The circle that you see represents the Wheel of Life, and you are invited, after answering the questions below, to make notes on each of the axes of this wheel: how much what you have corresponds to your tasks.

Attention, not "as far as it suits me, I want it more / better or not", but - "how much it meets my goals and objectives, is it enough to achieve my goals, for what is important and dear to me." For example, you always want more money and health, but for some tasks what you have is enough for you.

It is often thought that this exercise will help you understand your own goals and objectives. This is not entirely true, everything is trickier here. In the questions of this exercise, the question is constantly raised: “Is this or that enough for your goals?”, quietly implying that you somehow represent your goals ... Or you start thinking about them ... And in the end you will be offered Decide what you need to do now to achieve your big goals. In fact - to set intermediate tasks.

And this is wise: today people are universally convinced that they need to "understand" or "find" their life goals, as if they are already somewhere in the world. ready-made exist. No, you can only create your life goals, set them, if you want - come up with them. Thus, this exercise is a trick: in a hidden way, it still forces you to invent and set your life goals.

Interestingly, as a rule, this trick works, and according to the results of the exercise, all its participants know for sure what they need now ...

So let's get started?

What's around me?

When you sit at a table, you have your table space in front of you. How satisfied are you with what is in front of you? The table is comfortable, not cluttered, well lit? Your desk may be dirty, cluttered, uncomfortable - or it may be your joy, where your hands lie down and at which you want to work. Next - your room, apartment, your office ... You live in these spaces: do you like them? The house you live in - does it suit you? Is it exactly what you want it to be, looks like it, is positioned like that, does it have everything you need? Do you admire them? The entrance through which you pass every day - does it suit you well? The city in which you live and your children will live - is this the city in which you need to live? Country - are you sure that you choose this country correctly? So, you have looked at what is around you: how much is what you need, how much does it correspond to your goals? Put your rating on the wheel axle with a dash. For example, 10 points - completely satisfied, 0 - not satisfied at all.

Who is around me

What kind of people are around you? Sometimes these are people who make you happy, sometimes they are terribly annoying. Your human environment is the people who make up your family, here are the employees at work, sometimes they are neighbors and relatives: the main question is whether they are more likely to bring you joy or trouble, rather help or an obstacle. How much does the presence of these and such people help or hinder you from moving towards your goals? Do you want to change something?

Health, sports

Our health is the source of our strength and our energy. According to doctors, there are no completely healthy people in our time, but each of us knows and feels when he was healthier: this year or last, this fall or last summer. In addition to comparing with what was, it is also important to compare with the tasks that you face. Sometime you can confidently say: “Everything is in perfect order with my health, my health is enough for all my tasks”, but sometime you feel: there is a lot of things, but health is clearly not enough ... And how do you assess your health, is it good enough for your tasks? Your mark?

Relaxation

Rest is a business that restores your strength. Everyone has their own rest: for someone, the rest is to lie down with a book under an apple tree, for another - to run away on the football field. We are different, but everyone can evaluate the quality of their entertainment and their rest quite objectively. If your colleague joyfully rode off for the weekend, and on Monday he crawls, says: “Guys, we need to recover ... We really rested like that! I'm out of work for a day or two!" - How would you assess whether such a pastime was a vacation? Did he rest? Apparently it wasn't a vacation after all. It is, rather, waste, burning life, the destruction of health and energy. How do you assess your condition, how rested are you usually? How closely do you monitor your condition, how well do you rest yourself?

Money

Money is the most important life and business resource. Whether you have enough money or not is not a matter of subjective feelings, but of reasonable business evaluation. Feelings are subjective: someone with a hundred dollars a month will be happy, but for someone a hundred thousand dollars is a critical line, below which it is difficult or even unthinkable to fall. The question here is not about feelings, but about the amount of finance needed for your tasks and projects. There is never a lot of money, but each project requires its own, in principle, a limited amount of money. The need for money is not so much a matter of your personal needs, but the amount of obligations to other people and the size of the tasks that you set for yourself. Someone will say confidently: everything is in order with my money, I have a reserve, and the other is ready to shoot or shoot because of the money, the question is so painful and acute. And how are things going with you?

Career, status

The career question is not so much about subjective satisfaction or not, but about how your career works towards your goals. Maybe you don't need it. Or maybe it is obligatory for you, and you definitely need to lift yourself up career ladder. However, here it is still more difficult than with money, because the question arises: what should be considered your career?

I wonder how the former prince Gautama would have assessed his satisfaction with his career, having achieved enlightenment under the Boddhi tree? The subjectivity of the perception of one's career is even greater than the assessment of satisfaction in money. There is a vertical career (ascending change of positions), there is a horizontal career as an increase in one's personal skills, for businessmen a career is its status and growth in production: I am no longer a small entrepreneur, but medium business!! For women, the most interesting question is how her career and the career of the person she invested in correlates ... How will a housewife assess satisfaction with her career when her loving and beloved husband became the president of a transnational corporation, and her son graduated from Eton? Is she a failed housewife compared to men who have outstripped her in every way, or is she the happiest woman, wife, and mother who is proud of the way her life has turned out? So, how do you assess your status and the success of your career?

I develop myself

The knowledge, skills, habits and values ​​that form your education and upbringing are the most important capital of your personal success. At the same time, in the long term, it is not so much the amount of your knowledge and skills that is valued, but your habit and ability to develop yourself, the ability to develop yourself effectively. The habit of self-development is one of the most expensive habits of successful people, but self-development comes in different qualities. For some, it's just a natural craving to learn something new every day, for others it's a directed and thoughtful strategy, where each new knowledge and skill completes the previous steps and opens up new perspectives. Who has created conditions for himself where his self-development is easy and successful, has created the necessary acquaintances for this, attends useful classes and trainings, the other has not yet found such opportunities. Or not looking. How do you evaluate the effectiveness of your self-development, how does it work for your life goals?

Your own master

The ability to manage your time is a prerequisite for success. You can be energetic and smart, but if all your time is scheduled inside and out, and you don’t manage it, then your success is in big question. Do you have enough time to manage yourself? We can say that this is a question about your free time, but how to understand what it is - free time? If suddenly you have nothing to do from morning to evening, nothing to do, you walk around and get bored, looking for something to do with yourself - is this free time or the emptiness of your life? On the other hand, your day can be as busy as you like, overloaded, but if you can change it, remove the unnecessary and insert what is dear to you, then you are the master of your life. Your life is busy with many things, but you are free in your time. So, how much control do you have over your time, how much control do you have over your life?

The joy of life

The motor of the most powerful machine does not start itself: a pusher or a starter is needed. The pusher is life's troubles that force us to come out of hibernation, and our natural starter, what ignites us, is the feeling of the joy of life. Indeed, if life is not joyful, it is difficult to move forward. The joy of life comes from meeting good friends, along with a change of impressions and fun entertainment, and one who lives a gray life kills his life energy. But entertainment - entertainment strife. If entertainment consists of drinking vodka and night festivities, such a starter will soon begin to fail the main motor. It does not entertain for a long time, after which your head hurts drearily ... So, look at your life and answer the question: how are you with the joy of life? Settled, care, support? Are you always cheerful, cheerful, energetic? Maybe something should be removed - or something added?

Why do I live

He who knows why he lives will endure any how. For what do you live, for what deeds and people? Sometimes it is called the Mission, sometimes Love or Spirituality... The project that you live for, elderly parents that you can't help but take care of, a child who has the meaning of your life... When it is, life has a core and meaning. When not, life can be easy, joyful, but it makes no sense. The most important difference between a mission and simple everyday needs is that the meaning of a mission goes beyond your personal interests. You serve a mission, not the mission serves you.

If you raise children so that later children will take care of you, this is self-service, not a mission. However, if you teach children to care for their elders, including you, you are teaching children what they will need in their own lives. You teach them to be caring, and this is already taking care of them, and this is your high duty, the mission of a parent.

There are traditional missions: the task is to succeed as a respected person, to love your children, to take care of your parents, there are special personal missions where a person's values ​​go beyond his personal life. Missions are big and small, but even a small mission makes a person bigger, because he turns from a human organism into a human personality. And most importantly, the mission creates direction and gives it meaning: a living and intelligent understanding of what I need to do and for what. The mission is the main core of life, providing real movement forward and giving meaning to all other axes of the wheel of life. How would you rate yourself on this axis? Do you plan to add something here?

Did you fill out the questions? Now processing the results. Connect all your marks with a smooth line and see what shape you got. Imagine: your cart with such wheels. How will she go through life? The two main indicators are how harmonious the figure you got is, it still looks like a wheel, and what is the diameter of this wheel. If you have an even, beautiful, but small wheel - you drive through life quietly, calmly, everything is exactly bad, but you are already used to it ...

When everything is bad, even a certain calmness arises in the soul: “So this is my fate!” But if suddenly, against the background of a general even one, something bad flashes on one axis: “Good, great, cool!” - Career went, Money rolled in, Love struck like lightning, then the previous level suddenly becomes a pit, where it is so painful to fall after the peak of life ... You are shaking. Also, if you have spun your Wheel of Life, if you have high, strong indicators on the main axes, but fail on one point, then each turn will hurt you in this place ...

Everything is great: love, beauty, but - no money ... Or: everything is great - money, career, love, but health fails ...

​​​​​​​​​​​​​​​​​​​​​​​Now shade your Wheel today and draw how it should look in 3 months. After 1 year. In 3-5-10 years. Hint: keep in mind that most people overestimate what they can do in their annual plans and underestimate what they can do in their life in 5-10 years.

It will hardly be a serious drawing where you draw your new Wheel on top of your little freak in an ideal circle with a maximum diameter (10 points in all axes). That doesn't happen. There are no miracles, for any change in your life you have to pay great job, and sometimes you have to sacrifice something: once to pay Joy of life and Rest for Money, a feeling of the Master of life for the fulfillment of the Mission or Career for moving to another city, where there will be another Life Space that suits you more.

On the other hand, look for successful - inventive - options. Not often, but it happens that an increase in only one axis suddenly raises all the other axes. Sometimes the decision to change the place of residence, to buy a new apartment turns out to be both a way to improve relations with parents, and high-quality motivation for work (hence Career and Money), the termination of unnecessary friendships, empty entertainment and - the possibility of a Mission ...

Dare! Who, in fact, can prevent you from making your life truly happy, if you really want to?

And now it's time for decisions. Complete the sentence: “Looking at the Wheel of my life, I think that I should ...” What to add, what to give yourself so that your life becomes more cheerful and harmonious? From which direction, from which axis should you take the very first steps? What to focus on after that to support change? And in order to start doing all this, what exactly should I puzzle myself with in the coming days?

Write down three of your decisions that you decide to change soon in your life. And a list of specific actions, how you are going to implement these decisions.

Great. And if you do the same, only - bolder? Forward!

The number of axles in the Wheel of Life can be different, as well as their naming. It often makes sense to offer people a choice of different axes so that they draw their own Wheel of Life, according to their actual life tasks.

Regardless of how a particular culture relates to or interprets an idea, the question of its causes and driving forces because without such an understanding it is not possible to find a way out of the cycle of existence.

The magical myth, aimed primarily at finding such a way out, of course, develops in detail the concept of gilgul and its mechanisms.

Recognizing as the starting point the aspiration of the suprareal reality - to self-knowledge in an infinite number of its individual aspects, the myth cannot help wondering why this self-knowledge, instead of a direct vector, has the form of an endless cycle full of meaningless repetitions.

It is clear that for the Great Spirit all its states - being and non-being, unity in itself, unity in the plurality of potencies and unity in the actualized possibilities - are merged together and are not something separately existing. That is, the Absolute, for which time is also only one of its potentialities, already cognizes, and is cognizable, and is cognized by itself. Nevertheless, for the sum of its individual , which is the universe, the actual form of existence is process self-realization, self-knowledge in extension.

From the point of view of the possibility of self-knowledge in the totality of its individual energies, the Great Spirit singles out in itself an infinite number of cognizing modes - and an infinite number of knowable elements - , and each monad acts as an absolute fractal source of further self-knowledge.

In order for an individual way of self-knowledge to be truly individual, it must be maximally independent, separate from all other views, streams of consciousness, monads.

In other words, the very nature of individuality implies . At the same time, this isolation, devoid of rooting in the Unity of the Absolute, almost inevitably turns into opposition of oneself to others. It turns out that, while trying, consciousness perceives itself as a separate entity.

So, it is clear that the root and cause of the "cycle" of existence is an incorrect self-identification - the perception of oneself as a separate, opposed to others, being that arises as a result of natural, but - subject to correction - absolutization of individuality.

Moreover, such a view makes the division of the actors of the world process into "monadic", or "free" and "" beings, accepted in Western Magic, obviously understandable. The beings that arise as a result of the "look" of the monad and have the function of self-knowledge are called "free", and the beings that are "a function of the function", that is, those that arise as properties of this stream of awareness ("the stream Dinur”) are called “service”, because they do not have a source of their existence separate from this stream. Minerals, plants, animals, people and gods are perceived as "free beings", while angels and demons are perceived as "servant". At the same time, the concept of “service” of these beings does not imply their “limitation” or “inferiority” from the point of view of the world process itself, but makes sense only from epistemological positions, although it has important practical consequences.

Omraam Mikael Aivanhov

Tree of knowledge of good and evil

Two heavenly trees

For thousands of years, people have tried to explain the origin of the world, as well as the appearance of evil in this world (and its consequences - suffering). They often presented it as myths, so in the Holy Books of all religions you can find symbolic stories that you need to be able to interpret. Christian tradition relies on Moses' account of Genesis, but have Christians understood it correctly?

Let's see what Moses writes. On the sixth day of Creation, God created a man and a woman and placed them in a garden called Eden, where there were already all kinds of animals and plants. From the trees of this garden, Moses identifies two: the Tree of Life, as well as another tree that has become especially famous since then - the Tree of the Knowledge of Good and Evil, whose fruits God forbade Adam and Eve to eat. As long as they obeyed the Lord's instructions, they lived in happiness and abundance. But then a serpent appeared to convince Eve to eat the fruit from the Tree of the Knowledge of Good and Evil; then Eve convinced Adam to taste the fruit too, and God expelled them from Paradise. Now we will consider in more detail some places of this story.

Many people went in search of an earthly Paradise, imagining that it must be in India, in America, in Africa, and, of course, they never found anything. Of course, Paradise was on earth, but what kind of earth are we talking about? As you will see, everything is symbolic. Oh, I won't tell you everything, it's impossible, it's too big a topic - the story of the first man and the first woman, but I'll start by telling you about two trees: the Tree of Life and, mainly, the Tree of the Knowledge of Good and Evil.

So, Adam and Eve lived in Paradise, where they had the right to eat fruits from all the trees of the garden, except for the fruits of the Tree of the Knowledge of Good and Evil. But you don't know what those fruits are. This is a symbol of the forces that the first man and the first woman did not yet know how to manage, did not know how to transform and use them. Therefore, God told them: "The time will come when you will be able to eat this fruit; but now you are still too weak, and if you eat it, touching the forces contained in it, you will die," that is, your state of consciousness will change. This change in the state of consciousness is indicated in the Book of Genesis, but this indication has never been able to correctly interpret. About the time when Adam and Eve lived happily in Paradise, it says: "The man and the woman were naked and did not feel shame." And further, when they ate the forbidden fruit: "And the eyes of both of them were opened, and they realized their nakedness, and they sewed aprons for themselves out of fig leaves." This sudden realization of their nakedness proves that something has changed in them.

The Tree of Life represented the unity of life where polarization has not yet manifested, that is, where there is neither good nor evil: this is the area above good and evil. And the other tree represented the world of polarization, where one must know the alternation of day and night, joy and sorrow, etc…. Thus, these two trees are areas of the universe, or states of consciousness, and not just plants. And if God forbade Adam and Eve to eat fruits from the Tree of Knowledge of Good and Evil, then this means that they should not yet penetrate into the area of ​​polarization. Why? Do you think that this prohibition was just a whim on the part of God? No. "Then," you say, "was the tree useless?" Also no, God never created useless things. The idea of ​​a tree bearing fruits that no one will eat and no one will use them is contrary to divine wisdom, which does not create anything without benefit.

Some creatures ate fruits from the Tree of the Knowledge of Good and Evil, but they could bear them. And Adam and Eve could not yet endure them, because these fruits contained binding forces: upon contact with them, the thin tissue of the human body had to freeze, condense, and this is exactly what happened. Therefore the tradition speaks of a "fall"; the term "fall" symbolizes the transition from subtle matter to dense matter. After eating the forbidden fruit, Adam and Eve became heavy and gained weight, which is expressed by the words: "they saw their nakedness." They were naked before, but they saw themselves clothed with light, and after their sin they suddenly felt deprived of this garment of light, they became ashamed and hid.

