Understanding the Principles and Evolution of Mathematical Algorithms
Much like the concept that 1 equals 1, mathematics serves as a cornerstone in understanding the world around us. The principle that 11 equals 2 might seem absurd at first glance, but in mathematical terms, it simply means that we are dealing with a different scale or a unique system. This concept includes the idea that 0.999 recurring is exactly equal to 1, showcasing the precision and beauty of mathematical patterns.
The Language of Proportions: A Comprehensive Overview
Mathematics is not just a language of proportions and dimensions; it's the fundamental basis for understanding our universe. Currently, there are six commonly accepted mathematical algorithms that serve as the building blocks for our understanding:
Arithmetic Algebra Trigonometry Geometry Integral Calculus Differential Calculus (or Quantum Mechanics)The primary purpose of these algorithms is to define proportional relationships between objects and phenomena, aiding humans in manipulating physical reality. Without these mathematical statements, the engineering of technology would become inconsistent and unreliable.
The Genesis of New Mathematical Algorithms
As we discover new phenomena that do not conform to our existing mathematical algorithms, we are compelled to develop new ones. This process begins with a deep understanding of the underlying mechanisms. For example, the discovery that varying frequencies of electromagnetic radiation (light) absorbed by matter would raise its temperature (heat) led to the development of new mathematical principles.
Newton's calculus, the standard scientific algorithm at the time, was not sufficient to describe these phenomena. When applying Newtonian calculus to the ultraviolet range, the formula produced a vertical asymptote, contradicting observed laboratory data. This discrepancy led to the term Ultraviolet catastrophe.
Max Planck: A Pioneer in Modern Mathematics
Max Planck, a contemporary and close friend of Albert Einstein, solved this problem by deducing that the underlying mechanism of atomic absorption was not "continuous" but based on the energetic frequencies of the outer shell electrons. This breakthrough led to the development of a new branch of calculus: differential calculus, which allows for the accurate processing of such phenomena. Planck referred to the changes in electron energy as "quanta."
The concept of continuity in Newtonian calculus assumed that there were no spaces between the points that form lines and curves. Differential calculus, on the other hand, introduced the idea that there can be spaces between these points, accurately modeling the behavior of electrons and photons.
Conclusion: The Continuous Evolution of Mathematical Language
In summary, mathematics is a language that is only bound by the principles of the underlying phenomenon it attempts to describe. While there are internationally recognized conventions, these conventions evolve as our need to describe the world changes. Understanding these principles and their evolution is crucial for advancing our technological and scientific capabilities.