Gottfried Wilhelm Leibniz(1646 - 1716) has suggested a unique idea called “Monadology”.
He thought that the universe consists of innumerable monads and another complete universe is concealed in each of them.
To consider this idea, you might start by understanding that it represents a kind of fractal structure of the universe; when a particle contains another complete universe in it, such a universe must be again composed of much smaller innumerable particles, in each of which another smaller universe may repeat.
In a fractal structure, this process continues endlessly.
If the universe were really formed in a fractal structure, you could say our cosmos might be a particle, too.
We may be living in a particle.
Such particles as the cosmos may exist innumerably.
And there may be a gigantic universe, and it may not be the end of all there is. In fact, it might be another particle in another greater universe.
Such a process would also continue endlessly in a fractal structure.
(In this essay, the <universe> is used for a universe in the fractal structure while the “cosmos” is used for the space which we belong to)
In a universe of fractal structure, infinity is the final answer.
Infinity - not only horizontally but also vertically.
This idea may be quite sensible in terms of philosophy, but in the aspect of science, it has been impossible until now.
Now, you will see the reality of the fractal universe in this essay.
You will see the ultimate substance of matter.
And you will see here the true face of time, too.
Big Bang Theory
I am going to prove in this essay that the universe is formed in a fractal structure.
However, since the Big Bang theory is dominating today's ideas of cosmology, I think I have to mention it beforehand.
There must exist only one ultimate truth of the universe.
If the Big Bang theory were definitely true, all other ideas would not be worth consideration because we have already got the truth.
But if the Big Bang theory proves to be not true, you will have to take another idea seriously.
So, I am going to indicate here the wrongfulness of the Big Bang theory before I start demonstrations of Fractal Cosmology.
According to the Big Bang theory, a particle of ultra-high density exploded about 15 billion years ago, and since then the cosmos has been expanding at the velocity of light.
So, cosmic history is said to be 15 billion years old and the cosmic radius to be 15 billion light-years.
Since time and space are inseparably related to one another, any theory upon the cosmos has to explain cosmic phenomena logically in the viewpoint of time as well as of space.
The Big Bang is a deduction drawn from the red-shift of galaxial spectrums.
Except several members of the Local Group, all galaxies in the cosmos are concluded to be receding from us, which has been thought the only reasonable explanation for all the galaxial spectrums showing red-shift.
If the cosmos has been expanding, there must have been a starting point of expansion - that was the Big Bang, physicists have concluded.
However, if you failed to explain cosmic phenomena in terms of time by means of Big Bang theory, you would have to search for another reasonable cause of the red-shift.
In the meantime, astronomers who have observed galaxies know the following facts;
(1) There are more than 100 billion galaxies in the cosmos.
(2) Galaxies are basically forming clusters here and there; several or dozens of galaxies gather to make up a cluster.
(3) Galaxies in a cluster system are combined because of gravitation.
(4) Galaxies revolve around the total gravitational center of a cluster system.
(5) The Milky Way Galaxy is also a member of a cluster called the <Local Group> which consists of 30 or so nearby galaxies, including the Andromeda galaxy which is about 2.5 million light-years away from us.
The Amdromeda galaxy at the opposite side of the Milky Way Galaxy in the Local Group, is nearing toward us in the course of its revolution around the total gravitational center of the Local Group.
(6) The pure rectilineal approaching speed of the Andromeda galaxy is about 50 km/sec.
The total rectilineal travelling distance of the Andromeda galaxy during its one time revolution around the Local Group may be about double the distance between it and us; that is 5 million light-years.
Consequently, you can simply figure out the revolution period of the Andromeda galaxy, through dividing 5 million light-years by 50 km/sec.
5 million light-years : 50 km/sec =
= (5,000,000 ∙ 365days 4hours 60min 60sec ∙ 300,000 km) : 50 km/sec =
= 9.46 ∙ 1017 sec.
When you convert 9.46 ∙ 1017 seconds into years, it makes 30 billion years. This means the Andromeda galaxy has not yet revolved once since the beginning of cosmic history.
It does not make sense.
However, somebody might maintain this supposition; as the cosmos had been expanding at the velocity of light, the cosmic radius was smaller in the past. Therefore, the radius of the Local Group must have been smaller, too.
In such a situation, intergalaxial gravitation had to increase to result inevitably in faster movements of galaxies.
