And experience is the son of difficult mistakes. Oh, how many wonderful discoveries the spirit of enlightenment is preparing for us! And experience is the son of difficult mistakes, and genius is a parade - Island MAN
And the genius of paradoxes, friend.
Experience is a lot of knowledge about how NOT to act in situations that will never happen again.
There are some looped situations in our lives when the same thing regularly happens to us, despite the fact that, it would seem, we have abstracted ourselves from it in every possible way, and voluntarily said - “that’s it, never again!”
You know, it happens that you run from something, you run, and then you still come back to it. And you stand dumbfounded over the conflagration - “well, how can this be?!”
Sometimes you meet in life different people, and after a while they all begin to behave the same. And you think - you need to change the person. You change a person, and he becomes the same again. The situation is going full circle.
I don’t want to get too deep into the weeds (“don’t dig deep - the cable is buried there”), but this all comes from the fact that by our action or inaction we constantly attract into our lives certain people. And after a while, consciously or unconsciously, we make them begin to turn towards us in some specific way.
They have other sides too - but this is the one they turn towards us.
If we don’t like it, then there is only one way to change something - to understand ourselves, to realize why and why I attract this particular thing into my life.
What am I broadcasting to the world that it mirrors exactly this to me? And the world - large mirror. When we experience a range of toxic experiences, it’s not the world that tripped us up, it’s us looking in the mirror.
There is no point in blaming the mirror if your face is crooked.
When the situation makes sense, behavior changes. Behavior changes - people change. Either they turn the other way, or some leave and others come.
When the situation is completely completed and meaningful, we know what to do with it. And then it turns into experience. The same one, the son of difficult mistakes.
Yes, any experience comes through mistakes. If you don't allow yourself to make mistakes, there will be no experience.
There will be a lot smart quotes, rules, references to the thoughts of the lives of the greats of this world, but own experience there won't be. And all these scatterings of wise thoughts will not help anyone.
You can, of course, give an Andamanese native a trigonometry textbook, saying (with absolutely no pretense) that it is necessary, smart and useful thing- but for the Andamanese native it will be completely in one place.
It's the same with experience.
What? “A smart person learns from other people’s mistakes, a fool from his own?” There are mistakes that you just have to go through yourself. To remember the experience with the body. So that the body remembers and does not remind.
If this experience is not wired into our body, no golden brain will help transform someone else’s mistake into our own experience.
When you have experience, the situation stops looping. When a similar situation comes and you have experience, it is already clear what can be done and what result you can get from it.
And then you can act differently, a choice appears, there is no longer a need to run like a squirrel in one wheel, to follow your own tail.
In a sense, this is such a lyceum - you pass the exam, close the topic - you rise to a higher level.
If you fail the exam, a little time will pass and you will have to retake it. Life will definitely throw up exactly the same situation - with another person, in another place, in seemingly different conditions - but the situation will repeat itself again.
And it will continue if you constantly fail the exam, even endlessly - unlike us, you have a lot of time.
Oh, you crafty old devil!
One thing pleases - whoever God loves, he tests. God gives tasks knowing exactly that I have the strength to complete it.
Sometimes, like a careless schoolboy, I meet him in the corridor. He squints with his gray eyes, winks at me - “Did he fail the exam again?” I nod. “Well, rest and come back for a retake,” he grins.
Yes, I'll come, damn it! Where will I go?
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March 30th, 2014
Paradox (from ancient Greek παράδοξος - unexpected, strange from ancient Greek παρα-δοκέω - it seems) is a situation (statement, statement, judgment or conclusion) that can exist in reality, but has no logical explanation. One must distinguish between paradox and aporia. Aporia, in contrast to paradox, is a fictitious, logically true situation (statement, statement, judgment or conclusion) that cannot exist in reality.
The most famous philosophical paradoxes of antiquity are Zeno's aporias, which prove the impossibility of movement: for example, the argument “Achilles and the tortoise”: theoretically, Achilles cannot catch up with the tortoise, which will always be ahead of him, even if just a little bit. Because in order to catch up with her, he must first come to the point where she was when he started moving, then to the point where the turtle had already managed to reach during this time, and so on ad infinitum.
Let's stretch our brains and think about these real and far-fetched, and often simply far-fetched paradoxes and aporias.
1. Banach-Tarski paradox
Imagine that you are holding a ball in your hands. Now imagine that you start tearing this ball into pieces, and the pieces can be any shape you like. Then put the pieces together so that you get two balls instead of one. How big will these balls be compared to the original ball?
