretan.

In science, this means that it is impossible to understand and explain a system based on the elements of this system only, the properties of these elements and the processes occurring within this system. To do this, one should consider the system as part of something larger - external environment, a higher order system of which the system we are studying is a part. Otherwise: in order to understand the particular, one must rise to the more general.

Paradox of Plato and Socrates
Plato: "Socrates' next statement will be false."
Socrates: "What Plato said is true."
That is, if we assume that Plato is telling the truth, that Socrates is lying, then Socrates is lying, that Plato is telling the truth, then Plato is lying. If Plato is lying that Socrates is lying, then Socrates is telling the truth that Plato is right. And the chain of reasoning returns to the beginning.

This paradox lies in the fact that, within the framework of formal logic, a proposition can be both true and false at the same time. This statement, which constitutes the liar's paradox, is neither provable nor refutable in formal logic. It is believed that this statement is not a logical statement at all. An attempt to resolve this paradox leads to trinity logic, complex logic.

This paradox shows the imperfection of formal logic, simply - its inferiority.

This paradox suggests that in order to characterize the elements of a system by the elements of this system, it is required that the number of elements in this system be more than two. The thesis and antithesis are not enough to characterize some element. If a statement is not true, then it does not follow that it is false. Conversely, just because a statement is not false does not mean that it is true. It is not easy for our mind to agree with this statement, because we use formal alternative logic. And the case with the statements of Plato and Socrates suggests that this is possible. Judge for yourself: we are told: "The ball in the box is not black." If we think that it is white, then we may be mistaken, since the ball may turn out to be blue, red, or yellow.

In the last two examples, we see that paradoxes are born from the inferiority of formal (binary) logic. Let's think about how the phrase should be constructed correctly: "History teaches a person, but he does not learn anything from history." In such a formulation, with such a clarification, there is no longer any paradox. The last two paradoxes are not antinomies, they can be eliminated within the framework of the laws of formal logic by correctly constructing a phrase.

The barber does not shave himself, Russell's paradox forbids him to do so. Photo from the site: http://positivcheg.ru/foto/837-solidnye-dyadenki.html

Russell's paradox: Does the set of all sets contain itself if the sets it contains do not contain themselves (are empty sets)? Russell popularized it in the form of the "barber paradox": "The barber only shaves people who don't shave themselves. Does he shave himself?

There is a paradox of definition here: We started building a logical construction without defining what a set is. If the barber is part of the multitude of people he shaves, then he must charge himself for shaving. So what is the definition? But even scientists often operate with concepts that do not define in any way, why they cannot understand each other and argue senselessly.

The concept of "empty set" is absurd by definition. How can a set be empty, containing nothing? The barber is not among the many people he shaves as a barber. After all, any man shaves himself not like a barber, but like a shaving man. And a man who shaves is not a barber, since he does not take payment from himself for this.

A paradox from the category of antinomies - generated by an error in reasoning, in the construction of a phrase. The following paradox also applies to antinomies.

In this case, we must remember that a person must learn to think, and not just memorize. Teaching as rote memorization great value does not have. Approximately 85-90% of what a person remembers while studying at school and university, he forgets during the first 3-5 years. But if he was taught to think, then he owns this skill almost all his life. But what will happen to people if, during training, they are allowed to memorize only those 10% of the information that they remember for a long time? Unfortunately, no one has done such an experiment yet. Although...

There was one man in our village who graduated in the early 30s from only 4 classes of school. But in the 60s he worked as the chief accountant of a collective farm and did a better job than the accountant who later replaced him with a secondary technical education.

But if a ship is defined as a system, the essence of which is determined by its properties as a whole: weight, displacement, speed, efficiency and other characteristics, then even when all parts are replaced with similar parts, the ship remains the same. The properties of the whole differ from the properties of its parts and are not reduced to the properties of these parts. Whole more than the amount its parts! Therefore, even at the age of 50, a person remains himself, although 95% of the atoms of his body have already been replaced by others many times during this time, and there are more atoms in his body than there were at the age of 10 years.

So it wasn't quite right. ancient philosopher, stating that it is impossible to enter the same river twice, since the water flows in it and all the time its molecules in the stream are replaced. In this case, it is implicitly postulated that the river is the sum of precisely these water molecules and no other water molecules. But this is not so, because we perceive a river not as a set of water molecules, but as a stream of a certain depth and width, with a certain flow rate, in a word, a river is a dynamic system, and not the sum of its parts.

