Isaev Alexander V.: другие произведения.

Section 100

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Isaev, Alexander V.

Sections 100

Fantasy Isaeva

Let me remind the reader that such reflektsiya (see Section 1, Chapter 3, "Initial concepts and definitions").

Reflektsiya (from pozdnelat. Reflexio - Reflection) - difficult to explain "reflection" of the world the numbers of real (physical) reality (the actual structure of space-time structure of the universe). I coined the term "reflektsiya" is intended to emphasize the difficulty of my analogy: no clear reflection, and "God knows that ..." - some reflektsii. Skeptics may feel that reflektsii - it's just ... reflection of the author, but it seems to me, not the worst use of our mind ...

My reflektsii - an attempt to prove that the abstract world of numbers and the real physical world - are isomorphic (at least partially, if at all possible). The concept of "isomorphism" can be explained as an example the following assertion: the number of partitions of a convex heptagon into triangles equals the number of options for placement of brackets to 6 letters. That is a triangulation of polygons is isomorphic (similar) problem of placement of the brackets (which leads to the Catalan numbers).

Reflektsii not form a unified picture, they may even contradict each other. But they have something attractive and certainly instructive for an inquisitive mind. In addition, reflektsii just curious scientific fact complement the main text of the book (if we ignore all of my "fantasy"). For example, many reflektsy devoted to the fine structure constant, which in itself - one of the mysteries of physics (see Section 1 Chapter 4, "Fine structure constant).


The Bible, as is known, begins with the words: "And God said: Let there be light. And there was light. "(Chapter 1, the first day of creation). And in the notes attached to the Bible, for example, AP Lopukhin explains that "The creation of light was the first creative-education act of divine creation. This primordial light is not an ordinary light in a perfect sense of the word ... and was the luminiferous ether, which, being in the vibrational [my italics] state, clocked a primordial darkness, and thereby create the conditions necessary for the future occurrence of all organic life on earth. "Here we see that this comment reflects the idea of light and life on earth, formed ... the natural sciences, and above all - physics. Therefore, we continued the conversation about light will conduct a scientific point of view.

In the physics of light - is electromagnetic radiation emitted by the hot or in an excited state of matter, which is perceived by the human eye. Under the light of understanding not only visible light (with wavelengths from 380 to 760 nanometers, that is, from violet to red), but also adjoining broad spectrum.

Nanometer (nm) - a unit of length in the metric system, equal to one billionth of a meter, that is 0.000000001 m. In that among the first significant digit (in this case - the unit) is on the 9 th position after the decimal point in science specified number is usually written as 10 ^ -9 (read as "ten to the minus 9-th degree," that is a unit divided by one billion). Nanometer - this is one of the most commonly used units for measuring small lengths. It is often associated with nanotechnology and the wavelength of visible light. For comparison, we can say that the distance between the carbon atoms in diamond is equal to 0.154 nm, and cutting-edge technology chip manufacturing operate with elements of size 15 nm.

In physics, light is studied in the "Optics". According to wave-particle duality - the principle according to which any object can be both wave and corpuscular properties of light, can be viewed in two ways:

1). Light - an electromagnetic wave (hence the "vibrational state in the commentary to the Bible, see above), the velocity of propagation in vacuum is constant and equal to c = 299792458 m / s (this rate - one of the fundamental physical constants);

2). Light - a stream of photons (light quanta): particles with a certain energy, zero rest mass and above, the speed (of light in vacuum).

Radiation of optical range (visible light and near infrared radiation) passes freely through the Earth's atmosphere, can be easily reflected and refraction in optical systems. Sources of optical radiation: heat radiation (including solar), fluorescence, chemical reactions, LEDs, etc.

Colors of visible light, corresponding to monochromatic radiation, called spectral. Spectrum and the spectral colors (the colors of the rainbow ") can be seen in passing a narrow light beam through a glass prism or any other refractive medium. Traditionally, the visible spectrum is divided in turn into 7 bands (colors): red, orange, yellow, green, blue, indigo, violet. The order of colors ("rainbow") helps to remember The simple phrase "Every hunter wants to know where to sit pheasants - the first letters (k, o, g, h, r, s, r), the words of this phrase indicates the corresponding color is" rainbow ". Why is traditionally distinguish seven colors of the rainbow (and not eight, or, say, nine colors)? The most "simple" answer to this question - because the number seven obviously has some ... magic (see Section 1). And to be more attentive, it is easy to see that in the surrounding real (physical) world, a kind of magic have a number in the range from 5 to 9 (all of these numbers are clearly "tend" it to the number 7, as there is no one "center") in other words, in terms of mathematics, one should speak about the magic number 7 plus or minus 2. Therefore, we, dear reader, that's how we will understand the word "magic number 7" (the numbers in the range of 5 ... 9 with the center in the form 7). From the standpoint of human aesthetics, an infinite (!) Series of examples of "magic number 7" logical place to start is with the biblical fact: The Lord God made the world (literally "from nothing"!) Was within seven days (with day of rest)!

Following the above, the "magic number 7" should not surprise us that the physics by considering light as electromagnetic waves, and emit just 7 basic electromagnetic band (the boundaries of which may overlap):

- Electromagnetic micro and radio waves (with wavelengths from 1 mm to 10 km and more);

- Electromagnetic terahertz radiation (with a wavelength of 0.03 mm to 3 mm);

- Infrared radiation (with wavelengths from 740 nm to 200 microns);

- Optical radiation (with wavelengths from 380 to 760 nm);

- Ultraviolet radiation (with wavelengths from 10 to 400 nm);

- X-rays (with wavelengths from 0.01 to 10 nm);

- Gamma-rays (with a wavelength of less than 0.01 nm).

Sharp lower bounds for the gamma radiation does not exist, but generally it is believed that gamma rays are emitted by the nucleus, and X-rays - electron shell of the atom (this is just a terminological difference does not affect the physical properties of the radiation). Gamma-rays emitted in transitions between excited states of atomic nuclei in nuclear reactions (eg, the annihilation of electron and positron decay of neutral pions, etc.), as well as rejection of energetic charged particles in magnetic and electric fields. Gamma radiation was discovered by Paul Willard in 1900 to study the radiation of radium.

To specify (of course, with a high degree of conditionality), the lower limit for the gamma radiation or, in other words, the lower limit of light (NHS), we use the following information. Jointly by the five countries (USA, France, Italy, Japan, Sweden), 06/11/2008, with the help of the launch vehicle, Delta-2 7920H "was launched spacecraft" GLAST ". On board was established unique equipment (gamma-telescope and another device), with which astronomers are going to explore the astrophysical and cosmological processes in active galactic nuclei, pulsars, and other high-energy sources, dark matter, and to study gamma-ray bursts in the universe. So, the upper threshold of the unique equipment "GLAST" is 100,000,000,000 eV (electron volts - an off-system unit of energy used in atomic and nuclear physics), which is equivalent to a wavelength 0.00000001240 nm. That last number we would accept as an NHS (which still somehow interested in academics?), But we will not rush into this and get back to the NHS after consideration of the CMB. But before we give an example of "disguised" "magic" number 7.

We introduce the following notation for the parameters of electromagnetic radiation:

E - energy of electromagnetic radiation, expressed in electron-volts (eV);

L - wave length of electromagnetic waves, expressed in nanometers (nm)

then between these parameters there is the following link:

L = e ^ ln1240 / E or (after taking logarithms): lnL = ln1240 - lnE, (1.1)

where ln1240 = 7,1228 ... - almost a "magic seven"! That is, physicists have entered (set to "their needs"), such units (eV, nm), which is a logarithmic scale, we almost get the formula lnL = 7 - lnE. In other words, the latter formula could really "work" (to exist) - If one wanted to physicists themselves (for this, say enough for the standard meter to 0.884382 ... are the current standard).

And now we'll talk about the so-called cosmic microwave background. This cosmic electromagnetic background radiation with a high degree of isotropy and with a spectrum characteristic of a black body with a temperature of 2.725 K. The existence of cosmic microwave background radiation was predicted theoretically in the framework of the Big Bang theory. It is believed that the CMB remained from the initial stages of the universe and it fills evenly. Experimentally its existence was confirmed in 1965. Along with the cosmological redshift, the CMB is regarded as one of the major confirmations of the theory of the Big Bang.

According to the Big Bang theory, the early Universe was a hot plasma consisting of photons, electrons and baryons. Due to the effect of Compton photons are constantly interacting with other particles in the plasma with them experiencing elastic collisions and exchanging energy. Thus, the radiation is in thermal equilibrium with matter, and its spectrum corresponded to the spectrum of blackbody.

As the universe expanded the cosmological redshift caused a cooling of the plasma, and at some point for electrons become energetically preferable, joining with the protons (hydrogen nuclei) and alpha particles (helium nuclei) to form atoms. This process is called recombination. It happened at about 3000 K, plasma, and the approximate age of the universe 400,000 years. Since then, the photons no longer scattered by the now neutral atoms and were able to move freely in space, almost no interaction with matter. Observable sphere corresponding to a given moment, is called the last scattering surface. This - the most distant object that can be observed in the electromagnetic spectrum. As a result of further expansion of the universe radiation temperature has fallen and now stands at 2.725 K.

Maximum of the CMB (IRI) corresponds to a wavelength of 1.9 mm (microwave radiation with a frequency of 160.4 GHz). This wavelength is close to 21 cm (this wave more MRI only two orders: 210 / 1,9 = 110), which is associated with a famous project SETI (born SETI, Search for Extraterrestrial Intelligence) - a project to search for extraterrestrial life . Beginning in 1959 SETI dates from the year when the international scientific journal Nature published an article Cocconi and Morrison, "The search for interstellar messages. In this article, it was shown that even at the then level of development of space communications, we may well rely on the detection of extraterrestrial civilizations, about the same as Earth's level, provided that they live not too far from us on the planets in nearby solar-type stars. Wave length of 21 cm, as a universal physical quantity (emission line of neutral hydrogen in the galaxy), we propose as a working program to search for SETI. As rational beings, are at a high level of development, should conduct extensive research space is at this wavelength (21 cm). Because hydrogen - the most abundant element in the universe, and therefore its radio link is like a natural benchmark rate, the benchmark to which inevitably must come every developing civilization on other planets.