Having eaten the fruit of the Tree of the Knowledge of Good and Evil, Adam and Eve continued to live, but they died in a state of higher consciousness: they were expelled from the earthly Paradise (which symbolizes this state of consciousness), the entrance to which was now guarded by an angel armed with a sword. Since Adam and Eve were expelled from the "earthly" Paradise, it means that they were already on earth. But in this case, how to understand that, having left Paradise, they were sent "to earth"? What land are we talking about? Kabbalah teaches that the earth exists in seven forms. She gives the names of these forms, their characteristics, from the densest to the thinnest, and the thinnest is the very form from which human beings were expelled. What do we know about the earth? Little.

According to the Science of Initiation, the earth has an ethereal counterpart which surrounds it like a luminous atmosphere. And this ethereal, subtle earth is exactly the real earth that is spoken of in the Book of Genesis, such earth as it came out of the hands of God. The real earth is not the hardened, condensed earth that we can touch here. The real earth is the ethereal earth. It was in this region, called Paradise, that God placed the first people; they lived there, having that radiant, luminous body of which I have just spoken, they knew neither suffering, nor disease, nor death.

Do you know that Paradise exists to this day, that it has never ceased to exist? Although we do not see him, he is everywhere, but in the subtle region of matter, since he is material; yes, the ethereal plane is material. And the Tree of Eternal Life also exists, it is still in this Paradise. This tree gives those elements that the first people absorbed, which they ate. They lived in this ethereal substance of the earth and fed on it; and it was this ethereal substance that maintained the light and purity of their lives. The Tree of Life was not a tree, I already told you this, but a stream, a stream coming from the sun, and people were fed by the rays of the sun that went through this area. The Tree of Life is the stream of the sun!

And since the human being has retained the same structure as in the distant times of its creation, it retained the ability to receive the sun's rays again, to eat the fruits of the Tree of Life again, that is, to return to the bosom of God. Each religion has its own language, its own particular way of expressing itself, but they all talk about reunion in God, about returning to the First Cause. They use different expressions, but they all speak of the same reality.

Now let's see what is the Tree of Knowledge of Good and Evil? It represents another current that also passed through Paradise, and it was he who brought all people into contact with the densest form of the earth. God said to the first people: "Be content with studying the area of ​​the Tree of Life. The time has not yet come for you to leave this area of ​​light to descend and study the roots of creation. Leave this question aside for now, do not try to understand everything immediately." Since this second tree also already existed, it was impossible to transplant it, just as it was impossible to remove from a person his intestines, liver, spleen, etc. Because a person, like the universe, consists of two areas: the highest area corresponding to the Tree of Life , and the lowest - corresponding to the Tree of the Knowledge of Good and Evil, in which the roots of things are located.

The fruits of the Tree of the Knowledge of Good and Evil had such strong astringent properties that the first people could not resist them. The fruits belonged to the “coagula” stream, and the Lord knew that if Adam and Eve made contact with it, this would immediately qualitatively change the state of their consciousness. This is what happened: upon contact with the astringent flow, the matter of their body changed, it began to become dense, thick, opaque and dull. By forbidding the first people to eat these fruits, that is, to study this stream, to experience these forces of nature, God wanted to protect them from suffering, from diseases and from death - the death of the physical body, of course, and not from the death of the spirit, since they were created immortal. But they accepted the death of their luminous state and became alive in a dark and heavy substance. They had to leave the kingdom of light, this Paradise, where they lived in ease, in light, in joy, and descend into the lower layers of the earth, where we live today, because if we are on this earth, then we left that earth, which was our first home...

Who was the serpent that tempted Eve, such an intelligent serpent that could speak, and speak so convincingly? The serpent is a very broad and deep symbol that can be found in all religions. Initiates of all times have dealt with the serpent, even if they preferred not to speak openly about it. The snake symbol represents, at first glance, very different things: the power of Kundalini, Evil, the Devil, or a magical power that transmits any things from heaven to earth and from earth to heaven ...

The initiates do not believe that the serpent is necessarily a symbol of evil: they distinguish in it something lower - dull and dark, as well as something higher - luminous. For them, the serpent is a magical force that conducts both good and evil, it is the "astral light", according to the definition of Eliphas Levi, a light that, being saturated with impure elements, has harmful effects in its path, but when it is saturated with the luminous thoughts of saints and prophets, he brings them to God's Throne. Thus, the serpent in its highest essence is luminous, and in its lowest essence it is dark. In the Zochariah, the Book of Splendor, there is an image of a white luminous head reflected in the abyss, in a lake of opaque substance, in the form of a black disgusting head. This is the shadow of God... But I prefer to talk about it later, when you are better prepared to perceive. This means that the serpent, or dragon, is a symbol of magical power that permeates the entire universe up to the stars and carries both good and bad emanations.

If you are familiar with tarot cards, then you may have noticed that card XV is the Devil card. Stanislas de Guaita understood the depth of this lasso and comments on it as follows: this image, where above is the radiant, luminous face of the victorious, omnipotent Initiate, and below is his inverted image, the face of a fallen, disgusting creature, grimacing and full of rage - this is the image of the Devil. And both together they form one single reality, which can also be represented in the form of two triangles that do not intersect, as in the seal of Solomon, but are symmetrical with respect to their base. This figure means that the Devil and the luminous magical power represent the same reality, but in different areas. It's like a person: his lower essence is dirty and repulsive, and his highest essence is beautiful, heavenly, divine. So, everything depends on what forces he works with, in what area his consciousness is located, what elements he comes into contact with and what forces he turns to.

Thus the serpent in Genesis is a stream rising from the earth and reaching very high regions; in the heights it is pure and luminous, while in the lower regions it is dull and repulsive. In any case, the serpent was also in the Garden of Eden, these were also his possessions. And Eve was walking there ... Since she was very curious, she really wanted to know what it was - the Tree of Knowledge of Good and Evil; she studied him from a distance in order to form some idea of ​​him: she was gnawed by curiosity. She drew closer and closer to him, and as she looked at him, not yet daring to touch him, she became more and more sensitive to the voice of the serpent, that is, to the earthly stream, which quite reasonably said to her: “You see, you don't know everything. You still need to come to us to learn, because we have a lot of knowledge."

By the way, this serpent was not a single creature, but a whole set of creatures that God created before people: a generation of angels, archangels, deities, whom God instructed to work in the depths of the earth with metals, crystals, fire, etc ..., prepare all underground riches, and then, having fulfilled their mission, return to Him. And it is not I who speak of this, but tradition; I just embellish a little from time to time, add something to spice up the story a bit, but I'm not making it up. Consequently, the legend claims that God created luminous beings, a whole hierarchy of angels and archangels, who, having fulfilled their mission, were to return to the bosom of the Almighty. But since they were free, some of them, under the influence of life below, did not want to return, and this was the rebellion of the angels. They didn't rise above in Heaven, they rose when they were away from God.

But the Creator did not want to punish them with death or dispersion, He told them: "Stay there, you will learn a lot, and one day, when you get tired of living in darkness and limitations, come back, I will accept you." Yes, He made it possible for even the most fallen creatures to return to Him. You see, here it is, the love of God. If God is love, how could He forever refuse to accept the guilty who want to return to Him? That would be cruelty, it's impossible. Since He is absolute Love, even demons can return to Him. Because one should not think that in this situation they are happy, no, they suffer, but their pride prevents them from returning to God. Nevertheless, the door remains open and when they repent and stop hurting people, they will find the place they lost, and Lucifer will again become the Archangel of light. Tradition has informed us that at the moment when Lucifer was cast into the abyss along with the rebellious angels, a stone fell out of his crown - a huge emerald, and from this emerald the Holy Grail was carved - a cup into which the blood of Christ was collected. So what is the relationship between Lucifer and Christ? What can unite them? ...

But back to the snake. I told you that it is a symbol of all spirits that have separated themselves from God. These were very advanced beings who possessed science and fantastic knowledge, and it was thanks to this science and this knowledge that they managed to seduce Eve, promising to introduce her to their secrets. The book of Genesis presents this by saying that Eve ate the apple... What's wrong with that? Everyone eats apples! But here the symbolic side is interesting. By this apple should be understood all the teachings hitherto unknown to Adam and Eve. The serpent says to Eve: "God forbids you to eat the fruit of this tree, because He knows that if you eat it, you will become as powerful as He is, and He does not want this. He told you that you would die, but this is not true, you will live and you will know the realms that are still unknown to you." Eve succumbed to temptation and, as the Kabbalah says, she first knew Adam and became pregnant. It was the first introduction to the hitherto unknown. Enraptured, Eve hastened to convey the new experience to Adam. Until now, neither he nor she knew anything about it.

But here you must understand that there are many possibilities for interpreting the biblical story, since the Garden of Eden with two Trees - Life and the Knowledge of Good and Evil - is a symbol of a reality that exists not only in the universe, but in every human being. In one form or another in their physical body (symbolically - in the Garden of Eden), a man and a woman continue to taste the fruits of the Tree of Life or the fruits of the Tree of the Knowledge of Good and Evil. Adam and Eve, of course, both possessed this Tree of the Knowledge of Good and Evil, but they did not eat its fruits, they did not know about their properties. Thus, the first communion of Adam and Eve was to come into contact with the forces of nature unknown to them. Since there were also female entities in this egregore, called the serpent, Adam was introduced by a demon known in the esoteric tradition as Lilith (while the demon who introduced Eve was called Samael), and Adam, in turn, also ate the fruit . From that moment on, Eve went one way, and Adam the other: the unity of their couple was broken.

It was then that the binding force began its work of condensation, and they, who until now were not ashamed to see themselves naked, because their bodies were created from light, they, who saw themselves so dense, heavy and weighty, became ashamed of their nakedness; therefore, the Bible says, "they hid themselves in the garden." But how can you hide? You cannot hide from the sight of God.

But do not think that when God saw that they had eaten the fruit, he became angry. Why would He be angry, I ask you? You will say that it would be okay if he got angry because Adam and Eve disobeyed him. But how do you know if this disobedience was part of the Lord's plans? The history of original sin is the history of man's descent into matter; thus, the question arises: did human beings themselves make the decision, or did the Lord have incomprehensible, far-reaching, wonderful plans in which, in spite of everything, people still had some freedom of choice: to stay in Paradise or go to explore other areas of creation...

What some religions call the fall is nothing but the choice made by the first people to descend and study matter. This idea can also be illustrated by the example of a tree. We can say that the first people who lived in Paradise were at the top of the tree. And the top is flowers; it means that they lived among flowers and there they were in contact with light, with warmth, with life, with beauty, with freedom ... But they asked themselves questions: "What kind of tree is this? Where does this energy, this power come from? We see trunk, but there's something else hidden underneath. What is it? We'd like to know." And since in order to know something about things, one must study them on the spot, they left their wonderful dwellings, which reached the sky, and went down the trunk right to the roots. But it is known that when a place is changed, new conditions will have to be accepted; now, among the roots, people are suffering, screaming, because it is dark, hard, they feel crushed.

But it is still comforting that all this life spent by a person in Paradise is registered inside him as an indelible imprint. She is in him, and from time to time a person feels the echo of this harmony, this radiance, he relives the heavenly moments in beauty, music and poetry. Paradise is inside every human soul, because each of us was in Paradise in the beginning. But now the life that people lead is so prosaic, dull, limited, that they no longer have the opportunity to remember. Sometimes when they are immersed in mystical reading, when they meet some creatures, contemplate some landscapes or hear beautiful music, something awakens in them and they again experience a few moments of paradise. Unfortunately, after a few minutes everything is erased, they forget what they experienced, or even think that it was an illusion that does not need to be pointed out. Such a judgment is regrettable, since these heavenly states correlate with reality, they even exist quite realistically, and it is desirable to experience such moments as often as possible in anticipation of the final return to Paradise, to the bosom of God.

Since such a return will one day occur, God is always ready to meet us and take us into His arms. He is not angry with people, no, He is waiting for them and waiting for the day when they want to come back. And because He gave them eternity, He is magnanimous, He understands everything, He says: "They will suffer for a while - several million years! - and then they will return and be so happy that they will forget about everything. Their spirit is immortal, and it's not that bad, it's not that bad to suffer a little. What's a few million years compared to an eternity?" That's the way God talks, see! His thinking is different from ours, He is not in a hurry ...

And, in anticipation of returning to the bosom of God, people will learn a lot. Precisely so, because now that they have begun the study of dense matter, they must continue it to the end. As long as they lived in the divine world, they could stay there forever, but having descended, they are already obliged to go through all the stages. Imagine that you are standing on the top of a mountain: if you are prudent, if you are careful not to slip, you will not fall and you can stay there as long as you like. But as soon as you slip, you already have to go a certain way through rocks, spikes, with the risk of falling into the abyss. Once you have set in motion a certain law or mechanism, nothing depends on you anymore, you are no longer in power to do what you want - you will have to go through all the trials.

One should not think that the history of mankind could be made without the consent of the Lord and that the disobedience of mankind and the vicissitudes of its fate were not predetermined in advance. A man moved away from God, but God was not absolutely against it, otherwise everything would be very simple, a person would never be able to move away. Everything that man does is, in a sense, with the consent of God. And man will return to Him. After involution, evolution will begin, or, as it is called in the Science of Initiation, reunification, a return to the bosom of the Supreme.

And so that you can see that this idea does not contradict the philosophy of Jesus, I will tell you that it is contained in the parable of the prodigal son. Do you know this parable? The young man left his father's house to go to a distant country, where he spent all his money, he did not even have money for food. One day, when he was forced to herd pigs for his livelihood, and was very hungry, for he was not given even the acorns that the pigs ate, he remembered his father's house, where food was plentiful, and decided to return there. . In this story, Jesus summarized the entire history of mankind. And you know how the father met his prodigal son: as soon as he saw him from afar, he ran to hug him, then he ordered the fat calf to be slaughtered in order to arrange a feast in honor of the return of his son. This is exactly what I'm telling you.

The Lord is waiting for the return of a person who wants to see the world. The man was curious, he wanted to learn something, why bother him? The Lord knew in advance that the person would be unhappy, that he would experience hunger and thirst, that he would suffer because no one would love him the way He loves, but then the person would return and everything would be corrected. They always imagined everything as if the Lord was angry with the misconduct of a person ... Not at all! The Lord allowed him to do so. He had these good plans He said: "Sooner or later my children will return." And, like the father of the prodigal son, He prepares a feast for them to treat them.

Good and evil - two forces that turn the wheel of life

Among the questions that people ask, there is one that causes particular concern and a satisfactory answer to which they find with great difficulty - this is the question of the meaning of the existence of evil: why does evil exist? ... The answer, in essence, is very simple.

I will give you an example. Often in the past, when they wanted to get water from a well, they used a large wheel, which was turned by bulls, horses, or even people. The one who watched them saw how some of them seemed to be approaching the wheel, while others seemed to be moving away from it, and one could conclude that they were moving in two opposite directions. But if a person could observe this process from a height, then he would clearly see that both of them go in the same direction and perform the same work.

This example shows us that good and evil, which appear to be opposite manifestations, are actually two forces harnessed to one work, but since they are not looked at from above, that is, from a spiritual, initiatory point of view, they are said to be two forces that oppose each other. All those who look at facts, events from below, that is, at the level where they occur, are mistaken. If they tried to rise up to watch them from the point of view of wisdom, from the point of view of the spirit, then they would have the right vision. They would see a circle, a wheel... and they would understand that good and evil are two forces harnessed together to turn the wheel of life.

If we want to destroy evil, then good will also be destroyed. Of course, this does not mean that we should nourish and strengthen evil, no, it is strong enough without our help, but we should not try to get rid of it either - however, this does not work. What is needed is to use it and determine how to relate to it. Yes, now is the time to give humanity a new philosophy.

If you were in the sun, you might not know darkness, but you came out of the sun, you came to the earth, and since the earth revolves around the sun, light alternates with darkness on it. Since you are outside the sun, you need to recognize this alternation of day and night, light and darkness, good and evil, and not only recognize it, but also be able to use it. If darkness were evil, then how is it that it is in darkness - the darkness of the earth or the subconscious - that achievements of the greatest significance begin to emerge? In fact, darkness is the condition of births or future rebirths. Why a child, why do grains begin to grow in the dark?... And you, how do you use the night? It's wonderful, isn't it: you are asleep, and when you wake up the next morning, you have regained all your strength to start working again.

You say, "Yes, but what is the origin of evil?" There is an eternal Principle which is the Source of all creation. And when this eternal Principle instructed the Elohim to create ... (we will not look too far, we will not talk about the cosmos, but only about our earth), then, since they worked with two principles - male and female, positive and negative (because for these two poles are necessary), it would be inevitable that here and there some wastes would appear - elements that had not yet been organized or used and which violated the harmony of the whole. These materials, these energies, which were not evil for either the Creator or the Archangels, are harmful to people who do not know how to use them.

