Want to learn how to get information out of nowhere? This rare technique will teach you to read information directly from Space!
This technique is suitable for those people who strive for self-development, as well as those who want to develop the superpower of reading information.
Thanks to this technique, ancient magicians discovered the secrets of the Universe!
It was later refined by parapsychology experts and adapted for modern man, making it even more effective and easy to use.
Pros and cons of reading information using the Universal Spheres!
- Doesn't take much time.
- 85% of the subjects were able to find out the answers to their questions after the first lesson.
- At regular training allows you to quickly become a master in the field of working with the information field.
- Requires some special training (you will also learn about this).
- It works best for those who naturally have a penchant for creative visualization¹ and the ability to work with energy.
What can this practice give you personally?
Imagine that you have gained access to an archive that stores all the information about your life, the lives of other people, as well as all knowledge in general - about those that humanity already possesses, and about those that are yet to be discovered!
And from this archive you can find out what is interesting to you!
You just give the archivist a request, and after a while he gives you the information you need!! Incredible? It seems that yes, but in fact, masters who know how to connect to the information field can do this.
Do you think brilliant discoveries are being made?
In fact, everyone has access to this repository of information, but not everyone develops this ability. Some people from birth unconsciously connect to the information field and become brilliant scientists, inventors, artists, composers, sculptors... In this case, “narrow-profile” ideas come to them, and the person uses his talent in one particular area - the one that interests him most interested.
But how to receive information consciously?
There are people who can connect to the information field at will and receive information based on various requests. This is exactly the gift that clairvoyants, mediums, psychics have...
Yes, there are not many such people, and they have reached the level of a master in obtaining information. But what prevents you from becoming a master?
With this unique technique, you can train your ability to receive information to the level you desire!
How to receive information using the universal spheres?
To obtain accurate information quickly and easily, specific training is recommended.
First part of preparation– this is self-tuning that everything will work out. To do this, you can work with affirmations, with sensations or willpower to create the desired mood - it all depends on your gift.
Second part of preparation– a special attitude towards the energy of the Earth.
Why is the setting connected specifically with the Earth? Because we are on it, and it is much easier for us to receive its energy. At the same time, the Earth is a component of the Universe, part of cosmic energies.
By connecting to it before the main practice, a person significantly enhances his ability to work with cosmic energies and increases the effectiveness of the main technique.
Attunement to Earth Energy
1. The practitioner takes a comfortable body position and closes his eyes.
2. Mentally releases all tension in the muscles and relaxes. If desired, you can take several deep and slow breaths for greater relaxation.
3. Having felt a sufficiently deep relaxation (when the body has become very heavy or has ceased to be felt at all), the practitioner imagines the center of the Earth in front of him. It represents the accumulation of a huge amount of energy in it. The power of this energy is so great that the center of the Earth continuously emits a bright light.
4. The practitioner focuses on the glow and mentally feels love for it.
5. He imagines that from this feeling the energies located in the center of the earth “seemed” and began to rise to the surface. Gradually they come close to the earth's crust. And the practitioner, in turn, strengthens his love for them.
6. Eventually, the energies of the Earth “come out” to the surface and penetrate the practitioner’s body, connecting him with the forces of the planet. The visualization lasts about two minutes.
7. Then the practitioner stops imagining anything and opens his eyes.
It is very good to use a special audio program during this meditative attunement, which allows you to quickly and easily tune into the frequency of the Earth. The audio program can be found
After preparation, it is advisable to take a walk in the fresh air, listen to music or relax a little. After some time (no earlier than 10 minutes), the practitioner moves on to the main exercise.
Techniques for obtaining information using the Universal Spheres
1. The practitioner takes a comfortable body position and closes his eyes. Lets go of all thoughts, worries and tension.
2. Then he relaxes and takes a deep breath and exhales.
3. After which he imagines that his body has been transported into outer space. There is nothing there, only somewhere very far away the stars shine dimly.
4. Having felt himself in this space, the practitioner imagines that a sphere has appeared in front of him.
5. He focuses on this area and thinks about what information he would like to receive.
7. After 1-2 minutes, the practitioner imagines that the Universe begins to emit vibrations, which manifest themselves in the form of vibrations in the surrounding outer space.
8. These vibrations form new circles around the sphere: first one, then a second, a third, and so on until nine.
9. The practitioner imagines that each of these circles begins to make a certain movement - for example, the first quickly spins to the left, the second slowly to the right, etc. (this visualization will be individual for everyone).
11. This ball contains all the necessary information. The practitioner mentally takes this ball in his hands and feels the energies with which the ball is filled.
12. Then he intuitively (as he introduces himself) absorbs these energies, after which he returns the ball back to the sphere and imagines how the Universe directs not one, but several rays into the sphere at once.
13. The energy of these rays charges the sphere with a special power that can speed up the decoding of the information received.
14. Thinking about the meaning of the knowledge gained, the practitioner again takes the ball into his hands and mentally absorbs its power.
15. After this, he thanks the Cosmos for the help provided and stops the internal dialogue, focusing on external sounds.
16. After two to three minutes the practitioner opens his eyes.
This technique helps in two directions at once - it allows you to obtain information of interest and gives you the ability to decipher it. As a rule, this happens intuitively. After some time, a person realizes that he knows the answer to the question that interests him.
This technique has shown the best results among those people who have a penchant for creative visualization and whose personal gift is associated with the ability to work with energy. To find out about your personal gift, get your free individual diagnosis >>>
Notes and feature articles for deeper understanding of the material
¹ Visualization is the general name for techniques for presenting numerical information or a physical phenomenon in a form convenient for visual observation and analysis (Wikipedia). A proven way to quickly
Services, search operators and interesting tricks.
We continue to talk about advanced ways to search the web. We started with the article:
I am sure that many of the techniques will be a revelation for you. For example, do you know how to find out a girl’s apartment number using her home phone number?
