**Isotropy and the growth rings of a tree**

Isotropy is uniformity in all orientations. So, in this lecture, the reader will find a brief inquiry into an old alchemic principle. Our universe shows everywhere uniformity and auto-similarity. So it appears the same from any position. In order to explain this reality, Einstein elaborated and achieved his special relativity theory.

## Isotropy and the cosmological principle

Isotropy is in complete harmony with the definition of the cosmological principle. It is the notion that the spatial distribution of matter in the universe is homogeneous and isotropic. This is a consequence of the fact that we expect the forces to act uniformly throughout all the universe. They should, therefore, produce no observable irregularities in the large-scale frame of our cosmos.

Isotropy is derived from the Greek *isos* (ἴσος, “equal”) and *tropos* (τρόπος, “way”). We indicate exceptions, or inequalities, by the prefix *an*, hence anisotropy.

Astronomer William Keel explains:

The cosmological principle is usually stated formally as ‘Viewed on a sufficiently large scale, the properties of the universe are the same for all observers.’ This amounts to the strong philosophical statement that the part of the universe which we can see is a fair sample. As a consequence, the same physical laws apply throughout. In essence, this in a sense says that the universe is knowable and is playing fair with scientists.^{[1]}

## Isotropy: large scales are not necessary

Anyway, as far as flat earth is concerned, in order that the cosmological principle could be respected, large scales are not necessary. For any phenomenon on the Earth’s surface, the distances are small enough that light signals appear instantaneous. This is a consequence of the fact that the flat circle we live on has a just a small radius. Thus light (admitting it had a real speed limit of 299792,458 km/s) is able to cover it 15 times in just one second. This means that a ray of light could run all the earth from the North pole to Antarctica in 4/60 of a second. It also means that a sun’s ray reaches any point of the tropic of Capricorn in 1/45 of a second. Three times faster. This actually nearly equals instantaneity.

### Isotropy and the Michelson and Morley experiment

After the Mickelson Morley experiment, Einstein himself was forced to take the subject of isotropy into consideration. ( http://earthmeasured.com/explanation-michelson-morley-experiment/ edited on this blog the 20th of December 2016) The results showed that starting from experiments made on the basis of the speed of light, it was not possible to demonstrate that the Earth rotates.

When deeply considering the topic, since the Earth rotates around its axis and around the sun, the system could not be considered as being isotropic. And this as a consequence of its not being inertial. An inertial system is stationary or moving with a uniform rectilinear speed without rotation because a rotation means acceleration and inertia. Since the Earth is said to rotate, there could be no isotropic behavior in every direction. In fact, physical laws should behave differently around the globe, whether moving eastward or westward. But isotropy means there are no special directions to the Universe and Mickelson and Morley proved that the previous hypothesis could not be true.

### Einstein ‘s special relativity theory

Einstein was then forced to posit that the rotation of the earth is not measurable by any optical means and the ether does not exist. For this reason, he posited that the light speed is of 299792,458 km/s and had to remain the same, independently of the reference system. His special relativity theory was then elaborated. It had to provide a framework for translating physical events and laws into forms appropriate for any inertial frame of reference. That is to say, it had to justify the fact that the isotropy evident everywhere on the earth could not be otherwise explained.

A corollary to the cosmological principle is that the laws of physics are universal. The same physical laws and models that apply here on the Earth also works in distant stars, galaxies, and all parts of the outer Universe – this, of course, would simplify scientific investigations immensely. Note also that it is assumed that physical constants (such as the gravitational constant, the mass of the electron, the speed of light, etc.) are also unchanging from place to place within the Universe, and over time.

## Constance in time will fail

**That the sun will not rise tomorrow is no less intelligible a proposition, and implies no more contradiction, than the affirmation, that it will rise.**

*This line was written by the philosopher David Hume in *An Enquiry Concerning Human Understanding*, published in 1748*

So, about this late assumption that physical constants will be unchanged even over time, we could discuss at length. For instance, knowing our earth-system is a capacitor and a battery we also understand the skies are wearing out. So the factor time could immediately be put into doubt. The same could be said for the physical constants in the course of time. Constance in the universe cannot be judged by simple mortal men. Everything could be changed at the right moment.