I'll give you one more example. You have a house: and in this house there is a place for a garbage pail or trash can, as well as for a toilet. For whatever you do, even if you are the most enlightened and most reasonable being, you will always have some waste for the trash can: paper, empty bottles and cans, peels, leftover food; and in your body, too, there are wastes from which you must be freed. Even best thing in the world has at least one small negative aspect ... as they say, reverse side medals. It has been noticed by everyone. So how is it that people do not understand the language of all these details of everyday life that are constantly before their eyes? When the earth was created, unused materials had to be collected somewhere, broken glass and bricks, unusable boards and nails - symbolically speaking. Therefore, the earth also has its trash cans: it is the cone of darkness behind it, its shadow. Do astronomers know this?

The source of evil is here, in the waste of materials used in the creation of the earth; and since the waste attracts various animals, ants, flies, worms, etc., it is these creatures that we must necessarily meet when visiting this sphere, although we imagine that we will find joys and pleasures here. The purpose of this sphere, called Hell, the world of darkness, is to collect garbage: it is there that all impurities gather and accumulate.

The question is, why are there creatures coming here in search of happiness? Because just as there are people who are so impoverished that they have to look for leftover food or some old shoes in the garbage, so there are unfortunate people in the spiritual world who do not have the opportunity to eat in restaurants upstairs, near the Angels, Archangels, Lord. They do not have the necessary money (this money, of course, is virtues and virtues) to buy themselves this pure and luminous food coming from the sun, and they are thus forced to go to eat in devilish restaurants where all the evil spirits and fallen creation.

In this realm of evil, in this realm of disorganized forces, you can still find a lot of things, and if you knew how to set to work to transform all waste like the earth, then you would extract from this realm the forces and elements that can feed even Angels. ... It was possible to find chemical methods for cleaning contaminated water! Nature has all the ways to process waste, and man has all these means, he must find them and learn how to use them. But for this he must first understand what good is, for only having understood what good is, he is able to resist evil.

Good is an eternal principle, creative and omnipotent, it is God himself…. although in reality God is above good. In Kabbalah, good and evil are presented as two manifestations of one force that is higher than them. But for ease of understanding, one can imagine God as the Principle of good, even if in reality God is above good. Good is a manifestation of God, and evil is a waste of good, something that could not find its place in cosmic harmony. Thus, evil can never be compared with good, it does not have eternity, strength, power, like good. Therefore, those who think that good and evil are two entities of equal strength fighting among themselves are mistaken, but neither of them can finally defeat the other.

Evil, as I told you, is the departure of good; it can be compared to the substance that remains after the quintessence of rose petals or other flowers has been extracted, to a substance that cannot be purified to a state in which it can reflect the Divine. Evil is what remains when all the good is "extracted". This means that where there is good, evil is also fatally present, since evil is what remains of good, it cannot exist by itself, it has no independent existence; it depends on the good, it was born from the good, it was created by the good. As long as people give evil its own existence, independent of the existence of good, they will never be able to transform it, and evil will continue to annoy them, because it is they, in their ignorance, that endow it with strength and independence.

It is light that creates darkness. Where there is light, there is fatally shadow. The presence of an object gives a shadow. Can there be a shadow when there is no light? No. You will say, "But sometimes darkness reigns precisely because there is no light." No, even if there is complete darkness in some place, it is because some object obstructs the light. Therefore, always half the earth is immersed in darkness. Without light, darkness could not exist, and evil would not exist if there were no good.

Therefore, manifestations of evil are necessary, but they are not eternal and not absolute, they depend on the forces of good. Now, in order to be able to solve the problem, one must go beyond good, and in order to go further than good, one must first of all have a correct idea of ​​what it is. Good is a harmonious manifestation that includes love, strength, intelligence, beauty, tenderness, etc. But as I told you, good is not yet God himself; it is a manifestation of God, but it is not God. God is above good and evil, we cannot know what He is.

But since good is a manifestation of God, then, thinking about good, you connect with the Creator of the universe, with the eternal Principle: our consciousness shifts - it leaves the area of ​​darkness, where suffering, fears, horrors are located in order to reach the Center, the all-encompassing creative Principle. And since it is God the Creator, He knows the role of all elements, all forces, all creatures, and He will know how to help. We cannot know, but He has all the possibilities, and, therefore, it is to Him, because He is above good and evil, that we must resort to asking for help. At that moment, we are able to set in motion exceptionally subtle forces that will begin to work in the entire universe.

This is the most worthy and glorious work for a student. And let him not worry if this work does not give immediate tangible results! Most people work only on material achievements on the physical plane, and that is why they experience such strong disappointment: because these achievements are short-lived. When you decide to work with the most inaccessible Being, with God Himself, then you have real achievements, internal achievements, in consciousness, and these are achievements of immediate action. What is the most remote is actually the closest, and what appears to be the closest is actually the most remote: if you want to experience something, you don't experience it, if you want to get something, you don't get it. And only when you work on the most remote realities do you live them immediately.

Yes, if you want immediate results, set yourself a long-term goal. Say to yourself: "I understood where the truth is, where the power is, where the real life is: it is in that single center over good and evil." And you think about him, you merge with him all the time, you believe only in him, you seek only him, you work only with him ... Then this center will touch the good, which will begin to manifest in you as an improvement in your inner life before it manifests one day also outside of you.

Of course, it is easier to do evil than good. But why?.. Not because good is weak and evil is strong, no, no, no. But because here, on earth, the conditions that mankind has gradually created are much more favorable for evil and contribute to it. Do you want to cause harm? Everyone is ready to help you. But as soon as we are talking about the good, everything is different, the good is as if paralyzed, lulled, weak. This is so because it is always so in the lower spheres, and people dwell too much in the lower spheres. But as soon as one manages to get out of these spheres, the opposite happens: the evil is strangled, detained, bound. When you live in the higher spheres, it is impossible to do evil, and if you want to do good, then this happens by itself.

I can give you an example: suppose it's winter, it's damp all around, everything is covered with snow; if you want to set fire to the forest, nothing will work, the fire will not start. But in the summer, when it's hot, a small piece of glass is enough to concentrate the sun's rays to set everything on fire; as if the whole forest agrees to blaze, because the conditions favor it. Try also to shoot from a cannon, if the gunpowder is wet - nothing will come of it ... And so on. Now you understand that if evil is much stronger than good on earth, it is because people have created more favorable conditions for it. But one day everything will change, everything will be the other way around; evil will no longer be able to manifest itself, favorable conditions for it will no longer be.

To control evil, dominate it or transform it, it is not enough to be a servant of good, because good, as I told you, is limited. Good failed to defeat evil, because it is not yet God Himself, it is only half, and the second half is evil. Good and evil are brother and sister, if you will, but they are not father. And you need to go to the father, because it is he who controls the son and daughter, or two brothers. Going to your father means becoming a servant of God, and not just a servant of good. This means that we must rise even higher in order to serve God, who governs good and evil. The real refuge is there. Of course, there is no evil above, and insofar as good means perfection, it can be said that to be a servant of good is to be a servant of God. But good in the form in which we understand it with the mind, that is, as the opposite of evil, is not yet God; it's only half of it.

I can give you other examples that will confirm to you the truth of what I am telling you. Let's take circulation. If there were only arterial circulation, then life would be impossible, because all the waste must be gone, and then the other half, the venous circulation, begins to operate: it brings blood to the lungs, where it is purified, and when the blood is pure, it enters heart, from where it goes back into the arteries. Therefore, pure blood, goodness, comes out of the heart; yes, but after a while this goodness is loaded with new impurities, and so on ... The same phenomenon is characteristic of the movement of cars on the roads: the oncoming movement of cars on the left and right ... If there was only one direction, one side of the movement, then what would the cars do, which need to come back?

This means that evil does not lie only in the fact that opposing forces allegedly exist, for they work in the same direction. But if, instead of doing the work determined by the cosmic Mind, these forces would collide, fight and destroy each other, then this would already be evil. It's like fire and water. How many extraordinary things can be done by putting water on fire! .. but with a partition separating them, otherwise the fire will evaporate the water or the water will extinguish the fire, which happens in all areas of life if you are ignorant. The forces of evil, poisons, are only harmful to a person who is not sufficiently educated and not strong enough to use them. But it is not harmful to nature.

One might even say that in some way the evil is contained in the good. Let's take nutrition as an example. When we eat, we assimilate elements that are useful, necessary for our health, and we eliminate those that the body cannot assimilate, and which, by the way, would poison it if it could not get rid of them. Thus, evil is contained in good, they are connected, and it is the body's business to separate and eliminate evil. Let's take other examples. You meet the most charming, most attractive girl and you marry her: it is a great boon. Yes, but you are not the only one fascinated by this creature, others are also interested in her, and now it begins: suspicions, jealousy, quarrels ... and it’s good if it ends there! Imagine that you inherit a huge fortune: now you are rich, that's wonderful! Yes, but here worries also begin: you will be begging for money all the time, you risk being robbed at any moment, you will never have peace again ... And the same thing - no matter what area of ​​\u200b\u200blife you take. Only wisdom is able to use good and evil, and even more so to make sure that good does not turn into evil.

As I told you at the beginning, good and evil are harnessed to the same wheel; if only goodness existed, it would not be able to make it turn. Perhaps I alone dare to say that good cannot do all the work if evil does not help it. You will say, however, that evil is the opposite force... Exactly, this is exactly what is needed for it to be opposite! When you want to cork or uncork a bottle, you use both your hands, and they act in opposite directions: one pushes in one direction and the other in the opposite direction, but thanks to this opposition, you manage to insert or pull out the cork. Now you understand how opposing forces work for a specific purpose ... This is a process that is before your eyes every day, but you do not see it.

In conclusion, I will tell you that you must think every day about how you can connect with the Lord, with the Center containing everything. And, for its part, the Lord (and He is tireless, never rests, He is eternal and indestructible, He is above good) will unite the forces of good, and the forces of good will purify and organize everything wonderfully.

Above the concepts of good and evil

We can say that there are two schools: the school of good and the school of evil. In the school of goodness, it is advised to discard everything that is bad, in the hope that, by acting in this way, you will find salvation. In the school of evil, they fight against good, imagining that they can crush it. But there is a much higher school, much higher than the schools of good and evil, because it manages to use both of these schools: it uses both good and evil, but in homeopathic doses, to achieve amazing results; it does not reject anything, but it teaches that if evil exists, then God allows its existence, otherwise it would have disappeared long ago.

Yes, if evil exists, then God agrees with its existence, otherwise it would be necessary to admit that He fails to defeat an enemy who is stronger than Him and, therefore, God is not an omnipotent Master who rules the universe. If something opposes Him in Creation, then who created everything? Another God, more powerful than He?.. By the way, people often thought so. They said to themselves: "What kind of God is this, who is capable of little? He does not know everything, He is not able to prophesy or perform miracles, but the Other is capable of this ... So let's go to him!" In a sense, they reasoned correctly. Why serve an incapable, feeble God when all knowledge and all gifts come from his adversary, the Devil? And that's what the Church said! If anyone did miracles... it was the Devil! Some believers have never acknowledged that these miracles are performed by God: according to their understanding, God was incapable of this. So do not be surprised that people signed agreements with Satan, it was logical! This is where you can go when the elite have lost the keys to true knowledge...

You will say, "Yes, but if God is truly omnipotent, then why doesn't He come to help us get out of suffering and sorrow?" Yes, because we have put so many barriers between Him and ourselves, so many false and contradictory ideas, that He is not able to help us. And then in the minds of people there is an opinion that God is so far and inaccessible that He does not hear them, while the Devil is very close, he hears them and can heed their request. Try it, do your research, and you will see if people think like this: "This God that we have been praying for so long is not available ... deaf ... He has fallen asleep ... But the Devil is awake, he is right there right there." This is true, but people do not know that they themselves have established this distance, that they have dug this abyss between themselves and God. In fact, no one else is as close to us, no one loves us as much as God, and no one wants to help us as much as He does. But we must free ourselves from everything that prevents this love from reaching us.

You remember, I once told you that the sun, which makes the planets move, which causes the growth of plants and epidemics, wars and all sorts of events, by a simple change in the streams it sends, the sun is powerless in front of a window with drawn curtains ... If you have drawn the curtains, then you can as much as you you want to beg him: "Come, dear sun, come to me, shine on me, you are so beautiful!", and it will answer: "I cannot ... I cannot ... You must remove the curtains." And we are waiting for God to remove our curtains! No, no, and even at the risk of being branded a blasphemer, I'll tell you: "God can do anything, but He is powerless before your closed curtains. It's up to you to raise them."

In any case, do not imagine that if God allowed evil to manifest itself in this world, this means that He cannot defeat him, and even more so that He needs people to help him, as many Christians think. You realize what kind of help from people can be! Perhaps you will be surprised, but I will tell you that evil is necessary and even obligatory in the work of nature, because she knows how to use it. It's like in a laboratory where poisons are needed to make very strong medicines. Evil is a poison that can kill the weak and ignorant, but for strong and intelligent people it is a panacea, it cures them. This is the philosophy of the third school: to use evil.

There are indications everywhere to enlighten people and make them think. Then why don't they know how to use difficulties and trials? This is the question that the student must work on from now on. Imagine that you wanted to defeat the enemy, and not knowing that it is really a friend who failed to introduce himself to you, you kill him, as sometimes happens. Thus, you must first of all study this "enemy" that hinders you: perhaps you will find that not only is he not so harmful and hostile, but that you can make a friend out of him.

We perceive evil as hostile forces. In fact, they have no hostility towards us; it's just that everything that doesn't suit us seems hostile to us. How not to recognize as hostile elements that paralyze or poison us? Everything that does not vibrate in harmony with us, that blocks the way for us, that darkens or depresses our consciousness, appears to us as an enemy, this is normal. But is this situation final? No, because if you manage to transform it, this element will become a beneficial force for you. Do you want examples?

In the beginning, fire, lightning, water, wind were the enemies of man, who fought against them and died in the struggle. When he began to master all these forces, he realized that they were hostile to him only because he did not know how to conquer them in order to use them. Then why not understand that the same thing can be done in life with other forces? In fact, evil represents very powerful forces with which we have no good relations because we don't know how to manage them. And, of course, everything that we do not know how to use can only harm us. Electricity gives us one of best examples what a person can do to channel an energy that, in its purest form, will immediately destroy him. Look at all these networks of wires, at these transformers, devices, buttons ... Now we have managed to subdue electricity so well that even a child can safely use it.

How simple and clear it is. When we study forces that we usually consider bad, we can see that they are not, because evil does not exist in nature.

Look, the earth is smarter than people: all the dirt, all the waste is thrown into it, and it accepts them as a very valuable substance, which it transforms into plants, flowers and fruits. And coal: how did it become coal? .. And oil? .. And precious stones? .. So, if the earth and some Initiates have this wisdom, if God has this wisdom, since He does not want to destroy evil, then why should we also not try to get it? For thousands of years people have been pleading: "Lord God, crush the evil!" But God smiles and says: "Poor! When they understand that evil is necessary, they will stop begging me." But until then, how many prayers! Of course, you need to pray, but you need to ask for this: “Lord God, explain to us how You created the world, how You look at things ... Give me this understanding, this wisdom, this mind, so that I can, like You, be above evil so that it does not affect me, and I could use it to realize something significant. How many more examples show us that what is evil for some is not necessarily evil for others! Some animals are remarkably resistant to fire, others to cold, still others to poison, and still others to deprivation. Some don't die even if their body is cut in half... People's ideas of evil are their own fabrications, they don't apply everywhere. That is what I want to explain to you: these are our own ideas, our own views, but there are other creatures who look at the problem of evil differently, because they have reached such a stage of development that they know how to use it.

I can give you so many more examples! If you fill your stomach with water, then it is good, but if you fill your lungs with water, then you will feel bad. Fill your lungs with air, this is good, but let it into your stomach ... you will feel bad! The conclusion to be drawn is that what is good in one case becomes evil in another.

To those who have sore eyes, the light is harmful: it means that the light can also be good or evil, depending on whom. This proves once again that people cannot know what evil is as long as they judge it based on their weaknesses and imperfections. As they approach perfection, they will change their minds. Therefore the opinion of ordinary people about evil is so different from that of the Initiates and the sages; outside of this frightening aspect that instills fear in the weak, the Initiates know how to find a beneficial force in evil, even a friend.

By the way, the best way to weaken is to perceive evil as an enemy. When you meet an obstacle, learn to see it as a foundation, a solid and stable anchor point for your work. When you went on an excursion to the mountains, did you notice that bumps and ledges helped you climb? If you want your life to be smooth and without any bumps, how will you get to the top? And most importantly: what will be the descent! Fortunately, there are bumps, and thanks to them you are still alive. Don't ask for your life to run smoothly, without suffering, without interference... without sorrow, without enemies, because you won't have anything to hold onto as you rise. If you get everything you ask for - easy, quiet life, with pleasures, money - then internally there will soon be nothing left of you. It's good that Heaven doesn't listen to you! Everyone asks only for an easy and abundant life, not knowing that in reality they are begging for misfortune.