Knowing the maximum of the CMB (IRI = 1.9 mm), we can assume that as the lower limit of light (NTS) "should" take the light with a wavelength of 0.0000026 nm, which is only 210 times (two orders) larger than the wavelength characteristic of the upper limit of sensitivity of the unique equipment of the spacecraft "GLAST" (see above). A "must" is of such a relation:

MRI / NHS = 1900000 nm / nm 0.0000026 ≈ 731.000.000.000. (1.2)

That is, starting from the values of IRI = 1.9 mm = 1,900,000 nm, we find such an imposter, at which the ratio of IRI / NHS will still ... i-trillion (in this case it represents the number 731.000.000.000 - almost a trillion).

Let me remind you that i-trillion - is one of the key parameters in the late great length (for N = 8 ∙ 10 ^ 60 Evie, that is, in our modern age). "Mathematical" sense of i-trillion - is the ratio of largest to smallest type type: Tmax / Tmin, where Tmax = 7 ∙ 10 ^ 11 - the highest number of integer divisors of natural numbers at the end of the Great segment, and Tmin = 1 - is the smallest number of integer divisors of natural numbers (a number of N = 1). In cosmology, the concept of a virtual i-trillion is introduced in Section 2 (in the chapter "Types of numbers (the worlds number)").

Thus, considering the scale of electromagnetic radiation, we have established:

- "Center" of this scale - it is MRI with a wavelength of 1900000 nm (1.9 mm);

- "Lowest point" of this scale - it is an NHS with a wavelength of 0.0000026 nm, which corresponds to the typical size of a proton (an elementary particle is of paramount importance in nuclear physics, for example, a proton is a part of the nucleus of any atom).

Note that from the MRI before the NHS - a huge (long) scale electromagnetic radiation (the ratio of wavelengths - almost a trillion, or nearly 12 orders!). However, the nature of the visible light had brought a man with a narrow "window" width of only two orders of magnitude - 380 nm (wavelengths from 380 to 760 nm). Indicated a narrow "window" on the background of a large scale (2 orders against 12 orders) - this is a very remarkable fact that we have only to remember and fully we will be able to appreciate it later.

It is obvious that we have to identify "the tipping point" scale of electromagnetic radiation - the upper limit of light (HCV), which lies somewhere in the radio (or even "above" them "). In connection with this we can only say that the extra-long waves - radio waves with a wavelength of 10 km. They are easy to bend around the Earth, poorly absorbed by the earth's surface, is well reflected by the ionosphere. To satellite communications systems of distant radio with submerged submarines is carried out mainly in sverhdlinnovolnovom range (requiring colossal power transmitting antennas) and in the link "beach - a submarine." That is, from an underwater position (through the water), boat, generally speaking, technically unable to send a message to the bank (alas, the boat can only "listen" to shore). Extra-long radio waves are two decisive advantages - they are, first, able to penetrate deep into the sea water and, secondly, can spread over very large distances, while not being sensitive to ionospheric disturbances caused by a recent solar activity or nuclear explosion.

Using the concept of "i-trillion" and considerations of symmetry (with respect to the "center" of our scale - IRI), we arrive at the following definition: the upper limit of light (HCV) - is electromagnetic radiation with a wavelength of 1,390,000 km, that is numerically equal to the ... diameter of the sun (very mediocre, typical star, which is characteristic for each galaxy in the universe). The numeric value of HCV derived from this relationship:

HCV / IRI = 1,390,000 km/1900000 nm ≈ 732.000.000.000. (1.3)

That is, starting from the values of IRI = 1.9 mm = 1,900,000 nm, we find a GHS, in which the ratio of HCV / MRI will be equal to i-trillion (in this case it represents the number 732.000.000.000 - almost a trillion).

So now we can say that light - is electromagnetic radiation with a wavelength, generally speaking, the characteristic size of a proton to the typical diameter of the star (like Sun), and the center of the specified range (in logarithmic scale) is for a maximum of cosmic microwave background radiation (or at a wavelength of 21 cm? ", ie the reference frequency to communicate advanced civilizations from different planets). To this we can make two clarifications. First, often the overall (global) picture of the universe is convenient to consider it on a logarithmic scale (meaning "the immensity of" scale of the universe). Secondly, we can assume that the specified range of wavelengths (the size of a proton to the diameter of the sun) get 99.7% of all possible wavelengths in nature, which follows from the so-called "three-sigma rule" (it is the standard deviation in the well-known theory of probability).


What is our universe? The most common, the fundamental answer to this question is a science called cosmology which is based on mathematics ("queen" of all the sciences!), Physics and astronomy. Cosmology allows us to describe the universe in the following, extremely simple manner.

To start, imagine cosmic vacuum whose density - much less than 1 hydrogen atom per cubic space of side 3 m (less than one atom in a small room - it's almost empty!). Immediately, we note that the share of hydrogen and helium (the most "simple" and light atoms!) Has 99.9% of visible matter in the universe (dominated ... mysterious dark matter that scientists have not yet learned to see). Now imagine that this space vacuum fills the whole sphere (symbolizing our universe in terms of its size) with a radius of about 130086000000000000000000000 meters, that is, roughly speaking, a unit with 26 zeros or, more scientifically, the radius of the universe - it's about 10 in a 26-degree meter (ie, the number 10 should be multiplied by itself 26 times!). Inside this sphere (in space vacuum), "loaded" to a trillion galaxies (this is 1,000,000,000,000, or 10 in a 12-degree or 1000 billion). Galaxy - these are the basic building blocks of the universe.

To imagine that such a galaxy - we are mentally reduce the universe to the size of our Earth ... - is the ball diameter of 12,742,060 m. Then our galaxy (in which we live, and which is one of the largest galaxies in the universe!) Would have a diameter of 46 meters and 46 centimeters thick ... that is, the Galaxy is similar to a thin "pancake" (from the stars, see below)! It is clear that the size of the galaxy against the size of the universe - is practically nothing, because even with aircraft flying to, say, at an altitude of 10 km, we barely visible 46-meter sites (in the form of tiny dots) on the background of the Earth's surface! In that scale, the average density of the location of galaxies in the universe is such that for each galaxy ("pancake" of up to 46 m in diameter) have suspended spherical space (space vacuum) with a radius of 700 to 1400 meters, ie, galaxies in the universe is very ... "amply !

Galaxy - a stellar pancakes-islands "in which the stars are held between a gravitational force. This same force is tightening all the stars in an endless rotation around the center of (their) galaxies. Most large galaxies (like our Galaxy) contain up to ... a trillion stars. It's an amazing coincidence: in each of the largest galaxies the same stars, so many galaxies in the universe (of course, that it is on the order of values: these values are the order of a trillion, ie 10 ^ 12). Such a beautiful coincidence, quantities, and the most mysterious number (a trillion) - is still no clear explanation in the framework of mainstream science (cosmology, physics). So here I offer my "mad" the hypothesis of a virtual cosmology: the specified number (a trillion stars and galaxies) "dictated" ... the world of natural numbers as i-trillion (7 ∙ 10 ^ 11) - is the maximum possible number of integer divisors of natural numbers at the end of great length, symbolizing our modern age [see Section 2, Chapter Types of numbers (the worlds number) "].

As for the stars. Our Sun - is the most unremarkable star, whose mass is about 1989000000000000000000000000000 kg (ie about 10 to 30-degree kg), and diameter - 1.391.980.000 m (109 times larger than the diameter of Earth, the Earth is in the sun - is as a large pea on the background m ball). If the Galaxy - is a 46-meter "pancake", then on this scale the Sun would look like ... an atom (with a diameter of 0.00000007 mm), and from the Sun to the nearest star would be ... 2 millimeters (4.2421 light-years). Generally, in this scale the average density of the stars in the Galaxy is that for every star (the size of an atom!) Has suspended spherical space (space vacuum) with a radius of 0.6 millimeters, that is, stars in the galaxy, in general, much more "spacious "than the galaxies in the universe!

It is worth mentioning that around most of the other stars (as most other galaxies) also rotate their planetary systems - so-called extrasolar planets. And some of them (in many respects similar to our Earth) can also live sentient beings, and in their size, they simply must be close to us: from tens of centimeters - a few meters (that is, to put it scientifically, the order of a meter) .

In scale, characteristic of a person (this is the scale of the order of a meter) the universe has three spatial dimensions (a, relatively speaking, "length", "width" and "height" of the room where you are now) and one time dimension, which is absolutely equal footing spatial dimensions. From the viewpoint of mathematics description of space and time were very similar, in fact, in reality it is two sides of a single structure, called "space-time." And in modern physics (quantum theory) in space and time play a central role, there is even a hypothesis, where the substance (including you and me, dear reader!) Is considered no more than a disturbance of this basic structure. But such a paradoxical statement now should not surprise the reader, because the above cited figures allow meticulous reader to get the most important cosmological parameters of the universe - visible matter density, which is approximately equal to 0.0000000000000000000000000000001 grams per cubic centimeter (about 10 to minus 31-degree r / cc). That's why our universe (the whole universe) - is in some sense, indeed, almost "empty" space-time! Therefore the main task of theoretical physics (her theories, including string theory) - to create a mathematical (and other - and can not be!) Model of space-time (IRP), which describes the "foundation" (fundamental principle) of the universe. And in their theories of physics have already proved that in the description of the "basement" of the universe can not do without the so-called Planck units (after the German physicist Max Planck), which including the following are the fundamental physical constants (constants):

0.00000000000000000000000000000000001616252 m, ie about 10 to minus 35-degree (m) - is the Planck length (the unit length). Submit such a meager amount is impossible, but here are some pertinent analogy, for example, if the (paltry) atom is increased to the size (huge) of the universe, the Planck length becomes equal to the average tree height .... Science predicts that you can not measure with a precision that exceeds the Planck length.

