Non-stationary processes and their reduction to a stationary form. The process of getting the system to its best condition

The process of getting the system to its best condition

First letter "o"

Second letter "p"

Third letter "t"

The last beech letter "I"

The answer to the question "The process of bringing the system to its best condition", 11 letters:
optimization

Alternative crossword questions for the word optimization

The process of bringing the system to the best (optimal) state

The process of choosing the best option available

Definition of the word optimization in dictionaries

Wikipedia Definition of a word in the Wikipedia dictionary
Optimization - modification of the system to improve its efficiency. The system can be a single computer program, a digital device, a collection of computers, or even an entire network such as the Internet. While the goal of optimization is to get the optimal ...

Economic Dictionary terms The meaning of the word in the dictionary of the Economic Glossary of Terms
determination of the values ​​of economic indicators at which the optimum is achieved, that is, the optimal, best state of the system. Most often, the optimum corresponds to the achievement of the highest result with a given resource consumption or the achievement of a given result ...

Encyclopedic Dictionary, 1998 The meaning of the word in the dictionary Encyclopedic Dictionary, 1998
the process of choosing the best possible option. The process of bringing the system to the best (optimal) state.

Big Soviet Encyclopedia Definition of the word in the dictionary Great Soviet Encyclopedia
(from Lat. optimum ≈ the best), the process of finding the extremum (global maximum or minimum) of a certain function or choosing the best (optimal) option from the set of possible ones. The most reliable way to find the best option is ...

Examples of the use of the word optimization in the literature.

Additional optimization is achieved by filtering the table before sending it, i.e.

The purposes for which mirroring is used are high availability and optimization read operations.

But even in this case, on many machines it is possible optimization if you put such an array into write-protected memory.

With his direct participation and support, the main scientific directions: network planning and control, scheduling theory and scheduling, nonlinear and stochastic programming, differential games, dynamic models of economics, methods of discrete optimization etc.

Quite complex methods are used optimization operators, which we will consider in detail in the following lectures.

To understand how to bring the initial data series to a stationary form, let us first consider what types of non-stationary processes are distinguished by classical econometrics. And there are only two of them:

  • 1) a process that is stationary in finite differences;
  • 2) a process that is not stationary in finite differences.

The first can include various processes described by trend models, as well as processes with the transition of an indicator from one level to another. They are shown in fig. 8.5.

All other non-stationary processes belong to the second type of processes.

The upper left graph in Fig. 8.5 is a non-stationary process described by a linear trend

This process will be stationary in the first differences, since taking them in such a situation entails getting rid of the tilt angle:

which leads us to permanent mathematical expectation and variance.

The lower left graph in Fig. 8.5 demonstrates a non-stationary process described by a parabola.

Rice. 8.5.

By analogy with the linear trend, it can be shown that this process will be stationary in the second differences.

In the upper right graph in Fig. 8.5 shows a non-stationary process with a change in the level of a row. Attention is drawn to the fact that until about the 20th observation, the value at t fluctuates around one constant value, and after that - around another. This series also becomes stationary in the case of taking the first differences, since in this case the constants are eliminated and all fluctuations occur already at the zero level. Note that in the series in the differences, an outlier appears corresponding to the transition to a new level after the 20th observation.

Finally, in the lower right graph in Fig. 8.5 shows a non-stationary process with a change in the angle of inclination. Until about the 20th observation, the dynamics of the process is calmer than after it. Taking the second differences in this case also brings the process to a stationary form.

Obviously, only these types economic processes are not limited (we have given only basic ones as an example) and taking the differences, unfortunately, does not always increase the forecast accuracy. And in the case of evolutionary processes, in which constant changes in all statistical parameters occur, taking the differences can, on the contrary, reduce the forecast accuracy: the series can indeed become "stationary" from a statistical point of view, but there will be little benefit from this, because already in the forecasting period, the outlined the trend may change. Therefore, bringing the series to a stationary form cannot be considered a "panacea".

To include differences in an ARMA model, the lag operator is commonly used. For example, first-order differences can be written as follows:

The second differences in the same notation take the form

Now applying the lag operator to (8.40), we obtain

In general, order differences d using the lag operator are written in the form

A difference-based moving average autoregressive model is denoted as ARIMA ( p,d,q), where the letter 1 responsible for order d integration (taken difference), and is written in a compact form

Usually in case d> 0, the constant from (8.43) is removed, since when passing from the differences to the initial data, a trend appears in the model due to it c t, and trend components in ARIMA should be described by autoregressive elements. However, sometimes the constant is left, and then such a model is called the ARIMA model with drift ("with drift").

Let us now consider, for example, what the ARIMA (2,1,1) model will represent. It is written as

To understand what such a model corresponds to, let's expand this entry:

Let's rewrite the difference in terms of the difference operator:

and expand the brackets in (8.45):

We will transfer everything except the value of the difference to the observation t, to the right:

Now to get the final value y t, you need to use formula (8.39). We get

or, equivalently,

Using the model (8.47), you can easily get a forecast one step ahead:

Unfortunately, in order to get a forecast for a larger number of steps forward, you need to use the recursive procedure we described in Section 8.1.

Note that usually when constructing an ARIMA model, the order of the differences is limited by the number d= 2. This is due to the fact that taking the second differences usually makes it possible to bring practically any non-stationary data series to a stationary form.

As you can see, the difference tool is quite convenient and fits perfectly into the ARMA model, but, of course, it is not the only tool for reducing a non-stationary series to a stationary form. Let's talk briefly about other methods.

One of the most simple methods reduction to stationarity is building a trend model based on the original data series. Having built a model of the selected trend, the researcher calculates the residuals for the model and builds the ARMA model based on them.