Consequently, though they are moving slowly at the moment, they must have revolved many times already while the cosmic radius was much smaller than now.
This sounds plausible.
But let's see the reality, not the deduction.
Astronomers have observed that the cosmic structure is uniform to as far as 100 billion light-years.
This means that you can say galaxies in the cluster systems have not revolved once during at least 100 billion years.
Now, let's think about the future this time.
The cosmos is expanding in the viewpoint of the Big Bang theory.
Therefore, if the cosmic radius becomes double the present one, the extent of the Local Group will also be double the present one.
After 15 billion years when the cosmos has expanded to 30 billion light-years in radius, the extent of the Local Group should be 5 million light-years.
By then, the Andromeda galaxy may be reaching the position where the Milky Way Galaxy is presently located.
However, the Andromeda galaxy would not be able to reach there because the extent of the Local Group will become wider and wider while it travels and, to the contrary, its travelling speed will become slower and slower with the decrement of the gravitational interaction.
Though the Andromeda galaxy has reached the position where the Milky Way Galaxy was once located, Andromedans will never be able to finish a revolution around the Local Group. That is because it will take another 30 billion years or longer to carry out another half of their itinerary.
You can tell this story at any point in the future.
Therefore, you may conclude that the Andromeda galaxy can never complete a revolution in the future as long as the cosmos expands.
Now, we have obtained two definite points in case we regarded the Big Bang theory as true; one is that galaxies in cluster systems have not revolved once during at least 10 billion years in the past, and the other is that they will never be able to carry out a revolution in the future.
Therefore, the conclusion seems to me that galaxies are not revolving.
Galaxies can not revolve if the cosmos is ruled by the Big Bang theory.
However, this is in contradiction to reality.
The reality is that galaxies are combined in gravitation and they are revolving around the total gravitational center of the cluster.
It is a reality that astronomers have concluded through observations.
Those two contradictory conclusions can not be true at same time.
So, we have to choose one of them. We have to choose one between the reality and the deduction.
I would like to choose the reality, for I think any theory can not surpass the reality.
As the Big Bang theory failed to explain the time factor of cosmic phenomena, so it might be said to be untrue.
Now we might consider Fractal Cosmology.
In the Fractal Cosmology, the cosmos is substantially the same as a particle.
The cosmos is replicated in each particle which comprises cosmos.
As man is also a component of the cosmos, you could describe the fractal universe by laying stress on man, too.
That is, you could imagine a gigantic being in which numerous cosmoses are included, and our cosmos is just one of them, and there are numerous particles in your body, each of which may be thought to be a complete cosmos by ultra-small men who may be living in it.
If this idea were true, you might be able to prove it.
It is a question of similar figures. I will show you a simple example.
Here is a triangle. You expand it to double the size in a duplicator.
Now you have two triangles; the one is small and the other is large.
These two triangles are similar shapes.
In similar shapes, the ratio between the corresponding sides of each other is always constant.
So, they retain a substantial identity.
When you expand the small one to double the size or reduce the large one to half the size, they will meet exactly.
There is no method to tell the difference between them.
Therefore, if two triangles prove to be similar shapes, you can regard them as retaining substantial identity.
This logic can be applied regardless of the size of triangles.
Suppose you start to expand the one larger and larger, and reduce the other smaller and smaller.
Though the large one has became larger by a million times than the small one, there will not happen any change in the fact that the two are substantially identical.
Now, let's suppose you expanded one to the size of the cosmos and reduced another to the size of a subatomic particle.
Even in such a case, as far as you are able to measure every corresponding side, you will not have any difficulty to prove them to be similar shapes.
This is a simple and unquestionable logic.
If you could measure all the elements both in the gigantic being and in your body and then show all the ratios of corresponding elements to be always constant, the idea that the gigantic being and yourself are substantially the same might be recognized as true.
This is the method to prove the fractal structure of the universe.
Stages Of The Universe
Let's call the large world inside the gigantic being 'the macro-world' and call the small world replicated in your body 'the micro-world'.
Then you can arrange all the stages of the universe from subatomic particles to the gigantic being as follows;
(1)Micro-world : subatomic particles - (atomic nucleus) - atoms - molecules - macromolecules - morphological elements - cells - man
(2)Macro-world : stars(the sun) - (galaxial nucleus) - galaxies - clusters - great clusters - superclusters - the cosmos - gigantic being
Above line-ups include all stages of the universe, and no outstanding stage exists other than above.