0.0000000000000000000000000000000000000000000539121 with, that is about 10 to minus 44-degree (second) - is the Planck time (elementary time interval). It is for this time of photons (quanta) of light, moving with the greatest possible speed in the universe, are the Planck length. You can also say that the Planck time - it is the smallest moment of time required for the occurrence of any conceivable physical event. The traditional view of space-time is not applicable at distances less than the Planck length, or for periods of time less than the Planck time.

The most miserable that is still able to "catch" our eye - this is, say, one hundredth part (1 / 100) mm: 0,01 mm = 0.00001 m (10 in the minus 5-degree meter). But the maximum depth of penetration of experimenters in a microcosm of today is estimated as 10 to minus 18-degree meter (this number is called attometrom) - is the Compton wavelength of the particles accelerated in the most powerful of modern accelerators. That is, everything that happens in nature at distances less than attometra - scientists observe until given (No such device). However, theoretical physicists have almost no doubt that at the Planck time, the values cease to be a "smooth and continuous" (this is only an illusion of human perception of time!) At the deepest level of the analysis - at the "basement" of the universe - the time has already ... discrete ("grain") the structure! It is obvious that the simplest idea of discreteness gives us a number of natural numbers: 0, 1, 2, 3, 4, 5, 6, 7, ... (this is the positive integers, reaching up to infinity).

Time seems to us (humans) as a continuous ("smooth"), without any hint of its discretion (grain) only because attometr (more accessible to physicists in the experiments) than the Planck length is ten to 17-degree time ( Giant Value!). For comparison: even on an airplane flying over the taiga at a height of H = 10000 m, we see only a smooth green carpet, instead of piling up the trees (height h = 10 m), although in this example (with a plane), we have only the ratio of H / h = 1000, and is only 10 in the third degree, which is 14 (!) orders of magnitude smaller than the above ratio, which is characteristic of the microworld (where there is much more "windfall" of space-time than in the taiga, but we just do not see at least, in our ordinary life on earth!).

And now, dear reader, we have come, perhaps, to the most intimate question - where and how did our universe? Perhaps I disappoint many when I say that our universe was "born" ... literally from nothing (?) And as a result of the so-called Big Bang - it's just a conditional (and beautiful) name of the first moments of the universe. Because in fact it was not an explosion, and (in many ways still mysterious) sverhstremitelnoe extension originally a "point of the bunch" of space-time. And, most interestingly, all physical theories that describe the nucleation (creation) of the Universe, Creator of the participation of a certain (the Creator), generally speaking, is not required (that is, it seems that science can explain almost everything!).

Science has been reliably established that from the inception of the universe (since the Big Bang) was about 13.75 billion years or T = 433620000000000000 seconds or

N * = 8021970000000000000000000000000000000000000000000000000000000 Planck time (approximately 10 to 61-degree Evie - elementary time intervals).

At birth, the universe began his endless running and the first photons (quanta) of light (which, generally speaking, can not "stand still"). A velocity (C) light in a vacuum - it is, as we have said, the fastest that can be in the universe, because C = 299.792.458 m / sec. This, of course, magnificent speed, however, say the light from the sun reaches the earth for a minute ... 8.32 - so far away from us is a glowing star that gives us life (up to the Sun - 149,597,870 km). Multiplying the speed of light C in time T (the age of the Universe) - we get the distance traveled by the photons of light during the existence of the universe - this is the radius of our universe, from which we started our story (see above). On this I finish my brief description of the actually existing universe, though, because more of it can be read on the Internet (eg, Wikipedia).

Next, I turn to the description of a very different - the virtual universe of which you, dear reader, have never read (except in my books and articles), since the virtual universe - my "know-how" (invention), "by accident" arose back in 2000, my technology to explore the world of numbers (as some "mirror" universe.)

Virtual universe - is a series of natural numbers: 0, 1, 2, 3, 4, 5, 6, 7, ..., N *, or, to put it scientifically, it is a segment [0; N *] of the natural series, which includes as the first natural numbers (starting from scratch!) - as the Planck time (Evie, see above) is contained in the real age of the universe. Specified interval of natural numbers I have called long periods, because he seems to be "generated" (in my imagination) the Big Bang. Needless to say, "the queen of all sciences," commonly known mathematician paid attention (infinite) number of positive integers - it is studying the theory of numbers - one of the most difficult (as it is strange you know!) And the most "worked" sections of higher mathematics. However, virtually the only practical application of the theory of numbers is cryptography - the study of methods to ensure confidentiality (inability to read the information to outsiders) and the authenticity of the information.

I am not at all interested in cryptography (not interested), but that's the beauty, harmony and perfection of the world of numbers - I was completely captivated! Moreover mathematical ("internal") structure of a large segment so beautiful and has so many amazing properties, which certainly should be pointed at something more profound! And without hesitation, for some reason I just (still in 2000) decided that the world of numbers indicates the device ... "basement" of the universe! That is, the structure of the world of numbers - this is the simplest model of a real space-time (the real universe), and "theory", which explores this phenomenon, I finally called virtual cosmology, as the main instruments to explore the world of numbers for me was the computer and guileless Mathematics (available from most ordinary high school students).

It is appropriate to recall the ancient Latin proverb: "Simplex sigilum veri" ("Simplicity - it is a sign of truth"), as well as visionary words of Einstein: "Our experience convinces us that nature - a combination of very simple mathematical ideas" (lying in the "basement" universe, and has all other "architecture" of the universe can be extremely difficult!). And what could be easier when I say that the mathematical model of real space-time (as a number of its discrete time quanta), possibly in something (and nothing more!) Similar to that of the Greater of (0, 1, 2, 3 , 4, 5, 6, 7, ..., N *). And if, say, string theory - is a complex model of space-time (IRP), my virtual cosmology - this is the easiest refraction (of many possible) that models "explain" the physical world are fragmentary and primitive, but very useful (although would be from a philosophical point of view).

Virtual cosmology - is primarily a mind game that allows to attach the widest possible audience to the beauty of the world of numbers to a simple but very useful in mathematics (which most of us "hate" - that we must honestly admit). And here I go again (already in some time!), Repeating the words of the famous English philosopher and scientist Roger Bacon (c. 1214 - 1292): "Whoever does not know mathematics can not learn any other science and can not even detect their ignorance. "Still it is possible to quote the genius of Leonardo da Vinci (1452-1519)" He who blames the supreme accuracy of Mathematics, fed by the confusion and never give up the tricks Sufi sciences, generating endless chatter. " ... "No no confidence in the sciences, where you can not make any of the Mathematical Sciences.

Virtual cosmology also initiates the reader to the well-known cosmology (see top of article), microphysics, philosophy, etc. Figuratively speaking, the laws of the world an amazing number "reflect" ("explain", ...) the most fundamental laws of the universe. Moreover, the virtual cosmology can even have predictive power, for example (and similar examples in my books and articles - a lot more):

1). The number of all sorts (types) of elementary particles of the order of 807,430 (physicists suggest that their number is indefinitely great, although it is open no more than 1000?)

2). The mass of the lightest of the fundamental particles (electron neutrino) would be just a trillion times smaller than that of the heaviest fundamental particle (t-quark, 174100 MeV);

3). Size (diameter) of the largest closed strings (string theory) will be just a trillion times greater than the smallest of the string (of the order of the Planck length);

4). The ninth digit after the decimal point in a numeric value of fine structure constant (1/PTS = 137.0359895 ...) will increase by one after about 1934, eight-digit increases by one after about 134 years, the seventh figure - through 1141, the sixth digit - through 11209 years, the fifth digit - by 111,885 years.

Of course, you can completely differently to treat my virtual cosmology, but still curious about what skeptics say, professionals (physicists, mathematicians, philosophers), when the "prediction" of my "crazy" theory will come true one day ... (as long as they are The Outer Limits of Experimental Physics).


Leading master of Taoist school of sexology in the West - Mantak Chia in his best-selling "Sexual secrets that everyone should know the man" says that the average time of intercourse - three minutes (or slightly more). We will take it for granted, and for longer sex, so characteristic of healthy people, this article will not discuss. Because it is so clear - literally at any career a person for some reason (well, really, why?) "Does not know the steps and bring everything up to the full limit, including their sexual pleasure! For us, in this case is important only the fact that God (the Creator, if it exists) "chose" just three minutes as the time of creation (conception) of a new life for the sake of continuing the human race (by the way, the irrational animals the time of conception can be quite different and different for each animal species). Of course, the "three minutes" - it is rather arbitrary and do not attempt to define a specified time to the nearest second - this is not essential for our future "research."

Let's move on to more secular subject (although the author himself - not a prude and the beginning of our conversation, he especially did not bother) and ask ourselves the important question: what is a man ... (sentient beings in general)? Scientists believe that intelligent beings can live on an extrasolar planet (outer planets), which circle around distant stars (our Sun - this most ordinary star). Science has long been in no doubt that the man - a kind of center (crown) of the universe - a real physical world that surrounds us. Below we "prove" this assertion with figures in hand, not by appealing to religion and to the rest endless humanitarian verbiage, which, alas, is not able to bring us closer to the truth, and not even able to make us just a little better (that is now happening with humanity on the planet - do not you tell me).

The smallest building blocks (denoted by the symbol K) is the universe, quarks and leptons that make up the elementary particles, and already from the last - is all the visible matter in the universe. These "building blocks" have size, relatively speaking, equal to K = 0, m (after the decimal point is 25 zeros!). In other words (to say the scientific zykom), the characteristic size of the smallest building blocks of the universe - is the order of 10 to minus 26-degree meter - the number is certainly an incredibly miserable. And here is the natural logarithm (ln) of the number-crumbs quite visible even number: ln (K) = - 60. That is a logarithmic function as it's inflated to the tiny number of visible values, thus attributing to them a minus sign, which indicates only that the number of crumb-less than one (in our case, the number K is less than 1 m).

The most that can be in the universe - is itself "marker" size (L) of our enormous universe, is estimated as L ~ meters (roughly speaking, a unit with 26 zeros!). It was such a rushed way (with incredible speed, almost equal to 300.000.000 m / s!) Photons of light during the existence of the universe - about 13.75 billion years (about 433,620,000,000,000,000 seconds). In other words (to say the scientific zykom), the characteristic size of the universe - it's about 10 in a 26-degree meter - the number is certainly huge. And here is the natural logarithm of the number of monster quite small: ln (L) = 60 (log-like "squeezes" ungodly medical benefits of up to tangible value).