This method has one significant drawback - inflexibility. The trends themselves do not in any way take into account the new incoming information, therefore, the models built on their basis will be frozen. However, the use of trends in bringing the series to a stationary form allows in some cases to obtain more accurate forecasts in the long term.

A rather promising, but not very widespread alternative to taking differences is the method proposed in 1982 by E. Parzen. Its essence consists in describing the initial data series by a non-stationary AR model, and then constructing an ARMA model based on the obtained residuals. The resulting model is called ARARMA.

Another option for bringing a series of data to a stationary form is taking non-integer differences(when d becomes a non-integer number), which is achieved by expanding (l-B) d in Taylor series. The essence of the method is that taking integer differences may be redundant for some data series (stationarity may lie somewhere between d = 0 and d = 1). Difference order d in this case, it is selected automatically. ARMA is being built again on the basis of the converted row. The resulting model is called ARFIMA (AutoRegressive Fractionally Integrated Moving Average).

In addition, there is a method used to obtain constant variance (usually solving the problem of heteroscedasticity in many cases), - taking the logarithm of the original data series. It allows you to obtain a series with constant variance in cases where the error in the model is of a multiplicative nature.

Seasonal data series can also be considered non-stationary (since the variance, for example, at the beginning of the year may differ from the variance in the middle). To get rid of seasonality, you can either use one of the seasonal decomposition methods or take seasonal differences. The first solution to this problem was discussed by us in Section 6.1, and we will turn to the second in Section 8.4.

  • Makridakis Spyros, Hibon Michele. ARMA models and the Box-Jenkins Methodology // Journal of Forecasting. 1997. Vol. 16. P. 147-163.
  • Parzen E. ARARMA Models for Time Series Analysis and Forecasting // Journal of Forecasting. 1982. Vol. 1. P. 67–82.
  • Granger C. W.J., Joyeux Roselyne. An Introduction to Long-memory Time Series Models and Fractional Differencing // Journal of Time Series Analysis. 1980. Vol. 1. Issue 1. P. 15-29.

By tradition, England is considered a classic "land of ghosts", almost their homeland, if such a concept is applicable to this kind of non-material phenomena. Indeed, according to the Dictionary of the Russian Language, a ghost is "a ghost of a person, absent or dead, who appears to people with a sick imagination." In turn, a ghost is defined as “something that only appears to be real; what appears to be. " And in Encyclopedic dictionary no such phenomena are mentioned at all.

However, in England, the attitude towards ghosts is very serious. And a clear evidence of this is the existence of such at first glance, but rather respectable organizations such as the commercial company "Ghostbusters" and "The Club of Ghost Experts."

The first is headquartered in Grimsby, off the east coast of Central England. It is led by Robin Farman, a paranormal researcher and lecturer in parapsychology for 20 years. The company has a small staff: Farman's wife Sheila, a clairvoyant nicknamed the Immortal Aisha; his son Andy; two otherworldly experts, Janice Paterson and Rodney Mitchell, and Newfoundland Ben, a Farmen dog with a phenomenal flair for parapsychological manifestations.

All employees of the firm wear the same half-faith with the inscription "Ghostbusters", adorned with the corresponding design and the Grimsby coat of arms. On calls they go in the aristocratic black limousine "Austin Princesses" 1959, formerly owned by the mayor of the city. At the same time, these catchy attributes, which outwardly look like clownery, are in fact a deeply thought-out result of many years of serious work and are intended primarily to calm down frightened people by their very appearance. Because it is this category that makes up the vast majority of Farmen's clients.

When many of us read about ghosts making creepy groans or noisy poltergeists throwing a bedlam in the house, we probably think, "This will never happen to me," says Farmen. - But if, unexpectedly waking up at night in a cold sweat, you see a ghostly luminous figure in the twilight and this repeats itself over and over again, and visits to a psychoanalyst doctor do not give results, all your skepticism will surely evaporate. When furniture begins to inexplicably move around the apartment, and household items fly through the air and you hear the slamming of doors and the steps of some invisible person, then you, no doubt, will passionately want to call specialists from our company for help ...


"Ghostbusters" do not refuse anyone, no matter where the challenge comes from and no matter how fantastic it may seem. One of the company's employees - usually Farmen himself - is immediately sent to the site to meet with the person asking for help. According to Farman, the first thing to do is to establish the nature of what is happening: whether it is physical or psychological; optical illusion, play of light or the result of the special sensitivity of certain unusual people. A professional is needed here. The first person you meet is no "ghost hunter". After all, it often happens that someone was confused by a dress thrown on the back of a chair, and someone was confused by the reflection in the mirror or even on the door of a polished cabinet.

One day we went to an extremely serious man, says Farman, and during the preliminary investigation we noticed that he had a strong smell of what we thought was disinfectant in his house. When we asked what was going on with him, the owner replied that he was being attacked by some disembodied creatures. I really think such a phenomenon is possible in principle, and therefore I was ready to believe in his story.

We had already begun to negotiate about the upcoming visit of our team, when suddenly my counterpart jumped to his feet. “Look - there, there it is! - he shouted, pointing his finger somewhere in the void. - There it is! I'll finish him off now! - Taking out from behind the chair a huge canister with amanita tincture (as it turned out later), the owner of the house began fiercely puffing out of him in all directions. - Here, finished! - in the end he declared triumphantly, wiping the profuse sweat from his forehead. - With them, you understand, only like this ... ”. It turned out that cylinders with a fly agaric were prepared by him everywhere in the house and even in the car. It became absolutely clear to me that the person has hallucinations ...