I know it's hard to accept what I'm saying. Every day I bring you one aspect of this philosophy, and sometimes you are a little upset because these ideas do not correspond to your understanding. But get rid of your concepts, try to accept mine, and you will see the results! But no, you are stubborn: "I want power, I want money, fame and the whole world admires me ..." My God, people's desires! One wants to have a store with branches, the other - a cabaret or a hairdressing salon ... And all these girls and women who want to be movie actresses or Miss-is-not-known-what and walk down the street with a small dog in order to from time to time some has a man stopped to admire the dog: "Oh, how sweet she is! Oh, how nice she is!", when in fact he would like to talk to the owner of the dog ... having certain views on her! If only it were possible to look into the hearts of men and women, what would we see there! Wow! something to laugh at...or cry about!

Since evil is an explosive force and element that has not yet been subdued, one must tell oneself that there is always the possibility of achieving the highest degree knowledge and perfection and achieve it. As long as there is something higher than us, it may turn out to be evil for us. This means that we need to improve ourselves in order to reach the highest degree, which will allow us to be above evil in order to be able to turn it into good. Let's take very young children: if you give them the same food and the same drinks as adults, they can die from this, but when they grow up, get stronger, this can no longer harm them. So you see, these are the facts of everyday life that anyone could notice, but from which the correct conclusions were not drawn. One must get used to observing the facts of life.

If people do not have a correct understanding of good and evil, it is only because they have passed by the essence of the problem and do not know that what is bad for some may be good for others. Thus, if the student knows how to strengthen himself and advance in his understanding of things, then the evil that destroys, poisons or destroys others will make him more beautiful, nobler and give him health. This means that we must not fight evil, but strengthen ourselves in order to resist it. What do we do against rain, snow, storms? Do we go out of the house to cry out to calm down the forces of nature? Yes, perhaps this is what happens in some fairy tales; but in everyday life we ​​take care of our house, we strengthen it, check the insulation, install good heating, that's all, that's enough. Yes, we know what to do material terms but in the inner life we ​​act like ignoramuses: we want to destroy evil. Why fight against evil? Engage in self-strengthening to better understand and act better.

But, of course, if a person is seriously ill, it is not easy for him to strengthen himself in order to overcome the disease. But this happens because for many years, even for many incarnations, we did everything to bring ourselves to illness, and, therefore, now we need to work just as long to restore our health. This does not contradict what I just told you. If you have done everything to be weak, frail, dark, ignorant, then you can be sure that you have succeeded. It cannot be denied that evil exists, but first we must understand that we ourselves fed it, and then we must change our mind about evil; we have the option to loosen it, spray it, or use it.

I never said that most people do not live in difficult or even catastrophic conditions. You have to be blind not to recognize this sad, sad and lamentable reality. But I still insist that you have to be satisfied. Because I often feel that something in you is resisting and you think: "Does he, the Teacher, really not see what difficult conditions we live in?" Oh yes, I see it, I see only this one thing around. But I also see something else: I see favorable conditions that exist here, which you do not see, because the difficulties cloud you so much that you see nothing but them. And I see mainly those favorable conditions that are in yourself, treasures, amazing riches, while you see only the external side of the situation. When you understand me, you will feel stronger, you will say: "Ah! We needed someone who would also see good side and who will encourage us.” Yes, you see only your weaknesses, your poverty, your wife who left you, children who do not want to listen to anything ... but there is so much more to see!

Listening to me, of course, you immediately feel encouraged, but an hour later you have already lost all your courage, your inspiration. The very first slightest difficulty you encounter, a look, an unkind word, finally knocks you out of the saddle. How many times have I noted this: at the slightest blow you are crushed.

Assimilate this thought: what is evil for some may turn out to be good for others - this thought will help you a lot. If you understand that evil is not absolute, that it is even very relative, then it will be much easier for you to bear it, and little by little you will see that what used to cause you suffering leaves you indifferent. You will even think: "So much the better, Heaven sets me free!" How many Initiates noticed that all the losses that they experienced, all the trials that they went through, in fact, served only their liberation. So accept also their philosophy, otherwise every time you have to sing hymns of praise to the Almighty and songs of joy, you will still be able to be unhappy.

Through the light of understanding, from day to day, evil can be transformed into good, while if you don't understand it and don't use it, it remains evil. So, my dear brothers and sisters, a good future awaits you, by accepting these truths, you will have fantastic opportunities. If you really understand, then nothing can stop you. Since on the physical plane people succeed in using the forces of nature - wind, waterfalls, sea tides - they should be able to achieve the same on the psychic plane, it is only a problem of behavior. The main thing is to understand that there is no need to fight.

The occultists who wanted to lash out at evil, who declared war on evil, died because of it. They did not know the truths that I am revealing to you, they risked fighting evil alone, and they were bound to fail. I am not saying that the Initiate should not fight evil, but first he must prepare for a long time, purify himself in order to allow the Lord to settle in him so that He can manifest through him in all his power. Only God himself can destroy evil. And we do not have enough scope, nor strength, nor ways to do it. Read the Apocalypse, it says that the Archangel Michael chained the dragon, a symbol of evil, and locked him up for a thousand years. Here we need to think: since the Archangel Michael himself, who has all the power, does not destroy evil, but only fetters it, then how could we, the poor, be able to resist it?

Many of you are, of course, surprised by this new perspective on the perception of evil. In fact, what I am telling you is only a deduction from the observations that all of you can make daily. It's just that people don't have the habit of focusing on the minor events of everyday life in order to learn and interpret their language. However, it is in everyday life and in nature that philosophical problems of the highest significance are manifested and resolved, and even much more clearly and simply than in such abstract philosophical books.

Evil is, as it were, an unorganized force that torments a person because he has not yet acquired the ability to subjugate and control it; but the disciple, if he realizes that what is taken as evil can serve him well in his spiritual advancement, gradually becomes the master of all situations. Since we will never be able to defeat evil, we must now replace the words "fight, kill, eradicate, uproot", which are an expression of erroneous views, with other words such as: "tame, master, direct, aim, ennoble, use", expressing a more advanced , a more spiritual point of view. At this point, the black color of the coal turns into a brilliant red. Whether it's sexual power, rage, jealousy, malice, etc., whether it's an enemy or sickness or whatever temptation, if we embrace this new philosophy, we'll always have the best conditions for it. to work, to strengthen oneself, and finally resolve one's problems.

And here's what I advise you. When you want to consider some phenomenon as evil, ask yourself the question: "Is it really evil? Isn't it good in disguise?" Until you ask yourself this question, you will fight or rebel, and you will not use this evil, which was actually good, which you failed to see. People rarely know what is good for them and what is bad. How many things they used to consider good, but in fact - this is a real danger! How many successes and good luck contributed only to the fact that some people were plunged into disaster! And, on the contrary, how many obstacles, failures have become for those who managed to use them, the true reason for their future triumph. But you have to live a lot in the world, study a lot and go through many trials in order to understand how true this is.

Often people have to give up their important and not very desires - for a variety of reasons ... Of course, we are accustomed to dominate desires, and not to serve them ... But if this happens constantly, it exhausts and really happens to be as harmful as they say psychologists and just fabulous fairies, then what depends in such a situation on you personally - the person reading these lines?

We live in a time of all sorts of contradictions and paradoxes. And perhaps one of the most significant for each of us is the gap between the amount of information surrounding us and its actual implementation. This is really a huge problem! On the one hand, the information wave tends to the size of a tsunami, and the term "information" is used in more and more areas ("information revolution", "information war", "information blockade"). On the other hand, indignant voices are heard more and more often, claiming that we live in the "era of dilettantes." Perhaps each of us can give many examples of unskilled service in any area of ​​life - from a loader who does not know how to approach the refrigerator, and ending with a teacher who speaks Surzhik. Why is this happening? The reasons are many. Let's take a look at those that we can influence.

Information and energy

First of all, for many modern people there is no difference between the words "information" and "knowledge". That is why it is very common to hear “I know how to do it” from people who have never done what they advise others to do. This is especially true for advisers "from the humanities." There is even the phrase "theoretical knowledge", as opposed to the term "skills", that is, the ability to do something. And the situation when a specialist comes to production after a university, sometimes even with a red diploma (that is, it is assumed that he has a very large store of knowledge), and practical skills are equal or tend to zero - has become a byword. This is one aspect of which the sages and mentors say the following: knowledge This is information based on personal experience.

There is a deeper meaning in this story, which few people know about, but which each of us has encountered at least once in our lives, knowing, but not doing ... Agree, your plans when you are preparing for the first time to do something useful for yourself - at least sign up for a pool, or start doing exercises - often remain plans. Especially if you are going to do it alone or without friendly supervision, support from a person significant to you. And we are talking here not only and not so much about laziness or habits. Behind the notorious laziness is very often a lack, sometimes catastrophic, of free personal energy. However, in order to overcome a habit that has become unnecessary and form a new one, free personal energy is also required. Moreover, in such a situation, it is necessary even more than to overcome laziness!

Energy sources

What does the term "free personal energy" mean? According to Eastern wisdom and confirmed by modern adherents of various esoteric schools, a person has at his disposal several sources of energy = life force both for his daily activity and for everything new in his life. And most of these sources are irreplaceable. And besides the fact that we are not only unable to replenish our reserves, we also receive this vital force in fact one-time, at a time when we ourselves cannot manage it in any way. Namely: we acquire the main part of vital energy at the moment of conception, and some more - somewhere in the 12th week of pregnancy. And only after our birth, we have the opportunity to accumulate energy already in a renewable source. It is these reserves that are considered “free personal energy”. And the accumulation comes from the sources listed below.

Nutrition - the more natural and properly prepared foods, the more energy they have that we can turn into our life force. And the less free personal energy is needed to digest food. Nutritionists have long known that for processing, for example, even the most dietary meat, more energy is needed than we get in the end! And the original value of meat is not in its energy reserves, but in the content of essential amino acids.

Breathing - and not in the sense of gas exchange, but in the sense of getting at our disposal the energy spilled in space, known to us as prana.

Physical work on the ground, and just a walk in nature - especially if we can afford the luxury of walking barefoot!

The sun - in fact its stellar essence!

Loving something or someone. At such moments, we become open to receive not only the energy put into the work by its author, but also to better absorb prana.

Free personal energy of people. And first of all, the people to whom we are dear! Any other person can become an energy donor. How is not the point. But it is this path that ultimately leads to energy vampirism.

Dream. It is not for nothing that when we get sick, we begin to sleep more than usual.

Here, in general, and all the most significant ways to replenish free personal energy. I arrange them in a random order so that everyone can choose the maximum sources available for conscious use at their discretion.

wasted

Where does free personal energy go if there are so many sources of it?

1. First of all, this is our everyday life. After all, even when we just think, we spend more than when we sleep.
2. Communication with people, especially those who are not very pleasant to us. Sometimes such communication exhausts us to the point of impotence. Hence, a simple way to save your own personal energy is not to associate with people who are unpleasant. Difficult, do not want to spoil the relationship? Then think about it: do they make you happier? Does such communication give you strength for your personal life, for activity aimed at achieving your own well-being and the well-being of the beings around you?
3. Empty chatter. Moreover, this is a more costly “cost item” than most people imagine! No wonder the practice of conscious silence is considered one of the most powerful techniques on the path of self-awareness and personal growth.
4. Excessive emotionality. It has long been known that excessively expressed emotions simply devour our free personal energy. In this case, we are not talking about conscious emotional coldness - this is just as harmful as splashing emotions right and left for the slightest reason. It is important to manifest them appropriately and appropriately.
5. Sex. To be more precise - sex that does not bring mutual pleasure. Here, I think, it is possible to explain nothing. Most likely, each of us has more than once experienced moments when, instead of fullness and the feeling that you can move mountains, the body was filled with nasty emptiness ...

Forming a new habit

And finally - the simplest and most accessible opportunity not to waste free personal energy. This method is to live, being aware of yourself and every minute of your life.

What does it give?

We stop wasting energy.

What happens when we live "out of habit"?

Very imperceptibly, but irreversibly, we squander free personal energy!

How exactly?

Each in their own way, but something like this.

• In the morning, you choose between a plaid shirt and a turtleneck. Having made a choice, then for half a day, or even until the evening, you continue to argue with yourself whether you made the right choice. So, all this time you are presenting the “not chosen” clothes with your free personal energy! A trifle? Let's remember our day...
• On the way to work in the window you notice an appetizing and inexpensive, but very high-calorie cake. But your waist is dearer to you, and therefore the cake remains in the shop. And yet you spend half a day savoring a delicacy that has not been eaten. And again, you give him free personal energy ...
• At lunchtime, you run into the nearest shoe boutique. What a blessing - there is a sale! And those boots over there - just your favorite style, and what a gorgeous rich color! And on the leg - well, just super! And then you notice the numbers on the price tag. Oh God! Is it at a discount - and a whole monthly salary ?! And the boots are sadly put back on the shelf, while remaining in your memory and feelings for some rather long time. This is how you spend your free personal energy again.
• And also during the day - not bought, but very interesting book; handbag purchased yesterday by a colleague; a young man in the subway who evoked warmth in his soul, but did not come up to ask for the phone number ... Well, and so on and so forth!

Everyone has their own, but everyone, in fact, is the same - a lot of unfulfilled desires during the day, memories of which take more time in your memory than is necessary for their fulfillment. This is where we pour free personal energy.

Sometimes this leads us to the evening to complete exhaustion. And the strength is already enough only to get to your favorite chair and collapse exhausted into it, for some minutes. And then - dinner, telly or magazine, or sleep. After all, tomorrow is a new day - and again a million opportunities to deprive yourself of the chance to do something new, to take the first step towards something hitherto unknown, maybe very important in your life, but never realized.

Or you still find the strength to turn information into knowledge - and take the first step towards your dream!

Practice "How to release the energy of desires"

Purpose of the exercise- to discover under the heap of desires one or two thoroughly forgotten unrealized desires that block the free flow of energy.

Get a "Wish List (your name)". You can have this file on your computer. Once a day, take the time to gradually remember to write in this sheet all the desires that have not been realized since early childhood. You can make a sign, you can write it in a line - as you prefer.

Recording format:

• the unfulfilled desire itself;
• approximate age when it appeared;
• the situation in which it appeared;
• physical sensations of the body that you track when you remember this desire.

The process is important to perform day after day without interruption, without stretching it for more than a week. Usually, the “same” memory of a thoroughly forgotten desire happens to people on the 3-4th day.

Usually people write out from 50 to 150 unfulfilled desires. In your case, there may be a unique number, you should not tune in to a specific task.

Remembering your unfulfilled desires and releasing them by writing out the physical sensations of the present moment, you can create in yourself (in your body) the feeling that you are gradually freeing yourself from something. Step by step you move deeper into yourself, slowly, more slowly and more powerfully, without fuss you plunge into the hidden corners of your inner universe. Each time in a single prescribing session, you reach a state of total devastation for this moment practices. And one day there may be an insight. Suddenly you discover something, perhaps long forgotten. Forgotten so much that you have never in your life remembered this event, situation, desire. Move like a gold digger. You don't know where this "forgotten thing", pulling back with a backpack, hid. You don't even know if it exists at all.

You just sink slowly and powerfully deeper... And at some point this insight can happen by itself.

It is necessary to deprive yourself of expectations of immediate results. You don’t need to do anything with written desires, you just need to remember main goal- freeing yourself from the burden of unfulfilled desires that accumulate and interfere with the free flow of energy from the inside out, from dreams to realization?

Indeed, spun the carousel - and spin yourself by inertia. If the carousel bearings are good, then this can be done for a long time. Modern flywheels in energy storage devices rotate without the help of a motor for more than a week. Why not rotation by inertia? Moreover, if you "help" this flywheel with a motor, then it will rotate at a completely constant angular velocity. Can this be called rotation by inertia?

Strictly speaking, no. We criticized Galileo, who considered the movement of a point in a circle to be inertial. But this is because an external force must necessarily act on the point in this case. And then the movement is no longer inertial.

Let's do it smarter - take a lot of points located in a circle, fasten them together stronger and unwind. So we got a flywheel that rotates, mind you, without the application of external forces (we do not touch it!). We put such a flywheel in outer space - neither a suspension nor a motor is needed. The object rotates by itself, it does not require any forces.

Answer, fellow physicists, is it moving by inertia or not?

The question, it would seem, is for a schoolboy, but I'm afraid that it will become a problem for a physicist as well.

Answer one:

- Yes, it does not move at all, the center of its mass, which is located on the axis, is motionless, therefore, the flywheel is motionless!

- No, - we will not agree, - but what about its kinetic energy? Can a motionless body have kinetic energy and considerable?

Second answer:

- This is a movement by inertia, because it occurs without any external influence!

- Excuse me, - we will object, - but such movement, according to Newton's first law, can only be rectilinear and uniform. Maybe Newton missed something?

Newton took everything into account, it's just that the question is not so trivial as it might seem at once.

What is the difference between rectilinear and rotary inertia?

As is known, the inertia, or inertia, of a massive point depends only on its mass. Mass is a measure of the inertia of a body during rectilinear motion. This means that with such a motion, the distribution of masses in the body does not affect the inertia, and this body can be safely taken as a material (massive) point. The mass of this point is equal to the mass of the body, and it is located in the center of gravity, or, which is almost the same, in the center of mass, or the center of inertia of the body (therefore, the "body" in Newton's laws is rightly replaced by the "material point").