Average height (H) of man on earth can be written as H = 1,62 m (it's due to the Chinese, which is almost 20% - every fifth person on the planet!). And here is the natural logarithm of this number is practically equal to zero: ln (N) = ln (1,62) = 0,48 [almost zero compared with a numeric value 60 of the quantities ln (K) and ln (L)]. On the real axis (going from minus infinity, passing zero, and then going into the plus infinity) is zero in the middle between the numbers of minus 60 and plus 60 (between the logarithms of the numbers K and L, see above). Thus, the average height of a man, the man himself - is the middle (tsentr!) logarithmic scale between the extreme values of the universe (from the "building blocks" - to the entire universe as a whole).

Note that the extrasolar planets far simply must be similar to our Earth (the physical parameters), otherwise there is no reason to appear, do not survive, not evolve. Therefore, any intelligent beings (on any extrasolar planets) should have increased the order of a meter, and place scientific term "order" in this case means that it is a reasonable increase in "green men" from tenths of a meter to several meters (all of them - about a meter !). Natural logarithm of this magnitude (about a meter) can also be conventionally assumed to be zero on a background of 60. And anyway, we should not "picking on" to the numerical value of K, L, H, since we are talking only about the order of their values.

More appropriate to explain how even in our conversation a logarithmic scale. The thing is that we live in an exponential world, that is, in his scientific description of the fundamental role played by an exponential function of [its simplest form is as follows: y = exp (x), often for the sake of brevity it is called a prime exponent]. Exponential growth (or decrease) of anything - it's generally a quick process, for example, we can say that human civilization is at an exponential rate, ie a rapid pace. After just 300 years ago, mankind did not even exist ... textbooks in mathematics (which is considered the queen of all sciences!), But now, after only 300 years, people have managed to calculate the ... trajectory to Mars (on the plans - landing astronauts on the planet happen until 2033). So, the logarithmic function (x = lnu) - is the inverse of the exponential function, just as, say, raising a number N in a square (multiplication of N by itself) - this action, the reverse recovery of the square root of N. And the whole wide range of scales of the universe (from its smallest building blocks - to the universe as a whole) is simply the most convenient to consider it on a logarithmic scale, just as the distant stars is most conveniently viewed through a telescope, a tiny microbes - through a microscope.

Thus, we take for granted the fact that people (sentient beings in general) - the center of the universe! By reason we mean the individual's ability to explore the world through the natural sciences (mathematics, physics, astronomy, chemistry, biology, etc.). It is these sciences have been able to paint a fascinating picture of our universe literally from its first moments - the so-called Big Bang - so far (and even much further until the complete disappearance of the universe ... ").

And now attention dear reader! Science is well established that our universe was created in the first three minutes .... Who created (and literally out of nothing?) - This science does not know yet, there is only a number of scientific hypotheses, against which the best science fiction books and all religions together look pathetic baby talk (naive, stupid, worthless). In other words, for the first three minutes there was all that "programmed" shape our modern universe, already existing for nearly 13.75 billion years old (it is about 7,227,000,000,000,000 minutes). Detailed information can be found in a very popular and fascinating book "The First Three Minutes," which was written by Steven Weinberg (b. 1933) - the largest American physicist, Nobel laureate in physics (1979).

Now, the reader should understand why a person (the crown of his creation!) "God" appointed "just three minutes for such an important process - the creation of human beings like themselves (see top of article). This once again reminds us that man is connected with the universe (with more spaces) is much more closely than we used to think about it. Rather, we did it was never thinking in everyday life! Well, say, for example, who among us knows, remembering that we, like all living things on Earth, "designed" by nature, literally from the ashes of the dead ... the stars in the universe (and it's the way it is)!

If you, dear reader, for the first time you hear about the hidden meaning of three minutes and not inclined to believe the author directly, then try to type in any Internet search engine the words "three minutes" - and you'll see that we unseen hand (besides the Creator?) "Laid" exactly three minutes (as a period of time) in a very very many sides (aspects of) our surroundings. You can even make a very comprehensive and interesting collection of various facts on the subject of three minutes. Here are some facts that could form the basis of this collection.

Clinical death - it is a reversible stage of dying, the transition between life and death. At this stage, stops the heart activity and breathing completely disappear all the trappings of life of the organism, but hypoxia has not yet caused irreversible damage to her most sensitive organs and systems. So, the state of clinical death in humans, except in rare and casuistic cases, on average, lasts no more than 3-4 minutes.

Free-diving (or sleep apnea) - is scuba diving man, based on breath-hold. Every dive is limited to factors such as time of breath and oxygen deficiency. This is usually a minute or less. However, with the help of training can bring this time up to three minutes (and even up to five minutes or more, and is the world record ... 11 minutes 35 seconds!).

According to the Guinness Book of Records, Eugene Andreev set a world record free-fall: November 1, 1962 he made a jump (with a folded parachute behind) from a height of 25,500 meters, 24,000 of which he overcame in free fall with a maximum speed of 900 kilometers per hour (250 m / s). Means to opening the parachute at Andreeva its free fall lasted about three minutes.

Ending high school (10 th grade in June 1974), I made several parachute jumps in the sky over the airfield in the picturesque town of Moldovan Vadul-lui-Voda, located on the right bank of the Dniester River, 23 km from Chisinau. We, the boys and girls aged 17, jumped from the aircraft AN-2 (popularly known as simply ... "for maize). The most terrible were to approach the open door of the plane and step into the void at an altitude of 850 meters. Curiously, that is about as make their first jumps novice parachutists and today (after almost 30 years!). So, under these (best for beginners) jumps, while in the sky by parachute in the middle as well ... just three minutes (full of indescribable joy, jubilation, true happiness)!

Recently I found a disc DVD, which was recorded 200 of the most popular national songs to karaoke (I myself am not fond of it). The CD also has been shown (among others) and total time of all the songs - 730 minutes, so I just figured out the average playing time of one song: 730/200 = 3.65 - that is, I got a secret (almost) three minutes!

Usually, the rounds in boxing are the length of three minutes. This time is determined by the physiological characteristics of the human body. Obviously, the multi-faceted sport there are many examples on the subject of three minutes.

Inflatable bed Eazy Bed (Easy Bed) built-in pump inflates - less than three minutes! These words are taken from the text ads. Advertisers will probably just feel that three minutes - is a kind of Rubicon for a man (for his patience?). You can probably assume that if a stranger to you a man says three minutes, you can form your complete opinion of this man (his words).

The author would be very grateful if the observant reader will send him (in the comments or e-mail) their three-minute examples from various spheres of our life, full of amazing facts.

Three minutes into the virtual cosmology

Curiously, that the fundamental role of the first three minutes, managed to "discover" even in the world ... of natural numbers (0, 1, 2, 3, 4, 5, 6, 7, ...) which, like the mysterious "mirror" reflect the physical laws of the real world . Extremely short of it discussed below.

The minimum possible time interval that is required for the occurrence of any conceivable physical event, called the Planck time. The magnitude of the smallest interval of time (time quantum) is 0.000 ... 0001 seconds, where after a point is worth 43 of zero, then there is the Planck time - this number is about 10 to minus 44-degree (of seconds). However, do not even attempt to somehow imagine such a tiny moment of time - it lies far beyond our imagination!

Theoretical physicists are not seriously believe that such a "thorough" review (at the Planck time) space-time is indeed quantized starts - the time shows like "granular" in nature. And if the scales characteristic of everyday life, it seems to us that time is gradually "flows" (from the past through the present into the future), then at the Planck time the flow of time is already comparable with a number of natural numbers 0, 1, 2, 3, 4, 5, 6, 7, ..., and this is a discrete ("granular") values - between integers there is no (integer) "bridges" - and time is beginning to change the "jump" (physicists say about the bustling "froth" of space -time). Here the author came up with each number of natural numbers identified with ... Planck time - this amazingly simple idea allowed to create an unusual theory (game thoughts), called virtual cosmology.

Age of the Universe (about 13.75 billion years) we will be in the form of ... a segment of the natural numbers containing a huge number of integers - the order of 10 to 61-th degree - so much the Planck time fit into the age of the universe (see for yourself with figures in hand). Said a huge segment we call the Great segment. This name was inspired by the cosmology of the so-called Big Bang - the moment of "birth" and early expansion of the universe, to which the universe was in a mysterious singular state (in terms of its physicists have lots of questions).

If the end of the Great segment - corresponds to the date (in which we live), then any segment of the natural numbers correspond to the first three minutes (after the birth of the universe)? Obviously, the first "3-minute" segment includes 10 to 45-degree natural numbers (starting with one) - this is easy to see, after working with numbers (see above). So, within a virtual cosmology shows that in a world of numbers the first "3-Minute" segment, as it were "programs the" parameters of the entire Great segment. That is all the basic (mathematical) specification of the Greater segment differ from similar parameters of the 3-minute "segment, generally speaking, negligible. Figuratively speaking, the overseas "3 minutes" segment was nothing "interesting" happens - and this is a "mirror" reflects the profound essence of the processes that took place in the evolution of the real universe! We can therefore say that the world of numbers (virtual cosmology) as if ... "predicts" (models, controls), the real physical world. The universe is subject to mathematical laws that are "generated" ... the world of natural numbers!

Theoretical physics (and indeed, it is - solid rocket science!), Which describes the universe, is incredibly complicated, and it fully able to understand only God's chosen people (some of the professional physicists). But a number of positive integers (0, 1, 2, 3, 4, 5, 6, 7, ...) seems simple to the extreme. And not for nothing is a series of integers is the first abstract truths, which opened early man in his early life (at the expense of various real objects - "nature"). However, only the (rare), dedicated people know that the mathematical structure of a number of natural numbers so beautiful and has many remarkable properties, which certainly should be pointed at something more profound! It is appropriate to recall the ancient Latin proverb: "Simplex sigilum veri" ("Simplicity - it is a sign of truth"), as well as visionary words of Einstein: "Our experience convinces us that nature - a combination of very simple mathematical ideas." It is possible that one of these ideas is part and VIRTUAL cosmology, which is considering a number of natural numbers by an unexpected angle.