1. How to find a person’s pages in all social networks at once?
Several years ago, Yandex launched a service to search for people’s personal pages. It is available at yandex.ru/people. Currently, the search is carried out on 16 social networks:
You can search not only by first and last name, but also by nickname:
If you are in doubt about how a person identifies himself on the Internet, you can use the logical OR operator (indicated by a vertical bar):
2. How to find a person’s latest posts on all social networks at once?
12. Does ICQ store any interesting information about your stormy youth?
14. How to find out location by IP?
The method does not guarantee the accuracy of the information. After all, there are many ways to hide your real address, which are used by both providers and users. But it's worth a try.
1. Take a letter from a person and look at its original text:
2. Find the sender’s IP address in it:
3. Enter it into the form on the service ipfingerprints.com :
15. How to find out a person’s apartment number using their home phone number?
The last trick makes a lasting impression on women:
1. Accompany the new girl to the entrance. You casually ask for her home phone number;
2. In between times, go to the Sberbank mobile application and go to the section for paying for MGTS services;
3. Enter the phone number and find out the apartment number;
4. Before saying goodbye, you tell about your second cousin who participated in the “Battle of Psychics” and offer to guess her apartment number;
5. Call the desired number;
In life, we sometimes come into contact with people whom we see for the first time. If we are interested in the interlocutor, we want to know more about him, we want to structure the conversation in such a way as to also interest him. For business, information is money. And the more information you have, the less uncertainty, the easier it is to reach your goal.
How can you get information from your opponent and about your opponent?
I offer some observations, methods that people most often use in business to promote their opponents for information.
These methods are not always honest; sometimes it is a conscious manipulation, sometimes an unconscious one. I am a proponent of a win-win situation.
But, you see, it is better to know the ways to be armed and not give away any secret information when someone uses them.
Or understand what kind of weapon you own and use it for its intended purpose and in the right situations.
This article is for those who want to know how and in what ways people influence each other in order to obtain the desired information.
Ways to promote information
1. Pass off a variant of a possible action, an opponent’s decision as valid
using affirmative phrases “ I know», « You surely... (you do this, such and such a person, feel this way...)"
And carefully record your opponent’s reaction.
The more incorrect the option, especially the assumption about the interlocutor’s feelings (talking about feelings unconsciously turns off part or all of logic), the more frank his reaction.
Sometimes several options for solutions are given on behalf of the interlocutor, although he did not voice them. Information is obtained by comparing reactions to both situations.
List the problems that most likely exist.“Surely...” And ask your opponent what is interesting from the list and what is not important? Ask an alternative question: either this or that is interesting?
Even if a person doesn’t guess correctly, the opponent is more likely to reveal himself when he is credited with something that is not what he is.
Say what are the reasons for refusal. But at the same time make a challenge: “If I say that all this does not apply to us and prove it, will you sign?”
2. Start a topic with your interlocutor that is indirectly related to the topic of interest.
Moving from a safe, related topic to a relevant one is easier to do, and information can often be obtained by listening to the opponent's beliefs.
For example, someone wants to know about a person's problem, starts a conversation about what causes it.
Do you want to know human diseases? They start talking about food, smoking, stress...
Want to know about a competitor's prices? They start talking about the high cost of supplies, the labor market...
Start a conversation about competitors. About their clients, about their prices... About the differences and advantages of the opponent with them. About the market situation in this segment.
Sometimes described a similar situation that allegedly or actually happened to him with his opponent’s competitor.
Bring up the topic of personnel in conversation. It is always relevant for the manager, just like sales. Start talking about what's new in these matters. Often the opponent himself begins to talk about plans.
Talking about dreams, drawing the desired image. Often managers easily talk about plans that are in dreams, i.e. ideal, not real. But if you listen carefully and encourage conversation, the person himself moves on to real plans and possibilities.
3. Find common ground with your interlocutor.
“I know that...” “I also had a similar experience...” “I came across...” “I’m from the same area, so I know what problems there are...” “I talked to everyone like you, and they have...”
It is clear that experiences bring us closer together, give us more understanding and trust. And information is given to those who are safe and trusted.
Link to authority.
Sometimes it’s easier to do what someone else has already done before you. And if it was authority...
4. Put the interlocutor into an emotional state.
This can be done through an emotional topic or a “different level” topic of communication.
An emotional theme is a theme that “transfers”, “switches” a person to the sphere of “emotions”. And both pleasant and unpleasant. If you make your opponent scream and start asking the right questions, he can answer, because control over logic is sharply reduced.
Emotional topics are topics that may concern your interlocutor. Money, prestige, his status, driving on the roads and brands of cars, extreme sports, relationships (including with staff, competitors)…
Call for a discussion of a controversial topic in an opponent’s area, where there is no right-wing 50% to 50%.
It can be in the form of a request from your opponent for advice. “You are an experienced person, I wanted to know the opinion of a specialist on such a controversial issue...”
Now I'll tell you about usage different levels communication to obtain information in business.
There is one system that distinguishes 3 levels of communication: business, friendly and sexual.
Each level of communication implies its own specific behavior, its own vocabulary of words, its own topics, its own gestures, permitted postures, even its own breathing...
The business level involves talking about facts, the friendly level is about feelings, the sexual level is about sensations.
To put your opponent into a trance, or temporarily remove control over the main topic, it is enough to use one level as the basis of the conversation, and insert some element from another level.
For example, men can talk about serious things using sexual or friendly language.
Even phrases to a subordinate woman when concluding a serious contract “I want you” or when concluding a supply contract “I love large sizes” can unconsciously switch the opponent to another level, which already implies a different attitude. And it doesn’t matter whether the opponent agrees to move to another level, it is important that he switched and the thoughts that appeared led him off the main topic, and when they lose control, people can give out information.
5. Give original and on-topic compliments.
Recognize your opponent's advantages.“I know that you have a decision without me. But all my clients also had a solution. And they refused, because... ...But they were interested...Are you interested in development...?”
This method works according to the rule - give your interlocutor the opportunity to win by recognizing the merits, and he will be ready to give it to you.
6. Record your opponent’s negative or incomprehensible reaction
(a person’s silence, his “resistance”), even at the level of “Your feelings,” and describe this reaction out loud to your interlocutor.
For example, “I see that you are silent. You are not interested? What is important to you?” “I see that you don’t want to talk. What should I do differently?
When voicing one’s own feelings or guessing the feelings of another, interesting fact– “sharing of responsibility” for the emergence of these feelings.