According to set theory, the two resulting balls will be the same size and shape as the original ball. In addition, if we take into account that the balls have different volumes, then any of the balls can be transformed in accordance with the other. This suggests that a pea can be divided into balls the size of the Sun.
The trick to the paradox is that you can tear the balls into pieces of any shape. In practice, this is impossible to do - the structure of the material and, ultimately, the size of the atoms impose some restrictions.
In order for it to be truly possible to break the ball the way you like, it must contain an infinite number of available zero-dimensional points. Then the ball of such points will be infinitely dense, and when you break it, the shapes of the pieces can turn out to be so complex that they will not have a certain volume. And you can assemble these pieces, each containing an infinite number of points, into a new ball of any size. New ball will still consist of infinite points, and both balls will be equally infinitely dense.
If you try to put the idea into practice, nothing will work. But everything works out great when working with mathematical spheres - infinitely divisible numerical sets in three-dimensional space. The solved paradox is called the Banach-Tarski theorem and plays a huge role in mathematical set theory.
There are a dozen more similar paradoxes under the cut...
2. Peto's paradox
Obviously, whales are much larger than us, which means they have many more cells in their bodies. And every cell in the body can theoretically become malignant. Therefore, whales are much more likely to get cancer than humans, right?
Not like that. Peto's Paradox, named after Oxford professor Richard Peto, states that there is no correlation between animal size and cancer. Humans and whales have about the same chance of getting cancer, but some breeds of tiny mice have a much higher chance.
Some biologists believe that the lack of correlation in Peto's paradox can be explained by the fact that larger animals are better at resisting tumors: a mechanism that works to prevent cells from mutating during the process of division.
3. The problem of the present time
For something to physically exist, it must be present in our world for some time. There cannot be an object without length, width and height, and there cannot be an object without “duration” - an “instant” object, that is, one that does not exist for at least some amount of time, does not exist at all.
According to universal nihilism, the past and future do not occupy time in the present. Moreover, it is impossible to quantify the duration that we call "present time": any amount of time that you call "present time" can be divided into parts - past, present and future.
If the present lasts, say, a second, then this second can be divided into three parts: the first part will be the past, the second - the present, the third - the future. The third of a second that we now call the present can also be divided into three parts. Surely you already understand the idea - you can continue like this endlessly.
Thus, the present does not really exist because it does not continue through time. Universal nihilism uses this argument to prove that nothing exists at all.
4. Moravec's paradox
People have difficulty solving problems that require thoughtful reasoning. On the other hand, basic motor and sensory functions like walking do not cause any difficulty at all.
But if we talk about computers, the opposite is true: it is very easy for computers to solve complex problems. logic problems like developing a chess strategy, but much more difficult to program a computer so that it can walk or reproduce human speech. This difference between natural and artificial intelligence is known as Moravec's paradox.
Hans Moravec, a postdoctoral fellow in the robotics department at Carnegie Mellon University, explains this observation through the idea of reverse engineering our own brains. Reverse engineering is most difficult for tasks that people perform unconsciously, such as motor functions.
Since abstract thinking became part of human behavior less than 100,000 years ago, our ability to solve abstract problems is conscious. So it's much easier for us to create technology that emulates this behavior. On the other hand, we do not comprehend actions such as walking or talking, so it is more difficult for us to get artificial intelligence to do the same.
5. Benford's Law
What is the chance that a random number will start with the number "1"? Or from the number "3"? Or with "7"? If you know a little about probability theory, you can guess that the probability is one in nine, or about 11%.
If you look at the actual numbers, you will notice that “9” is much less common than 11% of cases. Also, far fewer numbers than expected start with “8,” but a whopping 30% of numbers start with “1.” This paradoxical pattern plays out in all sorts of real-life cases, from population size to stock prices to the length of rivers.
Physicist Frank Benford first noted this phenomenon in 1938. He found that the frequency of a digit appearing first fell as the digit increased from one to nine. That is, "1" appears as the first digit about 30.1% of the time, "2" appears about 17.6% of the time, "3" appears about 12.5% of the time, and so on until "9" appears in as the first digit in only 4.6% of cases.
To understand this, imagine that you are numbering lottery tickets sequentially. When you number your tickets from one to nine, there is an 11.1% chance of any number being number one. When you add ticket number 10, the chance of a random number starting with "1" increases to 18.2%. You add tickets #11 through #19, and the chance of a ticket number starting with "1" continues to increase, reaching a maximum of 58%. Now you add ticket number 20 and continue numbering the tickets. The chance of a number starting with a "2" increases, and the chance of a number starting with a "1" slowly decreases.