Bald orangutan. Photo from the site: http://stayer.35photo.ru/photo_125775

Balding dandelion. Photo from the site: http://www.fotonostra.ru/4101.html

Often the answer to the question of baldness lies in a different plane than the one in which it was formulated. To answer such a question, it is necessary to leave one plane of reasoning and perception into a completely different one. For example, publications of one scientist are cited 100 times a year, and another 1 time per year. Question: which of them is a brilliant scientist? There can be four different answers to this question: 1 - none, 2 - both, 3 - first, 4 - second. And all four answers in this case are equally likely, since the number of citations, in principle, cannot be a sign of genius. The correct answer to this question can only be obtained in 100 years or a little less.

The absurdity in this case stems from the lack of a clear definition of the concept of "democracy". If the social system (the state) is to be democratic, then equal representation should be made precisely from the voters. Equal representation from the states, if the population in them is different, is not a principle of democracy, but something else. Equal representation from parties is something third, from religious associations is fourth, and so on.

But in politics, even formal logic is not held in high esteem, and often it is deliberately violated in order to fool the electorate. In the United States, brain-powdering technologies are simply excellent. Their elections are not democratic, but majoritarian, but the Americans firmly believe that they have a democratic state and are ready to break anyone who public system thinks otherwise. They manage to pass off the aristocratic form of government as democratic. Is democratic elections possible in principle?

But in practice, Monte Carlo's conclusion can be false for another reason as well. After all, the condition on the independence of elementary events when playing roulette may not be satisfied. And if elementary events are not independent, but "linked" to each other in ways known to us, as well as unknown yet... then in this case it is better to bet on black, not on red.

It may turn out that there are other carriers of energy and information in the Universe, and not just electromagnetic field fluctuations and flows elementary particles. If at its core the Universe is not discrete (vacuum), but continuous, then this paradox is inappropriate. Then every part of the Universe is influenced by the rest of it, then every atom of the universe is connected and interacts with all other atoms, no matter how far they are from it. But in the infinite Universe of atoms there must be an infinite number... Stop! The brains are starting to boil again.

This paradox stems from our misunderstanding of what time is. If time is a stream of the world with many channels (as is often the case with a river), and the speed of the flow in the channels is different, then a sliver that has fallen into a fast channel will then again fall into a slow one when the fast channel merges with the slow one in which another chip floats with which they once sailed alongside. But now one sliver will be ahead of its "friend" and will not meet with her. In order to meet them, the lagging "girlfriend" must fall into another fast channel, and the one who is ahead of them should swim in the slow channel at this time. It turns out that the twin brother, who flew away on a sub-light ship, cannot, in principle, return to the past and meet his brother. The slow flow of time (sub-light ship) delayed him in the flow of time. During this time, his brother not only got older, but he went into the future, with him everything that surrounded him went into the future. So the brother, who is behind in time, will not be able to get into the future in principle.

And if the river of time does not have channels with different speeds, then there can be no paradox. Maybe the theory of relativity is wrong, and time is not relative, but absolute?

Paradox of the dead grandfather: you travel back in time and kill your grandfather before he met your grandmother. Because of this, you will not be able to be born and therefore will not be able to kill your grandfather.

This paradox proves that travel to the past is impossible. In order to get into the past, a person needs to turn into a different entity - go into a five-dimensional space-time, in which the past, present and future exist together - are merged together, he will have to be born, die and live, and all this in the form of a kind of consubstantial phenomenon when "born, live and die" are not separate from each other. To become such a being for a person means certain death - disintegration into subatomic particles. In general, we live in a four-dimensional world, and the path to the five-dimensional world is barred for us.

And thank God! Therefore, grandfather is not threatened that his grandson will come from the future and kill him. And there are many such grandchildren who have smoked marijuana today.

Recently, China's Central Bureau of Film, Radio and Television banned time travel films because they "show disrespect for history." Film critic Raymond Zhou Liming explained the reasons for the ban by saying that now time travel is a popular topic in TV shows and movies, but the meaning of such works, as well as their presentation, is very doubtful. “Most of them are completely fictional, do not correspond to logic and do not correspond to historical realities. Producers and writers are taking the story too lightly, distorting it and forcing that image on the audience, and this should not be encouraged,” he added. Such works do not rely on science, but use it as a pretext for commenting on current events.