To check this, try saying out loud “I have a bad headache” or “it’s stuffy in the room”, and those around you will most likely begin to offer solutions to your problem or suddenly begin to get angry, because... the appearance of a feeling of guilt that they cannot help can cause such a reaction. 🙂
7. Arouse curiosity, interest through a promise or disclosure of one’s own secret.
For example, “I have several solutions, several proposals, but I don’t know which one will interest you? So that you don’t waste time, I want to know the answer to one question, after which I will tell you exactly what is interesting to you...”
Curiosity operates at the level of instincts; it is difficult to refuse to find an answer. And when a person reveals secrets, it’s as if he’s giving up his weapons and becomes safer. And when there is nothing to fear, people relax more and have less control and tension in relationships.
It is not necessary to give away secrets, the disclosure of which could bring trouble to you or someone else, there are simply some revelations or new information for the opponent.
8. Play the role of the client. Ask questions as if you were an opponent’s client who is about to purchase his product or service.
Everyone wants to sell goods and willingly talks about this topic.
It is better to build questions based on possible problems with this product or service.
“Is this being done on time?” “How can I check the quality of your product?” “What if there is...?”
9. Find out the criteria in the opponent’s understanding of a “good client”, His benefit
i.e. “What is important to you in this product? (in this matter?”). “I can talk for a long time about how I can be useful, but to save time, I want to hear the answer to one question”
This is the most honest and effective way!!!
P.S. For those wishing to receive a description of additional observations of “games” in the business environment, please write to me.
Sincerely, Ekaterina Gordeeva, business coach
Receiving (perceiving) information is the process of purposefully extracting and analyzing information in any physical system.
Like living organisms that perceive information from external environment with the help of special organs (smell, touch, hearing, vision), technical systems perceive information using special devices - sensors, sensitive elements, analyzers (perception of visual, acoustic and other information).
An information perception system can be a rather complex set of software and hardware that provides several stages of primary processing of incoming information.
The simplest type of perception is the distinction between two opposite (alternative) situations: “YES” and “NO”; “+” and “-”; "closed" and "open", "1" and "0".
A more complex type of perception is measurement, i.e. obtaining external information and comparing it with certain standards. As a result, the measured quantities are determined in statistics or in dynamics (in their changes in time and space). In the latter case, perception systems that operate in real time are especially distinguished, i.e. at the same pace as changes in the physical system.
Subsequent stages of perception (if necessary): analysis, recognition, prediction of situations. In this case, various practical and theoretical techniques are used: analytical, statistical, logical, heuristic, etc.
The criterion for the quality (effectiveness) of perception can be the amount of information received while ensuring high reliability (low probability of error) of perception.
Devices that receive information from a physical system (sensors, analyzers, etc.) usually express input information in the form of equivalent physical signals (mechanical, electrical, etc.)
In this regard, let us move on to consider the concept of “signal”. “Signal” is a material carrier of information, a means of transferring information in space and time. The signal carrier can be sound, light, electric current, magnetic field, etc.
The entire variety of signals in nature can be divided into two main groups - deterministic and random. All signals, in turn, are divided into continuous and discrete. Let's look at these concepts in more detail.
Signals are deterministic and random.
Deterministic is a signal whose values at any time are known quantities. Otherwise, the signal is called random or stochastic (from the Greek word stochastic - guess). Each specific type of random signal X(t), which is a function of time, is called a realization. Each implementation can be represented by an infinite collection of dependent or independent random variables.
A random signal is described statistically using various probabilistic characteristics.
Let us assume that there are N realizations of a random signal. Fixing the argument t(t=t i) we obtain N values of the random variable ξ.
Specifying the probabilities of its possible values is equivalent to specifying the so-called distribution function (integral law) F ξ (x,t i). The value of the distribution function F ξ (x,t i) at point x is the probability that the random variable ξ will take a value less than or equal to x, i.e.
Rice. 1.1. Distribution function random variable(integral law)
To obtain one ordinate of the distribution function, for example F(x j,t i) for x=x j (Fig. 1.1), you need to calculate the ratio of the number of times n when the value ξ in all N implementations turned out to be less than or equal to a given value x j to the total number N values of ξ, i.e. .n/N. This ratio is called frequency, and the limit of this ratio at N∞ is called the probability that the random variable ξ will be less than or equal to the value x j, i.e. 
. Obviously, if you change the values of x, then the frequency (probability) will change, and for x-∞F ξ (-∞,t i)=0, and for x∞F ξ (∞,t i) =1 (n =N), i.e. 
. The distribution function is a complete statistical description of a random variable in the sense that it can be used to determine all possible values of the random variable and their corresponding probabilities. For example, the probability that the random variable ξ is in the interval (x 1 , x 2 )
The random variable ξ is also described by the distribution density (differential law)
As an example in Fig. 1.2 function shown fξ (x,t i). Having N values of a random variable, you can construct a step function - a histogram of the distribution of the random variable (step function in Fig. 1.2). To do this, the area of change x is divided into a certain number of intervals ∆x and each interval is assigned the ratio n/N for this interval. As the interval ∆x decreases, the function will approach continuous.
Rice. 1.2. Random distribution density
quantities (differential law)
From (1.2) it follows that
or
,
those. area limited by function f ξ (x,t i) and the x axis is equal to 1. Using the function f ξ (x,t i) we can approximately calculate the probability that at time t i the random variable ξ is in the interval (x,x+∆x):
(shaded area in Fig. 1.2).
Note that random variables whose distribution functions are differentiable with respect to x for any x are called continuous.
In some cases, there is no need to completely describe a random variable by its distribution function. Most practical problems can be solved using a few averaged characteristics of the distribution m , formed from moments ν of the order of the random variable ξ relative to the number a - i.e. mathematical expectation of a random variable (ξ-a) ν.
m =M(ξ-а) ν , (1.3)
where M – denotes the operation of mathematical expectation. The initial moment of the first order (ν=1) is determined relative to a = 0 and is called the mathematical expectation of the random variable ξ, i.e. m 1 =M(ξ)=a.