4. Omnipresent EXHIBITOR

Do the humanities have become a good habit in public (say, from the TV screen!) And coyly say something like: "I am at math (with tsifiryu) is not in trouble ...." But the famous English philosopher and scientist Roger Bacon (c. 1214 - 1292) has long and rightly remarked: "Whoever does not know mathematics can not learn any other science and can not even detect their ignorance." Therefore, I suggest the reader to overcome horrible aversion to math and still read this chapter (and you probably understand all ... ").

Talking about the exhibitor can not start except with a story about so-called "number of deaths", about which we all at one time attributed at school in mathematics lessons. The number of e - is the base of natural logarithms and the most important mathematical constant (denoted by lowercase Latin letter "e"), which occurs in higher mathematics at every step, it is especially important in the differential and integral calculus. Sometimes the number e is called Euler number. Leonhard Euler (1707 - 1783 gg.) - Is the most prolific in the world (opening) a brilliant mathematician. It was Euler first introduced the symbol e (without a sense of false modesty, because with that letter begins his last name - Euler) and has done so many discoveries related to the number e, which in the end, e were called Euler number (not to be confused with the Euler's constant : C = 0.577 ...). The numerical value of the specified number of the following:

e = 2,7 1828 1828 459045235360287471352662497757 ...

where the 1828 - year of birth is ... Leo Tolstoy (the great Russian writer and thinker), that allows even readers in the humanities is easy to remember 9 digits after the decimal point in the value of e.

The number of e - a transcendental number (Hermite proved in 1873), that is, it is not the root of any polynomial with integer coefficients, and there is no law that alternate digits after the decimal point in the value of e (in 1961 with using a computer has been received 100,265 decimal places). It is assumed that e - is the normal number, ie the probability of occurrence of different digits in it (beskonechnoy!) records are identical.

Sometimes the number of e maloobosnovanno neperovym call number, the name of the inventor of logarithms by John Napier (1550-1617), which is used as the basis of the number 10000000 = 0.9999999 ^ 0.367 ... (less than 1 / e, but the differences begin in the eight digits after the decimal point! ).

The number e can be defined in several ways.

Number of e indicates the limit to which tends the expression e = (1 + 1 / N) ^ N, where the integer parameter N tends to infinity: N = 1, 2, 3, 4, 5, 6, 7, ... [caret ("Cap") in this article would mean the "exponentiation", ie the expression in parentheses (1 +1 / N) raised to the power N]. In short, the expression e * rushes to the number of e = 2.718281828459045 .... The relative error [by definition: OP = (e - e *) / f *] decreases, in general, according to the law: OD <1 / (2  N) - this is my assessment of the virtual cosmology. See also the Wikipedia article "Remarkable limits" (the number of e called the second remarkable limit in mathematics.)

The number of e - is the sum of an infinite series: e = 1 / 0! + 1 / 1! +1 / 2! +1 / 3! 1 / 4! + 1 / 5! + ... (In the denominator are integers 0, 1, 2, 3, 4, 5, 6, 7, ..., reaching up to infinity).

The number of e - is the only number for which the following condition: the area under the graph of y = 1 / x on the interval from x 1 to x = e is 1.

The number e can be represented as an infinite continued fraction (it opened Euler):

e = 2 + 1 / (1 +1 / (2 +2 / (3 +3 / (4 +4 / ... )))).

There are many interesting problems with the number e. We can only give four examples.

1). The best approximation of f are fractions 87/32 and 878/323 (the numbers, palindromes, the difference between them - is also a palindrome: 878 - 323 = 555).

2). The expression y = x ^ (1 / x) has a unique maximum and that is when x = e.

3). If you add random numbers (from a certain "number generator" operating in a range from 0 to 1) up until their sum is greater than 1, the mean (expectation) of the terms will be equal to the number of E. ...

4). Curious card game "Solitaire" (my code name), who is also an interesting example ... imperfection of our intuition. Suppose that a player has recorded N cards in any order (made up my list - as he wanted). Thoroughly shuffled these N cards, leading lays them on the table for one (top picture), while the player is called a (regular) card out of his (written, see above) list. What is the probability of coincidence named and laid on the table cards?

So, it turns out that for any N, is greater than or equal to 7 ("Magic Seven"), the probability of this match will be 1 - 1 / e = 0.632 (ie almost 63%, and almost "golden section")! For example, from 30 parties "solitaire" player win about 19 parties, but our intuition believes it is difficult, is not it? Explanation for this result is that the number of "promiscuity" of permutations of N objects is equal to the integer closest to the fraction N! / e (where N! - the so-called factorial of N). Another permutation of N objects is considered to be "messy" if neither the subject does not occupy its original place (before the beginning of permutations).

Maps (described above game "Solitaire") - only one of this amazing task. And in theory, probably a lot of problems in which our intuition leads us to make incorrect conclusions. Such failures of intuition suggests that the human brain is far from perfect. In this case, it becomes obvious that intuition may not serve as the arbiter of truth in mathematics (as well as in all other aspects of our life and work). Performs the role of arbiter of Truth, our logic, and only in mathematics logic is flawless! [The idea of the knowability of the world was apparently destroyed all of Kurt Gödel in the 30 years of the last century, but this issue goes far beyond the scope of this book, designed for beginner readers.]

Maybe that's why mathematics education around the world - the first candidate to destroy, among other exact sciences. But in the favor - a religion, "science" of economics (the crisis of the crisis!), Law, etc. But, say, the Russian law of logic is simple ... No, rather, it reduces, in general, to a simple "formula": that one does, who has more money and (or) power (this is not always the same). Therefore, the Russians live (or rather - just mayutsya) is not in a legal state - it has become an axiom requiring no proof, and highly symbolic that for 10 years as president of Russia on his basic education ... a lawyer!

After a small lyrical digression (in terms of logic) we finally turn to the very remarkable features - to an exponential function (or, more simply, to the exponential function - is common in science and technology title). The simplest form of this function as follows: y = e ^ x, ie the number of e = 2.717 ... raised to the power x, for example, when x = 2 we get: y = e ^ 2 = 7.387 ... The formula y = e ^ x is often written in another notation: y = exp (x) - just as often it is more convenient (by analogy with the way I often convenient to call Sasha, not Alexander).

Thus, the exponential - this is the usual exponential function y = a ^ x, which lies at the base of a number equal to e. The laws of (higher) mathematics follows the unique property of the exponential: it coincides exactly with its so-called derivative: (e ^ x) '= e ^ x. The concept of "derivative" - one of the most fundamental in mathematics and its applications to science and technology, it is this and explained the reason for the frequent occurrence of the exponential in the formulas of mathematical analysis - the section of higher mathematics, studied at the first course of any technical college. That is why, even the most careless student "techie" hundreds of times I heard a lecture about ubiquitous exponential!

Exponent is very common in applications of mathematics to science and technology, where the rate of change of any quantity y is directly proportional to its present value: dy / dx = ky (where k - coefficient of proportionality). The solution of this differential equation is exponential, having this kind of

y = C  exp (k  x)

where C - the initial value of the exponent, k - the intensity exponent (coefficient).

Obviously, the exponent is a direct consequence of the fact that the magnitude of changes in an independent manner, by accident (we live in a world ruled by His Majesty Chance!), As its rate of change is proportional to only the most value at the material moment:

If k is greater than zero (k - the constant growth), then the exponent of the argument x increases rapidly (exponentially) increases, and expresses the so-called law of natural (organic) growth, for example, the growth of bacteria colonies, the increase in cash deposit at a constant percentage increment.

If k is less than zero (k - decay constant, decay), the exponent with the increase of the argument x approaches zero. Since flows, for example, the process of radioactive decay, damped oscillations, wave propagation, etc.

Inverse to the exponential function is the so-called logarithmic function, the simplest form of which is x = lny. In other words, the number e is the base of natural logarithms (this tells us the mathematical symbol ln). "Flip" the function is called, because we use it to search for the value (x) from the known value of the function (y), ie, here we solve the inverse problem (in the direct formulation of the problem are looking at the value of the specified parameter x).

Because the geometrical progression Yn = Y1  a ^ (n-1) (where Y1 - the first term of the progression, and - the denominator of the progression, n = 1, 2, 3, ... - the serial number of each member of progression) can be regarded as the exponential function where the argument x takes only discrete values (x = n - 1), it is obvious that any geometric progression corresponds to the exhibitor:

Yn = (Y1 / a) exp (n lna).

Converse is also true. If the exponent y = C  exp (k  x) the argument x takes a number of consecutive integers, the value of y varies in a geometrical progression, in which: the first term of Y1 = C  exp (k), and the denominator a = exp (k ).

In short, any (any kind!): Exponential, logarithmic functions, geometric progression - all this "litmus test" is exponential in the surrounding universe. Take a look through and any solid reference book on natural history (especially, of course, in physics) and technology - you'll see that most of the formulas given there contain the exponential (with the number of e), a logarithmic function or a geometric progression.

Of course, that the exponent - the main feature in all technical sciences, and their endless applications. Here are some examples of what was said.

In technology, there is such a thing as the preferred number - the decimal system of parametric series of numbers, constructed in a geometric progression with denominator 10 ^ (1 / n) (that is, exponentially!), Where n = 5, 10, 20, 40, 80 - numbers series, unlimited in both large and in the smaller side. Such an approach provides the basis for an optimal standardization of the technique (which is another proof of the exponentiality of the world).

The wires, ropes, chains, ropes and even ... pautinovoy thread (that is, any flexible uniform and heavy inextensible filaments, whose ends are fixed) is described by the "catenary" (this is also eksponeta): y = 0,5 a [e ^ (x / a) + e ^ (-x / a)].

Exhibitor invisibly present in our daily lives. For example, since 1961. Russians have used seven (again, "magic" Seven!) of treasury bills: 1, 3, 5, 10, 25, 50, 100 rubles, and their numeric values were close to an exponential form:

y = 0,5406  exp (0,7518  x), where x = 1, 2, 3, 4, 5, 6, 7 - serial number of the ticket.