More often, however, it happens that the expert comes to the conclusion that a detailed study is necessary. Then the whole group leaves for the "haunted house" with their unique equipment for detecting ghosts. The kit includes a temperature sensor connected by a long cord to the block, which gives a digital display of temperature fluctuations in the room, since, as the "ghostbusters" have established, with mysterious phenomena, it is usually observed a sharp decrease.

To measure the light radiation, "Robogost" is used - a personal computer "Eikorn", capable of recording even the smallest light radiation of living and inanimate objects. In addition, it has two more special sensors - one registers sound waves the other is vibration. The acoustic output is equipped with an amplifier, which makes it possible to hear even the "inaudible" flight of a piece of paper. In this case, if necessary, the speaker itself can be turned off, limiting ourselves to observing the screen, where the luminous ray shows the strength of the sound that occurs in the room with the sensor.

I must warn you that ghost hunting is a boring business. After the equipment is installed, it remains only to wait for the ghost to deign to appear. And because their behavior is unpredictable, the wait can drag on indefinitely. In order not to feel the hospitality of the owners, one has to set up a temporary headquarters in a local hotel, only from time to time visiting the "haunted house" to take cassettes with recordings of instrument readings.

And yet, if paranormal manifestations do take place, in the overwhelming majority of cases, sooner or later, it is possible to catch the culprit of the disturbance red-handed, - assures the head of the unusual company. - Despite the name of our company, we do not hunt for ghosts in the literal sense of the word, we do not shoot at them from some kind of neutron cannon, - he continues. -

This is nonsense, invented by journalists in pursuit of sensations. It all depends on what is happening in the client's home. It can be a ghost, a ghost, a poltergeist, his own mania - whatever. And yet - we act depending on the attitude of the owner to the observed phenomenon. People do not always want to get rid of their ghosts, it is not so rare that they just want to understand. We also come across those in whose houses ghosts sometimes appear, but the owners keep on friendly terms with them - the spirits become almost family members.

If someone perceives him as a threat, we can use pentagrams or pyramids - they help. We can invite a medium, and he will ask the ghost to state what is troubling him. After that, appropriate measures should be taken, and the unwanted visitor, most likely, will "move out of the apartment." It happens that the rooms themselves create a special atmosphere. In such cases, it is enough to simply re-paint the walls, open windows and doors, and ventilate the room well in order to change this atmosphere and calm the owners.

The phenomenon of poltergeist is another matter, says Farman. - You do not see any ghost, but suddenly a knocking starts on the walls, some footsteps are heard, trinkets fall from the mantelpiece, otherwise things start flying around the room. It scares people insanely. A poltergeist has a tendency to show up in places of misfortune and collapse of hopes, most often in the neighborhood of young people, much less often in the elderly. You cannot drive him out - he does not give in. But in order to help the possessed by him, it is possible to use the services of a priest. Besides, poltergeists are very "shy". Sometimes it is enough to start an instrumental investigation to get rid of it.

For many years, Farmen and his comrades have been dealing with mysterious phenomena, but they prefer not to dwell too much on their essence.

When we are asked: "Do you believe in ghosts?" - this is a question with a double meaning, because the word "ghost" usually means some deceased who suddenly appears to terrorize the living. I do not believe in such phenomena. But a lot of people observe ghosts of one kind or another, and I am interested in finding out what it is - something from some other, otherworldly world or some anomalies of time. There are a lot of hypotheses on this score, so a rather extensive field for research opens up here ...

This is what the Ghost Club, led by its president, Peter Underwood, does. Evidence of ghost appearances is as old as the world, and examples of this can be found in every civilization, culture, habitat around the world, he argues. Plutarch, Pliny, Socrates, Cicero - they all took the existence of ghosts for granted, and so did many other prominent personalities in human history.

The most reliable evidence, both ancient and modern, describe these phenomena not at all in the form of something ephemeral, transparent, but as ordinary people of flesh and blood, whose immaterial nature betrays itself when they suddenly disappear under the most mysterious circumstances.

Ghosts do not appear only in human form. People often see animals, especially horses and dogs, perhaps because they have long lived next to humans. Ghosts and inanimate objects have been observed, including something like; (there is a dangerous turn on one road in Scotland, where, according to evidence different people, a small blue car appears and disappears); ghost trains (Abraham Lincoln's funeral train is said to have been seen for several years, each time in April, at New York Central railroad slowly and sadly returning to Illinois). After all, there is a lot of evidence of "ephemeral" furniture, such as armchairs, which some ghosts like to sit in.

Over the years of research, the club's experts have revealed interesting facts about the "localization" of ghosts. It turned out that, for example, among public buildings they prefer churches, and among residential buildings - houses of priests. It is not surprising, therefore, that most often ghosts appear in the form of a monk or nun, although they have many other images as well.

There is an interesting photograph of the ghost on the Tulip stairs at the Queen's House in Greenwich. It was taken in 1966 by Priest Hardy and his wife, who repeatedly saw someone's ghost at this place and finally decided to try to photograph it, says Peter Underwood.

At first glance, it seems that the lens captures one figure, covered with a hood, creeping up the Tulip's stairs. But if you look closely, you can see that there are two figures in the photo, and one almost completely obscures the other. You can clearly distinguish between the left hands with the same wedding rings on the same finger. Such a ring could belong to the unfortunate Queen Henrietta, whose house was built by order of her husband, King Charles I. It seems that both figures are one and the same person, captured in motion.