The central moment of the second order (ν=2) is determined relative to the center of the distribution and is called the dispersion of the random variable ξ, i.e. D ξ =M(ξ-a) 2 .
The mathematical expectation and variance of a discrete random variable ξ are determined by the formulas:
(1.4)
(1.5)
In the case of a continuous value ξ:
(1.6)
, (1.7)
Where 
denotes the standard deviation of a random variable.
The mathematical expectation M ξ and the variance D ξ are functionals that describe the properties of the distribution of a random variable ξ: M ξ characterizes the “weighted average” position of the value ξ, and D ξ is its dispersion relative to the mathematical expectation.
The considered characteristics F ξ (x,t i) and f ξ (x,t i) are one-dimensional, because they are obtained with a fixed value of the argument t=t i . A more complete characteristic of a random signal x(t) is the two-dimensional distribution law f ξ (x,t 1 ;x,t 2), which contains the connection between the values of the function at two points in time. Obviously, the most complete characteristic of a random process could only be an “infinite-dimensional” (n-dimensional) distribution law (due to the continuity of the argument - time) f(x,t 1 ;x,t 2 ;...x,t n). However, in practice, there are some types of random signals that are better studied, the properties of which are completely determined by the distribution law for a small number n (usually for n< 3). К такому классу случайных сигналов относятся чисто случайные сигналы, характеризующиеся независимостью значений х(t) в различные моменты времени (для таких сигналовf ξ (x,t 1 ;x,t 2 ,…,x,t n)=f ξ (x,t 1)·f (x,t 2)·…f ξ (x,t n). Чисто случайный процесс является идеализацией, т.к. в реальных процессах всегда существует статистическая связь между значениями х(t) в достаточно близкие моменты времени. Другим примером являются марковские (по имени математика А.А. Маркова) случайные сигналы, для которых, в силу их безынерционности, любаяn– мерная плотность вероятности их значений может быть получена из двумерной плотности вероятности.
Obtaining a multidimensional probability density in the general case is a very difficult task. Therefore, for many practical areas of application when determining the statistical characteristics of a random signal, as well as a random variable, it is quite sufficient to know some integral (averaged) characteristics, but instead of moments of order ν in the case of random variables, moment functions of various orders of ν
(1.8)
At 
(1.9)
This time function is called the mathematical expectation of a random signal X(t). It is obvious that the mathematical expectation of a random signal represents some average curve around which its possible implementations are located.
Signals of the form 
usually called centered. The initial moment function of the second order (ν=2) characterizes the mathematical expectation of the square of the process, i.e. M, and the central moment function of the second order (ν=2)
is called dispersion
The correlation (autocorrelation, autocovariance) function is the mathematical expectation of the product
Random signals are usually divided into non-stationary (statistical characteristics depend on the origin of time) and stationary. Strictly speaking, stationary random signals, like stationary physical systems, does not exist. However, stationary random signals are a very “convenient” idealization and play an extremely important role in practical problems. Random signals can be stationary to a “greater or lesser extent”: in the narrow and broad sense. Stationarity in the narrow sense is complete stationarity; in this case, all probability densities of random signal values do not depend on the position of the reference point, i.e. do not depend on the same time shift t 0 of all points t 1 ,t 2 ...t n along the time axis:
Stationarity in a broad sense implies that the least constraint is imposed on a random signal. This is a signal whose statistical characteristics do not depend on time - the mathematical expectation is constant, and the correlation function depends only on the argument 
, i.e.
.
In the further presentation, unless special reservations are made, we will talk about stationary, in a broad sense, signals.
Among stationary random signals, a special group of ergodic signals is distinguished, which obey the ergodic theorem. This theorem states that for ergodic signals, the results of averaging over many implementations coincide with their average values over an infinitely large time interval of one single implementation. From here it follows that for ergodic signals it is always possible to choose such a finite implementation length, the results of averaging over which will coincide with the sample average estimate obtained for a given number of implementations. The last point is especially important in the field of measuring the statistical characteristics of random signals, since the measurement procedure and hardware implementation of various algorithms in this case are significantly simplified.
The mathematical expectation is defined as the time average
.
(1.13)
Dispersion (power)
(1.14)
Correlation function
For centered signals the correlation function is:
When instrumentally determining the numerical characteristics of random signals, an approximate value is often used - an estimate (hereinafter, the “asterisk” sign is used to denote estimates):
(1.17)
(1.18)
(1.19)
or for a centered signal 
(1.20)
Expression (1.17) determines the estimate of the mathematical expectation - the average value of a random signal. The closest to it, in the case of a signal specified by N values of x i, is the arithmetic mean of N values of a random signal or a sample mean (Fig. 1.3)
(1.21)
Figure 1.3. Estimation of the mathematical expectation of a random signal
Expression (1.18) gives an estimate of the dispersion 
, which characterizes the spread of values x i from the mathematical expectation. The closest to it in the case of a signal specified by N values x i is the arithmetic mean of the squares of N centered values of the random signal or sample variance
(1.22)
Where 
- standard deviation.
Expression (1.19) gives an estimate of the correlation function. In practice, to find one of its values, for example, 
For 
, for one implementation of a random signal x(t) (Fig. 1.4a), you need to take a certain number of products of values x(t), separated from each other by the amount 
, and find their arithmetic mean, i.e.
Rice. 1.4. Construction of the correlation function R XX (τ), for the value τ=τ 1
Magnitude 
(Fig. 1.4b) shows the average strength of the statistical connection between random values of signals x 2 and x 1, x 4 and x 3, x 6 and x 5, etc., spaced apart by an interval 
. If the value 
large - then the strength of the connection is large (knowing one value of the signal you can predict another), if the value 
is small – then the statistical relationship between these values is small (knowing one signal value, for example x 1, it is difficult to predict another – x 2). The values of the correlation function for other values can be determined in a similar way 
. To automatically measure many ordinates of autocorrelation functions, special devices are used - correlometers.
From (1.19), (1.20) it follows that 
is an even function, i.e. 
=
At 
is maximum and equal to the variance estimate, i.e. 
. With increase 
the statistical relationship between two values of a random signal weakens when 
.