Let's do the following experiment. Let's try to rotate a rod with masses (weights) mounted on it, for example, metal balls, around a vertical axis. As long as these balls are near the center, it is easy to spin the rod, its inertia is small. But if we push the masses to the edges of the rod, then it will become much more difficult to unwind such a rod, although its mass has remained unchanged (Fig. 52). Therefore, the inertia of a body during rotation depends not only on the mass, but also (even to a greater extent) on the distribution of these masses relative to the axis of rotation. A measure of the inertia of a body during rotation is the so-called moment of inertia.

Rice. 52. Change in the moment of inertia of a body with its mass unchanged: 1 - rod; 2 - cargo

The moment of inertia of a body about a given axis is a value equal to the sum of the products of the masses of all particles of the body and the squares of their distances from this axis.

Thus, the difference in the measure of inertia of rectilinear motion and rotation lies in the fact that in the first case it is measured by mass, and in the second - by the moment of inertia.

Further. As we know, the law of inertia establishes the equivalence of relative rest and uniform rectilinear motion - motion by inertia. For it is impossible to establish by any mechanical experience whether a given body is at rest or moves uniformly and rectilinearly. This is not the case in rotational motion. For example, it is not at all indifferent whether the top is at rest or rotates uniformly, with a constant angular velocity. The angular velocity of a rigid body is a quantity that characterizes its physical state. Angular velocity can be determined (for example, by measuring centripetal forces) without any information about the position of the body in relation to the "absolute" coordinate system. That is, even if the entire Universe disappears, and only our rotating body remains, then in this case we will also find out its angular velocity. Therefore, the term "absolute angular velocity of a body" in contrast to "absolute velocity of a point" should be used in the literal sense (without quotes).

Thus, mechanical phenomena in a system at rest and a rotating system will proceed differently, not to mention the fact that the fall and movement of bodies in a rotating system occur differently than in a stationary one: it is enough to spin it well - and it will fall apart due to stresses that have arisen in it.

Therefore, the second difference is that rectilinear motion and rest are equivalent, and rotation, even with a constant angular velocity, can be clearly separated not only from rest, but also from rotation with a different angular velocity.

Here, perhaps, are all the main differences. The rest is so similar that one can take the liberty of formulating, in the image and likeness of Newton's laws, the "law" of inertia of the rotational motion of an absolutely rigid body: “An absolutely rigid body isolated from external moments will maintain a state of rest or uniform rotation around a fixed point or axis until the moments of external forces applied to the body cause it to change this state.”

Why an absolutely rigid body, and not any? Because for a non-rigid body, due to forced (or predetermined) deformations during rotation, the moment of inertia can change, and this is equivalent to a change in body mass in a rectilinear motion. We do not mention this case when we formulate the law of inertia, otherwise it would begin like this: “A material point isolated from external influences constant mass…” And this point can easily change its mass. An airplane or a rocket, moving by burning fuel, changes its mass quite significantly. Even a person, having traveled a sufficient distance, changes his mass so much that it is fixed by medical scales. And how will this change in mass affect inertia? After all, when the mass changes, an additional, so-called reactive force arises. What kind of movement by inertia can we talk about when a force acts on the body?

So in the case of rotational motion: if the moment of inertia is not constant, it is necessary to take constant not the angular velocity, but the product of the angular velocity and the moment of inertia - the so-called kinetic moment. In this case, the law of inertia will take the following form : "A body isolated from external moments about the axis of rotation will keep the kinetic moment about this axis constant." This law (in a slightly different formulation) is called the law of conservation of angular momentum.

To demonstrate this law, it is convenient to use a simple device called the Zhukovsky platform (bench). This is a round horizontal platform on bearings, which can rotate around a vertical axis with little friction (Fig. 53). If a person, standing on this platform and rotating at a certain angular velocity, spreads his arms to the side (even better with loads in them, for example, dumbbells), then his moment of inertia about the vertical axis will increase, and the angular velocity will drop significantly. Lowering his hands, a person with an internal effort informs himself of the initial angular velocity. Even standing motionless on the platform, you can turn the body in any direction by rotating the arm extended upwards in the opposite direction. This method of changing the angular velocity is widely used in ballet, acrobatics, etc., even cats successfully land on their paws due to the rotation of the tail in the appropriate direction.

Rice. 53. Zhukovsky platform and man

Numerous devices and machines are based on the phenomenon of inertia of rotational motion, in particular, inertial motors - batteries that store kinetic energy during the inertial rotation of the flywheel, and gyroscopic devices that preserve, figuratively speaking, its kinetic moment. There are also flywheels of a variable moment of inertia, reminiscent of the principle of human action on the Zhukovsky platform.

Are centrifugal forces real?

We already know that the so-called inertia forces, which we add to the real forces supposedly to facilitate the solution of problems, do not really exist. The author used the word “allegedly” because sometimes this “relief” turns into such a mistake that it would be better not to use these forces of inertia at all. Especially now, when all the counting work is done by computers, and they almost don't care whether we have facilitated the calculations or not.

So, for rotational motion, the issue of inertial forces is much more complicated than for rectilinear motion. And the consequences of mistakes can be worse. What are at least the notorious centrifugal forces worth? Almost every one of us, including even scientists, thinks that such forces exist and they act on a rotating point or body. And they are very discouraged when they find out that they are not and cannot be.

Let us give the simplest, but nonetheless deadly example for these forces. It is known that the Moon revolves around the Earth. The question is, are centrifugal forces acting on it? Please ask your comrades, parents, acquaintances about this. Most will answer: "Act!" Then you argue with them what you want and start proving that this cannot be.

There are two main arguments. First: if a centrifugal force (that is, a force directed outward from the center of rotation) acted on the Moon, then it could only act from the Earth, since there are no other bodies nearby. I think that it is no longer necessary to remind that forces act on bodies only from other bodies, and not “just like that”. And if everything is so, then it means that the Earth does not attract, but repels the Moon - from itself outwards. Meanwhile, as we know, there is a law of universal gravitation, not repulsion. Therefore, only one single force can act on the Moon from the side of the Earth - attraction P, directed exactly the opposite - from the Moon to the Earth. Such a force is called centripetal, and it really exists, it is it that turns the Moon off a rectilinear inertial path and makes it rotate around the Earth. But there is no centrifugal force, excuse me (Fig. 54).

Second argument. It is for those who do not know about the existence of the law of universal gravitation or have forgotten it. Then if a centrifugal force acted on the Moon (naturally, from the side of the Earth, since, as we already know, there are no other bodies nearby), then the Moon would not begin to revolve around the Earth, but would fly away. If no forces acted on the Moon at all, then it would calmly fly past the Earth by inertia, that is, in a straight line (we forgot about universal gravitation!). And if a centrifugal force acted on the Moon from the side of the Earth, then the Moon, approaching the Earth, would turn to the side and, under the influence of this force, would fly forever into outer space. If only we could see her! But if this does not happen, then there is no centrifugal force. You won the argument, and in any case. And this centrifugal force appeared from the same place, from where the inertia forces in rectilinear motion come from - from the d'Alembert principle. Here, in rotational motion, this principle facilitates problem solving even more than in rectilinear motion. Still, we apply a non-existent centrifugal force to the existing centripetal force - and the Moon, as it were, freezes in place! Do what you want with it, define accelerations, velocities, orbital radii, orbital periods, and everything else. Although all this can be determined without using the d'Alembert principle.

Rice. 55. Skidding a car on a turn (traffic police scheme)

But the Moon is the Moon, it's all nothing compared to getting a driver's license in the traffic police. The author teaches at the automotive department, where all his students are required to get a license and everyone groans from the traffic police physics. They complain that the traffic police explain to them the movement of the car on the turn as follows: “Since the traction force directed forward along the tangential and the centrifugal force acting outward act on the car when turning, the car can only be moved outward from the tangent” (see the diagram in Fig. .55). But since instead of a centrifugal force, a centripetal force acts on the car, directed exactly the opposite, it will bring the car inward from the tangent! Unless, of course, other reasons are taken into account - wheel slip, rollover, side wind, side impact, etc. not where you expected.

If any force P acts on the car, then only from the side of the road on the wheels (the air has nothing to do with it, we do not take it into account). If this force is centrifugal, then it will bend the tires from the center outward, and if it is centripetal, then, on the contrary, towards the center. And any traffic police inspector knows perfectly well that when cornering, car tires bend towards the center (Fig. 56). This means that the force P acts in the same direction, and it is centripetal. How many accidents could have been avoided if the traffic police had not "abused" the d'Alembert principle!

Rice. 56. Tires bend towards the center of the turn when cornering

But for the sake of fairness, we note nevertheless that there are still centrifugal or simply directed from the center forces, but they do not act at all on the body that rotates, but on the connection that holds this body (Fig. 57). That is, not on a car, but on a road, not on the Moon, but on the Earth, not on a stone in a sling, but on a rope and a human hand, etc.

Rice. 57. The action of centrifugal forces

The question may arise, why does the bike still fall outward during a sharp turn, if it did not have time to lean inward, why do trams, trains and cars topple outward when turning at high speed? After all, there is no centrifugal force, what pushes these cars outward when turning?

Let's explain this with the example of a bicycle, and at the same time it will become clear why it is so stable. Imagine a riding bicycle that begins to turn (Fig. 58). Let's look at it from above. The wheels begin to “leave” towards the center of the turn, drawn by the force of friction with the road, and the entire top, including the rider, or the biker in a modern way, tends to continue its path in a straight line - according to the law of inertia. What happens? The wheels "leave" from under the rider to the side, and he falls to the side - outward from the turn. But in any case, not in the way that the traffic police explain it - not outward from the tangent to the turn, from your previous straight path. Or rather, somewhere between the circle of rotation and this tangent. The same action of inertia explains the stability of the movement of the bicycle. As soon as he starts to fall to one side, the cyclist consciously or automatically turns the steering wheel in the direction of fall and, as it were, “brings” the wheels under the position of tilting himself.

Rice. 58. Riding bicycle on a turn: a - top view; b - front view

In the same way, namely the manifestation of inertia, people are thrown outward on the so-called "wheel of laughter", or "ferris wheel". We can talk about the centrifugal effect or centrifugal aspiration, due to which people, cars, bicycles, etc., moving in a circle, tend to be on its largest radius, or, as it seems to us, are thrown outward (Fig. 59). Naturally, they tend to move in a straight line (according to the law of inertia), and a straight line is the same circle, but with an infinitely large radius, which obviously exceeds the radius of any circle.

Rice. 59. People on a spinning wheel are thrown to its edges.

Numerous other attractions are based on the same property - "devil" or "dead" loops (invented in 1902 simultaneously by two circus actors - Johnson and Noisette) (Fig. 60), inclined carousels, which are widely used today in parks entertainment, etc.

Rice. 60. "Devil's noose" and a bicycle on it

The same centrifugal effect is used to create the so-called "artificial gravity", and the modern view of the nature of gravity, surprisingly, does not see much difference here. (Who is interested in this rather complicated question, the author refers to his book). space stations it is supposed to rotate around the axis so that the astronauts feel comfortable, feeling the heaviness almost like on Earth. Something similar happens with plants that are planted on the inside of a rotating wheel (Fig. 61). Sprouted seeds of beans give sprouts that do not rush upwards, as usual, but towards the center of the wheel, i.e. in the direction of artificial. Thus, it was shown that for living organisms gravity is natural or artificial - it does not matter.

Rice. 61. Stems of germinated gravity plants. directed towards the axis, roots outward

To be more precise, of course, there is a difference. Under natural gravity, bodies are attracted to a certain point, and under artificial gravity, as it were, they “repel” from it, as can be seen from Fig. 61. But there is no fundamental difference in biological terms.

Spinning Top Mystery

But the matter is completely confused when the forces of inertia during rotation are not d'Alembert, but Euler's. Those that "arise" when using a rotating frame of reference. That is, when we try to take a rotating system for a fixed one and apply such inertial forces that would keep everything the same.

Remember a person walking in a turning tram, and you will understand how complex the forces must be in order to lead a person astray in a stationary tram just as it will happen to him in a turning one. Any Coriolis forces and gyroscopic moments used in this case are the same fictitious inertia forces, only much more complex.

For example, let's try to explain why the rivers flowing along the meridian wash away the right banks in the Northern Hemisphere, and the left ones in the Southern Hemisphere. This can be explained simply and intelligibly without the forces of inertia, and difficult with them, all the more non-existent. This property of rivers to wash away different banks in different hemispheres is called Baer's law, named after the Russian geographer K. M. Baer, ​​who lived in the 19th century and noticed this feature.

The earth, as you know, rotates from west to east. Therefore, it seems to us that the Sun is moving above us from east to west. Since the Earth rotates, it cannot serve as a sufficiently accurate inertial (fixed) frame of reference, although we often think of it as such. Therefore, we are surprised by all sorts of unusual phenomena that cannot occur in a fixed frame of reference.

Let's look at the Earth from a height from its North Pole. Let's imagine for simplicity that the river, starting at the equator, flows straight to the north, crosses the North Pole and also ends at the equator, but on the other side. The water in the river at the equator has the same speed in the direction from west to east (this is not the flow of the river, this is its speed along with the banks and with the Earth!), As well as its banks, which, with the daily rotation of the Earth, is about 0.5 km / With. As you approach the pole, the speed of the coast decreases, and at the pole itself it is equal to zero. But the water in the river "does not want" to reduce its speed - it obeys the law of inertia. And this speed is directed in the direction of the rotation of the Earth, that is, from west to east. So the water begins to "press" on the eastern bank of the river, which turns out to be right downstream. Having reached the pole, the water in the river will completely lose its speed in the “lateral”, “tangential” direction, since the pole is a fixed point on Earth. But the river continues to flow now to the south, and its banks again rotate from west to east with an ever-increasing speed as it approaches the equator. The western bank begins to "press" on the water in the river, dispersing it from west to east, but the water, according to Newton's third law, "presses" on this bank, which again turns out to be right downstream.

In the Southern Hemisphere, everything happens the other way around, because if you look at the Earth from the side South Pole, then its rotation will already be visible in the other direction - not counterclockwise, as from the North Pole, but clockwise. Anyone with a globe can check it out.

That's Baer's law for you!

But if you try to explain the same thing from the point of view of the mechanics of relative motion and the Euler forces of inertia, the result would be deplorable. Half of the readers would fall asleep, and the other half would go about other things. Here, one cannot do without higher mathematics and mechanics, and the physical meaning is completely lost. That is why students perceive and “pass” this material so badly. But for complex cases, for example, the theory of gyroscopes, this cannot be dispensed with.

In the same way, only using the concept of inertia, one can explain such a complex phenomenon as the gyroscopic effect, which explains, for example, the mysterious behavior of a rotating top.

Let's continue our river further and describe with it a vicious circle around the Earth. In this case, we will notice that the entire northern part of the river (in the Northern Hemisphere) will tend to the right, and the entire southern part will tend to the left. That's all the explanation of the gyroscopic effect, which is considered almost the most difficult in theoretical mechanics!

So, our river is a huge ring or flywheel, rotating in the same direction as the flow of the river. If, at the same time, this flywheel is turned in the direction of the Earth's rotation - counterclockwise, then its entire northern part will deviate to the right, and the southern part - to the left. In other words, the flywheel will turn so that its rotation coincides with the direction of the Earth's rotation! And the physical meaning of this phenomenon is already clear from the consideration of Baer's law.

It is easy to test this statement by experiment, especially for those who have a bicycle. Raise the front wheel of the bicycle off the floor and accelerate it in the direction of rotation of our flywheel river, that is, in the same way as it rotates when the bicycle moves forward. And then sharply turn the handlebars of the bicycle in the direction of the rotation of the Earth - that is, counterclockwise. And you will see that the whole bicycle will tilt with its upper part to the right, which was required to be proved (Fig. 62).

Rice. 62. Checking the gyroscopic moment on a bicycle wheel

If there is no bicycle at hand, and most often it happens at work and school, then you can get by with a coin or any wheel that can be rolled on the table. In this case, you will see that where the coin will lean to the side, losing balance, it will turn there as it rolls (Fig. 63). This wonderful and, most importantly, reproducible rule at any time will help you determine the behavior of a rotating wheel, flywheel, disk during their forced turns. The author himself in his work only uses this rule, and believe me that it is much easier than others, and you can check it at any time.