Benford's Law ubiquitous Pi = log (1 + 1 / i) contains in its records so-called logarithm (log), which can always be transformed into natural logarithm (ln), so ubiquitous manifestation of the law Benford - one of the main proofs exponentially in our world !

Thus, the reader should not now be no doubt that the real physical world - is very often an exponential world. One of the main ("lying on the surface and visible to us" naked eye ") properties of real space-time is its exponential character. The root cause of this by the very large lies in the supposedly "obvious" facts - we live in a world built on the likelihood (see, eg, probability theory in Wikipedia), we live in a world ruled by "His Majesty Chance." And with that, in principle, many scientists now agree ...

In my virtual cosmology is also very often "seen" exponential: in almost every formula - or the number of e, or logarithmic function. Therefore, I accept the following statement: mathematical (internal) structure of natural numbers (the "flow" of discrete numbers 0, 1, 2, 3, 4, 5, 6, 7, ...) to some extent (in a very primitive form? ) can "reflect" the mathematical structure of real space-time (stream its discrete quanta). And if this is indeed so (even if only in principle, there are grounds!), Then we are faced with a paradox, because in the world of numbers ... there is no room for the slightest chance, there is nowhere to hide, "His Majesty Chance"! All "internal" structure of natural numbers - it is literally a "concrete" design, deterministic (certain) once and for all (see Section 2, the head of the Pyramid of divisors)

And all the "randomness" in the world of numbers - it is nothing more than an illusion of our (still very imperfect) mind! In short, it may well be that the real world - it is strictly deterministic world, "Destiny" which was originally "painted" the most fundamental structure of space-time. Simply, we do not yet know how to read a specified "text" (we still have not found any form of equations or their solutions in string theory).

5. Number of elementary particles

C point of view of physics, the number of classes (types) of elementary particles, most likely indefinitely large (for example, it claims, and string theory). However, in our opinion, the world ... of natural numbers (1, 2, 3, 4, 5, 6, 7, ...), perhaps "tells" us that the number of varieties of all the particles is limited. In any case (conditional) number of 807,430 generated by the world of numbers, may be the most fundamental (but this is what exactly?).

If the reader has a notion of elementary particles, then it can go directly to the end of the article, which tells about the world of natural numbers.

 Elementary particle - a collective term referring to the microscopic to the subnuclear scale (with dimensions smaller than the nucleus of an atom). Most of the elementary particles have a complex internal structure, but split them apart is impossible. And only 28 elementary particles currently considered to be structureless and are considered as primary (fundamental) particles. Let's talk first about exactly these particles.

Fundamental particle - a structureless elementary particles, which hitherto could not be described as a constituent. Any (visible) matter in the universe for physicists is, more often - just stuff that (if you ignore the string theory) at the deepest level consists of 12 fundamental particles - building blocks of the universe (6 quarks and 6 leptons) as well as of 4 quanta fields (vector 4 fundamental forces in nature, the most mysterious of the four powers - that is gravity). Each quark and lepton has its own antiparticle, so a complete set consists of 28 fundamental particles.

The main building block of all atomic nuclei - is a proton, so it is considered a proton particle of paramount importance to nuclear physics. However, experiments in 1968 proved that the proton is composed of three quarks (u + u + d), and the neutron (a relative of the proton, only without charge) consists of three other quarks (d + d + u). It was later established that all elementary particles are not "elementary", and are a combination of fundamental particles. And in a free state quark can not exist - it is an axiom and the paradox of science. And all the fundamental particles of this kind (species) are identical to each other (for example, all protons - "one person").

All fundamental particles are clearly divided into three families, each of them: two quarks, electrons (or their relatives) and neutrinos. Properties of the fundamental particles in three families (denoted by numbers: I, II, III) are identical except for mass, which has consistently increased in each of the following family (family I - the most "easy"). The mass of the heaviest fundamental particle (t-quark), possibly a trillion times the mass of the lightest of the fundamental particles - the electron neutrino (see "Trillion Isaeva).

Taking into account the "color" (this is just the charge of nuclear power) and helicities of all fundamental particles are 45 Weyl states (equations of motion). It is such a large number of quarks and leptons suggests that they, in turn, may consist of preons (subkvarkov, pervochastits). However, the experiment has not yet given any indication of the existence preons.

All that we see on Earth and in space is, apparently, a combination of two quarks (u, d) and electrons, ie the fundamental particles of the family I (the most "light" - particles of this family have the lowest weight).

Even in the universe is a particle-ghost - of neutrinos, which interact extremely rarely with other forms of matter. Almost all the fundamental particles of the families II and III are not included in ordinary matter. These fundamental particles or there (for a moment) in accelerators, simulating the conditions of the early universe (such conditions in the universe there is no longer), or detected in cosmic rays (muons). Despite some "elusiveness" of fundamental particles from families II and III, allege physics: any substance (natural or obtained at accelerators) consists of 12 combinations of known fundamental particles and their corresponding antiparticles (I repeat, they have each particle).

In the generally accepted model of elementary particle physicists of all fundamental particles - a zero-dimensional point objects (mathematical idealization), devoid of any inner structure. Radically different view of the nature of fundamental particles demonstrates string theory.

We now consider the elementary particles.

In modern physics the term "elementary particles" is used not in its precise meaning (primary, not further decomposable), but less severely - for the name of the smallest particles of matter, is not associated in the nuclei and atoms (except for the proton). In addition to the 28 fundamental particles (see above) refers to the elementary hundreds of different particles, and their number continues to grow and most likely indefinitely large (in this case converge all physical theories, including string theory).

Most of the elementary particles are composed of different combinations of fundamental particles (and their antiparticles) and are the ultimate form of matter that still manages to capture in the experiments. Dimensions of the most "large" elementary particles (protons, neutrons, mesons) "only" 1000 times more attometra (equal to 0.000000000000000001 m, after a point is worth 17 zeros, then there are 10 in minus 18-degree meter) - limiting the penetration depth in a microcosm of experimental physicists. What happens in nature to the size of less attometra - scientists see is not given, although their physical theories they come up to the Planck length (10 to minus 35-degree meter).

All elementary particles (including all 28 fundamental particles) in this class (say, all 10 in 80-degree electrons in the universe) is absolutely indistinguishable (identical to each other), like atoms, constructed from them, but why this is so - so far remains a mystery of nature. And there is no, even the slightest, the differences (on the "slightly"), the mathematical apparatus of the modern theory does not admit - it just increases the number of discrete degrees of freedom (the number of species) of the particles and change their stats.

Every kind of particle is characterized by a set of properties, however, the total number of these properties have not yet been established. The majority of elementary particle masses are of the order of magnitude of the proton, which is equal to

0.00000000000000000000000000167 kg - a 10 in minus 27-degree kg.

Immortal yet considered only: photon, electron neutrinos (leptons), and possibly a proton.

All elementary particles (except the photon and the graviton), divided into two main classes: hadrons and leptons. Hadrons - particles are involved in all types of interactions. Leptons - a particle not participating only in the strong interaction (neutrino does not participate in electromagnetic interactions). Hadrons are divided into baryons (including protons and neutrons) and mesons. The total number of species (species) of hadrons in the hundreds, but there are theories where the bill goes to the thousands.

In a free state, all hadrons (all their varieties) are unstable (except for perhaps only a proton). Hadrons which decay due to nuclear forces and have a short lifetime, are called resonances (most of them, more than 300). Time of their lives close to the nuclear time (0.00000000000000000000001 seconds, ie 10 to the minus 23rd degree seconds - during which time a photon of light crosses the proton). The so-called conditionally "stable" types of hadrons lifetime may exceed the nuclear time a trillion times (see "Trillion Isaeva).

Each group of elementary particles is characterized by its own specific conservation laws. Currently, the elementary particles known seven "charges", the sum of which should remain unchanged in nuclear processes: the baryon number, lepton electronic charge, the muon lepton charge, the tau lepton charge, strangeness, charm, charm ("magic" number 7).

The electric charge of any elementary particles (in free form) is one of the 4 possible values: "minus" e (elementary charge), zero charge, "plus" e, "plus" 2e. The law of conservation of electric charge - one of the fundamental laws of nature, consisting in the fact that the algebraic sum of charges of any closed (electrically isolated) system remains unchanged, whatever the processes may occur within the system.

Behavior of elementary particles due to quantum properties. The most important of these - the ability to be created and destroyed (emitted and absorbed) in interaction with other particles. In search of new particles, scientists are building ever more powerful accelerators. The most astonishing experiments designed at CERN - the leading European Institute for Nuclear Research, located in Switzerland and France, employing 5,000 scientists from 40 countries (with the Russians - on the first cast!). There are completing the construction (reconstruction) of the Large Hadron Collider (LHC). Its length - 30 km, it deepened into the ground at 100 meters at the LHC in collisions of protons and antiprotons are created beams of particles with great energy - 7,000,000,000,000 eV (the characteristic energy at the age of the universe 0.00000000000001 seconds.) This is close to the conditions of the Big Bang, after which the matter existed in the form of quark-gluon plasma. Note that the maximum possible accelerator on Earth, which is equal to the length of Earth's equator (!) Will achieve the energy that only once in 1400 will surpass the capabilities BAC (the most expensive experimental setup as of today).

So, how much is now open "classes (types) of elementary particles? In Wikipedia there is no clear short answer to this question, however, by following links on the Internet can, in principle, to count all the particles are very open science. According to the author's already opened more than 350 species (kinds) of elementary particles (mostly unstable), and, thanks to the experiments, and their number continues to grow. With rare exceptions, it will be very heavy particles, which are usually split into lighter particles.


Within the virtual world of cosmology in numbers each class (type) of elementary particles can be (complete insanity?) To compare all of the number N of a specific type T, then there is a certain number of integer divisors. T Type of N - it is simply the number of all integer divisors of the number N. For example, the number N = 20 a total of six subgroups (1, 2, 4, 5, 10, 20), so its type is T = 6. All prime numbers N (2, 3, 5, 7, 11, 13, ...) type is T = 2 (after all primes N divider only two - one and the number is N).