So how do you explain that ghosts are to humans? According to Underwood, there is no single overarching reason. As for individual special cases, he put forward an interesting hypothesis to explain them. It is now recognized that in tragic circumstances or when severely injured, people acquire an increased susceptibility. Besides, in extreme situation hidden reserves of the human body, primarily in the field of the psyche, can be released, and other unusual effects can also occur. But in order to confirm or refute this hypothesis, parapsychologists and psychoanalysts must study and systematize precisely the conditions under which people can see - and see - ghosts.

There are other types of ghosts, for example, crisis or near-death visions, while they appear no more than 4 days. Such phantoms usually appear to their relatives, friends or relatives, and later it becomes known that during these 4 days the person whose phantom they saw died or that he was sick and experienced a crisis at that time.

This kind of phenomenon was quite common during both world wars, when people were seized by deep concern for the fate of loved ones, especially if they fought somewhere thousands of kilometers away. There are many testimonies of trustworthy, mentally perfectly healthy individuals who clearly saw a relative who visited them for a moment and immediately disappeared. They later learned that the one they saw died at the very moment when his phantom appeared to them.

However, according to Peter Underwood, prolonged encounters with ghosts are much rarer than many believe, and much less frightening than we are used to thinking. Of all the cases of "meetings" with them that people talk about, 98% are due to natural reasons. And it is impossible to find them only for 2%. Moreover, recently it has been possible to find an objective criterion that makes it possible to reliably judge the authenticity of a particular ghost.

When it appears, a decrease in temperature by 8-9 ° C is invariably recorded in the immediate vicinity of the phantom in comparison with the temperature of the surrounding space. A large number of checks with the help of sensitive equipment revealed another interesting phenomenon: in the "haunted houses" in the usual places of their appearance "cold spots" are formed, which persist for a long time. At the same time, none of the experts of the club undertakes to explain why this is happening.

Underwood himself believes that this phenomenon is most likely associated with the "withdrawal" of energy from our space for the "materialization" of a ghost in it. Maybe his physical nature can be unraveled if we turn to the latest work in the field of quantum theory. We are talking about the so-called quantum inseparability, implying a "non-force", "out-of-space" and "timeless" connection of particles.

According to this hypothesis, interacting with each other elementary particles can no longer be considered as separate objects, even if they go beyond the zone of conditional interaction. They seem to eternally "remember" each other. This "quantum inseparability" essentially means that all objects that once interacted with each other, in a sense, remain connected forever.

Moreover, this fixation of quantum connections is of a “nonlocal”, “out-of-space” nature. Unlike gravity and electromagnetism, it does not arise due to any fields, but absolutely independently. Since in this case nothing real, tangible is transferred through the space separating the particles, the matter between them cannot slow down such a connection.

Extra-dimensional connections do not go anywhere, and, therefore, they are not afraid of distances. At a distance of a million miles, they are as powerful as they are in a millimeter. And because these connections "ignore" space, they also do not care about time. For an outside observer, in accordance with the theory of relativity, this effect - which occurs instantly, ahead of light, the mutual influence of particles - should seem to be moving backward in time. It is possible to assume that it is in this way, literally passing through the walls, that ghosts appear, taking energy from our space for their "materialization". And the evidence of this is the drop in temperature at the place of their appearance.

There are no firm, well-established rules in "ghostology", and in our club we are always looking for corrections for our hypotheses and ideas. We always try to keep our minds liberated and admit that there are things in the world of mechanization, standardization and automation that we cannot explain, says Peter Underwood. “And Dr. Samuel Johnson, a medieval English writer and author of the philosophical treatise Russellas, Prince of Abyssinian, was not the only person who believed that the ghost phenomenon was“ one of the most important issues, which can appear before the human mind ... This question is still not resolved now, after thousands of years of the existence of the human race. "

It seems increasingly likely that the border between that world and our world, so familiar and comfortable, is just one step away from us. The data we have collected suggests that in the course of each study of the "Club of the Ghost Experts," we may be walking along the border of the unknown all the time ...

Although Dr. Donald Carpenter, a theoretical physicist from America, was not a member of the English Ghost Club, it was the work of this society that played a major role in his decision to pursue such a mystical field as ghosts. At the same time, the matter was not at all in the physical hypotheses of Peter Underwood, although they probably contained a grain of reason. Carpenter was much more interested in the statistics of temperature fluctuations given in the works, obtained with the help of modern measuring equipment.

However, to be completely frank, it should be noted that interest in the investigations of English ghost historians, accidentally seen on the shelf of the university library, was awakened by one childhood memory of Carpenter himself. At the age of 9, he and his mother were at home when the ghost of his father, who had gone on business to another city, suddenly appeared in the room.

Later they learned that he died that very night. As an adult, Carpenter once again encountered a ghost. 1971 - He was talking to a railroad worker who, as Carpenter later found out, had died in an accident a few hours earlier.

The task that this physicist has set himself, at first glance, may seem absurd - to calculate the mass of a ghost.

To appreciate the courage of an American, one must take into account that, with rare exceptions, scientists, and especially physicists, a priori consider ghosts, spirits, and ghosts to be complete nonsense. The well-known formulation perfectly suits their attitude: "This cannot be because it can never be." In fact, they refuse in advance to consider anything that goes beyond modern scientific knowledge besides, it is difficult to reproduce with the help of experiments. Moreover, this applies not only to ghosts, but to a wide range of strange phenomena, such as UFOs, telepathy, poltergeist.

By the way, it can be recalled that at one time the French Academy of Sciences did not allow the possibility of meteorites falling to Earth, and back in the 30s it was considered an illusion.

Because the problem of the other world and everything connected with it is too vast and contradictory, before proceeding with the solution of the task, Carpenter tried to clearly define the conditions necessary for this. Studying the works of the English club took a lot of time. But in the end, he had several starting points to facilitate the work ahead.