### Isotropy and the fractal universe

Now, let’s go back to our subject and take into consideration the fact that our universe has a fractal geometry behind. “Fractal cosmology is a set of cosmological theories which state that the distribution of matter in the Universe, or the structure of the universe itself, is a fractal across a wide range of scales. More generally, it relates to the usage or appearance of fractals in the study of the universe and matter. A central issue in this field is the fractal dimension of the universe or of matter distribution within it, when measured at very large or very small scales”. (Wikipedia)

Nature, of course, can offer an enormous number of fractal geometry examples. Think, for instance, to the forest trees, the ramifications of lightning, of rivers, the many dendritic patterns in the mammals and human bodies: bronchi, bronchioles, lungs, kidneys, brain neuron dendrites, circulatory systems… So, in this manner, on a larger and a smaller scale, the universe can show an underlying, constantly repeated, self-similarity.

### Isotropy and the old alchemic principle

Ancient micro-macrocosmic theories were a powerful theoretical construction able to unify the laws governing the human body with the laws governing the earth and the whole universe.”As above, so below”, was the old alchemic principle. It means that what happens in our cosmos, from the very large to the very small, is always affected by the same laws.

In writing his Timaeus, Plato noticed that the frame of our body is similar to the framework of the earth. Inside of us body fluids flow like rivers, lungs are full of air, our skeleton can be compared to stones, fire to energies emanating from the mind. He considered the universe as a living organism possessing a collective soul, the so-called Anima Mundi.

There is no doubt that since the modern times’ discovery of the atoms, the hypothesis that the living human body and the celestial stars could have the same fundamental structure, has had an astonishing confirmation. The chemical reactions inside our cells are similar to those developing in the above space. Everything that happens in the furthermost distant parts of the universe can have a deep influence on the rest of the earth’s system, even without any visible, evident energy movement transmission.

### The theory of the entangled particles

Alain Aspect, David Bohm, Karl Pribram’s theories concerning the new physic could shake the foundations of the traditional science. From the subatomic particles to the gigantic galaxies, all is an infinitesimal part and a totality of the whole. Alain Aspect and his team found that, in particular conditions, electrons can instantly communicate with all the universe, independently of the distance. It appears that every single subatomic particle knows what all the others are doing.

However, the distances in space are said to be vast. They are measured in hundreds of millions of light-years. Thus, the time for light to travel from the remotest galaxies is said to be on the order of hundreds of millions of years up to billions of years for the most distant objects.

### Instantaneous signal transmission

So, what about the distant stars? The only answer is that our cosmos is tiny enough so that the speed of light can reach every part of the universe in a fraction of the time. Instantaneously. Our firmament has measures that are far lower than the about 300.000 kilometers the light can cover in a second. Many physicists deny the possibility to find major speeds than that of the light. But the Aspect experiment could prove that the ties among the subatomic particles have no local limits and are instantaneous.

David Bohm suggests that every part in the universe system can be informed by the same structures and models. So, as I have already explained in a series of different posts, and according to the principles above introduced, the earth and the dome are made of a series of concentric and similarly spaced rings. Something like the growth rings of a tree. This reminds me of Cantor’s theorem with nested intervals.

Cantor’s theorem with Nested Intervals

Here I don’t pretend to give a rigorous mathematic explanation inside this theorem. I simply want to give an easy, elementary sample. You should consider an interval as a box, a sort of Matryoshka with a second box inside, a third box inside the second, a forth inside the third and so on. Every box has to be a bit smaller than its container. Now we could go infinitely on in order to reach the smallest box, a simple point, a single subatomic particle. That point belongs to all the boxes that are nested one in the other. You can, at this point easily understand that Cantor’s set is nonempty. So is the universe we live inside.

### The Dome and the human eye

In order to show how the Dome’s layer can be compared to many different things and realities on the earth, I would like to compare it to the layers of the human eye: the Sclera, the Choroid, and the Retina. To study them, could help to understand a lot about the framework of the firmament and the fact that the Universe has only a finite number of stars.

These are considerations I will cover in a later lecture. Bye, bye, my reader.

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