If the universe were replicated in fractal structure, the magnitude ratios of corresponding elements between the two extreme worlds would be all constant.
To compare the appearances roughly at each stage, you may become aware that elements in the two line-ups are likely to match each other as the sequence as arranged above.
I decided the sequence after deliberately comparing their appearances, distances between colleagues and so on.
In the above sequence, atoms correspond to galaxies.
However, you may be familiar with the idea that the atom is similar to the solar system. This idea looks rather widespread because, according to the classic atomic model, electrons have been described as turning around an atomic nucleus.
However, this idea is far from the reality.
In the material world the distance between atoms is very close; their neighbors are mostly in the range of their diameters or so.
But the distance between stars is exorbitant; stars are normally separated in the distance of some light-years which is equivalent to tens of millions of times the average stellar diameter.
Consequently, the idea that atomic structure may be similar to that of the solar system is not worth consideration at all.
Now let's pay attention to the above sequence.
By the way, it is indispensable that you must confirm each size first of all when you intend to calculate the ratio of two elements.
However, as you may easily notice, to decide the definite sizes of elements in the above line-ups is not possible. It is because the sizes of all the elements are ranging within some extent.
For instance, galaxial diameter: 10,000 ~ 100,000 light-years
estimation of cosmic radius: 10 ~ 30 billion light-years
cellular diameter: 10 ~ 100 microns
Like this, every element has not a single value but is distributed within some range.
But, in the material world, things are arranged in quite fair order.
When you survey the magnitude range of members at each stage in above line-ups carefully, you may notice the fact that in general cases the upper value does not exceed 10 times of the lower value.
Now, my suggestion is that you calculate every ratio using mean values and admit a tenfold variation at each result.
Somebody may assert that comparing things of indefinite magnitudes is meaningless, but I think it's quite a fair method for dealing with the material world in which members of each stage, various as their sizes may be, are distributed within quite limited ranges.
Demonstrations In The Aspect Of Space
From now, I'm going to calculate each ratio one by one.
All data used in these demonstrations are from the findings of modern science.
The purpose of these demonstrations are, as you understand, to confirm if all ratios would be constant or not.
First, I will start with [atomic nucleus : galaxial nucleus].
The ratio of [subatomic particle : star] will be calculated in the end, for it needs some complicated explanation.
For some calculations, I'll use the mean radius of elements, the shapes of which are mostly spherical and compact.
But for some others, I'll use a mean diameter or a rough magnitude of elements, the shapes of which are mostly irregular.
(1) The atom has a nucleus at its center.
The nuclear radius is about 1/100,000 of the atomic radius, i.e. 10-13 cm.
A galaxy generally has a nucleus at its center, too, and its diameter does not exceed 1 light-year.
In case of the Milky Way Galaxy, the nuclear diameter is observed to be about 0.65 light-year.
Recently, quasars have become understood as being nuclei of active galaxies and their diameter is estimated to be no larger than 1 light-year.
Therefore, you may regard the nucleus of the Milky Way Galaxy as a standard.
Then the mean radius of galaxial nuclei can be decided as 0.33 light-year.
Radius of atomic nucleus : radius of galaxial nucleus =
= 10-13 cm : 0.33 light-year =
= 10-18 km : 3.12 ∙ 1012 km =
= 1 : 3.12 ∙ 1030
(2) The atomic radius is generally said to be 1 angstrom, i.e. 10-8 cm.
Galaxial diameters are ranging from 10,000 to 100,000 light-years so that you may take 30,000 light-years for the mean galaxial radius.
Atomic radius : galaxial radius =
= 1 angstrom : 30,000 light-years =
= 10-13 km : 2.84 ∙ 1017 km =
= 1 : 2.84 ∙ 1030
(3) There are so many kinds of molecules and their sizes so various that it is very hard to determine the mean molecular size.
To regard their shapes as spherical, small molecules are said to be ranging from 1 to 10 angstroms in diameter.
In an organism, proteins are the typical macromolecules, and they consist of amino acids.
Therefore, amino acids may be regarded as the typical molecules in an organism.
The size of amino acids in an alpha-helix, one of the typical protein structures, is about 5 angstroms.