The dimension of the correlation function, as follows from (1.19) (1.20), is equal to the square of the dimension of the random signal. In practice, this is not always convenient (for example, when comparing correlation functions of two different signals). Therefore, they use the concept of a normalized (dimensionless) correlation function 
obtained by dividing the correlation function by the variance:
(1.23)
ABOUT 
it's obvious that 
. At 
; at 
. An approximate form of the normalized correlation function is shown in Fig. 1.5.
Rice. 1.5. Normalized correlation function
For random signals one can find the following time interval 
, that at 
the values of the signals x(t) and x(t+τ) can be considered independent. Time interval 
, called the correlation interval, is the value of the argument τ of the normalized correlation function, for which (and all large values) the inequality
where ε is any, however small, positive value. In practice, the value of τ k is determined by setting ε to a value of 0.05.
The correlation interval is used in determining the time step of sampling during analog-to-digital conversion and signal transmission, in estimating the entropy of a signal, in predicting signals, in the analysis and synthesis of automated information systems.
The equivalent number N of practically independent samples processed during the signal observation time T (for example, when estimating mathematical expectations, correlation functions, etc.) is determined by dividing the observation time T by the correlation interval 
, i.e.
(1.24)
Among various random processes, a normal or Gaussian process is distinguished, which is completely determined by specifying the mathematical expectation and the correlation function. This process takes place under the influence of a large number of independent and non-prevailing factors. The one-dimensional probability density of the centered signal values has the form
IN 
the probability of a random variable not falling into the zone 
is less than 0.05 (Fig. 1.6).
Rice. 1.6. Probability density of a normal process
In practice, there are often cases when not one random signal x(t) is studied, but a system consisting of two random signals x(t) and y(t). One-dimensional distribution function of such a system of random variables
(1.25)
One-dimensional probability density
(1.26)
In this case, in the general case
Where 
provided that the value of the signal y(t) is equal to y(t j);
- one-dimensional probability density 
provided that the value of the signal x(t) is equal to x(t j).
In the special case of independent random signals x(t) and y(t), the one-dimensional probability density 
does not depend on the value of y(t j) and
Finding one-dimensional probability densities (1.27) is quite difficult task. An even more difficult task is to find the two-dimensional or more probability density of a system of two random signals. Therefore, in practice, the simpler, although less informative, numerical characteristics of random signals discussed above are used. To assess the cross-correlation of two random signals x(t) and y(t), the concept of cross-correlation (cross-correlation) function R xy (τ) is used, which characterizes the strength of the statistical connection between the random values of these signals spaced from each other by an interval τ.
By analogy with (1.19), (1.20):
Or for centered signals x(t) and y(t)
(1.30)
At t=0 
is maximum and equal to the estimate of mutual dispersion 
, i.e..When 
, which means the independence of the values of the signals x(t) and y(t).
Dimension 
is equal to the product of dimensions x(t) and y(t), which is inconvenient when comparing mutual correlation functions of two pairs of random signals. Besides 
characterizes not only the statistical relationship between x(t) and y(t) but also the spread of the values of these signals relative to their mathematical expectations. Therefore, in practice they use the normalized (dimensionless) cross-correlation function:
(1.31)
It's obvious that 
(at τ=0 
at 
)
Note that the correlation function R z () of a random signal 
, which is the sum (difference) of two stationary signals x(t) and y(t)
(1.32)
In this case, the mathematical expectation of the sum (difference) of random signals is equal to the sum (difference) of their mathematical expectations. In the case of independent signals (the cross-correlation function is zero), the correlation function
(1.33)
When analyzing information systems, the task is often to determine the measurement (sampling) period T of input x(t) and output y(t) random signals and determine the shift time δ t * of measurements of the values of the output signal in relation to the values of the input signal.
The first part of the problem is solved by finding correlation intervals 
(for x(t)) and 
(for y(t)), and choosing the largest of them, i.e. 
(1.34)
The second part of the problem is solved by constructing a cross-correlation function 
.
Determination of quantity 
for one time shift value, for example 
For 
(Fig. 1.7a, b) is practically carried out in accordance with (1.29) by calculating the arithmetic mean of the products
Rice. 1.7. Construction of the cross-correlation function R XY (δt)
In a similar way, the values can be obtained 
for other values 
and ultimately – the cross-correlation function 
(Fig. 1.7b)) The maximum of this function corresponds to the time shift of interest to us 
, at which the effect of values x(t) (at the system input) on values y(t) (at the system output) manifests itself with the greatest statistical force.
Meaning 
gives a time shift in the measurement of values y(t) relative to the measurement of values x(t).
In Fig. Figure 1.8 shows the input x(t) and output y(t) random signals, the sampling period T and the shift 
between measurements of output and input signal values. The values x 1 , y 1 ; x 2 , y 2 ; x 3 , y 3 etc. will be measured (sampled). .
When analyzing random processes, along with correlation functions, spectral functions are widely used, which characterize the energy distribution over the frequency components of a random signal. The most widely used among such functions is power spectral density 
, which 
is defined as the derivative with respect to frequency of the average power (dispersion) of the random process, determined by expression (1.14),
Figure 1.8. To determine the measured values of the input and output signals
(1.35)
Obviously, the average power (average intensity, mean square) of the process will be the integral of the spectral density 
, i.e.
(1.36)
From definition (1.35) it is clear that the function 
characterizes the density with which the dispersions of individual harmonics (frequency components) of a random process are distributed over the frequency spectrum. For example, a random signal with a constant spectral density is theoretically possible 
in an unlimited frequency band. This random signal is called white or functional noise. In reality, such a signal cannot be created. Therefore, they practically limit the frequency band within which the spectral density can be considered constant. It is practically believed that if the width of the frequency range within which the spectral density is constant is at least an order of magnitude greater than the bandwidth of the system under study, then this source for this system can be considered the equivalent of a white noise source.
Power Spectral Density 
and correlation function 
for a stationary process that takes only real values, are interconnected by the direct and inverse Fourier transform
(1.37)
(1.38)
Spectral density is an even, non-negative function of frequency. This circumstance makes it possible to use modified dependencies in practice.