First, only "pure" ghosts were subject to consideration, leaving out spirits, poltergeists, ghosts of animals and inanimate objects. Further it was necessary to proceed from the fact that, since the considered phenomena are homogeneous, they must have the same main characteristics.

After all, since ghosts in at least one aspect - the temperature jump when they appear - surely interact with our world, all known physical laws and no reference to magic and miracles is allowed. And the last thing. Based on the fact that, according to the descriptions of eyewitnesses, the ghosts looked like ordinary people from blood and flesh, the size of phantoms in three-dimensional space on average should be equal to 0.07 cubic meter(this is exactly the volume of a person weighing 70 kg).

It would seem that it is not so difficult to formulate the above 4 points. But this is only at first glance. Carpenter had to read hundreds of pages of eyewitness accounts, tabulating recurring points, before drawing definitive conclusions about appearance ghosts.

As a rule, it appears in front of a person face to face, and only in those cases when there are several people in the room, someone sees it from the side. A faint white glow emanates from the phantom, less often bluish or greenish, sometimes with a reddish tint, with a power of one to 20 watts. In some cases, a faint odor may be felt in the vicinity of the ghost.

Behind the impossibility of comparison, eyewitnesses define it with one word: "Strange." The sounds that the ghost makes are often limited to groans, although sometimes you can hear howls, screams, ringing of chains, some kind of "burial" laughter, very rarely - single words... The duration of the phantom phenomenon ranges from a few seconds to 10 or more minutes, with short visits being the most frequent.

So, the generalized portrait of the ghost robot is ready. And then the question arises: how does a person see a phantom? From a scientific point of view, three options are possible: the ghost excites electrochemical processes in the retina, which are transmitted along the nerves to the visual center in the cerebral cortex, forcing to see it; he can achieve the same result by acting directly on this center where the visual sensation arises; in the end, a ghost can give birth to a stream of photons in the space bordering it, and a person sees it in the same way as an image on a TV screen.

Without categorically rejecting the first two options, I still lean towards the third, - says Carpenter. - And that's why. When a ghost is observed by several people, each sees it from a different angle depending on where he is, as if he was looking at a TV screen, albeit three-dimensional. But that's not all. Since the ghost seems to be hanging in the air, it is the latter that is the substance that emits photons that "paint" the phantom. And since we have excluded magic, then the only possible explanation of this process looks like this: the flux of photons is the result of a change electronic structure atoms and molecules of air. In turn, this requires a certain amount of energy. Without going into details, suffice it to say that it is these costs of it, obviously, that cause the temperature drop in the place where the ghosts appear.

To further prove the correctness of this conclusion, Carpenter made simple, but rather convincing calculations. A ghost with a maximum luminous power of 20 watts, drawing energy from a decrease in the ambient temperature, should cause it to fall at a rate of 14.5 ° C per minute until it reaches the dew point. That is, such a temperature at which the air cools to such an extent that the water vapor contained in it is saturated and begins to condense into separate droplets.

In a normal climate, this would take just over a minute. At the same time, the ghost should have been shrouded in fog. However, this does not happen, because the air has thermal conductivity and manages to partially replenish the energy costs at the phantom boundary due to the influx of heat from the surrounding space. But where the humidity is high - on the seaside and even in England in general - and, consequently, the temperature of the dew point is higher, ghosts can often be observed as if surrounded by a light fog. A similar effect occurs when the ghost makes loud moans, for example. After all, energy is also needed to induce sound waves.

Among other things, one very important conclusion follows from the above, - says Carpenter. - Namely, that ghosts are capable of manipulating energy - converting heat into electromagnetic or sound waves. But this is only possible if they are composed of matter or energy. Because none of the thousands of observations contains any indication of the material nature of the phantom, it is possible to assume that its essence is energy. Although what this energy is, we do not yet know. Another thing is important. According to the principle of equivalence of Einstein's theory of relativity, a certain amount of energy must correspond to a certain mass, the so-called mass equivalent.

On the other hand, energy doesn't come out of nothing. It only changes its shape. Therefore, the energetic essence of ghosts is inherited by them from human body v . This is what is traditionally called "the human soul" in religion and everyday life. Therefore, the expression: "The soul left the body" - in physical sense means that this material object has lost its energetic essence. As a consequence, according to the principle of equivalence, its mass should also decrease. The difference between its initial and final size will be the mass of the ghost.

Let's move on, ”Carpenter continues. - Because we proceeded from the fact that all ghosts obey the same laws, and all energetic entities have the same mass equivalent, originally embedded in material objects, no matter who - God, a higher mind or someone else - this means, that the mass of a person's body decreases by the same constant value, which does not depend on its size. In other words, it makes no difference whether we are talking about a child or an adult ...

Unfortunately, Carpenter was unable to find reliable data from the corresponding measurements at the time of death. The only thing that the American managed to firmly establish concerned babies and boiled down to the following: it was never noted that the surface of the cradle was even slightly straightened. As a result of the experiments, the scientist was able to find out that the latter is possible only if the change in the object's mass does not exceed 1% of the original.

For babies, this figure is 22.7 grams. This means that the mass of the ghost cannot be more than this figure. As for the lower limit, then through complex calculations, Carpenter was able to calculate it - 6 grams. In other words, the mass equivalent of a phantom is in the range from 6 to 22.7 grams. To clarify and confirm Carpenter's conclusions, it would help, in his opinion, conducting further experiments using the latest highly sensitive measuring equipment and involving, for example, thousands of adult hopeless patients and elderly volunteers in them.