Benford's law does not apply to all cases of number distribution. For example, sets of numbers whose range is limited (human height or weight) are not covered by the law. It also doesn't work with sets that only have one or two orders.
However, the law applies to many types of data. As a result, authorities can use the law to detect fraud: when the information provided does not follow Benford's Law, authorities can conclude that someone has fabricated the data.
6. C-paradox
Single-celled amoebas have genomes 100 times larger than those of humans; in fact, they have perhaps the largest genomes known. And in species that are very similar to each other, the genome can differ radically. This oddity is known as the C-paradox.
An interesting conclusion from the C-paradox is that the genome may be larger than necessary. If all the genomes in human DNA were used, the number of mutations per generation would be incredibly high.
The genomes of many complex animals like humans and primates include DNA that codes for nothing. This huge amount of unused DNA, varying greatly from creature to creature, seems to depend on nothing, which is what creates the C-paradox.
7. Immortal ant on a rope
Imagine an ant crawling along a rubber rope one meter long at a speed of one centimeter per second. Also imagine that the rope stretches one kilometer every second. Will the ant ever reach the end?
It seems logical that a normal ant is not capable of this, because the speed of its movement is much lower than the speed at which the rope stretches. However, the ant will eventually reach the opposite end.
When the ant has not even begun to move, 100% of the rope lies in front of it. After a second, the rope became much larger, but the ant also walked some distance, and if you count it as a percentage, the distance it must cover has decreased - it is already less than 100%, albeit not by much.
Although the rope is constantly stretching, the small distance traveled by the ant also becomes larger. And, although in general the rope lengthens with constant speed, the ant's path becomes a little smaller every second. The ant also continues to move forward at a constant speed all the time. Thus, with every second the distance he has already covered increases, and the distance he must travel decreases. As a percentage, of course.
There is one condition for the problem to have a solution: the ant must be immortal. So, the ant will reach the end in 2.8×1043.429 seconds, which is slightly longer than the existence of the Universe.
12. Paradox of the Wheel
People first started talking about the paradox of the wheel even before Aristotle, but he was the first to study it closely. Then Galileo Galilei struggled with solving this problem. Although to many this will seem completely obvious. But let's take it in order...
Aristotle's wheel is the name usually given to an apparent paradox that appears when a wheel moves around an axis, when the wheel itself rolls on a plane in a straight line. It is believed that Aristotle was the first to notice this strange paradox, which for this reason retained the name “Aristotle’s Wheel”.
Let us assume that a circle, revolving around its center, rolls at the same time in a straight line and, with a complete revolution, describes a straight line whose length is equal to the circumference of the circle. If in this circle, which we call main, let us imagine another, smaller one, co-centered with the first and moving with it, then after the large circle completes a full revolution, the small circle will describe a straight line, no longer equal to its own circumference, but to the circumference of the main circle. An example of such an apparent paradox can be seen in the movement of a carriage wheel, the hub of which, during its rotation, will cross a straight line greater than its circumference and equal to the circumference of the wheel itself. The above example is known to be confirmed by daily experience.
But here the question arises: how to explain that the circle of the hub describes a straight line larger than this very straightened circle?
13. Russell's Paradox
Here is one of the popular formulations: In one country a decree was issued: “The mayors of all cities should live not in their own city, but in a special City of Mayors.” Where should the mayor of the City of Mayors live?
There are many popular formulations of this paradox. One of them is traditionally called the barber's paradox and goes like this: One village barber was ordered to “shave anyone who does not shave himself, and not to shave anyone who shaves himself,” what should he do with himself? "
Or: A certain library decided to compile a bibliographic catalogue, which would include all those and only those bibliographic catalogs that do not contain links to themselves. Should such a directory include a link to itself?
Russell himself formulated it this way: “Let K be the set of all sets that do not contain themselves as their element. Does K contain itself as an element? If so, then, by the definition of K, it should not be an element of K - a contradiction. If not, then, by the definition of K, it must be an element of K - again a contradiction.”
14. Levinthal's paradox
The mystery of the phenomenon of spontaneous self-organization of proteins (and RNA) is summed up by the “Levinthal paradox”. The mystery is this. A protein chain has a myriad of possible conformations (each amino acid residue has about 10 possible conformations, that is, a chain of 100 residues - about 10 to the power of 100 possible conformations). So the protein must look for “its” spatial structure among about 10 to the power of 100 possible ones. In this case, the protein can “feel” the stability of the conformation only if it gets directly into it, since a deviation of even 1 Å can greatly increase the energy of the chain in a dense protein globule. And since the transition from one conformation to another takes ~ 10-13 seconds at a minimum, searching through all 10 to the power of 100 structures would have to take about 10 to the power of 80 years, against which the lifetime of our Universe is 10 to the power of 10 years - the value is infinitesimal... Question: how was the protein able to “find” its structure in minutes.
