Man continually seeks deeper understanding of the world around him. From the deepest reaches of space, to the depths of our oceans, to the smallest particle, Humanity seeks to gain ever more profound insight into this world we all experience together. However, what if the clues to gaining some insight into our existence lie right before our eyes?
As I journey through my life, it continues to amaze me how complex and yet simple our existence really is. Humans have a remarkable ability to discern patterns. Repeating patterns are a phenomenon seen throughout nature, such as the fractal. Could our ability to discern those patterns and their existence be an indication of deeper truths for this reality?
Example of a Fractal
A fractal is defined as a “natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale.” No matter what magnification the observer uses, the same pattern is evident, just at a larger or smaller scale depending on the magnification used. The Mandelbrot Set is one such fractal and is illustrated to the left. Mandelbrot described the fractal as “…a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole…” (New World Encyclopedia, n.d.)
One example of a fractal is seen in a hyperbolic fractal tessellation. A tessellation is a closed, countable set of tiles arranged so that they do not overlap with a repeating pattern. They essentially form a two-dimensional shape within the Euclidian Plane. A hyperbolic fractal tessellation combines the traits of a tessellation and a fractal in a manner similar to the illustration at the right.
Fractals can be seen in our daily lives. The manner in which this article was assembled has fractal patterns – start at the highest level, build a framework (outline), select one of the subsections and write to that, inserting a sub-framework around which the words are assembled, repeat until the depth of detail desired is reached. The antennas used in cell phones are fractal in design as well. This design was selected to solve an early problem with cell phones – the large number of different frequencies each phone had to receive. The length of an antenna must be a whole fraction of the wavelength of the signal for the signal to be received. Dr. Nathan Cohen discovered in 1988 that an antenna designed as a fractal could receive multiple signals because a fractal antenna realized antennas of multiple different lengths, either matching or a whole fraction of the wavelengths of the received signals.
Fractal Pattern in Nature
Fractals are ubiquitous throughout nature as well. From a certain perspective, the fractal antenna above was successful because it replicated the concept seen in nature. Some of the more commonly seen fractals include trees and ferns. For trees, think about how the trunk is the base for multiple large branches, which form the foundation for smaller branches, so and so forth to the leaves at the end of the smallest branches. Certain sea shells also exhibit a fractal pattern. You may wonder why natural systems behave in this manner. As quoted from Dr. David Pincus:
Essentially, fractal systems have many opportunities for growth, change and re-organization. Yet they also are very robust. They maintain their coherence; they hold together well, even under tough circumstances. They are balanced in this respect, between order and chaos. They are simple, yet also very complex. This balance is often referred to as “criticality.”
And the term “self-organized” is often added because systems tend to become fractal on their own, simply by putting a lot of system components together and allowing them to exchange information. Think of a party. All you need to do is come up with enough people at the same place and time and they will start to form complex patterns of connection with one another.” (Z.McGee, n.d.) I like to think that fractals are so complex that they are simple.
Fractal Pattern in the Brain
It turns out that the brain is fractal, both in the way it is organized physically and functionally. On the physical level, at the smallest scales are the pyramidal neuron, which is the most common neuronal structure in the brain. These form into cortical columns, consisting of numerous pyramidal neurons. Finally, the Columnar Complex consists of a number of cortical columns. All of these structures exhibit branching both into and out of the arrangement. (The Fractal Brain Theory, n.d.)
Indeed, illustrations of the neuron and its surroundings depict a fractal type of construction. Even the way the brain works is fractal in nature. Psychologists discovered in recent years that behavior patterns and social behavior adhere to those principles. So Humanity exhibits a fractal nature from the smallest to the most gross scale, which may explain our connectivity to Nature itself. One author describes this connectedness as “broadband connectivity” and explains how that may be related to our consciousness. (Ph.D., 2009)
To Pythagoras, the number 10 was the holiest of numbers; the tetractys is a triangle form of 10 dots, created by interlinking the dots into nine triangles forming the 10th, larger triangle. It is used to symbolize the creative forces of the universe. From ancient-symbol.com, “In the figure, the first row has a single point that is representative of the Creator, the active principle, the divine power behind all creation and is associated with wisdom. The second row contains two points that represent the passive principle and are associated with friction, movement, impulse, strength, and courage. The third row with three points signifies the world coming out of the union of the above two, a union of physical and mental balance and is associated with harmony. The fourth row has four points that represent the four liberal arts & sciences that complete the world. These four points symbolize the four elements of earth, fire, air, and water.” This was, generally speaking, the first time that the philosophical meaning of a number, its holiness and perfection, being derived from pure mathematical reasoning rather than from inductive reasoning. It was more than the total of our fingers on our hands. Another interesting article on the triangle and tetractys, among other things, can be found here: 
In the alchemical writings of the Middle Ages, the classical elements of hermeticism were based off the form of the triangle, turned upward or down, with a line to denote the opposite or without to indicate the base elements. The conjoining of fire and water is indicative of balance and achieving perfection. The triangle is also seen in the “triangle of art” also known as Solomon’s Triangle. The circle in that triangle represents the space where spirits are called, with the triangle representative of the safe space from which the magician worked.
know much more about the word than we really do.
unexplained scientific laws that we do not understand quite yet?
of Western medicine has cropped up in many personal conversations over the years. Ideas such as Flat Earth have come back to the scene in modern discussions and often with contention. 
make an idea become an organism of knowledge?
boosters landed on Earth again. This shouldn’t be happening, I told myself. Side boosters don’t come back, they just don’t. Again, the wonderment had me re-watching several times over until the busy day I had, had dragged my eye lids closed.
unreachable? I cannot help but to understand Elon Musk’s strategy. He needed to pull our eyes off the ground by wowing us with his fancy car whizzing around Earth’s orbit because a rocket that brings us one step literally closer to Mars, wasn’t and isn’t enough.
Claudius Ptolemy (100-170 CE) was a Greek mathematician living in Alexandria. His work The Amalgest was one of the most influential astronomical works until Galileo’s discoveries in the 17th C. The Amalgest documents many mathematical and astronomical treatises, including works by other mathematicians – works thought to be lost. The most significant piece of this Amalgest (total of 13 books), is the documentation of the geocentric model of the universe. Ptolemy’s work became the accepted theory of the structure of the planets and stars, with the Earth central to all. 
Leonhard Euler, a Swiss mathematician of the 18th Century solved, sort of, the problem of the Seven Bridges of Koenigsberg (Russia, at the time). Koenigsberg had two islands connected by seven bridges. The problem is to decide whether it is possible to follow a path that crosses each bridge exactly once and returns to the starting point (touching every edge only once). Euler proved that a necessary condition for the existence of Eulerian circuits is that all vertices in the graph have an even degree, and stated without proof that connected graphs with all vertices of even degree have an Eulerian circuit. The bridges did not meet this condition and therefore, no solution could be found to the problem.
networking, and computer programming. For example, the Eulerian cycle or path is used in CMOS circuit design to find an optimal logic gate layouts. For anyone wanting to read the paper outlining these paths in the original Latin, it can be found 
For the serious student of the classics, all of these philosophers, in their original Greek or Latin (with English translations alongside the original) can be found in the Loeb Classical Library series. Many used book stores, especially near universities, carry these books and they can be had for about 10$ each. There are hundreds of books but all are quite good as original references (See NOTE below) Back to the Quadrivium…
and without a Freemasonic connection. It’s up to you, the reader, to decide what you’d like to do with the information.