I believe that the Chinese hit the nail on the head when they realized the harm of such films. Fooling people with nonsense, passing them off as science fiction, dangerous. The fact is that such films shake people's sense of reality, the boundaries of reality. And this Right way to schizophrenia.

Salvador Dali showed the absurdity of our ideas about time by means of painting. The current clock is not the time yet. But what is time? If there were no time, there would be no movement. Or maybe it is more correct to say this: if there was no movement, then there would be no time? Or maybe time and movement are one and the same? No, rather, with the help of the categories of time and space, we are trying to characterize and measure movement. In this case, time is something like an arshin of malalan. In order to travel in time, one must stop being living (living) people and one must learn to move within the movement itself.

There is no time, there is movement, and movement is time. All the paradoxes connected with time come from the fact that properties of space are attributed to time. But space is a scalar and time is a vector.

Past and present. If it were possible to connect the past with the present in this way, then in the evenings we could go for a walk in the courtyard of our childhood and meet childhood friends there, and childhood friends would be children, and we would be adults. But this is impossible. Time is not a characteristic of any movement, but a characteristic of an irreversible movement. Even if you start moving in a circle - loop, then each cycle will differ in something from the previous one. Photo from the site: http://kluchikov.net/node/76

The turtle felt sorry for Achilles and stopped. Only then, exhausted and aged, was Achilles able to catch up with her and finally rest. Drawing from the site: http://ecolours.pl/life.php?q=zeno-of-elea&page=2

In mathematics, an attempt to escape from the captivity of formal logic was the creation of differential and integral calculus. Both presuppose a continuous change of some quantity depending on the continuous change of another quantity. Bar charts depict the dependence of discrete phenomena and processes, and graphs (lines) - continuous processes and phenomena. However, the transition from diagram to graph is a kind of sacrament - something like sacrilege. After all, all experimental data (results of specific measurements) are discrete. And the researcher instead of a diagram takes and draws a graph. What is this? If we approach strictly, then the situation here is as follows: a graph is a transformation of a diagram into a graph that approximates this diagram. Building a graph in the form solid line, we make the transition from the world of discrete phenomena and objects to the world of continuous. This is an attempt to break out of the limits of formal logic and thereby avoid its paradoxes.

In philosophy, already in the 19th century, scientists realized the inferiority of formal logic, some began to try to solve this problem. They started talking in unison about dialectics, about the triad (Hegel), about a different theory of knowledge. Philosophers realized before scientists that formal logic leads cognition into a dead end. The result of the introduction of dialectics into science was, for example, the doctrine of evolution (development). After all, if one is strictly on the positions of formal logic, then development is impossible in principle. Preformism is a pathetic attempt by formal logic to explain the evolution going on everywhere. Preformists argue that everything is predestined in some program in the bud, and the observed development is only the implementation (deployment) of this program. Formal genetics was born out of preformism, but it could only explain the development of an organism in ontogeny. But formal genetics could not explain the change in species and macroevolution. It was necessary to attach a new building to that initial formal genetics, which turned out to be several orders of magnitude larger than the building of classical genetics, up to the negation of discrete genes. But even in such a modified form, genetics could only explain microevolution, and macroevolution was too tough for it. And the attempts that geneticists make to explain macroevolution give rise to paradoxes similar to those discussed above.

But even today the positions of formal logic are very strong in the minds of scientists: biologists, biophysicists, geneticists, biochemists. Dialectics finds its way with difficulty in this science.

The paradox says that someone omnipotent can create any situation, including one in which he will be unable to do anything. In a simplified version, it sounds like this: can God create a stone that he himself cannot lift? On the one hand, he is omnipotent and can create any kind of stone. On the other hand, if he cannot lift the stone he created, then he is not omnipotent!

In reality, this does not happen, since in the world there are no identical things, phenomena, bundles of hay, equivalent types of execution. Even if the bundles of hay are the same in taste and size, then one of them may be a little further than the other, or one donkey's eye may be sharper than the other, etc. Unfortunately, formal logic does not take this into account, so it should be used carefully and not in all judgments, and not always trusted.