In the infinite set of natural numbers (1, 2, 3, 4, 5, 6, 7, ...) the number of different types of T (more precisely, the number N of type T), of course, is also infinite. In a virtual cosmology of our universe (her age was taken to be 13.75 billion years, or about 10 to 61-degree Planck time) is equivalent to the so-called Great segment containing the same number of integers (1, 2, 3, 4, 5, 6 , 7, ...) - as the Planck time is contained in the age of the universe, then there is a large amount of time - it's about 10 to 61-th degree of natural numbers. And it is clear that within the great length of the number of different types of T (number N of type T) will be limited. According to research by the author on the large segment contains: odd types of T - about 120,000, and even types of T - about 687,430. Specified number of varieties (species) of the parameter T (different types of T) are controversial (conditional) numbers, but their order - without a doubt. [See Section 2, Chapter Types of numbers (the worlds number) "].

Inquisitive reader can find myself number of varieties (species) of the parameter T (check my numbers 120000 and 687430) in great length - it's very exciting (and very useful?) Mathematical problem!

In moving along the natural numbers (to the right of units), new types of T will appear less and less, so much so that at the very end of the big segment of "pause" between the appearance (the last, largest) of new types of T will be about 3 - 4 billion years (and themselves the types of T reached values almost equal to a trillion (see "Trillion Isaeva).

At the specified flow along the natural numbers, each new type of T (which is becoming "harder" and "harder" until i-trillion), figuratively speaking, will "fall apart" on a "light" types, since the very high probability of occurrence is small ( "light") types of T (not new, and from among previously appeared). Thus, early in the natural numbers, for example, a lot of prime numbers (2, 3, 5, 7, 11, 13, ...) in which the type of T = 2.

Thus, if we believe the virtual cosmology is currently in the universe of sorts (types) of elementary particles is (conditional) number 807430 (the sum of two conditional numbers: 120000 and 687430, see above). Will the Large Hadron Collider to check absolutely "mad" the hypothesis of the author (after all, the LHC should open many new particles)?

In any case (conditional) number of 120,000 and 687,430 (or their sum - 807,430) generated within a virtual cosmology, can be found in physical theory and experiments. Let this be not the number of all sorts (types) of elementary particles, but these numbers certainly represent one of the greatest mysteries of the universe (not yet an enigma)!

6. Benford law

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ....


Do you believe that in our time can open a new fundamental physical constants? I confess - I do not believe that personally I could have done it, but it's not about me .... And in any case, my "discovery", for sure, will surprise the reader to think and make the most inquisitive minds. After all, this new "constant", in particular, suggests that human civilization in its rapid development came to no one Rubicon (for whom - the death of civilization?).

Let me remind the reader that in contrast to the inviolable (eternally unchanging) mathematical constants, physical constants are likely to change ... (!) During the evolution of the universe - some scientific evidence of this (though still highly controversial) have appeared in recent years. However, even if the physical constants and vary with time, very slowly, and any significant changes should be expected only at scales of order the age of the Universe (about 13.75 billion years). In other words, the rate of change of physical constants are so minuscule that they are still beyond the technical capabilities of experimental science. It is difficult to overestimate science (including philosophy), the value of physical constants, since they characterize the properties of our world (Universe) in general and arise in mathematics (the only true!) Describing the world through theoretical physics (see Section 1, chapter "The initial concept and definitions ").

So we start talking about the opening (?) ... The author of the new dimensionless physical "constants"! Its numerical value is probably a little less than a trillion (10 to 12-degree), so this "constant" will be called i-trillion, that is trillion Isaev (see Section 2, Chapter Types of numbers (the worlds number) ")

Let me remind you where generally appears (tochnoe!) the numeric value of i-trillion. To this end, the reader enough to grasp just three uncomplicated postulate (virtual cosmology):

Postulate I. Each whole number of the infinite natural numbers (1, 2, 3, 4, 5, 6, 7, ...) will be identified with the quantum of time, ie the Planck time (the basic time interval - Evie). This is the time in which rays of light are the Planck length. In other words, the Planck time - this is the minimum possible time interval, which is required for the occurrence of any conceivable physical event. Planck time - this number is about 10 to minus 44-degree (of seconds). However, do not even attempt to somehow imagine such a tiny moment of time - it lies far beyond our imagination!

Postulate II. Age of the Universe (about 13.75 billion years) we will be in the form of ... a segment of the natural numbers containing a huge number of integers - the order of 10 to 61-th degree - so much the Planck time fit into the age of the universe (see for yourself with figures in hand). Said a huge segment of the natural numbers we call long periods. This name was inspired by the cosmology of the so-called Big Bang - the moment of "birth" and early expansion of the universe, to which the universe was in a mysterious singular state (in terms of its physicists have lots of questions).

Postulate III. My i-trillion - is the maximum possible number of integer divisors, which may be in a certain whole number (Ni) in the great length (it is clear that the number of Ni is located somewhere at the end of great length, but very specified number of Ni I is not known but some of my readers probably will be able to find it!). As part of the integral divisors explained that, for example, the number N = 20 has six divisors of integers (1, 2, 4, 5, 10, 20), but the number of N = 1 (one) - is a unique number, which only a divider (by the way, within a virtual cosmology unit is fantastic, "rich", diverse, unique object!).

In a natural number N is the number of all integral divisors (including 1 and the number is N) is conveniently called the type of N. We assume that a unit (N = 1) - is a very special number, the type of which is equal to 1. Obviously, all primes type is 2 (they only have two divider).

Thus, we can say that i-trillion - is the highest possible integer type within a larger segment (ie, during the existence of our universe). Moreover, we can say that i-trillion - is the ratio of the maximum possible type (Tmax) on the large segment to the smallest possible type (Tmin = 1)

i-trillion = Tmax / Tmin (7.1)

Generally speaking, this is what the definition of i-trillion (as a ratio of Tmax / Tmin) should be remembered in all the examples below (from the physical world).

I will add that in the virtual cosmology ten billion years ago (there we "are moving" when reduces the length of the Great segment in 3,7 times) i-trillion was 17% lower than at the end of great length (the end of it - is in our modern age). Compare the specified rate of change (in time) i-trillion to possible changes (in time) the most mysterious of physical constants - the TCP (see Section 1, the head of the fine structure constant).

At the same time the author stops "torturing" the reader's theoretical arguments, because now every reader should be clear that such an i-trillion. It remains the last (already largely practical) question: why, strictly speaking, one can assume that the i-trillion - is the physical "constant"? The simplest answer is - yes, if only because that i-trillionth of "discovered" when considering the real (physical) world. Below are the most obvious manifestation (incarnation) i-trillion in the real world.

The mass of the heaviest fundamental particle (t-quark) is 174100 MeV, and the lightest weight of the fundamental particles (electron neutrinos) does not exceed 0.0000022 MeV. Hence, the neutrino mass may well be 9 times less than the (experimenters to date), but then the ratio of the mass of the heaviest particles to the mass of the lightest particle will be equal ... i-trillion, that is against the very "hard" numbers to the most "easy" to those within the Greater segment (virtual cosmology, see above).

The explanation of this equality of two relations (of real physics and cosmology, virtual), the author believes, is as follows. A number of positive integers (its a long stretch, see above) has a kind of "internal" structure (it is formed integral divisors of each number, etc.), and this structure (you will not believe!) ... Daunting, because the theory of numbers - is a complex section of the highest Mathematics! In this world of numbers (the mathematical structure), as it were "copies" the real physical world (the fundamental mathematical model, relations, relationship). Figuratively speaking, the world of numbers is like a kind of "mirror" universe - about this and tells my virtual Cosmology (worlds Isaeva). Moreover, the world of numbers like "indicates" the physical world how it should be now (in a virtual cosmology - this is the end of the Great segment). It is the world of numbers "dictates" to us that the ratio of mass to the heaviest particle mass the lightest particle must be equal to i-trillion (which can also be interpreted as the ratio of the maximum possible type in large stretches of the smallest possible type: Tmax / Tmin, see above ). And if this "crazy" hypothesis (and not much else!) Gets too annoying knowledgeable reader, I beg him to tell me why this relation from the physics of numerically coincides exactly with the i-trillion, including all the examples listed below! And how would I have been accused that I allegedly "attract the number of ears (to get my" cherished "i-trillion) - all the same this i-trillion (or something very close to it!) Clearly discern in the surrounding physical world (like, say, and it is clear "magic" number 7, see Section 1).

In all other examples (below) we'll just "discovered" the coveted i-trillion, assuming that the underlying explanation for this will be the same (just a world of numbers - a "mirror" universe "). The above examples on their own (without i-trillion) - very informative. In principle, this should be read every cultured man!

Thus, we extend concrete examples of "discovery" i-trillion.

Studying the properties of top quarks (t-quarks) - one of the challenges facing the Large Hadron Collider (LHC), built near Geneva. BAK is the largest research facility in the world, whose main task - the capture of "the so-called Higgs boson. According to the scientists, this boson would appear no more frequently than once in the i-trillion collisions occurring in the detector of the LHC for about one day. From this fact implies that the Earth Day - a time interval characteristic (vital) to any alien civilization. In other words, intelligent life is possible only on the planets that are similar (in its physical parameters, parameters of their orbits) to our Earth (more on that another will be discussed below, see about exoplanets).

Atom - the smallest (chemically) indivisible part of a chemical element that is a carrier of its properties. An atom consists of a nucleus (a heavy nucleons) and the surrounding electron cloud (which is more than 1836 times lighter nuclei). The ratio of the atom to the volume of the nucleus of an atom - the i-trillion. Therefore, by the way, we can say that in some sense, an atom of any chemical element that ... "empty" space!

According to string theory, the size of closed strings (like "diameters" them "vibrating ring") can vary widely. In this case, it is likely that the ratio of the maximum possible size (not exceeding the size of quarks and leptons) to the smallest possible size of the string (of the order of the Planck length) will be exactly equal to i-trillion.