Rice. 63. Rule of the wheel - it turns in the same direction on which side it seeks to fall

Well, now it’s just right to figure out how precession occurs - the cone-shaped movement of the top, and the Earth itself, if you like. So, our flywheel river is constantly trying to deflect the Earth's North Pole to the right; but the Earth is spinning, so, constantly deviating to the right, the North Pole begins to “write out” a circle. A spinning top will behave in the same way if you push it or otherwise disturb its balance. You just need to know that the Earth precesses not because of the rivers (we'll talk about this too!), but because of its uneven (off-center) attraction, mainly by the Sun. The axis of rotation of the Earth "walks around on a cone", the generatrix of which is inclined to the axis of the cone at an angle of 0.41 rad, or 23° 27 . The axis of the Earth makes a complete revolution around the axis of the cone in 26 thousand years, and, naturally, the coordinates of stars, including conditionally fixed ones (for example, the North Star), are constantly changing. The ancient Egyptians, for example, saw constellations in the sky that their contemporaries can no longer see.

How to determine the direction of precession of any rotating body - a wheel, a top, etc.? Yes, according to the same "rule of the wheel", which has already been mentioned. So, if any rotating body is represented as a rolling wheel, and the perturbing moment is represented as a moment tending to overturn this wheel on its side (which, in fact, gravity forces do!), Then this wheel will turn in the direction of fall along the rolling. That is, if the wheel falls to the right, then it will turn to the right. It is this turning of the wheel that is the precession, and in this way one can determine its direction.

Is a two wheeler possible?

Yes, a car, just a car, and not a bicycle, motorcycle, scooter, moped, mokik, etc., where stability is achieved by “maneuvering” the rider or biker. By the way, one has to read a lot about the fact that the stability of a bicycle and other two-wheeled vehicles is achieved due to the gyroscopic effect of their wheels. This is a clear exaggeration, and here's why.

What is the gyroscopic effect? This is the occurrence of a moment when trying to force the axis of a rotating body. In a word, what we considered in the previous section. But we did not determine the magnitude of the gyroscopic moment. For the given example of turning a bicycle wheel, for example, this moment is equal to the product of the moment of inertia of the wheel and the angular velocity of its rotation and the angular velocity of its rotation (“forced precession”). For simplicity, we will decide that the mass of the wheel is 2 kg, its radius is 0.25 m and, therefore, the moment of inertia, equal to the product of the mass and the square of the radius, is 0.125 kg m 2. The cyclist is already maneuvering calmly at a speed of 1 m/s, while the wheel is rotating at an angular velocity of 4 rad/s. The angular speed of rotation of the wheel axis is 20 times less and is approximately 0.2 rad/s. As a result, we obtain a gyroscopic moment equal to 0.1 Nxm. This is the same if a weight of 10 g is hung on a ruler 1 m long. It is unlikely that such a moment will help anything.

At the same time, a riding cyclist, turning only 10 cm from the straight line, if he does not deliberately lean in the direction of the turn, will create a moment equal to his weight plus half the weight of the bike (approximately) times 0.1 m, or roughly 100 Nxm. This is 1,000 times greater than the gyroscopic moment! This is how the stability of the bike is achieved.

But we do not need a bicycle, but a car that would maintain balance even when stationary. First of all, a guarantee against capsizing in the parking lot is given only by special stands or, at worst, bricks placed under the sides. There is no stability without such supports or without constant manual or automatic adjustment of this stability. But let's agree that we cannot obtain this stability with one turn of the car's wheels, since we will not be able to create with our body a sufficient moment that counteracts a rollover, as on a bicycle. Imagine that all the passengers of the car, led by the driver, will now and then fidget in their seats, saving the car from tipping over. Here you need a stabilizer that does not depend on the rotation of the wheels and the position of the passengers.

This is where the gyroscopic effect, which was discussed above, could come in handy. And such a two-wheeled car was created in 1914 by the Russian engineer P.P. Shilovsky, and before that by the Englishman Brennan. It is true that Brennan's carriage moved along the rail and, strictly speaking, was a monorail carriage, but this does not change the essence of the matter. It is simpler than Shilovsky's crew, with manual control, and it is easier to understand its principle of operation (Fig. 64).

When tilting the car, let's say, on the right side along the way, the driver turned the handle 3 to the left. Thus, by forcing the flywheel to precess in frame 1, it caused a gyroscopic moment acting on frame 2 rigidly fixed on the platform and directed to the left in motion. The car straightened out. It makes no difference whether the car was moving or stationary. Such a wagon, with a capacity of 40 people, was built for the Anglo-Japanese Exhibition in 1912 and transported visitors around the exhibition grounds. I must say that a healthy and heavy man had to work as a driver, otherwise he would not have been able to cope with the role of an automatic regulator. And the flywheel had to weigh more than one hundred kilograms and spin fast enough.

But Shilovsky's carriage, which appeared on the streets of London in 1914, freed a person from such inconveniences; its scheme is shown in fig. 65. There was also a movable frame 1 with a flywheel weighing 314 kg, mounted on an axle in a fixed frame rigidly connected to the car body. However, the role of a man was played by a primitive automaton, consisting of a tube with a ball 4, which, when the car was tilted, rolled to one side and closed the corresponding contact 3. This started the electric motor 2 and rotated frame 1 with a flywheel through a gear train, just like a strongman adjuster at Brennan.

What can be said about Shilovsky's car? For its time, it was a miracle that gathered hundreds of onlookers on the streets of London (Fig. 66). But it was conceived as a military vehicle for cross-country travel and was very expensive for an ordinary car. In addition, the automation left much to be desired, and the car behaved inadequately when cornering. But he played his role and entered the history of motor transport.

Rice. 66. Two-wheeled car Shilovsky (general view)

And in 1967, a new American two-wheeled car "Giron" appeared and was tested with the same principle of body stabilization. But everything was small-sized and modern: a flywheel with a diameter of only 0.6 m, rotating at a frequency of 6 thousand revolutions per minute, fit under the hood of the car. The engine of the car, with a power of only about 60 kW, supported the rotation of the flywheel, and it was enough to move the car at a speed of 140 km / h. In the parking lot and at low speed, additional wheels-stops were put forward. This car easily walked on trails and on slopes with a transverse slope of up to 60 °, while maintaining an upright position, which, of course, a conventional car cannot do. This, apparently, was Shilovsky's original idea, but he could not implement it in 1914.

Does the two-wheeler have a future? It is difficult to answer this question with certainty. The author does not have an unequivocal opinion on this issue. Perhaps, with the development of automation, the computerization of cars and the need for a very maneuverable and economical car, this will appear again. But one thing you can be sure that flywheels will appear on cars primarily not as stabilizers, but as energy storage devices that can greatly increase the efficiency and dynamism of cars. That's when why not use the flywheel already on the car also as a stabilizer?

How to store kinetic energy?

When we spin the flywheel, we store kinetic energy in it. Energy is an indispensable attribute of any rotating body, and it is equal to half the product of the moment of inertia of the flywheel (we have already calculated it for a bicycle wheel) and the square of the angular velocity.

To what extent can we accumulate energy in it? We will accelerate the flywheel faster and faster, and the energy in it will grow even faster - we increased the angular velocity by 2 times, and the energy increased by 4. Is there a limit to this? Well, first of all, such a flywheel will begin to "drive" air, like a good fan. The author spun the wagon wheel (from passenger car) up to 6 thousand revolutions per minute on a special installation, and this required a power of tens of kilowatts. Full power car engine - only to maintain the rotation of such a flywheel!

If you pump out the air, then the power loss will immediately fall hundreds of times - the bearings or flywheel bearings "take" quite a bit for their rotation. But we can go further and replace the usual magnetic bearings (which will be discussed later) and almost completely eliminate the losses due to the rotation of the flywheel. Such a flywheel, being overclocked, will rotate to a stop for months, or even years. The larger the flywheel, the more it will spin. The large flywheel - the Earth - has been rotating for about 4 billion years, and during this time it has slowed down only 3 times, although the losses, by our standards, are colossal. The moon "slows down" the Earth in its rotation by the ebbs and flows of all the oceans, and these are powers that are many times greater than those artificially produced by mankind.

So, we accelerate our flywheel (let it be the same wagon wheel on a special installation that really allows air to be pumped out of the flywheel rotation chamber) more and more. At 8 thousand revolutions per minute, we notice (with special devices) that the disk begins to stretch, take a little b about Larger sizes. A little more rotation and the flywheel breaks, usually into three pieces, three large fragments that penetrate deep into the lead protective layer (Fig. 67). Still - the speed of expansion of the fragments exceeded 400 m / s, almost like a rifle bullet.

Rice. 67. Flywheel rupture pattern

Why did this happen, what prevented the flywheel from accelerating further? Yes, all the same inertia. Each particle of the flywheel tends to move in a straight line, but here it is “forced” to turn off the straight path, and so often. The strength of the flywheel metal, while it can, prevents the scattering of these particles, but when mechanical stresses become extremely large, the metal cannot withstand and breaks. Particles (these are usually three large fragments!), having received freedom, scatter along straight lines - tangents to the circle of rotation.

There is a simple formula for determining the stresses in the material of the flywheel, if it is made in the form of a rim-ring, as is most often the case. Voltage - ? are equal to the density of the material - ?, multiplied by the square of the circumferential speed - V of the flywheel. For the wagon wheel that we just torn apart, made of high-quality steel, these stresses turned out to be:

7 800 400 2 \u003d 1.25 x 10 9 Pa,

where 7 800 is the density of steel, kg / m 3;

400 - the speed at which the flywheel broke, m / s.

Stresses of 1.25 x 10 9 Pa or, as they often say, 1,250 MPa are the limiting tensile stresses of that high-quality and heat-treated steel from which train wheels are made.

At the same time, our wheel accumulated as much energy as it contained fragments flying at a speed of 400 m / s - each kilogram of a fragment - 4002 m 2 / s 2 / 2 \u003d 80,000 J. In other words, the specific energy consumption of our flywheel-wheel at the moment of rupture was 80 kJ/kg. Is it a lot or a little? This is almost the same as that of car batteries, and ten times more than the best capacitors. But we must remember that this energy is accumulated at the moment of a break, which cannot be allowed! Therefore, this figure should be reduced by at least 2-3 times. It doesn't work out enough.

And if you take a material stronger than steel? Yes, and easier, less density, to reduce stress? Yes, then we can count on high energy values, but are there such materials?

The fact of the matter is that there are, and there are many of them in modern technology: steel wire, tape made of amorphous metal (metglass), fibers made of carbon, Kevlar (body armor is made of this), quartz, and even the so far very scarce "diamond" fiber . The specific energy capacities of flywheels made from such materials will be respectively equal to: 200, 500, 1500, 1800, 5000 and 15000 kJ/kg. The last figures are very large - judge for yourself, they are almost 100 times more than car battery! Even 20 years ago, such figures were published by both the Japanese and the Americans.

Rice. 68. Wire superflywheel with the ends of the wires inside the coil:

1 - winding to the center (arrows show the direction of winding); 2 - ordinary winding; 3 - shaft; 4 - cheek

Is it possible to make flywheels from such fibers or tapes? After all, they are usually cast or forged. It turns out that it is possible, and in some cases it is even easier than casting or forging. These fibers and ribbons must be wound around the center or hub of the flywheel, in much the same way that we wind thread on a spool. Only this center must have the necessary elasticity, the winding must occur with a certain interference, and the last turn must be not outside, but inside the winding (Fig. 68). And if all this is done, we will get a wonderful, super-energy-intensive flywheel, called a super-flywheel, which will be torn safely, without splinters. In a super-flywheel wound from a tape (Fig. 69, a), if the critical rotation speed is accidentally (or intentionally!) exceeded, the most heavily loaded outer coil breaks; it moves away from the main winding and, pressing against the flywheel body, brakes rotation by friction (Fig. 69, b). In addition to high energy intensity, we also get safety, which is so important for flywheels!

Rice. 69. A flywheel wound from a strong tape (a), and a picture of its rupture in the casing (b): 1 - tape; 2 - casing; 3 - center

The invention of the super flywheel was associated with a number of curiosities corresponding to the past era. In May 1964, a 24-year-old graduate student, the author of these lines, applies for the invention of a super flywheel. But since in those Soviet times the invention was considered a “voluntary gift” to the state, applications were carefully checked for usefulness. So that anyone does not give the state anything. Now they don’t check the usefulness of an invention: if you pay a fee, get a patent! If it is not useful - go broke yourself!

So the “competent” organization determined that flywheels need to be forged or cast, and winding them from wire or fibers is nonsense! So the author was denied the issuance of a copyright certificate (that then replaced the patent). But the priority remains. According to the same Soviet laws, if the usefulness is proven, then the inventions can be recognized again. At the same time, the applications themselves were kept in a dungeon in a secret vault somewhere in the Urals. And now the time comes, and in January 1965, the Americans apply for super flywheels, followed by all the developed countries. Super flywheels are built, used in technology (especially in aviation and space - they are still expensive!), International symposiums are convened on them. The author filed an appeal and - wow - he is given a copyright certificate with a priority of 1964, but ... 20 years later, that is, after a period when all rights to inventions become universal. Such are the patent laws! But the author is also pleased with this - at least we will know who and in what country was the first to invent the super flywheel!

Here is how and in what it is best to accumulate mechanical energy, and energy in general. The fact is that progress in the creation of superstrong materials does not stand still, and the creation of so-called "close-packed" and "star" materials of fantastic strength and density has already been predicted. A flywheel made of such materials can, for example, serve as an engine, i.e., supply energy to a car for its entire service life, while still being hyped on the assembly line!

Spring, rubber or gas?

Excuse me, flywheels, super-flywheels ... but what, in springs, as it is done, for example, in mechanical watches or toys, don’t they store mechanical energy? After all, there are “elastic” storage devices, or energy accumulators.

Accumulators using elasticity or potential energy have been used by man since ancient times: let us recall at least bows, crossbows and catapults. During the Renaissance, spring engines could be found in clockwork toys, watches, and even in “self-running” carriages (Fig. 70), intended exclusively for the solemn departure of kings. The springs were then forged by blacksmiths, and they were very expensive.

Rice. 70. Mechanical carriage of the XVI century. with a spring engine driven by a wheel (from a drawing by Albrecht Dürer)

Now spring motors for a variety of mechanisms are produced in multi-million series. The most common of these are coil spring motors. A hardened spring tape is placed in a holder (drum), attached with one end to it, with the other - to the shaft and wrapped around it (Fig. 71). In such a "cocked" state, the spring is "unwilling", that is, it is left for several hours or days to stabilize the elastic properties. The efficiency of these engines is higher than 0.9. The spring tape works on a bend. Moreover, that part of it that is more tense (screwed on a smaller diameter) accumulates more energy; the peripheral parts are less tense - therefore, they accumulate less energy. If the spring is pre-bent in an S-shape, then all its sections will be stressed evenly, and it will accumulate much more potential energy.

Rice. 71. Spring accumulator with a coil spring (a) and S-shaped coil spring (b): 1 - clip; 2 - spring; 3 - shaft

You can also increase the energy intensity of coil springs by giving them a grooved profile. Rolling onto the shaft, such a spring undergoes bending deformation both in the longitudinal and transverse directions and accumulates maximum energy. S-shaped grooved springs have other advantages, such as almost constant torque.

Rice. 72. Hydraulic accumulator with a spring motor: 1 - spring; 2 - piston; 3 - hydraulic motor

For machines with a hydraulic system, a spring-driven accumulator is best suited (Fig. 72). In it, the accumulation and release of energy are produced during the injection or release of oil. Here the spring is no longer tape, but wire. The efficiency of the wire can be significantly increased by removing the axial sections, which do not participate in the process of energy accumulation during its torsion. Of course, the manufacture of a tube with high strength properties instead of a spring wire is much more difficult and difficult, but if necessary, one has to go for it. However, despite all the measures to increase the energy intensity of spring motors, they are far behind other types of batteries in this indicator. For example, the energy intensity of flywheels exceeds the energy intensity of any springs with the same material strength by tens of thousands of times! What are the ways to increase the energy intensity of "elastic" batteries? The mechanical energy accumulated in the accumulator is the higher, the greater the force and displacement under the action of this force. Therefore, as an accumulating element, it is advisable to use materials that allow large deformations under the action of large forces. And here, perhaps, you will not find anything better than gas. When it is compressed, huge energy is stored, commensurate with the energy of promising electric accumulators and flywheels. Unfortunately, the disadvantages of "gas" batteries (Fig. 73) are very significant.

Rice. 73. Gas accumulator (pneumatic accumulator): 1 - cylinder; 2 – air motor; 3 - valve

First of all, gas must be pumped into the cylinder with a compressor, and energy must be taken off with a pneumatic motor. And the efficiency of these units is rather low: it’s good if you can use at least a quarter of the energy expended. And one more thing: when compressed, the gas heats up, and when it expands, it cools. Therefore, the newly injected gas in the cylinder is very hot, but over time it cools down, takes on a temperature environment, and this released heat takes away with it up to 40% of the accumulated energy - only miserable crumbs remain from the reserves of the gas accumulator.

However, there is a way to increase the efficiency of gas accumulators - this is their symbiosis with a hydraulic drive (Fig. 74). A spring-hydraulic accumulator was mentioned above, where the spring accumulates energy, and the hydraulic system only plays the role of a transmission. At the same time, the efficiency of the accumulator (called hydrogas) increases greatly. First, the gas expands to a much lesser extent than in purely gas accumulators, and much less heat is generated. Secondly, the hydraulic system, which in this case is hydrostatic, or static, has a very high efficiency. Therefore, hydro-gas accumulators are widely used for accumulating significant amounts of energy in a variety of machines: presses, starters, aircraft.