People in life and in their activities (including economic ones) do not behave at all like "ideal" balls in theory. In addition to benefits, people strive for stability and comfort in the broadest sense of the word. The unknown risk can be less than or greater than the known risk. You can, of course, win more and become richer. But you can lose more and become bankrupt. And non-poor people give money in growth, they have something to value, and they do not want to be homeless.

Let's say I took 100 rubles from a friend, went to the store and lost them. I met a friend and borrowed another 50 rubles from him. I bought a bottle of beer for 20 rubles, I had 30 rubles left, which I gave to my friend and owed her 70 rubles. And I owed a friend 50 rubles, a total of 120 rubles. Plus I have a bottle of beer for 20 rubles.
Total 140 rubles!
Where are the other 10 rubles?

Here is an example of a logical error embedded in the reasoning. The error lies in the incorrect construction of the reasoning. If you "walk" in a given logical circle, then it is impossible to get out of it.

In space physics, the theory of black holes has become very fashionable today. According to this theory, huge stars in which thermonuclear fuel "burns out" shrink - collapse. At the same time, their density increases monstrously - so that the electrons fall on the nuclei and the intra-atomic voids collapse. Such a collapsed superdense extinct star has strong gravity and absorbs matter from outer space(like a vacuum cleaner). At the same time, such neutron star getting tighter and heavier. Finally, its gravity becomes so powerful that even light quanta cannot escape it. This is how a black hole is formed.

This paradox casts doubt on the physical theory of black holes. It may turn out that they are not so black. Rather, they have structure and therefore energy and information. Moreover, black holes cannot absorb matter and energy indefinitely. In the end, having "overfed", they "burst" and throw out clots of superdense matter, which become the cores of stars and planets. It is no coincidence that black holes are found in the centers of galaxies, and in these centers there is the highest concentration of stars escaping from these centers.

Any contradiction in the theoretical dogmas of science should encourage scientists to change (improve) the theory. Such a large number of paradoxes in logic, mathematics, and physics shows that not everything is going well in these sciences with theoretical constructions.

In 1850, the German physicist R. Clausius came to the conclusion that heat passes only from a warm body to a cold one, and never vice versa, which is why the state of the Universe must change more and more in a certain direction. Physicist William Thomson argued that all physical processes in the Universe are accompanied by the transformation of light energy into heat. Consequently, the Universe is waiting for "thermal death" - i.e. cooling to absolute zero -273 degrees Celsius. Therefore, an infinitely long existence of a "warm" Universe in time is impossible, it must cool down.

The theory of heat death of the Universe, in all likelihood, is a beautiful theory, but false. Something thermodynamics does not take into account, since its postulates lead to such a conclusion. However, the physicists love this theory too much and do not want to part with it or at least severely limit its applicability.

Another revolution in physics is brewing. Someone brilliant will create a new theory in which energy can not only be dissipated in the Universe, but also collected. Or maybe it is going to black holes? After all, if there is a mechanism of dispersion of matter and energy, then there must necessarily be an opposite process of concentration of matter. The world is based on the unity and struggle of opposites.

Photo from the site: http://grainsoft.dpspa.org/referat/referat-teplovoy-smerti-vselennoy.html

Clausius wrote about it this way: “The work that can be produced by the forces of nature and contained in existing movements celestial bodies, will gradually turn more and more into heat. The heat, constantly passing from a warmer to a colder body, and thereby striving to even out the existing differences in temperature, will gradually receive a more and more uniform distribution, and a certain equilibrium will also come between the radiant heat present in the ether and the heat located in the bodies. And finally, in respect of their molecular disposition, the bodies will approach a certain state in which, as regards the prevailing temperature, the total scattering will be the greatest possible. And further: “We must, therefore, deduce the conclusion that in all natural phenomena the total value of entropy can always only increase, not decrease, and we therefore get as short expression The always and everywhere ongoing process of transformation is the following statement: the entropy of the Universe tends to a certain maximum. (http://msd.com.ua/vechnyj-dvigatel/teplovaya-smert-vselennoj-i-rrt-2/)

But everything goes well until a production crisis occurs. And with a production crisis in the United States, the balance of payments deficit disappears. A lot of capital has accumulated in banks, but there is nowhere to invest it. Capitals live only at the expense of turnover through production. As they say: "Airplanes live only in flight." And capital lives only in the processes of production and consumption. And without production and consumption, capitals disappear - they turn into nothing (yesterday it was, but today it is not), because of this, the balance of payments deficit in the USA is growing - the airbags of other countries in US banks have disappeared without a trace. The United States, having made the dollar an international currency, put itself on a dollar needle. The world economic crisis sharply aggravates the situation and the health of the dollar "addict". In an effort to acquire another "dose", the addict goes to any lengths, he becomes aggressive.

