A Universe Connected
In the year 1202 AD, a mathematician from Italy asked a very simple question: “A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?” A question notably found in the third section of a publication called Liber Abaci which was written by Leonardo Pisano Fibonacci. The above question led to a sequence of numbers that the Western world knows as the “Fibonacci Sequence”. Although most accredit Fibonacci with the discovery of this numerical sequence, its existence had been observed long before Leonardo’s lifetime.
With each turn of a Rubik’s cube creates a permutation (rearrangement of color tiles)The study of permutations and combinations has long been a subject of research in areas of South Asia, particularly in India. Variations in numerical arrangements became popular in ancient Indian society and applied to astrology, medicine, music, and architecture. The first notable hint of this sequence’s existence came around 200 BC through the work of an ancient Indian mathematician named Pingala through his work with Chandaḥśāstra (metrical sciences). Following the work of Pingala, various other Indian mathematicians such as Virahanka, Gopala, and Hemachandra contributed work that gave evidence of the existence of this numerical anomaly. Not to discredit the brilliant work of Fibonacci but his most recognized contribution to mathematics, not necessarily his most significant, led to the discovery of a ratio that has scientists in most practices mystified. This ratio, as observed numerically, appears to be ingrained within the fabric of universal order. Before going into too much detail about this ratio, it is essential first to understand how the Fibonacci sequence works and how through this sequence the ratio was discovered.
One of the most consistent and elusive numbers ever discovered is 1.161803398874989. The Golden Ratio, as it is known to those seeking to discern the underlying architecture of the cosmos, is a ratio apprised in quantum physics and in the overall construct of galaxies. This ratio has been applied to and observed in geometry, nature, and architecture.
The square labeled “2” has an area double of the 2 squares labeled “1”. At this point, the ratio between the sizes does not equal that of the Golden Ratio (Ratio 2:1 or 2), however, as the tiles grow larger by building on the base predicated by the previous two larger squares, the ratio approaches and will eventually equal that of the Golden Ratio. For instance: the area of the largest square of the image above is 21 units X 21 units or 21 units². The next largest squares have an area of 13 units² and 8 units² after that. Both the squares labeled 13 and 8 have a base that’s’ sum equals 21. Mathematicians have added additional geometry to the square Fibonacci tiling to create a spiral pattern. This is known as the Fibonacci spiral: illustrated below.
The Fibonacci spiral is incorporated into a tile pattern based on the sequence. As previously stated and observed in Table 1, ratios calculated from smaller integers of the Fibonacci sequence do not exhibit the Golden Ratio or Phi (φ)(Phi is the Greek letter denoting 1.61803…). As the numbers become larger throughout the calculation, the more a Fibonacci spiral resembles the Golden Spiral. A Golden spiral is based on geometrical square tiling similar to figure 1 except all correlating tiles are designed to have a ratio of φ (Phi) as seen below.
Sequence 1: a self-similar (mathematically identical continuous pattern) illustration of the Golden Spiral. Sequence 1 is a Golden spiral continuously winding through Golden-square tiles. This also resembles a Fib spiral at larger values as they approach affinity. Sequences, tiles, and spirals may all exhibit φ, but there are plenty of different ways to observe this ratio. The golden ratio isn’t just a number or proportion; it is a reminder of the inherent connectivity that exists within our universe. The existence of the Fibonacci sequence and Golden ratio preceded mathematics as it can be observed in nature within human DNA and even within the anatomical structure of certain flowers. Now that some fundamentals have been discussed, let’s dive into a few real-world examples.
Although mathematics has deep-seeded roots in human history, DNA and mammalian procreation preceded human existence and therefore arithmetic. In 2005, a team of genealogists led by Luke Hutchison stumbled across some interesting results. In their research article entitled “Growing the Family Tree: The Power of DNA in Reconstructing Family Relationships” Hutchinson et al. retroactively studied the number of ancestors that could potentially be the source of specific genes on a particular, heritable X chromosome (sex chromosome carried by both parents). This study used advanced genomic technology to discover what Leonardo Pisano Fibonacci had centuries ago, that in a controlled environment the Fibonacci sequence and Phi may be witnessed within aspects of mammalian lineage. This is one example of how the Fibonacci sequence appears to shape natural order, but another biological example is found in the anatomy of some flowers.