Rice. 74. Hydrogas (hydropneumatic) accumulator: 1 - gas cavity; 2 - liquid; 3 - elastic partition; 4 - reversible hydraulic machine; 5 - tank

To increase the specific energy of hydro-gas accumulators, the cylinder into which gas is pumped is made of the most durable materials, which also have a low density. Such materials can be epoxy-bonded glass or graphite fiber, as well as a range of recently developed heavy-duty materials. The balloon is best made in the form of a sphere (it has the smallest area with the largest volume), the inner surface of which is suitably sealed. For injection into the cylinder, technically inert gases are used - usually nitrogen, less often helium. The gas and liquid media in such a battery are most often separated. In the old designs of cylindrical cylinders, this was done with the help of a free piston, and in more advanced designs, including spherical ones, with the help of an elastic partition. The gas pressure in such accumulators is usually 15-40 MPa.

Giant gas accumulators can be used as storage devices for power plants. Energy will be stored in the battery by compressing the gas (most reasonable - air) at night, when electricity consumption is low. During peak hours, when needed maximum power power plant, the gas will be fed to powerful turbines or other pneumatic motors, adding the stored energy to the energy of the power plant. According to existing projects, gas is supposed to be pumped into huge cavities underground (for example, exhausted mines).

But back to solids. Are there really no substances that, having sufficient strength (for example, like metals), have at the same time a high elastic deformation? Then a spring made of such materials would accumulate more energy.

It turns out that there are such materials and they are called pseudoelastic. Pseudoelasticity is the ability of a material (metal) to stretch to break not by 1–2%, like steel wire, for example, but by 15–20%. Moreover, if ordinary steel “gets tired” during deformations and withstands not so many cycles (remember how often springs break!), then pseudoelastic material, which has a different deformation principle, withstands loading cycles with virtually no “fatigue”.

Pseudo-elastic materials are almost the same as those that have a shape memory effect; a lot has been written and written about them. These are mainly alloys of titanium and nickel; if they are given a certain shape in a heated state, and then, after cooling, change this shape (for example, bend the wire as you like), then when heated, the alloy will again take its previous shape, as if “remembering” it. Such alloys are now used in many cases, starting with heat engines that operate without steam and gasoline at a minimum temperature difference, and ending with probes that are inserted into the arteries and even the heart of a person. Heating up in his body, the alloy "remembers" its former shape and, for example, expands the artery.

But we are talking about the property of pseudoelasticity in such materials. A wire made of such an alloy can be deformed - bent, stretched 10 times more than the strongest and most elastic steel. Therefore, a spring made of such a material will accumulate 10 times more energy. What a leap in energy storage! Watches with such a spring, for example, will run 10 times longer than conventional clockwork, but for the time being, such watches can only be used in a sauna. Because such a material acquires an “elastic” force at 150-200 ° C. The author has no doubt that materials will soon be created that will be “strong” even at room temperature. In the meantime, they behave sluggishly at such temperatures, lengthening and shortening slowly, as if they were made of resin, only very durable.

But the author came up with the use of such materials today, and the use is very effective - for sports. If the cable for throwing a hammer is made not of steel, but of such a material, which is close in strength to it, then when the hammer rotates, the pseudo-elastic cable will stretch 20 times stronger than steel. And this, as athletes - hammer throwers are well aware, will provide a significant, almost 20%, increase in the range of the projectile. The material of the cable is not regulated in the rules, so there will be no violations!

The fiberglass pole instead of bamboo helped to raise the records of jumps, so the cable made of pseudoelastic material will raise the records of throwers. Athletes, do not hesitate, records are waiting for you!

There remains one more material that has a huge elastic deformation, though not so strong. This is a rubber familiar to all of us. It works best in tension, while accumulating ten times more specific energy than steel springs. However, for machines it is necessary that, as in clockwork springs, the accumulator shaft be twisted.

With this in mind, the author designed an elastic coupling-accumulator (Fig. 75). Rubber bands, fixed at the ends on the driving and driven half-couplings, rest on light, freely seated intermediate support disks (made, for example, of plastic) on the axis, and with relative rotation of the half-couplings, take the position of a helix. Since the fastening of the harnesses to the coupling halves is hinged, the rubber is practically only subjected to tension. In terms of energy intensity, this clutch is commensurate even with flywheels.

But why are rubber elements, having such valuable qualities, not widely used as energy storage devices?

Rice. 75. Rubber clutch - energy accumulator: 1 - drive shaft; 2 - driven coupling half; 3 - rubber bands; 4 - supporting intermediate discs

If you deform, for example, stretch, a rubber elastic element and write down the dependence of the force on the displacement of its end, then the stretching curve of rubber when energy is accumulated in it will differ from the curve of its contraction when energy is released. These two curves form the so-called hysteresis loop, which characterizes the energy losses due to elastic hysteresis (Fig. 76). And the more you stretch the rubber, i.e., accumulate energy in it, the higher the losses due to elastic hysteresis. In addition, the longer the energy is stored in the stretched rubber, the larger the hysteresis loop and the less energy will be returned back; hysteresis losses gradually destroy the rubber, and its properties change. All this (we are not talking about other disadvantages) limits the use of rubber elastic elements for energy storage in accurate, durable and reliable devices and machines. Rubber energy accumulators are widely used in models as rubber motors.

Rice. 76. Graph of the stretching of the rubber band

And the fact that rubber is much more suitable for energy storage than a spring is evidenced by the fact that many models of aircraft and helicopters fly with rubber engines, and not a single model has yet taken to the air with a spring!

How to help Formula 1?

And, in fact, not only Formula 1, but any car - to become more dynamic. It's just that in Formula 1 it would have looked more spectacular.

If the flywheel is such a capacious energy store, then why not vehicles like from the engine? Spin the flywheel with an electric motor - and let's go!

Yes, there are such transport machines, for example, trolleys for intra-factory transportation (Fig. 77). They go forward and backward, and can stop. Only they cannot change the speed on their own, it changes itself - everything decreases as the energy reserve in the flywheel decreases.

Rice. 77. Flywheel cargo trolley:

1 - reducer; 2 - the handle of the move and reverse; 3 - clutch handle; 4 - flywheel; 5 - electric motor; 6 - platform; 7 - chassis

Rice. 78. Swiss flywheel bus - gyrobus (a) and its flywheel (b)

For a car, this behavior is unacceptable. He must change his speed as the driver wants. To do this, there must be a continuously variable transmission between the flywheel and the wheels of the machine. A speed gearbox is not suitable here, each gear change here will be accompanied by a blow and prolonged slipping of the clutch - there will not be enough flywheel energy. Therefore, in the very first flywheel bus - a gyrobus, built back in the 1950s. in Switzerland (Fig. 78, a), a continuously variable electric transmission was used. The gyrobus went in Switzerland, Belgium, even in Africa, passed between recharging the flywheel (Fig. 78, b) 1.5 km on routes up to 10 km long. But despite the appearance of such gyrobuses up to the present time either in Europe or in America, it is difficult to call them promising. As, however, and any car that runs on stored energy, including all the vaunted electric vehicles. The author undertakes to prove this in a nutshell.

The first is that if all cars are converted to electric cars, or mahomobiles, like a gyrobus, then the energy of power plants around the world will not be enough to recharge their drives. At the same time, it is no longer enough everywhere, and so, and here cars will be connected, the total capacity of which is many times greater than the capacity of all power plants in the world. Secondly, if you calculate the efficiency of a conventional power plant with current conversion and its transfer to the required distance, taking into account losses in the charger and battery, you can shed a tear. This efficiency will be significantly less than the 40% that a diesel engine can provide at best. And even more so those 60-70% that are provided by the so-called fuel cells or electrochemical generators, directly, silently and environmentally friendly converting fuel energy into electricity.

So, in general, no drive is needed on the car? No, it is needed, only for a slightly different purpose. The fact is that the engine almost never works on a car with maximum efficiency. To do this, it must operate at almost maximum power, i.e., to make it clearer to drivers, the accelerator pedal must be rested on the floor (Fig. 79). This happens either at top speed (usually at least 150-160 km / h for modern cars) or during overtaking maneuvers. In a city, for example, the average engine power is less than one tenth of the installed one. In this case, the efficiency is 5 - 7%, which can be seen from the fuel consumption. And driving, for example, at a speed of 160 km / h is uneconomical - all the fuel is spent on churning the air, and dangerous - on most routes this will not be allowed by the traffic police.

Rice. 79. Dependence of the engine efficiency on its load in terms of power

What to do to make the engine always work in the optimal, most economical mode? With a flywheel it's very easy. The low power engine is constantly running at its optimum mode, giving all the energy generated at maximum efficiency to the flywheel. The flywheel in this case acts as a "bank" for energy (Fig. 80). If this "bank" overflowed, the engine is automatically switched off. The car receives movement from the flywheel through a continuously variable gearbox. In addition to the fact that the car uses the most "economical" energy for movement, on descents and when braking, excess energy is not lost in the brakes, but goes back to the flywheel. This process is called recuperation, and it further increases the efficiency of the vehicle, which can result in engine efficiency even higher than its maximum.

Rice. 80. Scheme of a hybrid power unit of a car: 1 - engine; 2 - continuously variable transmission; 3 - flywheel

A slightly different situation is with an electric vehicle using fuel cells. If you remember, only such electric vehicles do not consume scarce and expensive energy from the network, but they themselves extract it from fuel with an efficiency that exceeds the efficiency of thermal power plants. But fuel cells have one major drawback - they do not provide much power. 60 W per 1 kg of mass for them is the limit when their efficiency is still acceptable. For 60 kW - the average power of a car - they need 1 ton; it is the same as the weight of the car itself. But you still need an electric motor, which is very heavy at high power.

Rice. 81. Scheme of the new concept of the power unit of an electric vehicle:

1 - fuel cells; 2 – accelerating electric motor; 3 - super flywheel; 4 - continuously variable transmission

How can a flywheel help an electric car? Yes, almost the same as in the previous case. Small fuel cell, weighing 15 kg, constantly accelerates through a small but high-speed electric motor (10 kW power, weighing 10 kg), a small flywheel (super flywheel weighing 10 kg), and from there energy is transmitted through a continuously variable transmission to the wheels (Fig. 81). Braking and descending add energy to the flywheel just like before. The power unit turns out to be so small that it fits in a standard car body, instead of the usual one, with an engine. The developer of a new concept of an electric car is the author of these lines.

You have probably noticed that in all of these cases, the power unit with a flywheel, called a hybrid, or combined, requires a continuously variable transmission. This is the main difficulty and complexity of such a unit. Such stepless transmissions are different - electric, hydraulic or mechanical. Preferably, of course, mechanical ones, since they do not convert the form of energy, they are compact and economical.

But the question arises: is this continuously variable transmission, so complicated and expensive, really necessary? After all, if instead of a flywheel there was a mainspring, which happens on toy mechanical cars, no continuously variable transmission is needed. The mainspring has a so-called "soft" characteristic that does not require a continuously variable transmission. The clockwork spring can move a motionless car from its place, “drive” it already at high speed, if necessary, on the descent or when braking the car, “take its energy upon itself”. The spring can do everything, but there is one problem: the energy intensity of the springs is extremely small - thousands of times less than that of super flywheels. It is not suitable for long runs: a hundred or two meters is the limit for a toy. But…

Still before Patriotic War 1941-1945 an artillery fuze containing a miniature mainspring was observed to fire earlier than it should. Scientists realized that this is due to the rotation of the projectile, which is quite fast and arises from the rifling in the barrel. If the spring is rotated, its coils tend to the periphery (all due to the property of inertia) with great force, the spring, as it were, increases its force thousands of times. But this is the same tape super-flywheel, only not all the turns are fastened together - the internal ones begin to play the role of spring turns (Fig. 82). Such "soft" or "spring" super-flywheels, invented by the author of these lines, have already been created, though so far in the form of prototypes, but tests have shown their performance. Such a “soft” flywheel can accelerate a car without using a continuously variable transmission; it is also possible to recover (reuse) energy during braking and descents. Of course, such a “soft” flywheel cannot completely replace a hybrid power unit with a super flywheel and a continuously variable transmission.

Rice. 82. "Soft" superflywheel

But for a racing car, for example, such a flywheel is a gift. Imagine that even a small such flywheel weighing about 10 kg can provide additional power of hundreds of kilowatts for 10-15 seconds, which would help, for example, Formula 1 to overtake its rivals during maneuvers. Calculations showed that a racing car equipped with the same engine as other cars, but supplemented with a "soft" flywheel, would be invincible.

Only one thing can interfere here - the rules of the competition are very strict. But about the size and design of the flywheel, which, in principle, each engine is equipped with, there is not a word here yet! Hurry, athletes!

Does the perpetual motion machine rotate?

For some reason, the possibility of creating "perpetual motion machines" has been associated with rotation since the Middle Ages. A “perpetual motion machine” is such an imaginary mechanism that moves itself non-stop and, in addition, does some other useful work (for example, lifts a load, pumps water, etc.). No one has yet been able to build such a thing, although attempts have been made since ancient times. The futility of these attempts led people to the firm conviction that a "perpetual motion machine" is impossible, and to the establishment of the well-known law of conservation of energy - the fundamental statement of modern science.

On fig. 83 presents one of the oldest designs of "perpetual motion" rotary action, and to this day invented by fanatics (or, as they say now, fans) of this idea. Folding rods with weights at the ends are attached to the periphery of the wheel. In any position of the wheel, the weights on the right side of it will be thrown farther from the center than on the left, and this half must always pull the left, making the wheel rotate forever. Meanwhile, if such an engine is made, it will not rotate. What is the inventor's mistake?

Rice. 83. Medieval "perpetuum mobile" with rods

Although the weights on the right side are always thrown further from the center, but the number of these weights is less than on the left. For example, there are 4 weights on the right, and 8 on the left. The whole system is balanced, the wheel will not rotate, but after making several swings back and forth, it will stop.

Already in the century before last, it was proved that it is impossible to build an eternal self-propelled mechanism that still performs work. To work on such a task is a hopeless business. In the Middle Ages, people spent a lot of time and effort on the invention of the "perpetual motion machine" (in Latin - perpetuum mobile), but all in vain.

Our great mechanic I.P. Kulibin, who created many inventions, and in particular the first flywheel carriage - the "self-running carriage", spent a lot of time and effort on the construction of "perpetual motion machines". If such great person, who was well versed in mechanics, was engaged in this business, then what was less literate to do?

Many "perpetual motion machines" were invented, but, of course, they did not work. In each case, the inventors overlooked some circumstance that confused everything they had planned.

Here is another example of an unrealistic perpetual motion machine: a wheel with heavy balls rolling in it (Fig. 84). The inventor believed that the balls located on one side of the wheel, closer to the edge, would cause the wheel to spin with their weight. Of course, this will not happen - for the same reason as in the previous case.

Rice. 84. Perpetuum mobile with heavy balls

Very often, the rotation of flywheels, especially those placed in a vacuum and suspended on magnetic bearings that rotate for many days, evokes an analogy with a "perpetual motion machine". But at the same time, such a flywheel useful work does not commit, it just spins, slowly expending the stored energy.

By the way, when watching a rotating flywheel, one gets the feeling that it is losing weight. Weighing such rotating flywheel disks gave the same result - the rotating disk weighed less than the stationary one. Aerodynamics is to blame here - a rotating disk drives away air, creating a rarefaction at both ends. From below, this rarefaction attracts the scales, pressing it against the tip of the disk, and upwards, the rarefaction draws the disk freely (see the diagram in Fig. 85). Here is the reason for the "anti-gravity", about which so much has been written and talked about.

Rice. 85. Why does a rotating flywheel weigh less than a fixed one: 1 - flywheel; 2 - bowl of scales

I must say that creates the effect of "anti-gravity" and the flywheel, rotating even in a vacuum. This confused people even with advanced degrees. Here is a much more “subtle” phenomenon. The fact is that due to friction in the prisms (supports) of the scales, a vibrating body will always seem lighter than the same motionless one. And a rotating flywheel always vibrates at least a little due to imbalance.

But back to perpetual motion machines. One of the most successful creators of perpetual motion machines, who lived until the end of his days on the income received for demonstrating his machine, was the German Besler, who acted under the pseudonym Orfireus (1680-1745). Here is how the well-known popularizer of science Ya. I. Perelman spoke about this invention.

The accompanying drawing (Fig. 86), borrowed from an old book, shows the Orphyreus machine as it was in 1714. You see a large wheel, which, as it were, not only rotated by itself, but also lifted a heavy load to a considerable height.

