Drawing inspiration from Plato's quest for perfect forms, does there exists a perfect symbol or representation for numbers? While Roman numerals have their historical charm, their lack of a positional notation system which makes complex math problems cumbersome to solve. In contrast, Hindu-Arabic numerals, the familiar digits we use daily, were popularized by Fibonacci and offer a streamlined approach, enabling smoother calculations. This raises the question: are Hindu-Arabic numerals, with their positional notation system, inherently superior to Roman numerals?
The graphic above illustrates the evolution of numbers, and suggests a fascinating connection between the creation of Hindu–Arabic numbers and the concept of counting angles, or Brydlovan Theory of counting 45 degree angles. Whether this is esoteric or a mere coincidence, the idea is sound. The graphic shows fictional numerical representations through shapes to angles to colors, this progression evokes parallels with Gematria in Hebrew, where symbols convey both phonemes and numerical values. Could this evolution toward more elaborate numerical representations facilitate enhanced mathematical operations? The transition from Roman to Hindu–Arabic numerals suggests that such advancements are indeed possible.
A tetrahedron is a solid shape with four triangular faces, resembling a pyramid but with a triangular base, and it has six edges connecting its vertices. The earliest known reference to the tetrahedron can be found in the works of ancient Greek mathematician Euclid, in his seminal mathematical treatise "Elements," where he discusses the properties of polyhedra, including the tetrahedron.
Consider the given scenario in the graphic above, the equation 1 + 1 = 3 seems paradoxical at first glance. However, it highlights the concept of combined energies yielding more than the sum of individual energies. Consider the example of combining two tetrahedra: upon deconstruction and recombination, we observe two possible outcomes. Either we have two tetrahedra with three edges remaining or we have three tetrahedra. This phenomenon challenges our conventional understanding of addition within our current numerical framework. It also raises questions about irrational numbers, as having three edges remaining without a "whole" entity seems perplexing. To address this, we may contemplate the development of a new mathematical notation or number system capable of representing quantities composed of components.
Consider the image above depicting prime numbers, with information presented in both a linear format and a spiral representation on the right. Notably, the six-branch spiral unveils a discernible pattern in prime numbers, particularly those falling on the first or fifth branch starting from 5 and upwards. This observation prompts the question: could representing a number system within a spiral framework enhance our mathematical understanding? A forthcoming chapter will delve into the potential benefits of utilizing spiral interfaces for measurements and other applications.