In addition, there are other questions to be answered. In what specific place does the energetic essence of a person, or his "soul" leave the body and in what direction does it move? When does it enter the body - at the moment of birth or even earlier? Do animals have such an energetic essence? If so, which ones? What forces determine the interaction of entities with each other? How are they affected by radiation or penetration through matter?

The difficulties are enormous. But if unbiased scientists, experimenters and observers manage to overcome them, an important breakthrough will be made in revealing many mysteries of nature, man, religious beliefs, and even in the knowledge of the Universe.

It is not yet possible to fully assess the significance of the results obtained, says Carpenter. - Another thing is unclear. Namely, in what direction may further research go in the future. And yet I believe that an important step has been taken: now it is possible to consider as scientifically proven the fact that the mysterious "something" that gives rise to the phenomenon of ghosts does not belong at all to the field of the human psyche, but to the world of physical phenomena.

The future will show the validity of the hypothesis proposed by Dr. Donald Carpenter. Moreover, in the case of its confirmation, a revaluation of many of what is considered an immutable truth is inevitable. But even now, the clear and clear logic of Carpenter's conclusions convincingly testifies that there is nothing supernatural, magical in the phenomenon of ghosts, since the natural laws of nature apply to them. It's just that not all of them are known to us yet.

focus on how it will reinforce and enrich your initial understanding of your beliefs and values.

9. Transfer your vision, identification, beliefs and values ​​into the “ability” space. Notice how this enhances, changes, or enriches your sense of your own abilities.

10. Transfer your vision, identification, beliefs, values ​​and abilities into the “action” space. Please note that even the most seemingly independent actions are a reflection and manifestation of your experience at all higher levels.

11. Transfer all the experience gained to the environment space and note how it has changed and enriched.

12. Remember the feeling of the state of conformity. Imagine yourself in this state at that moment and in the place when and where you will most of all need it.

This procedure can be done alone or with another person who will act as a consultant or “guide”. Reproduced below is a recording showing how one person can lead another in the process of creating a match state.

RD I would like to demonstrate the alignment process with Jay. To begin with, we will designate the physical space for each of the levels: environment, actions, abilities, beliefs. a values, identity and spirituality. I usually prefer to line them up, so that you move backward from the environment level to the spirituality level, and move forward from the spirituality level to the environment level.

Jay. Good.

RD And what I want to ask you first of all is to stand in the position of the environment and think under what conditions you would like to be in a state of greater personal conformity.

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Jay. Well, I am a manager and I would like to be more consistent in my work.

RD Can you describe the conditions in which you act as a manager? Answer the question: where and when do you function as a manager? Tell us when and where you do your job.

Jay. I am usually in my office at our headquarters. I can also be in the conference room, which is similar to this, but slightly smaller. Lots of people come and go. I interact with about a dozen key people a day. This usually happens all week, sometimes on weekends.

R. D. So. Very good. (Audience) Note that Jay speaks exclusively in the language of facts, which is quite consistent with the description at the environmental level. Your environment is just what you see and hear around you. People often try to make judgments or interpretations about their environment instead of simply describing what they see and hear. If someone says, “I work in a hostile environment,” that is his judgment about the environment. In doing our exercise, it is very important at this level to describe only on the basis of the information provided by your senses, as Jay does.



(To Jay) Now I want you to move to the position of "action" and describe what actions you perform when you effectively manage people in the place and in specified time... Answer the questions: what do you want to do in greater quantity in the "where" and "when" indicated by you? What actions do you perform when you function in this place and at this time as an effective manager?

Jay. I can stand, sit or walk. Sometimes I talk, sometimes I suggest ideas, sometimes I negotiate with people. Sometimes I try to support the person by asking questions, saying or writing something down. So I listen, I ask questions, I try to get an idea of ​​what the person is saying and doing, and then I try to guide him or keep him on the right track.

R. D. Good. (Audience) Note again that Jay is simply describing certain actions without giving any interpretation. If he said, “I behave well or badly,” that would be a judgment regarding his actions. In performing this exercise, at the action level, describe what could

From vision to action

capture a video camera while it is at your workplace. The camcorder does not make judgments and does not offer interpretations, it just records.

(To Jay) I would like you to stay at this level a little longer and try to identify some "micro-actions" that can accompany your state of "greater conformity". Pay attention to your body and try to understand which postures correspond to the state of "conformity" when you are sitting, standing or walking in your office. How do you hold your body?

Jay(straightens up and takes a collected pose). I stand or sit more evenly and erect. I believe my head is tilted back and slightly raised.

RD And what do you do with your hands? What gestures do you make while in a state of "conformity"?

Jay(making appropriate gestures). I think that I more often stretch out my hands in the direction of the interlocutor and more often look into his eyes.

RD Do you notice any differences or peculiarities in your breathing when you are in a state of "conformity"?

Jay. It is slower and deeper.

RD Great. Now I want you to move into the position of ability. Here I invite you to answer how you manage to do these “what” in the conditions of these “where” and “when”. In other words, what know-how or mental strategies and skills do you need to listen, ask questions, and guide people in a balanced, direct, clear and even manner?

Jay. Well, I have to use the ability to structure and organize information. I need my professional knowledge to translate this structure into words and actions. I also need the ability to take the position of another person to see what is happening from his point of view. And I also need the ability to take the position of an outside observer in order to see the relationship between me and other people. Also I have to use the ability to create a picture of what I am going to do.