(1.39)
(1.40)
From the above mutual Fourier transforms it follows:
(1.41)
where f is frequency, Hz
Similarly, the value of the spectral density at zero frequency is determined as
(1.42)
From the above formulas it follows that for stationary random processes the equality
(1.43)
One of general characteristics random signals is the width of their energy spectrum, determined by the ratio
(1.44)
In practice, when modeling various stochastic systems using computer technology, there is often a need for special devices - generators to obtain real models of random signals that have given statistical characteristics - one-dimensional probability density and spectral density (correlation function).
Due to the difficulties of creating “specialized” generators that reproduce random signals with given statistical characteristics, generators are usually created that reproduce “typical” random signals, and with the help of linear and nonlinear transformations they provide random signals with given statistical characteristics.
The choice of the normal distribution law for a typical random signal is due to the fact that this law is most widely encountered in the analysis of real systems and is the easiest to reproduce and transform. The one-dimensional probability density of a random signal and its spectral density are interrelated. When one of these characteristics is transformed, the other usually changes as well. One of the most important exceptions to this rule is when a normally distributed signal is passed through a linear filter. In this case, the distribution law remains normal, but its spectral density changes. This is a property of a signal that has a normal distribution and is used if it is necessary to change its spectral density.
The choice for a typical random signal to have a spectral density characteristic that is constant in a given frequency range (white noise) is also due to the fact that such a random signal can be used in the analysis of many real systems and is convenient for the mathematical description of stochastic problems; at the same time, random signals with different spectral characteristics can be obtained from such a signal
Thus, the task of obtaining a random signal Z(t) having a given spectral density and one-dimensional probability density is practically reduced to the sequential transformation of a typical signal x(t) of a white noise generator in 2 stages:
1. receiving at the output of the linear filter a random signal y(t) with a given spectral density and normal distribution laws;
2. obtaining at the output of the nonlinear converter a random signal Z(t) with a given one-dimensional probability density and the spectral density obtained at the 1st stage (Fig. 1.9).
Rice. 1.9. Block diagram of the formation of a random signal Z(t) with given spectral density and one-dimensional probability density
1. To obtain a random signal with a given spectral density, the dependence of the spectral density of a stationary random signal S out (ω) at the output is used linear system on the spectral density of the input signal S input (ω) and the frequency response Ф(jω) of the linear system
Hence the frequency response Ф(jω) of the filter, which provides the required spectral density at the output S out (ω) with a known spectral density S input (ω) of the signal at the filter input
(1.46)
For an input signal that is white noise
(1.47)
Using relations (1.39), (1.40), which characterize the functional relationship between the correlation function and spectral density, it is possible to unambiguously relate the parameters of the shaping filter with the parameters of the correlation function. After determining the required frequency response Ф(jω) by a graphical or analytical method and constructing the filter transfer function from it, it can be implemented on various element bases.
2. The transformation of a continuous stationary signal x(t) with a one-dimensional probability density f(x) into a signal y(t) with a given probability density can be carried out using a nonlinear transformation
(1.48)
where y is a single-valued function of x.
The conversion probabilities of both signals in the dx and dy intervals are the same, therefore
(1.49)
(1.50)
To determine dependence (1.48), it is necessary to find such values of y that, for each value of x, will satisfy equations (1.49) or (1.50). Determination of dependence (1.48) can be performed analytically and graphically.
Correlation functions and spectral densities are widely used in computer science in the transformation, analysis, forecasting, identification and discrimination of random signals, as well as in the analysis and synthesis of automated information systems.
The practice of obtaining information shows that psychological factors play a decisive role in this process. In most cases, success here depends on the ability to establish psychological contact with the interlocutor and, in the process of communication, influence his conscious and unconscious areas of the psyche. Such influence is exerted for different purposes. One of them is to obtain certain information that he would not like to share with anyone. Based on practical experience, there are two main ways to obtain the necessary information.
The practice of obtaining information shows that psychological factors play a decisive role in this process. In most cases, success here depends on the ability to establish psychological contact with the interlocutor and, in the process of communication, influence his conscious and unconscious areas of the psyche. Such influence is exerted for different purposes. One of them is to obtain certain information that he would not like to share with anyone.
The general psychological basis on which it is possible to obtain information of interest is the theory of the unconscious. The term “unconscious” is used to designate such phenomena that occur in the human psyche, but are not conscious of it. The meaning of obtaining information through elicitation is to, based on the general patterns of the subject’s mental activity, encourage him to transmit information in one form or another. Since this subject, as a rule, does not want to consciously transmit this information, he must be encouraged to transmit it unconsciously.
Unconscious mental processes are a direct necessity for the normal functioning of the body. This reveals another function of the unconscious: it provides “unloading” of consciousness, which is reflected in the development of so-called “defense mechanisms” of consciousness. The meaning of defense mechanisms is that they displace or suppress all that information from consciousness that interferes with or contradicts the activities and behavior of a person in a particular situation.
If we turn to the psychological structure of the personality, then in its various substructures one can find many elements that are unconscious mental phenomena. For example, the main elements of biologically determined qualities - properties of temperament, inclinations, innate drives, etc., as a rule, are not recognized by a person. Many mental phenomena have elements of the unconscious. Stable elements of professional and life experience, as a rule, are not recognized by the subject. These are automated skills, abilities and especially habits. Many actions that a person performs repeatedly and have vital significance also remain outside his consciousness.
Finally, certain character traits inherent in a person, his inherent abilities, are also not always realized by him. Often, in order to realize these traits, the subject needs certain circumstances that will reveal these traits as elements of personality. Sometimes a person is not aware of his abilities and they are revealed as his self-awareness develops in the process of practical activity. Consequently, unconscious phenomena are not the realm of something mysterious; These are ordinary mental phenomena, but have not reached the level of consciousness.
Based on general theoretical principles and practical experience, we can distinguish two main ways to obtain the necessary information:
First- this is an inducement of the subject to involuntary statements of facts that are of interest to you.
Second- inducing the person of interest to involuntary physical and expressive actions containing relevant information. Within these methods, one can identify a number of specific techniques with the help of which the necessary information is obtained.