So, you may take 5 angstroms for the mean molecular diameter of organisms.
Several or dozens of galaxies gather to form a cluster.
The typical extent of clusters is observed to be about 1.5 million light-years in diameter.
Molecular diameter : cluster diameter =
= 5 angstroms : 1.5 million light-years =
= 5 ∙ 10-13 km : 1.42 ∙ 1019 km =
= 1 : 28.4 ∙ 1030
(4) The primary organic elements in organisms are macromolecules such as proteins, nucleic acids or polysaccharides.
There are many kinds of macromolecules so that determining the mean size must be very hard, too.
Therefore, it's better to find a typical one.
Protein occupies the largest portion of an organism.
And a typical protein consists of about 200 amino acids.
So, you may say the typical macromolecule in an organism is the protein which is assembled with about 200 pieces of amino acids.
The size of such a typical protein is about 300 angstroms.
Atoms are united to make up a molecule, and molecules are combined to organize a macromolecule.
Such a process is exactly repeated in the macro-world, too.
Nearby galaxies are combined to make up a cluster, and clusters gather to form a great cluster.
The great cluster is generally formed by more than 50 galaxies, and its extent is about 10 million light-years.
Magnitude of the macromolecule : magnitude of the great cluster =
= 300 angstroms : 10 million light-years =
= 3 ∙ 10-11 km : 9.46 ∙ 1019 km =
= 1 : 3.15 ∙ 1030
(5) The actual physiological processes of the cell are performed by morphological elements such as mitochondria, microtubules, golgi bodies, etc., which are organized with macromolecules.
There are many kinds of morphological elements and their sizes are all different, but you may notice that they are mostly measurable in microns.
The mean size of them all could be said to be 5 microns.
As the tenfold variation is permitted for these calculations, most morphological elements may be covered by it.
The last stage in the cosmos is the supercluster, the same as the last stage in the cell is the morphological element.
Since 1980, astronomers have discovered superclusters, the greatest structures in the cosmos, such as Bubbles, Stakes and Great Walls.
The extent of these superclusters generally reaches some hundreds of millions of light-years.
So, you may take 500 million light-years for the mean magnitude of superclusters, which may cover most of them to consider the tenfold variation.
Magnitude of morphological element : magnitude of supercluster =
= 5 microns : 500 million light-years =
= 5 ∙ 10-9 km : 4.73 ∙ 1021 km =
= 1 : 0.95 ∙ 1030
(6) The human body consists of around sixty thousand billion cells.
The shapes of cells are generally spherical, and their sizes are mostly ranging from 10 to 100 microns in diameter.
So, you may take 50 microns for the mean cellular diameter.
Then the mean cellular radius makes 25 microns.
The cosmic radius is often mentioned differently by scientists.
Their opinions may vary but converge in ranges from 10 to 30 billion light-years, among which 15 billion light-years is widely accepted.
So, you may take 15 billion light-years for the cosmic radius.
Cellular radius : cosmic radius =
= 25 microns : 15 billion light-years =
= 2.5 ∙ 10-8 km : 1.42 ∙ 1023 km =
= 1 : 5.68 ∙ 1030
(7) Now it is time to calculate the ratio of [subatomic particle : star].
Stars in the galaxial system are turning around the galaxial center, while electrons are turning, or distributed in the meaning of the quantum theory, around the atomic nucleus.
Therefore, you may regard them as corresponding to each other in fractal structure.
However, you may easily notice a great disharmony between them.
In the Milky Way Galaxy, for instance, there are more than 300 billion stars; on the other hand, there exist only a few electrons in the atom.
Hydrogen has one electron only, carbon 6, nitrogen 7, oxigen 8, and even uranium, having a very heavy atomic weight, has just 92 electrons.
Here, I am going to suggest a new idea of the electron.
As is known well, stars in the galaxial system are not scattered
at random but form spiral arms.
The book "Infinite Universe in a Mote" was published in 1994
from Sagyejul Publishing Co., one of the major
publishing companies in
It has 290 pages.
It explains the Fractal Cosmology precisely in easy words.
Any publishers who want to publish this book in your language may write a letter to the author by E-mail : firstname.lastname@example.org
This page (http://sergf.ru/fc.htm) is a copy from: http://www.fractalcosmology.com/ , Yun Pyo Jung.