China is also developing well under socialism. Not because there are few private property, but more of the state. It's just that the Chinese began to determine the price of goods by the demand for them. And this is possible only in a market economy.

The paradox of thrift. If everyone saves money during an economic downturn, then aggregate demand will fall and, as a result, the total savings of the population will decrease.

I would call this paradox the paradox of Angela Merkel and Sarkozy. By introducing austerity budgets in the countries of the United Europe, politicians have sharply reduced the demand of the population for goods and services. The reduction in demand led to a reduction in production, including in Germany and France themselves.

Europe, in order to cope with the crisis, must stop saving and must come to terms with the inevitability of inflation. In this case, part of the capital will be lost, but production will be saved through consumption.

Photo from the site: http://www.free-lance.ru/commune/?id=11&site=Topic&post=1031826

But inflation will inevitably lead to the loss of capital - the savings that the population keeps in banks. They say that the Greeks lived beyond their means under the euro, the Greek budget was in big deficit. But after all, receiving this money in the form of salaries and benefits, the Greeks bought goods produced in Germany, France, and thereby stimulated production in these countries. Production began to collapse, the number of unemployed increased. The crisis worsened in countries that considered themselves donors to the European economy. But the economy is not only production and its lending. It is also consumption. Ignoring the laws of the system is the reason for this paradox.

Conclusion

Finishing this article, I want to draw attention to the fact that formal logic and mathematics are not perfect sciences and, boasting of their proofs and the rigor of their theorems, are based on axioms taken for granted as quite obvious things. But are these axioms of mathematics so obvious?

What is a point that has no length, width or thickness? And how is it that the totality of these "incorporeal" points, if they are lined up, is a line, and if one layer, then a plane? We take an infinite number of points that do not have volume, line them up in a row, and we get a line of infinite length. In my opinion, this is some kind of nonsense.

I used to ask this question to my math teacher at school. She was angry with me and said: "What a stupid you are! After all, this is obvious." Then I asked her: "And how many points can be squeezed into a line between two adjacent points, and is it possible to do this?" After all, if an infinite number of points are brought close to each other without distances between them, then we get not a line, but a point. To get a line or a plane, it is necessary to arrange the points in a row at a certain distance from each other. You can’t even call such a dashed line, because the points have no area and volume. They seem to exist, but as if they do not exist at all, they are intangible.

At school, I often thought: are we doing arithmetic operations, for example, addition, correctly? In addition arithmetic, 1+1 = 2. But that may not always be the case. If you add one more apple to one apple, you get 2 apples. But if we look at it differently and count not apples, but abstract sets, then by adding 2 sets, we will get a third one, consisting of two sets. That is, in this case 1 + 1 = 3, or maybe 1 + 1 = 1 (two sets merged into one).

How much is 1+1+1? In ordinary arithmetic, it turns out 3. And if we take into account all combinations of 3 elements, first 2 each, and then 3 each? That's right, in this case 1+1+1=6 (three combinations of 1 element each, two combinations of 2 elements each and 1 combination of 3 elements each). Combinatorial arithmetic at first glance seems stupid, but it is so only out of habit. In chemistry, you have to count how many water molecules you get if you take 200 hydrogen atoms and 100 oxygen atoms. You get 100 water molecules. And if you take 300 hydrogen atoms and 100 oxygen atoms? You still get 100 water molecules and 100 hydrogen atoms remain. So, we see that in chemistry a different arithmetic finds its application. Similar problems take place in ecology. For example, Liebig's rule is known that plants are affected by chemical element in the soil, which is at a minimum. Even if all other elements in in large numbers, the plant will be able to assimilate them as much as the element that is at a minimum allows.