However, this paradox already has a solution:
A protein can fold not “all at once,” but by growing a compact globule due to the sequential adhesion of more and more links of the protein chain to it. In this case, the final interactions are restored one after another (their energy will fall approximately in proportion to the number of chain links), and the entropy will also fall in proportion to the number of fixed chain links. The drop in energy and the drop in entropy completely compensate each other in the main (linear in N) term in the free energy = - . This excludes the term proportional to 10 N from the folding time estimate, and the folding time depends on much lower order of magnitude nonlinear terms associated with surface enthalpy and entropy effects proportional to N 2/3. For a protein of 100 residues this is 10 100 2/3 ~ 10 21.5, which gives an estimate of the folding rate that is in good agreement with the experimental data given in.
But it has simply been established that the protein folds not after it is built, but as it grows.
Overall quite similar
I can remind you of something else interesting: for example, there is still a version of what or really. Let's remember about
"Oh, how many wonderful discoveries we have
Prepare the spirit of enlightenment
And experience, the son of difficult mistakes..."
These lines from a poem by Alexander Sergeevich Pushkin are a kind of parting word for people and make them think about the role of experience and mistakes in their lives. What is experience? Experience is knowledge accumulated throughout life. Is it possible to gain experience without making mistakes? Practice shows that no. You can learn from the mistakes of others, but it is impossible to live without making your own. Every person, when born, begins to gain experience, making mistakes in order to become better than they are. “Experience and mistakes” can be called relatives, since experience comes from mistakes. These two concepts are very close and one is a continuation of the other. What role do experience and mistakes play in people's lives?
These and other questions are cause for lengthy reflection. IN fiction The topic of choosing your own path, while making mistakes and gaining experience, is touched upon very often.
Let us turn to the novel “Eugene Onegin” by Alexander Sergeevich Pushkin. This work tells about the unsuccessful love of Evgeny Onegin and Tatyana Larina. Onegin at the beginning of the work is presented as a frivolous nobleman who has lost interest in life, and throughout the novel he tries to find new meaning of its existence. Tatyana takes life and people seriously, she is a dreamy person. When she first met Onegin, she immediately fell in love with him. When Tatiana writes a love letter to Evgeniy, she shows courage and puts all her love for him into it. But Onegin rejects Tatiana's Letter. This happened because he was not in love with her then. Having fallen in love with Tatyana, he sends her a letter, but then she could no longer accept his feelings. She learned from her mistakes and did not repeat them again, now she knew that by falling in love with such a frivolous person, she had made a big mistake.
Another example where the acquisition of experience from mistakes can be traced is the work of Ivan Sergeevich Turgenev “Fathers and Sons”. Evgeny Bazarov was a nihilist all his life; he denied everything, all feelings that could arise in a person, including love. His nihilistic views were his biggest mistake. Having fallen in love with Odintsova, his world begins to crumble. He could hardly talk about his feelings, which he so zealously denied. And although Odintsova loved Evgeny, she still chose a quiet life and refused him. Before his death, Bazarov made a testament to the one because of whom his world was destroyed, his love did not disappear. Before his death, he realized his mistake, but, alas, he could no longer correct anything.
So, mistakes are what allow people to accumulate life experience. And it doesn’t matter whose mistakes it is, a person must learn from his own mistakes, as well as from the mistakes of others. Only in this way will people be able to improve and develop as individuals.
Effective preparation for the Unified State Exam (all subjects) -
L.F. Kotov Or maybe the verse is not finished?
Oh, how many wonderful discoveries we have
The spirit of enlightenment is preparing
And experience, the son of difficult mistakes,
And genius, friend of paradoxes,
And chance, God the inventor...
Science in the works of Pushkin
Interspersed with “scientific” themes in Pushkin’s poetic works are quite frequent. But this five-line can be called the quintessence of the theme “Science in the Works of Pushkin.”
Just five lines, and what a coverage - enlightenment, experience, genius, chance - all the components that determine the progress of mankind.
Pushkin's interest in contemporary science was very deep and versatile (as, indeed, in other aspects of human activity). This is confirmed by his library, which contains works on probability theory, works by Pushkin’s contemporary, Academician V.V. Petrov, a Russian experimental physicist in research electrical phenomena and others (in Russian and foreign languages).