^ ШШ Chapter 2 _____________________________________________

R. D. Good. (Audience) Notice how Jay's physiology changes every time he goes to a new level. The number of gestures and movements increases. Each next level involves an increasing part of his personality and, consequently, the nervous system. At the level of the environment, he practically did not move at all. At the action level, he began to gesture and turn slightly. On an ability level, you might have noticed the movements of his eyes and the way he looked around as he listed his abilities and skills. You can also note the changes in the timbre of his voice at various levels. Now he speaks a little more slowly and in a lower voice. The vocabulary has also changed. All this points to the participation of an increasingly diverse personal processes... at

(To Jay) What kind mental processes do you need to maintain the physical manifestations of your "fit" state? What inner abilities allow you to be balanced and direct, make gestures towards the interlocutor, breathe more deeply and speak softer and more clearly?

Jay. This is the ability to clearly see the goal in front of you and realize how much it corresponds to the situation. It is also the ability to maintain feedback with oneself and with other people. I believe that first of all it is the ability to be aware of myself and what I want and the quality of my relationships with employees.

RD Wonderful. Now I ask you to move to the position of beliefs and answer the question: why do you use the listed abilities to "act in this way and in such conditions? Why did you decide to use your ability to structure information, put structure into words, look at things from different points of view , create a picture of what you are going to do, be aware of yourself and others, and get feedback What beliefs and values ​​have led you to use this know-how and act in that way at that time and place?

Jay. Well, I believe in respect, respect for other people. I also believe in good relationship... I believe that the support I give to other people and to myself will allow me to achieve more together. I believe that it is very important to achieve integrity and that it is good to have a lot of skills in order to do something.

RD So you value respect, attitude, support, skill, and integrity. These are important and weighty values. (Audience) On this

From vision to action

At the level we investigate the question: what beliefs do you have about yourself, people and your business? What beliefs are guiding you? Notice that Jay's voice has gotten even lower. It's like you can hear his words better. He speaks from the heart.

(To Jay) Now I invite you to move to the position of identification and answer the questions: “Who am I, in my essence, am I, the one who respects the lives of other people, wants to have good relationships, to support people who value skill and believe in integrity? Who am I if I use my mind to create structure, put it into words, see things from different perspectives, have a clear vision of the future, and maintain awareness of myself and my purpose? Who am I if I have to develop the strength to come up with ideas to sit, stand, stroll, listen, ask questions and answer people in those rooms during the week and sometimes on weekends in the part of the planet where my office is located? Who am I as a manager? "

What type of manager are you? What kind of person are you? What metaphor can you use for yourself and your mission?

Jay (pause). Well, one metaphor might be this: I am a kind of beacon. I am a beacon that shows people the way and helps them achieve their goals.

RD So, you are a kind of beacon that supports people and shows them the direction. It is a metaphor or symbol for how you are aware of your identity or mission.

Now I want to ask you to take the last step, to go beyond what you are a beacon, and move to a higher position, into what can be called "spirituality." While in this position, think about your vision. Imagine that you can see for a short time something that is beyond your life and your identification. What is your goal? How do you serve your identity as a beacon? What does this beacon show? What vision does your mission support?

The question here is: “What kind of vision is associated for me with the image of a beacon and a manager who values ​​respect, support, skill and integrity? What vision do I have as someone who structures and expresses the goals that he sees in his thoughts, who looks at things from different points of view, maintains awareness and receives feedback on what is happening within him and between him and others? What vision do I have when I sit walking

eV & STEP. Chapter 2

and I listen, breathe deeply and speak softly but clearly, stand up straight and level, addressing a group of twelve or so people, in that office, in that meeting room? "

Jay (long pause). It has something to do with congruence and integrity, but I don't know how to put it into words.

R. D. Take your time. These words are very important. There is no need to adjust them. Let them appear or emerge from your subconscious. Just describe what happens as you experience it. Maybe it's just a color or some kind of image.

Jay (pause). I see something that resembles big ball or a planet. Most of the planet is lit, but there are dark areas. Some areas are in complete darkness, while others are only slightly shaded. But in those places that are in darkness at this time, people need beacons that help them find their way out of darkness. I'm not the only lighthouse. There are many of them, but since they are very far from each other to better help travelers, they do not always realize that there are other lighthouses somewhere. But I hear some kind of noise, it is similar to those beeps in the fog, and this allows the beacon to understand that there are other beacons out there somewhere.

R. D. (audience). You can tell by the way Jay says that he is going through a very deep experience. Just look at how much his breathing has changed. We are extremely rarely open to such an experience, perhaps, with the exception of cases when we are close to death or are mortally in love. And yet in our nervous system there are always hidden resources for such an experience. We are completely absorbed in the “experience” of our daily life and forget that this life takes place within a much larger frame that is difficult to describe in words. Each of us has probably had an experience like this, but found it difficult to hold or relate to the experience of "everyday" life. Yet it is this level of experience that gives our “everyday” experience meaning and purpose. I am confident that it is possible to transfer this quality of awareness into our daily life and work.

(To Jay) Jay, I would like you to stand for a minute, continuing to fully maintain the state of awareness of this planet with areas of light and dark and beacons that recognize the presence of another beacon by beep. Be proud of him, hold him, anchor him. And then move into the identification space and transfer this state from

From vision to action

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yourself. That's right, take a step forward into the identification position and carry that vision with you. Note how being aware of the broader vision enhances and enriches your experience of who you are. If you want, you can make changes or additions to your description and metaphor for identity and mission.

Jay. I can feel it, but it's hard for me to put it into words. As if some excitement and awareness of oneself as a part of something bigger were added.

RD You are no longer just a lighthouse, it is the awareness of yourself as a particle of light and a whole network of lighthouses that help travelers find their way. And it is the thrill that this vision gave you as you brought it into your sense of identity and mission.