Mathematicians boast of their alleged independence from real world, their world is an abstract world. But if this is so, then why do we use the decimal system of counting? And some tribes had a twenty-fold system. Very simply, those southern tribes who did not wear shoes used the vigesimal system - according to the number of fingers and toes, but those who lived in the north and wore shoes used only fingers to count. If we had three fingers on our hand, we would use the six-digit system. But if we evolved from dinosaurs, then we would have three fingers on each hand. So much for the independence of mathematics from the outside world.

Sometimes it seems to me that if mathematics were closer to nature (reality, experience), if it were less abstract, do not consider yourself the queen of sciences, but be their servant, it would develop much faster. And so it turns out that the non-mathematician Pearson came up with the mathematical criterion chi-square, which is successfully used when comparing series of numbers (experimental data) in genetics, geology, and economics. If you take a closer look at mathematics, it turns out that it was physicists, chemists, biologists, geologists who introduced everything fundamentally new into it, and mathematicians, at best, developed this - they proved it from the standpoint of formal logic.

Researchers in non-mathematics constantly pulled mathematics out of the orthodoxy into which "pure" mathematicians tried to plunge it. For example, the theory of similarity-difference was created not by mathematicians, but by biologists, the theory of information by telegraphers, the theory of thermodynamics by physicists-heat engineers. Mathematicians have always tried to prove theorems using formal logic. But some theorems are probably impossible to prove with the help of formal logic.

Information sources used

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

The paradox is 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:

Players are no doubt aware of Monte Carlo's false derivation. Some, however, will be surprised to learn that this is a false conclusion - they then consider it a "Monte Carlo strategy." Well, that's exactly what the croupiers are counting on.

We all know that a roulette wheel has half black and half red sections, which means we have a 50% chance that red will come up when the wheel is turned. If we spin the wheel many times in a row - say a thousand - and at the same time it will be in good order and there will be no tricky devices on it, then red will fall out about 500 times. Accordingly, if we spin the wheel six times and all six times black comes up, we will have reason to think that by betting on red, we will increase our chances of winning. After all, red should fall out, right? No it is not true. On the seventh time, the probability that red will fall out will still be the same 50%, as well as every next time. This is true no matter how many times black is rolled in a row. So here's a very sensible piece of advice based on Monte Carlo's fallacy.

If you're going to be on a plane, for your own safety, take a bomb with you, because the chances of two guys with bombs meeting on the same flight at the same time are extremely small.

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Gambler's fallacy, also known as the Monte Carlo fallacy or mature odds fallacy, is the mistaken belief that if something happens more than usual over a period of time, it will happen less often in the future, or if something If something happens less frequently than it usually does for some period of time, it will happen more often in the future. As proof of this conclusion, people, and especially gamblers, often cite the so-called "balance of nature" or the "rule of justice." In situations where confirmation of this false conclusion is observed (i.e., a random result is accepted as a consequence of the correctness of judgment), the belief of a person is already appealing to the human mind, as a result of which false concepts turn into a proven theory. This error can occur in many life situations, although it is directly associated with gambling where such errors are very common among players.

Use of the term " false conclusion Monte Carlo" originates from the most famous example of this phenomenon, which occurred in the Monte Carlo casino in 1913. The most famous example A gambler's error occurred in a game of roulette at the Monte Carlo casino on August 18, 1913, when the ball landed on "black" 26 times in a row. This is, in fact, an extremely rare occurrence, though not more or less common than any other of the other 67,108,863 possible sequences of 26 red or black. Players have lost millions of francs betting against black, wrongly reasoning that the band was caused by an "imbalance" in the wheel's chaotic behavior, and that it should have been accompanied by a long red band.

The reverse fallacy also exists. According to Monte Carlo's reverse false conclusion, players can assume that "fate" is on their side and will continue to give out black, as in the case of August 18, 1913 for the 27th and even 101st time. Again, the delusion is the belief that the "universe" somehow carries a memory of past outcomes that tend to favor or unfavorably yield subsequent outcomes. However, this is not necessarily a delusion, sometimes this delusion is true, since for example, no matter how stupid it may sound, 2 + 2 will always equal four. Gambler's error also works in the theory of predicting the sex of a child. Many believe that the chance of giving birth to a boy in this particular girl, in the presence of one healthy fetus, is always lower, because "according to statistics, ten girls have nine guys," although this chance is 50 percent.

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