Demonstration of specific items,“revitalizing” relevant images in the memory of the person concerned and prompting him to make involuntary statements. For example, to find out some aspects of the life of a person of interest or to start a conversation on a political topic, you can use relevant newspapers or magazines.
In general, it should be said that personal belongings of this person (toilet items, books, etc.) can be used as specific objects that prompt the interested person to make involuntary statements; objects belonging to this person’s loved ones, or other objects accessible to perception. The presence of such specific objects gives a double psychological result.
It goes without saying that reviving images of the past in memory is a fairly conscious process. As for statements, they are, as a rule, unintentional, in the sense that the person of interest to us, talking about his life, does not realize that by doing so he is communicating the information that interests you.
Necessary conditions for the successful use of this technique:
the object chosen for demonstration must be associated with an object that would resurrect in the memory of the person of interest the events to be clarified;
the demonstration should always be natural and justified by the specific situation;
your actions and actions when demonstrating an item must be expressively justified.
It should be noted that the basic rule for using this technique is the following: the incentive to make an involuntary statement when demonstrating objects achieves its specific goal only if the person of interest does not realize that the given object serves as a reason for the statement.
Using a related topic of conversation. This technique generally makes it possible to conduct a focused conversation without resorting to asking questions. Such a topic revives a number of images in a person’s memory, inevitably capturing into its orbit images from the area of forbidden information, that is, information known only to him. What should be taken into account here is not the list of possibilities, but the way of posing the topic itself, that is, the ability to ask the main question with leading questions and get an answer to it. Switching to a related topic can be done using a variety of neutral questions.
The essence of this phenomenon is that practically identical reactions occur in a person to all words that are similar in meaning, that is, they belong to the same logical group, and almost do not depend on their sound or spelling.
Basic conditions for successful application this technique are as follows:
the topic of conversation used as a related topic must be known to the person of interest and have a certain personal significance and value for him;
the related topic should logically follow from the specific situation;
the actions and actions of the person receiving information must be psychologically justified and expressively confirmed, that is, correspond to the professional and individual characteristics of the individual.
Methodological conditions for using this technique:
a related topic should not be too close to the main issue to be explored, since otherwise it takes on the character of a poorly disguised direct question;
the topic should not be too distant from the main issue being clarified, because this evokes a lot of other images and leads to statements that do not contain the information of interest.
Thus, using a related topic of conversation to obtain information of interest to you is to revive the impressions stored in the memory of the person of interest, to mask the real meaning of the related topic, and as a result to induce him to inadvertently convey relevant information.
Using the sense of significance of a specific person. People generally try to maintain and increase their self-esteem. By touching this feeling, you can ensure that the person of interest, defending his prestige, speaks out on an issue of interest to you. In targeted conversations, you can use a person’s desire to defend his point of view at all costs and increase his personal significance in the eyes of others. In this case, the existing relationship with the interested party should be taken into account. Taking into account how this person treats you, certain prerequisites are created for receiving information. These prerequisites include the following:
the desire of the interlocutor to sincerely and selflessly help the partner. This desire is usually expressed in attempts to give specific advice, convince, etc.;
a feeling of gratitude experienced in response to the actions and statements of a partner. Therefore, the interlocutor can provide information that interests us, considering his actions as a kind of return of a “debt”;
the desire to surprise the opponent and cause him confusion. This factor is clearly manifested in the process of a dispute that affects the interests of both interlocutors;
the need to receive a response from the interlocutor to one’s statements. This factor is of particular importance when the partner enjoys authority from the interlocutor. Sometimes, when they say something, they want to get advice or an approving response from the person they value.
All this gives reason to use specific techniques of this method when obtaining information of interest, such as appealing to self-esteem, showing indifference, “playing” on the interlocutor’s self-esteem and showing participation. Let's briefly look at these designated techniques.
1. Appeal to self-esteem. This technique involves praise, flattery, a emphasized expression of respect, great interest and attention towards the interlocutor. The technique is especially effective when communicating with vain and ambitious people. Appeal to self-esteem allows you to establish close relationships with such people and promotes the manifestation of sincerity on their part.
You should always give a compliment before praising;
when giving praise, you should adopt an appropriate facial expression and posture;
It is better to emphasize the “advantages” of the person of interest by comparing him with his opponents. At the same time, you should know that everything is good in moderation, and this should not be forgotten.
2. Showing indifference. This technique is used when the interlocutor has a great desire to discuss the information he has, to bring up in a conversation news known only to him, to which he attaches great importance. Showing indifference to information that is important from the interlocutor’s point of view, neglecting it hurts his pride and thereby stimulates to the expression of additional data emphasizing the significance of this information.
you need to sense in time that the person of interest is “overflowing” with information. This is certainly noticeable in the behavior of this person: he casts frequent glances towards the person to whom he wants to say something, cannot sit quietly in one place, and begins to gesticulate vigorously.
You cannot at this time impose your topic of conversation on the person you are interested in;
a manifestation of indifference on your part can prompt this person to speak only in conditions of trust. This is recorded by the desire of the person of interest to be alone with you. In the absence of trust, an indifferent attitude towards this person will cause responses of this kind in him.
3. Use of emotional stress. In this case, emotional stress refers to a state of mental tension. In this state, a person’s control over his behavior and statements weakens. There are several stages in the development of this condition. Emotional stress occurs as a result of any sudden and strong impact on a person, exciting his psyche and disrupting normal orientation in the environment. The main stage is a period of violent experiences, poorly controlled actions and speech reactions. Emotional stress ends with a gradual transition to calm.
You can put the person of interest into a state of emotional stress by asking an unexpected question, making an inaccurate or false statement; report supposedly “important” information, show your knowledge of something.
4. Posing an unexpected question. This technique has two varieties. By asking an unexpected question, you can confuse the person of interest and convict him of something, for example, of deception. In the first case, this person may not be aware of the intentions of the interlocutor, in the second, these intentions are realized by him.
Conditions for successful use of this technique:
an unexpected question should not be related to the topic of the present conversation;
The basic rule for using this technique: if the task is to expose or incriminate the interlocutor, an unexpected question should confuse the person of interest; if it is necessary to confuse him, then it is necessary to provide for this person a way out of this situation.