The exact number of galaxies in the observable universe is unknown, but they shall not be less than 10 in 11-degree (galaxies) - at this point all the scientific sources. The theory predicts that the total size of the universe is much larger (than observed). Thus, we have a right to exist following hypothesis: in the present epoch in the universe of galaxies is equal to i-trillion. By the way, given the enormous size of the universe, we can say that in some sense, our universe is ... "empty" space (see above about the atom)! After all, the average density of visible matter in the universe - is one atom in a cube (space) with an edge of about 2,55 m.

The number of stars in the biggest galaxies (which include our galaxy, seen by us with the "edge" in the night sky and bears the name of the Milky Way) is close to i-trillion. In other words, the mass of most large galaxies can reach 10 to 12-degree solar masses (which, remember, is the most common, typical of stars in the universe).

Of all the currently known extrasolar planets Gliese only (more precisely, Gliese 581 c) is most similar in its parameters and the likely conditions on Earth (that is, on Gliese can also be intelligent life!). Therefore, it is Gliese is still one of the most "valuable" finds among the 500 exoplanets (400 "other" planetary systems). Distance from Earth to Gliese - about 20 light-years in the i-trillion times larger than the size of a large asteroid (4 Vesta), which man is still able to see in the night sky with the naked eye. In other words, the characteristic distance between the "brothers on reason" in space in the i-trillion times greater than the minimum possible distance between them (when the two "brothers" are on the same asteroid).

The typical diameter of the solid planets (such as our Earth) in the i-trillion times greater than the characteristic size of dust particles (in space ranging in size from a few molecules to 0.1 mm). That is a particle of dust - it is in some sense, the smallest firm ... "planet".

Largest possible mass of the planet (otherwise the planet into a star) in the i-trillion times the mass of the average (or slightly less than this) asteroid. Solar mass in the i-trillion times the mass of micrometeorites in the solar system.

According to science, called nucleosynthesis, the most common chemical element in the universe - is a hydrogen atom, and the least common - the tantalum atom. The ratio of these abundances - the i-trillion.

Absolute zero (0 degrees Kelvin or minus 273.15 degrees Celsius) to achieve the impossible. Obviously, the closer to it than just the temperature in the intergalactic space (average density - less than 1 hydrogen atom per 1 cubic meter). In 2003, experimenters in the lab was down "only" to a temperature of 10 to minus 10-degree Kelvin, that only two orders of magnitude of the reverse "i-trillion (10 to minus 12 th degree).

Chemical element with the highest density in the solid state - it's osmium (22,590 kg / m at 298 K). However, the density of neutron stars (and, in fact, the density of atomic nuclei) in the i-trillion times greater than the density of osmium!

Quasar - a bright object in the center of the galaxy, which is usually (?), Makes the i-trillion times more energy per second than our sun (and sometimes 10 times more than that!). It follows that the second - a unit of time are important (significant characteristic) for all intelligent civilizations in the cosmos. In other words, the "green man", surely has a "second" very close to "our" second.

The biggest black holes in the mass in the i-trillion times larger than the smallest stars - brown dwarfs, whose mass of about 0.08 solar masses (the most typical, ordinary star in the universe).

Physics Colin Froggatt and Holger Nielsen gave a new explanation for "dark matter": the foundation of it - superdense "dark balls" in diameter 20 cm and weighing 10 to 11-degree kg, which can be "hidden" inside the stars. The ratio of the diameter of the largest star to the diameter of the "dark world" is equal to i-trillion.

On Earth, there are up to i-trillion types of organic molecules - building blocks of living matter (though only 50 of them are involved in fundamental processes of life).

The largest living organism ever lived on Earth - is a blue whale. The heaviest blue whale (of a man caught) weighed nearly 177 tons (with a length of 33 m). It's in the i-trillion times more weight to the smallest of living matter. The latter include, for example, viroids - the smallest living object on earth. The smallest viroids (small cytoplasmic RNA) virus, rice yellow spots have a length of only 220 nucleotides.

The tallest tree on Earth (which is also a living system) - a sequoia, whose height reaches 115 m elementary living system, the basic structural and functional unit of all living organisms - is a cell (animal or vegetable), the minimum size is 0, 1 - 0.25 mm to 155 mm (an ostrich egg in the shell). Inside the cell carrier (overarching) genetic information is DNA. In turn, the DNA polymer composed of nucleotides, and the length of each nucleotide of about 10 to minus 10-degree meter that i-trillion times smaller than the height of redwoods.

Seychelles palm seed (the largest seed in the world) weighs 23 kg, and the seed of orchids (the smallest seeds in the world) weighs a few thousandths of a milligram. The ratio of the weights of these seeds tends to i-trillion.

The average height of a man on earth i-trillion/10 times smaller than the average distance from Earth to the Sun (and the distance - the most optimal for life on extrasolar planet). It is curious that the average man's height (1,62 m) - is the middle (tsentr!) logarithmic scale of the universe of all possible distances: the characteristic size of the quarks and leptons (10 minus 26-degree meter) to the characteristic size of our universe ( 10 in 26-degree meter). That is a logarithmic scale, in a sense a person (an intelligent being) - is the center of the universe!

The human brain contains a trillion i-cells (and the entire human body - is 100 times more cells). Capacity "long" human memory i-trillion/10 order bits of information, ie a person 70 years could "ship" in memory of 60 bits of information every second (!), But the nature somehow safely "hide" from the majority of our memories . The intensity of sound as perceived by our ears, may vary i-trillion/10 times.

The length of the DNA helix of human order i-trillion/100 links. In the women's blood near the i-trillion platelets, a man of little more. In lymph i-trillion/10 human lymphocytes. On the surface of the human body lives about i-trillion bacteria. The minimum length of life (1-2 days) - the cells of the intestinal epithelium, i-trillion/10 these cells are killed every day.

Number of people who have ever lived on Earth, is rapidly approaching i-trillionu/10 people. According to the theory of Kapitza SP in 2005, the rate of population growth has already peaked, and then - change of forms and parameters of human development, and nothing like this on Earth has ever had.

Power of most of the hydrogen bomb, man-made - 100 megatonnes of TNT (USSR, 1961). This is the largest man-made bomb is the i-trillion times the power of conventional manual fragmentation grenades (weight 0,3 ÷ 1,2 kg). Grenade - is, in fact, the smallest man-made bomb. Humanity has already recognized that the use of hydrogen bombs over 100 megatons - this is the end of our civilization.

Physical limit of miniaturization of semiconductor devices in i-trillion/10 times attometra - limit "penetration" into a microcosm of experimenters to date (soon to scientists "will sink" for another order, and then we will get the coveted i-trillion).

Radio waves: the ratio of hyper-high frequency to extremely low frequency (3 ÷ 30 Hz) is equal to i-trillion. Atomic clocks (by atoms of cesium 133) make almost i-trillion/100 vibrations per second, and the latest watches, based on a single mercury atom make more vibrations per second (the maximum number of oscillations - the i-trillion?). See also Section 100, chapter "Let there be light."

The tallest building built by man, has a height of about 1 km (for example, "Dubai Tower" has a height of 828 m). Nano - a conglomerate of atoms and molecules, the dimensions of such clusters in the i-trillion times less than 1 km. Such a cluster of nanoworld - it is like a minimal structure (the "Building"), created by mind and by human hands. The future of such small clusters of people going to design just about anything (including buildings up to 4 km)!

The biggest ship in the world (oil tanker) weighs about i-trillion grams. Recall that 1 gram - the weight of a (Soviet) a penny, that is, practically, the minimum weight, which is available to man in his senses when he was still able to do without the exact weights. By the way, now the world's annual production of about i-trillion liters of crude oil and about i-trillion cubic meters of natural gas.

According to the list of most expensive paintings in the world (painting sold at auction), the maximum value is close to i-trillionu/100 cents (the cheapest picture may well be worth just a few cents).

The total amount of money spent on defense and arms in 2004, the first time in history exceeded i-trillion dollars. In September 2008, U.S. president (even Bush) wanted to provide i-trillion dollars in order to avoid the inevitable crisis of capitalism (but congressmen by 13 votes against, then blocked a decision).

Status of the richest man in the world for almost reached i-trilliona/10 dollars. It is obvious that up to the amount of i-trillion dollars, there are very few. For information: for example, in 2004 almost one billion (!) People on the planet had an income equal to one dollar a day (now on the planet live 7 billion people). Thus, very soon the state's richest man in the i-trillion times the condition of the poor (this is the limiting factor of stratification in society?). And then what awaits mankind? Yes, it is likely to continue - ... NOTHING! For example, in 2029 (or 2036), human civilization may die from an asteroid hitting the Earth Apofes. And then the earth will be developed (almost from scratch) a new civilization, and until then, until once again in all areas of human activity (see the examples above) will not reach the proverbial ... i-trillion. Thus, socially, probably, i-trillion is a kind of Rubicon - the symbol of a certain boundary, the consequences of crossing that can not be predicted and prevented. Approaching all walks of life to the i-trillion, civilization should realize that most likely we are talking about the inevitability of its demise.

As a postscript to this chapter.

Number of all possible words in Russian is also close to the i-trillion. This assessment - is the number of possible placements, which can be formed from 33 Russian alphabet letters from 8 letters (talking about the usual combinatorial problem). After all, according to the authors on average word consists of 8 letters, in which, incidentally, shows the ubiquitous "magic" number 7 (see Section 1). Hence, the Russian language (his entire vocabulary - around 200,000 words), uses a tiny portion of the potential of the alphabet - no more than 0,001% of all words that could be drawn up of 33 letters. Next. If we assume that the average "length" short phrase-thought is 8 words (and it is quite likely!), Then the number of all possible phrases, thoughts would be enormous - about 10 in a 42-degree ". Therefore all is said and written by mankind in its history - is a tiny part of what in principle can generate "languages on planet Earth. However, alas, the mountain of verbal (humanitarian) debris that littered the Internet - no more than an empty phrase, practically, does not bring us to the truth (and not even making us just a little better), because the truth is written in the language of mathematics ... (cm . Section 1, the head of the great sayings "). That's about it reminds us of i-trillion (and the entire virtual cosmology). And the only regret that the vast majority of us can not stand math (in any form!) And relies on "the power of thought" the ignorant, but very influential people.

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