Pushkin's library in his museum-apartment includes many books on natural science topics: the philosophical works of Plato, Kant, Fichte, the works of Pascal, Buffon, Cuvier on natural science, the works of Leibniz on mathematical analysis, the works of Herschel on astronomy, the studies on physics and mechanics of Arago and d'Alembert, Laplace's work on probability theory, etc.
Pushkin, being the editor and publisher of the Sovremennik magazine, regularly published articles by scientists reflecting scientific and technical topics.
Pushkin could also learn about the achievements of physics of that time from communication with the famous scientist, inventor P.L. Schilling, creator of the first electromagnetic telegraph apparatus, the electric mine. Pushkin knew him very well and could easily see Schilling’s inventions in action.
The Poet's interest in Lomonosov's work can be assessed from the fact that, having read the Moscow Telegraph magazine "M.V. Lomonosov's Track Record for 1751-1756," he was amazed at the versatility and depth of the research. The poet expressed his admiration as follows: “Combining extraordinary willpower with the extraordinary power of concept, Lomonosov embraced all branches of education. A historian, rhetorician, mechanic, chemist, mineralogist, artist and poet, he experienced everything and penetrated everything...” And later he adds: “He created the first university. It is better to say that he himself was our first university.”
now look at what this poem could have been like if the Poet had tried to add a line with the missing rhyme.
Oh, how many wonderful discoveries we have
The spirit of enlightenment is preparing
And experience, the son of difficult mistakes,
And genius, friend of paradoxes,
And chance, God the inventor...
And an idle dreamer.
This Pushkin five-line poem was discovered after the poet’s death, during the analysis of his workbooks. In the first four lines the rhyme is adjacent, but the fifth line is left without a pair. It can be assumed that Pushkin did not finish this poem.
I read these lines and see how the poet hastily sketches out an impromptu, ripening in the subconscious, and suddenly pouring out into finished form when reading a report in a newspaper or magazine about another scientific discovery. I imagined “quickly,” but somehow this word doesn’t fit with writing with a quill pen; It is more plausible that Pushkin wrote rather slowly, which contributed to the birth in his subconscious of these brilliant lines, which included all the “engines of progress” - enlightenment, experience, genius, chance - already in a ready-made form. It seems to me that the first 4 lines were written impromptu, and the 5th, after re-reading what was written, the poet added after some thought. Added and set aside for later reading and possible use in some future work. But... it didn’t happen and the fragment remained unpublished during the author’s lifetime.
Of course, these are just my personal ideas, not based on anything, but I am writing them under the heading “Notes in the Margins.”
So I will continue. It seems to me that the poet put this fragment aside because he felt some incompleteness in covering in this poem the phenomenon of the birth of new discoveries. I put it aside to think about it later. But... it didn't happen.
Even Alexander Sergeevich Pushkin wrote that “experience is the son of difficult mistakes.” And people still love to say this line. This poetic line refers us to one of the most popular sayings: “You learn from your mistakes.”
You can give many examples from a person’s everyday experience that prove that mistakes help to gain experience. Almost every child learned to ride a bicycle. This skill only came after the student fell off his bike several times. Perhaps he even hit his knee. But in the end, he gained an experience that will stay with him for the rest of his life. Once you learn how to ride a bike, you will never unlearn it.
Essay No. 2 Experience son of difficult mistakes
People often make mistakes. Many people like to repeat proverbs that connect bad mistakes with experience. For example, the saying: “Learns from your mistakes.” Sometimes it seems strange. What you can learn from mistakes. A mistake is something stupid that a person has done. But in fact, mistakes often turn into experience and knowledge that helps a person in life.
People are purchasing more knowledge in practice. For example, in winter, many guys like to lick the swing. When they do this for the first time, they don't know that their tongue will freeze to the cold iron. They also don’t know that tearing their tongue away from the iron will be very painful. But when they make this mistake, they learn all this, therefore, gain experience. They may not know the laws of physics, but they already know that they shouldn’t “kiss” iron in the cold.
Experience is also gained when a person makes mistakes at school. For example, a first grader does not know what will happen if he fails homework. He doesn't bring his notebook and gets a bad mark. After this, he understands that he should not forget his notebook at home, because then he will be given a bad grade.
At the beginning of human history, many scientists comprehended our world experimentally. They did different experiments and got results. When the results matched, they could find different patterns. So, according to legend, Newton discovered gravity when an apple fell on his head. Perhaps his mistake was that he sat under the apple tree, but it turned into an experience.
Many examples can be given that experience is often associated with mistakes. And we can even call him the son of mistakes. Every person makes mistakes, but he should always learn from them. Only this will help him gain experience that will help him in life. And if you make mistakes, but do not correct them and do not analyze them, then no experience will be gained.
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