5. Inaccurate or false statement. By deliberately making a false statement or speaking incorrectly on any issue, we count on the fact that the interlocutor will want to clarify or supplement our statement. This technique is especially effective when communicating with emotional and impulsive people, who are easily unbalanced by distortion of facts. This technique is no less effective in relation to people who consider themselves “experts” or great scholars.
Conditions for the successful use of this technique:
the inaccurate or false statement must relate to the area of ideas that concern the person of interest at the moment;
such an action should create a certain difficulty for the person of interest in the form of a struggle of motives: to say - not to say, etc.;
the person using this technique must convince the interlocutor of the sincerity of his behavior.
The basic rule for using the technique: the falsity of the statement must be outlined basically correctly; only some specific detail of our information can be distorted.
6. Reporting “important” information. Using information that can change a person's mood helps direct the conversation and get the information you want.
Conditions necessary for the successful use of this technique:
when selecting “important” information, it is necessary to take into account the dominant needs of a person and his individual psychological characteristics;
it is required to be in a state of trust with the interested party;
the source of information must have the necessary respect and authority in the eyes of the person of interest.
7. Showing awareness. This technique is used when some details of the issue and events are already known and additional information is needed. Skillful handling of even a few known details can give the person the impression that the interlocutor is fully informed and encourage him to reciprocity and frankness.
8. Planting false evidence. It has long been known that a person trusts ideas that arise in his own head much more than those that are presented to him by other people. Therefore, people experienced in psychology try to avoid direct pressure on a person, but prefer indirect influence on his way of thinking. To do this, they seem to inadvertently throw certain information at him, from which he must draw conclusions himself. The art of obtaining information lies precisely in the fact that with the competent presentation of certain facts, the object of your interest should draw exactly those unambiguous conclusions that you are counting on.
9. Creating the image of a “simpleton”. The essence of this technique is to deliberately belittle one's own mental abilities, to create a feeling of intellectual superiority in the target. As a result, a person loses his vigilance, since he does not expect any trick from the “simpleton” with whom he communicates. In fact, it is he himself who is the simpleton, not you.
Methodology for obtaining information of interest
Preliminary study of the interlocutor is, of course, one of the most important tasks of the methodology for obtaining information. In practical terms, one should take into account those norms that regulate the behavior and relationships of people in the process of communication and significantly influence the process of obtaining information. Some of these norms are also determined by the national psychological characteristics of a person. These are also the character traits of the person we are interested in. You must correctly imagine which character traits of the person you are interested in can make it easier and which can make it more difficult to obtain information in a conversation. First of all, you should pay attention to the degree of his suggestibility and conformity, as well as such weakness of character as talkativeness. There are people who cannot keep within themselves a single thought that arises in their head, or a single piece of news heard from others. Until these people tell what they have to several people, each individually, they cannot be calm. This trait is often used and should be used in purposeful conversations that intentionally involve people who have similar traits. Knowing a person's character traits makes it possible to use people's vanity and ambition. Under certain circumstances, people with such character traits may take rash actions and statements only in order to attract attention to themselves and earn a positive assessment from another person.
It is also important to keep in mind that for most people, telling the truth is always easier than lying. Therefore, in situations where they have to tell a lie or hide the truth, many get lost and allow so-called “talks”, involuntarily expressing the truth, which must always be taken into account.
It is important to note the intellectual and speech abilities of the interlocutor, the features of his memory and observation. This helps to form a correct picture of the person and more objectively evaluate the data he reports. It is also important to know the degree of sociability of a person: how easily you can start a conversation with him, what position he usually takes in a conversation. The person’s mood during the conversation should also be taken into account. Events preceding a conversation can significantly affect the state of the interlocutor, his feelings, and his readiness to start a conversation and maintain it. Thus, various aspects of the personality of the subject of interest to us can lead to involuntary statements.
When making a final assessment of the personal qualities of the interlocutor, one should avoid prejudice and haste in forming an opinion. Bias interferes with a person's objective perception and leads to erroneous conclusions. In addition, there are cases when people who at first seemed withdrawn later turn out to be very pleasant interlocutors.
In order for a focused conversation to be successful, you must have sufficient general training to easily and naturally support the conversation and develop it in the right direction. Having erudition helps in conversations with people of different professions and interests, different social and age groups. General training and erudition should also include deep knowledge in the field of interest to the interlocutor.
Psychological preparation for focused conversations includes several components. One of them is the creation of an optimal psychological mood, which allows you to start a conversation without significant effort.
In order to free yourself from tension and maintain your interlocutor’s readiness to communicate, you should distract yourself from the upcoming action and remember situations in which you successfully solved similar problems. It is important to mobilize yourself for the upcoming action and constantly maintain it.
Another important aspect of psychological preparation is practicing the optimal line of behavior in the upcoming conversation. To successfully obtain information, you should behave freely, confidently and even somewhat condescendingly in a conversation. The choice of course of action depends on the individual qualities, character and temperament of the person you are interested in.
An independent component of psychological preparation for receiving information is predicting specific situations that may complicate the task: changes in the interlocutor’s mood, alertness, resentment, unfavorable emotional reactions. Good preparation for a conversation gives confidence and calm in a situation where there is practically no time left to think about a decision.
Practice shows that the conditions of the conversation significantly influence its process. An “informal atmosphere,” a calm place conducive to casual conversation, and enough time for a detailed conversation help solve problems of obtaining information. Focused conversations are best conducted in an informal setting, when the person you are interested in is free from professional responsibilities.
When entering a conversation, you should try to create a relaxed atmosphere. The initial topic should help to establish psychological contact as much as possible and allow you to further move the conversation in the direction that interests you.
Attempts to obtain information without a previously established contact usually do not lead to the desired result. However, you should not excessively delay the initial stage of the conversation to the detriment of solving the main tasks of obtaining information. Dragging out the conversation during discussion general topics may also lead to undesirable results. After receiving the necessary information, you should gradually reduce the conversation to a neutral topic and continue the conversation for some time.
Yuri Chufarovsky,
Doctor of Law, Candidate of Psychological Sciences, Professor of the Department of Criminal Law Disciplines of the Faculty of Law of the Moscow Academy of Finance and Law.