The disk florets of sunflowers have an arrangement that illustrates a spiral pattern that has Fibonacci undertones. In sunflowers, the spirals that are created within the disk florets’ pattern (reproductive buds at the center of the flower) often have 34 spiral turning clockwise and 21 moving counter clockwise. Another Fibonacci anomaly may be found in the number of petals on certain flowers. For instance, Lillies have 3 petals, Roses have 8 interior plus 5 exterior petals, and Pyrethrum have 34 petals: all Fibonacci numbers. Even the way plants branch from their trunk follow a Fibonacci pattern. Although there is an exact correlation between these numbers and the Golden Ratio, because these numbers are too low to give the precise value of Phi, these patterns may be dictated by some underlying force exhibited by Phi. This force appears to manifest itself within the human psyche as evidenced by ancient architects use of dimensions inspired by the Fibonacci sequence Golden Ratio.
In 432 BC the construction of a world renown temple dedicated to the Grecian goddess Athena was completed. The Parthenon isn’t just a testament to ancient Greek engineering, and it is also known as the first impression of the Golden Ratio on architecture. The Fibonacci sequence and Phi were not limited by culture concerning religious Temple architecture and practices.
Buddhism is rooted in Hinduism, in fact, Siddhartha Gautama ( known as Buddha) practiced Hinduism before finding enlightenment which is believed to have occurred in Bihar, a state of India. In ancient India, temple construction was a very well thought out process, veritably, ancient Hindu architects created a science designed to structure dwellings and temples to be in sync with the natural and cosmic order. Vāstu śāstra translates to “science of architecture,” is an ancient Sanskrit manual, which outlines appropriate geometry and alignment for temple construction. The general layout of a Hindu temple is called its “Mandala.” The Mandala of a temple did not always abide by Fibonacci sequence or the Golden Ratio, but some examples have been discovered. However, as Buddhism developed as a separate belief system, variations of Hindu practices were incorporated into Buddhist temple architecture and rituals.
As Buddhism moved East so has various aspects of Hindu practice. In Central Java, Indonesia resides Borobudur, the world’s largest Buddhist temple. The Mandala of Borobudur illustrates Phi when comparing the dimension of the square base to the diameter of the largest circular terrace. However, temple floor plans are not the only type of Mandala exhibiting the Golden Ratio.
If the term “Mandala” sounds familiar, that is because the word is still used today. Mandala: once used to describe the underlying architecture of Hindu and Buddhist temples is now a ritual synonymous with Buddhist meditation. In Vajrayana Buddhism, mandalas are created in the form of a sand painting, which is an incredibly tedious task. Tibetan monks are often recognized for their intricate, highly detailed sand Mandalas. These Mandalas are designed to encompass a Universal understanding as discovered in Buddhist teachings.
Although there is a direct correlation between this sacred design between Eastern religions, there are examples of Mandalas observed in Mayan (Tzolk’in: wheel of time), Aztec (Sun Stone) and even Christian cultures. Eastern Asian cultures have no historical connection with Mesoamerican cultures; however, many of the elements observed in Mandala’s across these cultures share sacred geometry (Fibonacci numbers, Golden Ratio, yantra and the flower of life). This is what makes the concept of the Mandala fascinating; it is a sacred design that spans across time and cultures that have no known physical connections. Mandala truly embraces the philosophy behind its concept: A Universe Connected.
The internet brought the world together, but with the emergence of Blockchain technology comes another mechanism of connectivity. Unity across the global society is bolstered through the instantaneous creation, transfer, and storage of data, in almost all forms, and Blockchain technology delivers just that.
As humans, we live in a world constricted by imaginary and physical barriers where financial institutions are required centralization to grant access. Humanity is seeing the dawn of a new era where technology is breaking barriers and Blockchain technology embraces our innate desire to share an objective. Two innovators with a mutual desire constructed a team that shares the same passion for creating a digital asset exchange that will bring aspiring and seasoned digital asset traders together on a platform designed with the hope of accommodating and educating the masses. With the goal of Connecting the Universe through Blockchain in mind, there is not a more appropriate name for a company striving to do so than Mandala.
Parallel to the explosion of new Blockchain based digital assets is a surge of Blockchain related exchanges. Digital asset trading differs from most traditional markets in that it is 24/7, this style of trade is international and never sleeps. For this market and Blockchain to exist the way that it does, speed and international cooperation are pertinent. With these two elements already in place and mass adoption under 5%, one could only imagine the potential of this technology across the global community.