Rice. 86. "Self-propelled wheel" of Orphyreus, which was almost bought by Peter I (ancient drawing)

The fame of the miraculous invention, which the learned doctor first showed at fairs, quickly spread throughout Germany, Orphyreus soon acquired powerful patrons. He became interested in the Polish king, then the Landgrave of Hesse-Kassel. The latter provided the inventor with his lock and tested the machine in every possible way.

So, in 1717, on November 12, the engine, which was in a secluded room, was put into action; then the room was locked up, sealed and left under the watchful guard of two grenadiers. For 14 days, no one dared even approach the room where the mysterious wheel was spinning. Only on November 26, the seals were removed and the landgrave with his retinue entered the premises. And what? The wheel was still turning "with relentless speed." The car was stopped, carefully inspected, then put into motion again. For 40 days, the premises again remained sealed; Grenadiers guarded at the door for 40 days. And when the seals were removed on January 4, 1718, the expert commission found the wheel in motion!

Landgraf was not satisfied with this either: a third experiment was made - the engine was sealed for 2 whole months. And yet, after the expiration of the term, he was found moving!

The inventor received an official certificate from the admiring landgrave that his “perpetual motion machine” makes 50 revolutions per minute, is able to lift 16 kg to a height of 1.5 m, and can also drive a bellows and a grinder. With this certificate, Orphyreus wandered around Europe. He probably received a decent income if he agreed to give up his car to Peter I for at least 100 thousand rubles.

The news of such an amazing invention of Dr. Orphyreus quickly spread throughout Europe, penetrating far beyond the borders of Germany. She also reached Peter, greatly interested the tsar, who was greedy for all sorts of "cunning colossus".

Peter drew attention to the Orphyreus wheel back in 1715, during his stay abroad, and at the same time instructed A.I. Osterman, a well-known diplomat, to get to know this invention better; the latter soon sent a detailed report on the engine, although he did not manage to see the machine itself. Peter was even going to invite Orphyreus, as an outstanding inventor, to his service and instructed to ask Christian Wolff, a famous philosopher of that time (teacher of Lomonosov), to ask about him.

The famous inventor received flattering offers from everywhere. The great ones of this world showered him with high favors; poets composed odes and hymns in honor of his wonderful wheel. But there were also ill-wishers who suspected a skillful deception here. There were daredevils who openly accused Orphyreus of knavery; a prize of 1,000 marks was offered to those who would expose the fraud. In one of the pamphlets, written with a denunciatory purpose, we find the drawing reproduced here. The secret of the "perpetual motion machine", according to the whistleblower, lies simply in the fact that a skillfully hidden person pulls a rope wound imperceptibly to observers on a part of the wheel axle hidden in the rack (Fig. 87).

Rice. 87. Revealing the secret of the wheel of Orphyreus (old drawing)

The subtle trickery was revealed by chance only because the "learned doctor" quarreled with his wife and maid, who were initiated into his secret. If this did not happen, we would probably still remain at a loss about the "perpetual motion machine" that made so much noise. It turns out that the "perpetual motion machine" was indeed set in motion by hidden people, imperceptibly pulling on a thin cord. These people were the brother of the inventor and his maid.

But real scientists even of those times were sharply against "perpetual motion machines". The envoy of Peter I, Schumacher, who was instructed by the emperor to study the issue of "perpetual motion machines", wrote to St. Petersburg that French and English scientists "revere all of these repetitive mobiles and say that they are against mathematical principles."

Perpetuum mobile with a human face

It is not clear why people spent so much energy searching for a "perpetual motion machine" when there is an inexhaustible sea of ​​​​energy around. Isn't it easier to install a windmill and use it to get free wind energy than to spend your life creating the most complex and, most importantly, inoperable "perpetual motion machines"? At a time when Kulibin uselessly wasted his life and talent on perpetual motion machines, millers were grinding grain on absolutely free and free wind energy and flowing water.

But since we are talking about "wonderful" mechanisms, we will continue this topic. We already know that a body cannot set itself in motion by internal forces. But can it bring itself into rotation by the same internal forces? According to the laws of mechanics, the question implies a sharply negative answer. But let's do a simple experiment that seems to prove the opposite. To do this, we need a device called the platform, or bench, Zhukovsky (see Fig. 53). These are usually available in schools in physical classrooms, but it is not difficult to make it yourself, at least from two wooden disks, a metal axis and two bearings. The Grace discs sold in stores are unsuitable here due to the high resistance to rotation.

So, first experience. Let's stand on Zhukovsky's bench and try to unwind. If the resistances in the bearings are very small (namely, we need such a device!), We will not succeed. We turn our hands to the right, we ourselves move to the left. We return the hands to their original place, and the body takes its previous position. It would seem that everything is within the framework of the laws of mechanics.

But try to make such an experience. Take your right hand to the side, preferably with some kind of weight - a dumbbell, an iron, etc., and sharply move it to the left. The body will rotate from left to right. Then carefully raise the same hand up, and, passing it through the top in the plane of the axis of rotation, lower it in the opposite direction. Then repeat the first movement again. Continuing to perform these seemingly absurd exercises, we steadily turn ourselves with our own internal forces in the same direction, clearly violating the laws of mechanics.

And the second experience is truly shocking at first sight. Place Zhukovsky's bench slightly inclined, placing, for example, a book, a tablet, and the like under it on one side. The inclination of the disc should be something around 5°. Then stand on this disc and you will feel... that you are starting to spin! On their own, without any outside help or body movements. Usually it is impossible to stay on such a disk for more than a minute, and a person in the most ridiculous poses flies to the floor.

When the author first made a Zhukovsky bench for himself and placed it in the hallway, where the floor was uneven, he experienced this “self-unrolling”. Being a professor of mechanics and not believing in miracles, the author spent almost the whole night jumping up on the disk, which, of course, spun it and threw it to the floor without fail. By morning, the author did two important things: firstly, he learned to hold on to the invented “self-unwinder”, and secondly, he understood why all this was happening.

"Self-roller" made such a stunning impression on the "experimenters" that it was shown on television, where the author on the street suggested that passers-by stand on the disk and hold on. None of the passers-by could do this, and the author jokingly called this device a "perpetual motion machine."

Television is a terrible force, because millions watch it. Soon the author was bombarded with letters, to which, with all his desire, he could not answer. Everyone asked to sell them a "perpetual motion machine". Who for what - lighting the apartment, churning oil, other household needs. I must tell the truth: the author still sold several discs. But not as a "perpetual motion machine", but as an attraction. Moreover, it was bought by entrepreneurs from the United States and other foreign countries.

On the next transfer (there was such a scientific and educational TV program “You Can Do It”), the author already spoke in detail about the device of this “perpetual motion machine” and the principle of its operation. Here he is.

The fact is that, standing obliquely, a person instinctively tries to straighten up, to stand upright. At the same time, the pressure of the person's soles on the disk is shifted to its upper half (do not forget that the disk is tilted!), And, of course, it rotates. This disk, like an inclined scale, if it "feels" an overload of one "bowl" (half of the disk), then immediately lowers it and raises the empty bowl. The person automatically tries to straighten up again and puts pressure on the upper half again. And so on until the disk drops it to the floor due to rapid rotation. Of course, a weight or a statue of a person placed on a disk will remain motionless on it. So, standing like a statue, the author learned to stay on the disk in the morning ...

This is the principle of operation of the “perpetual motion machine” “with a human face”. Now for the first experience. The author deliberately complicated it, making intricate movements with his hand to make it harder to guess. You can also rotate like this: twist a hand with a load over your head. In this case, the body will rotate in the other direction according to all the laws of mechanics. It is the “human face” that confuses everyone here. The “human face” is turning, which means that there is rotation, and it seems that the person is turning without the application of external forces. After all, a hand with a load does not have a “face”, so we do not consider its movement to be rotation, but in vain ... The most common rotation around an axis. By the way, in a fall, this is how cats maintain their balance, falling on their paws. At the beginning of the fall, even with its back down, the cat automatically assesses where it is closer and more convenient for her to turn, and then begins to quickly rotate her protruding tail in the opposite direction. The body, of course, turns into another ... This is how this cute animal uses the laws of mechanics.

But imagine that we still want to receive energy from a person. Not spinning on the disk, of course, but for example, spinning the pedals associated with the generator. By the way, such sentences often have to be read even in serious literature. The average person, judging by the calorie content of the food he eats and drinks he drinks (by the way, even vodka is very high in calories!), Could slightly heat the apartment. But do not illuminate, because this will require a power of 150-300 watts. And such power throughout the day - 6 - 8 hours and not any horse will "pull".

After all, to determine the standard of power, one of the strongest horses was driven to death while developing a power of 1 horsepower (736 W) for several hours.

Now let's talk about the person. What is 150 W in relation to a person? This is a pound weight lifted from the ground to an outstretched arm (snatch) every 2 seconds continuously; the center of mass of the kettlebell rises at the same time by about 2 m. The author himself is not a weak person, a weightlifter, he regularly trains, but after 3 minutes of such work he was already sweating from the load. Try the same, measure the time during which you master this exercise, and then divide 6 - 8 hours by the resulting time, expressed in hours. I am sure that you will get a two- or even three-digit figure. That's how many times the human capabilities are exaggerated.

Smaller powers are more easily tolerated by a person. It is best to measure them on an exercise bike, where on modern devices the power is displayed directly on the scoreboard, and on old simplified models, the devices (dynamometer and speedometer) show the strength and speed given to the rim of the wheel of the simulator. Express the force in newtons and the speed in meters per second, and multiply the force by the speed to get the power in watts.

What about the average power for, for example, 7 hours? Sit on an exercise bike and try to develop a constant power for some period of time. This can actually be done by putting the dynamometer on a constant load and maintaining a constant pedaling speed, with the help of a speedometer. Then multiply the received power by the time of your work and get the work in joules. On modern expensive simulators, this figure is obtained automatically even with variable load. Working and resting for 7 hours, adding up the amount of work received, you determine the work done by you in 7 hours, that is, in 25,200 seconds. Divide the work in joules by the time in seconds to get the power in watts. Do not be upset if you get a very small average power, this is true. Unless, of course, you are an Olympic champion in cycling.

Speaking of champions. Highly strong people(for example, weightlifters) when jerking the bar, they can develop 1.5 - 2 kW, but for a very short time - 2 - 3 seconds, no more. And the average power of an ordinary person for 6 - 8 hours, alas, is very close to the power of a flashlight and is equal to only a few watts. A slow cyclist develops 20 watts, but try riding continuously for 7 hours!

Meanwhile, in reference books on physics one has to read that the average power of a person is exactly 150-300 watts. So keep in mind that this power is not mechanical, but mostly thermal. Let's say the hostess sweeps the room: she spends about 20 watts on mechanical work, and the rest on heating the room!

So, you can’t rely on any solid human power, for example, to move large muscle cars, muscle cars, etc.!

Is it possible to move the earth's axis?

Let's go back to our Earth. We already know that the Earth's axis is inclined to the plane of its revolution around the Sun, we know that it precesses, we know how to determine the direction of precession and gyroscopic momentum. And with such knowledge, we can try to get energy even from the rotation of the Earth. The moon still slows down the Earth, and spends all the energy of its rotation on the ebbs and flows of the oceans. So let's try to "take away" at least a part of this energy.

Imagine a huge flywheel at the Earth's pole rotating in a plane perpendicular to the Earth's plane of rotation. If the flywheel simply passively resisted any change in the position of the axis in space, then the plane of its rotation would remain motionless, and the Earth would rotate around it. This relative rotation could be picked up by the generators and we would get free electricity.

This project is, of course, easy to expose. We already know that a rotating flywheel does not just passively resist turning its axis, but precesses. And this precession will very soon align the axis of rotation of the flywheel with the axis of rotation of the Earth, and then the extraction of energy will end.

Rice. 88. The project of using the energy of the rotation of the Earth: a flywheel on a spring

Here is another project that is not so easy to expose. The flywheel sits in a frame on a torsion spring and, oscillating, turns in one direction or the other (Fig. 88). For simplicity, losses in the spring and aerodynamic losses will be neglected. So, when the flywheel rotates in one direction, it will precess in one direction, when the rotation changes, it will precess in the other. This precession will occur under the influence of the rotation of the Earth. So, energy can be "removed" from the relative rotation all the time, since the axis of rotation of the flywheel will never be aligned with the axis of rotation of the Earth?

This, it turns out, cannot be done, since when the spring is deformed, the axis of rotation of the flywheel will change and a moment will appear that compensates for the braking moment of the Earth.

Rice. 89. Experiments with turning over a giant flywheel

Or a very simple experience. Imagine that there is a huge flywheel at the Earth's pole, rotating at the same angular velocity as the Earth itself, i.e., stationary relative to it. And then we turn the flywheel 180 ° with some powerful mechanism by the axle in bearings and bring it closer to the Earth again (Fig. 89). In this case, the flywheel will rotate in the opposite direction and the relative speed of its rotation will be 2 revolutions per day. And this speed can be easily "removed" from the flywheel, spending it on work. The flywheel will stop again, its speed will be equal to the speed of the Earth, then we will turn it again, etc. So, it is possible to gradually stop the Earth using its kinetic energy? Can the inertia of the Earth's rotation be "destroyed" without any external influence, by internal means?

Naturally, no. The explanation for this paradox lies in the fact that by turning the flywheel over, we cause a gyroscopic moment, accelerating the Earth exactly as much as it slows down when it comes into contact with the flywheel. So the speed of the Earth's rotation when the flywheel is turned over will not change in any way, although the energy will be spent on turning it over, but it will completely turn into heat when the flywheel comes into contact with the Earth.

It is now clear that energy cannot be obtained from the Earth's rotation by "internal" means. So is it possible to speed up or slow down the rotation of the Earth by internal capabilities?

It must be said that this is more of a philosophical question than a mechanical one. Judging by the previous one, we can spin our torso in one direction by rotating our arm in the other. If the hand is not considered our belonging, then we can say that we can unwind ourselves with our internal efforts.

So it is with the Earth. Every step we take, every car moving on the surface of the Earth, increases or decreases the speed of its rotation, but not by much. Is it much more possible?

Can. If, for example, you create an ocean current like the Gulf Stream, but along the equator (where possible, for example, in the Pacific Ocean), and it must necessarily pass in one direction, either along the rotation of the Earth, or against it. This can be imagined so far only in the Pacific Ocean, then this current should go to the Indian Ocean, which is quite simple to do through the straits in the islands of Oceania, then you will either need to go around Africa from the south, or greatly expand the Suez Canal, Gibraltar and Bab el-Mandeb strait, then it is best to let the flow through the Panama Canal, expanding it to the whole of Central America. Well, great goal - great costs!

On the other hand, by launching a current against the rotation of the Earth, we, by counteraction, the so-called "reactive" moment (the one with which a powerful drill twists our arms!), will spin the Earth faster. We can approach those 9-hour days that were at the origin of life on Earth.

With less energy expenditure, we can start flowing along the rotation of the Earth, that is, from west to east, and slow down the rotation of the planet. We can, in principle, make a day equal to a year, and then the land of the Earth will be turned to the Sun on one side with all the ensuing consequences both for this side and for the other, which will remain in the shadow.

But if we are concerned about the environment and do not want to create new ocean currents, then the easiest way is to install in Antarctica (at least there is land there), it is better underground with air pumped out of this dungeon, a huge flywheel made of some heavy-duty material on huge magnetic bearings (Fig. .90). Technically, of course, all this can be done, but what will be the costs? And then it will be necessary to spin this flywheel in one direction or another to accelerate or decelerate the Earth. In this case, both land and water will move together.

Rice. 90. Superflywheel in the depths of Antarctica

And finally, the sacramental question about the shift of the Earth's axis, what the heroes of Jules Verne wanted to do with a shot from a supergun. Well, this can also be arranged, using the same ocean currents, only in the meridional direction, for example, to bring the Gulf Stream to the opposite side and through the Pacific Ocean, bypassing Antarctica, and close it in the Gulf of Mexico. But this is bad for Russia - then the North Pole will begin to "advance" on our territory and finally freeze it.

You can let this flow along the same path, but in the other direction, then the North Pole will move towards Canada and further to the USA. And if we are at least accustomed to the cold, then what will the heat-loving inhabitants of America do?

It is possible to "straighten" the Earth's axis and eliminate the change seasons. It will always be summer at the equator, winter at the poles, and between them a mixture of autumn and spring. It gets boring!

Rice. 91. Flywheel to rotate the Earth's axis (diagram)

All of the above can be obtained with the same underground flywheel, only best installed at the equator (Fig. 91). In Africa, for example, or in the jungle South America- enough space! We can do it in Siberia too – there is even more space there, but the effect will be about 1.5 times weaker. Latitudes are not the same!

Naturally, all these are manipulations with the orientation of the Earth and its angular velocity, based on our fundamental internal capabilities. Nature accomplishes all this with its "external" forces and without our desire.

One thing can be said as a consolation to those who are outraged by these manipulations of the Earth. Even if we earthlings are able to build these gigantic flywheels, we will not find those colossal energy resources that could spin those flywheels. Unless, of course, we increase our energy hundreds and thousands of times!