Jay. It is also a feeling of gratitude ... an experience of gratitude. And at the same time, it gives more energy.

RD This vision has mobilized your nervous system and filled it with energy and strength. Now I want to ask you to accept this feeling of energy and gratitude, feeling like part of a large planet and a network of beacons that shine in the dark, and move forward into the space of beliefs. Take the feeling of your vision and your mission in your heart. How have your beliefs and values ​​become solidified and enriched? Maybe some new beliefs came from the depths of your heart?

Jay. Well, at one level, I can really feel the integrity of the entire system and the importance of relationships and support. It is also a belief in the importance of growth for its own sake. As if growth were a natural result of integrity and support. It may have a purpose, but I feel like growing is good in itself, regardless of other goals. This is the first thing. And then there is the realization that I am here at this time, that I also received support and can relax, enjoy what I am doing, and appreciate it more.

RD I would like to suggest that you focus again on feeling like a vast network of beacons. For example, you might mentally hear those beeps when you feel the value of respect, support, skill, and integrity. Also, do not lose the feeling that growth is good, even if it does not serve a specific purpose, and that you belong to the present moment and can appreciate what you do even more. I want you to bring it all into the space of ability. Link your vision, your mission, your sense of integrity and

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your heart with your mind. Realize that your skills and abilities are a reflection and expression of your beliefs and values, your integrity, mission and vision. Your mind is the way these deeper structures manifest themselves. When you are fully aware of these levels of your personality, how does it enhance and enrich your perception of the abilities you have to realize your values, beliefs, integrity and vision?

Jay. I am more capable of being myself and respecting my own point of view. It is also easy for me to see other points of view and look at them from a broader and broader perspective. It is easier to understand other maps and other thinking styles. It's as if I had fewer restrictions. I can better sense where the flow of people and events is going and give direction to that flow.

R.D. Now I suggest that you go forward into the space of actions and re-experience the actions that you spoke about: listen, ask questions, lead other people, being balanced and direct, making gestures towards the interlocutor, breathing more deeply, speaking softer and more clear. Transfer a sense of your abilities, beliefs, identification and representation into your actions. Link your strengths as a manager to your mind, heart, mission and vision. Has anything changed in your experience of these actions? How has your holistic image enriched the specific actions that you perform? Perhaps the quality of what you are doing has changed.

Jay. It has changed a lot. I am more aware of what is happening around me, what I do and hear. If I explain something, I know why it should be done. I have a much stronger sense of confidence and value in my work.

R.D. Finally, I invite you to return to the environment, to those specific "where" and "when", to your headquarters, to your office, to the meeting room, to those twelve people with whom you interact every day. ... Bring your vision and sense of purpose in line with your identification, your heart and mind - with your actions in this environment. How does your perception and experience of the environment change if you bring into it the awareness of yourself as part of a network of beacons that indicate to others

From vision to action

qi direction in this environment? Also transfer here your belief in the importance of relationships, that growth is beautiful in itself, your sense of belonging, your belief in the value of respect, support, skill, and integrity. Take your ability to receive feedback from yourself and others, to understand other people's cards and see a broader perspective, and that you are less constrained and able to direct the flow of your experience. Also, bring your physiology in a state of "conformity" here, your soft but clear voice and the feeling of awareness, confidence and significance that is associated with what you are doing. Pay attention to how your experiences change and become richer.

Jay. I feel that the job may require less effort, that I can be in more contact with the environment and my employees. I am more aware of my belonging. I also feel that I can be more creative in my work.

RD You can also point out that this environment is the place to which respect, support, skill and integrity are associated. This is a place associated with a broader perspective, where it is possible to understand other people's cards and where growth is valued, regardless of whether it has an obvious purpose or not. This is the place to which you belong and where you can go beyond the old boundaries and limitations. This is the place where you can let your vision and your values ​​manifest.

Jay. Yes, I think it is possible. Thanks.

Applause.

RD I find the level-matching process extremely important. In fact, I do this every day. For example, in the morning, as I prepare to run a seminar effectively, I imagine the seminar room and how I want to behave in that room. I also figure out what skills I will need to be an effective facilitator, and what style, beliefs and values ​​will support me the most. I also make sure that I have an understanding of my identity and mission, that is, the purpose, the reason why I am here. Then I reaffirm my vision for my life's work. And then I reconcile all of these aspects of my experience. This usually takes 5-10 minutes, but it is a very effective way of getting ready to do my best.

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Bringing to the state of conformity by levels in the group

The level matching procedure can also be used as an effective tool for team or group formation. When people are united by a shared vision, mission, values ​​and capabilities, they are able to work together much more effectively. This is undoubtedly the foundation of what is known as team spirit.

Group level matching is performed as an extended version of the individual procedure. After each participant has come to a state of "fit" (and served as a guide for the other participant), the group members can come together and exchange the answers they gave at different levels. By listening to each other, participants may find something in common in what they say about their environment, actions, abilities, beliefs, values, role, mission and vision. (It makes sense to choose one person to write the general answers in a notebook.)

After participants share their answers at all levels and find common themes, they can synthesize personalized responses to find a “group” vision and mission. If the group was originally formed to achieve some common goal, participants can focus on identifying group values, abilities, etc. 1.

I used this procedure even to help the team form group identifications: we identified shared values ​​and then tried to determine what kind of identifications the given values ​​could be added to, or the expression of what identification they were. Just like an individual, a group can define its identity through a symbol or metaphor.

This procedure has been successfully applied in companies such as Lufthansa, IBM and Fiat.

From vision to action

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