Cosmic Self-Similarity

Emanuele Meloni
Jan 24, 2021
5 min read

Planets revolving around stars and electrons revolving around atomic nuclei.

The ultra small reflected in the ultra large.

When dealing with scenarios of extraordinary scientific complexity, in which human understanding strives so hard that it touches on peaks of imagination hardly empirically demonstrable, it's always good to discern such scenarios and go for parts, follow the understanding with caution, especially when trying to explain nature, in which in a millisecond the order turns into chaos.

Optionally dividing this macro-theme into two mini-paragraphs, the fractal and the golden section, We will humbly try to strengthen the intention of these two theoretical concepts that underlie the existence of some of the most bizarre and fascinating scenarios enjoyable in nature. -THE FRACTAL: We speak of Fractals when referring to those natural geometric structures that, despite the irregularity of their shape, are subject to auto-similarity, or have the property of showing the same geometric profile on different scales of magnification.

This term was coined in 1975 by the French mathematician Benoit Mandelbrot, considered the creator of the same concept of fractal. A relatively recent subject, therefore, but of great importance for the description of phenomena that have always been almost paradoxical.

2. the structure of the whole Roman cabbage replicates in the peaks that compose it, which in turn are covered by even smaller peaks but always of identical shape.

They are recursive mathematical procedures applied to infinity and subject to the fractal dimension, that's, a number that indicates the degree of fragmentation and takes into account the irregularity of the object or phenomenon observed. Here, therefore, can be described the repetitive form of coastal lines, mountain profiles, cloud formations, molecular structure of polymers, aggregations of particles suspended in liquids, and in general of all those phenomena to which, despite their apparent irregularity, nature has conceded the surprising characteristic of self similarity. But the limits of understanding as always are touched on a cosmic scale, in which the concept reaches peaks of the highest imagination.

The Lambda-CDM model is the simplest physical model in accordance with observations that reproduce the genesis of the cosmos, its functioning over time and its large-scale structure and, thanks to its reliability, is considered the current standard model of cosmology.

Of all theories of multiverse bubble theory is among the few that faithfully follows the calculations of the Lambda-CDM model. It's also the only one to draw on experimental data: the multiverse would be an immense quantum foam hosting infinite bubbles. Bubbles are universes, whose formation is eternal (see Eternal Inflation) and connected to each other by space-time bridges.

The Big Bang itself could be the product of inflation of other universes, in a process that is endlessly repeating itself over and over, analogous to cellular self-replication involving animal and plant tissues and during which DNA is also replicated; Once again the ultra small that is reflected in the ultra large.

Evidence of this inflation (namely the theory that immediately after the Big Bang in an infinitesimal fraction of a second our universe would have expanded its radius by about a billion billion times, and then resume its previous expansion rate) were the detection in 2014 of primordial gravitational waves by radio telescopes of the base Amundsen-Scott, in the South Pole, then confirmed in part by the observation of the cosmic background radiation and theorized ninety-eight years earlier by Albert Einstein in the theory of general relativity.

-THE GOLDEN SECTION: is another concept in which nature can be explained through mathematical calculations, but this time it is the beauty that arises to have a key role. By definition the golden section is a number, the result of a mathematical division

Usually the division is between the values of two adjacent lengths.

3. the division of the diagonal BC to the BA segment gives one of the many gold numbers that can be found in the regular pentagon. The triangles that form the points of the star traced inside it are golden, and in the middle a new regular pentagon is formed F-G-I-J-H inside which it is possible to trace a new star and so on. Theoretically, the process can lead to infinity.

The origins of his study are traced back to the Pythagorean school and, in particular, to the observation of the square and the pentagon twenty-six centuries ago: it was noticed that the division between diagonal and side generated a number not representable in the form of a fraction, an irrational number therefore, and the two values of the quantities (diagonal and side) did not have any common sub-multiples. The value of the division is 1.618 and is considered golden any number resulting from the ratio between the sum of the values of two adjacent quantities (for example, the side and diagonal of a polygon) and the value of the first quantity taken into consideration, the result of which tends to 1.618. The ancient Greeks called it phi. In time it was considered synonymous with perfection, behind which was hidden the divine.

But where do we put beauty in this context?

4. The double DNA helix shall be impregnated with golden proportions.

In the next two and a half millenniums it was noticed that the forms, the structures, the creations, whether they were natural, whether they were generated by man, have to do with this number, with this rapport. Not only that: they are also beautiful and harmonious in most cases, and since (as with fractality) their forms follow a recursive pattern and are repeated to the bitter end, more repetitive they are and more beautiful and harmonious they become.

5. bounded by a golden rectangle the golden spiral is traced following the series of Fibonacci, and is attributable to a myriad of natural formations.

After the important treatise written on the subject by the greatest mathematician of antiquity, Euclid, in 300 BC, the study of this matter lived a stagnant phase until, 1,500 years later he was an Italian mathematician, unknowingly, to put black on white the most important numerical sequence linked to the golden section.

His name was Leonardo Pisano, known as "the Fibonacci", and he was a lover of Euclidean geometry and Arabic mathematical sciences. His intent was to study the reproductive sequences of rabbits, considering their periods of fertility and how many specimens were born month by month from a single initial pair.

The result was the writing of a series of numbers corresponding each to the pairs of rabbits in life of each month: 1 - 1 - 2 - 3 - 5 - 8 - 13 - 21 - 34 - 55- 89 - 144 - 233..... Note that each Fibonacci number is the sum of the two preceding it (for example. 8=3+5). It was, however, Kepler four hundred years later to note also that the division between two consecutive numbers of the Fibonacci sequence tended gradually more and more precisely to the golden number (for example 55:34=1,617) and applied the numerical sequence to trace the orbits of the planets around the Sun and thus improve the heliocentric model theorized by Nicolaus Copernicus in the previous century. Thus a new window was opened on the link between numbers, man and nature, and it was realized that the Pyramid of Khufu, as well as the entire plain of Giza,