Published on 11/03/23
We long have sought for the truth that is universal, absolute, and everlasting - so called Veritas in Latin. Even before the dawn of civilization, captivated by nature’s formidable yet beautiful wonder, primitive men worshipped and believed that veritas exists in glittering stars in the night sky, fire lightning up the dark, and valiant, mighty tiger. As civilizations flourished and the most fundamental of the stories spread, the subject of worship shifted from nature to transcendent beings, Gods, and their statue and pantheons were built. Circa middle age, one of those prospered, governing entire Europe under its influence. Worshippers described the Christian God as the candidate for veritas, conferring its characteristic-omnipotence and omnipresence. However, humans instead of God ruled the church, and soon they were corrupted. Yet, God’s alleged omnipotence didn’t punish those corrupted nor saved those suffered. Moreover, God-centered society lagged both social and scientific progress. To revive from the chaos, the Renaissance arose, and the industrial revolution followed, ending the era of God. Humans became the center of society again, and the reason retrieved veritas that had long belonged to God. Historians refer to this as a Scientific Revolution: a shift from the era where God was the answer to all questions to a reason-based society where we admitted our ignorance and sought answers with a mathematics-the new candidate for veritas. From such revolution stemmed marvelous developments and prosperous civilizations. Now mathematics appears to better display the characteristics of veritas that a God merely alleged to have, considering its phenomenal achievement and seemingly boundless potential. Yet, notable limitations have been discovered, suggesting that the era of mathematics will also decay as God’s did. Will mathematics eventually be proven to be inadequate? Or will mathematics truly explain the universe?
The language of God
The historical accomplishments and ongoing discoveries suggest the optimistic prospect for that question. Mathematics has contributed to a plethora of fields ranging from the movement of minuscule atoms to circulation of planets. It was also integral to the development of our society which is predicated upon the digital world, the world of computation. Thus, mathematics appears to be universal and absolute, capable of explaining the universe. The two examples below epitomize its such character.
Benford’s Law
Benford’s law is so-called law of leading digits. When data are arbitrarily chosen from a genuine data set, and the leading digits of each datum are collected, we expect each leading digit to appear in a uniform proportion of 11.11 percent. However, this law states that each leading digit of a datum will appear in certain proportion-in descending order from leading digit 1 to 9 as displayed in the graph below-calculated by the equation:
𝑃(𝐷)=log10(1+1/𝐷)
This law’s application is seemingly infinite. It appears in any naturally-occurring statistics: sports, finance, population, music, natural disasters, politics, diseases, criminal rate, birth, death, and even the choices of ours.
For instance, if we collect the population of all cities in China and form a data set, the cities having population number with leading digit 1 will account for about 30 percent of all data, cities with the leading digit 2 take a little less than 18 percent, and so on. The population number is determined by the combination of countless individual choices. Some decide to reside in Shanghai to find a job; some move from Beijing due to exacerbated heart disease from polluted air; some choose Guangzhou due to preference for Guangdong food. Shockingly, the product of such private and diverse decisions is also dictated by Bedford’s law.
Additionally, boxing is a sport that pursues unpredictability. Before the boxer steps into the ring, he and his professional coaches endeavor to identify the habit or pattern of the opponent’s playing style; simultaneously he endeavors to eliminate any pattern of himself. Despite athletes’ admirable efforts to destroy predictability in their game, Benford’s Law can also be found in any statistics in a boxing match. The number of jabs thrown, successful hooks, straight landed, and steps taken all yield the proportion of Benford's law.
Even the height of mountains, wideness of rivers, and molecular weight of compounds are no exceptions and whether produced by our personal choice or intentionally disrupted by human effort, such law appears to be ubiquitous in nature.
Euler Beta Function
Mathematics presents to us the potential not only to merge the twin most crucial yet seemingly unbridgeable concepts in our era-quantum physics and theory of relativity-but also to explain natures’ all four fundamental forces through a singular framework. If math succeeds to unify the most crucial concepts in the universe that are otherwise unbridgeable to each other, it may pose as definitive evidence for its absoluteness.
In the early 20th century, scientists first discovered the binding force between protons and neutrons: strong nuclear force, which constitutes the four most fundamental forces of the universe. To probe on the newly discovered force, scientists conducted numerous experiments with a particle accelerator and devised a mathematical formula to delineate the results. Then in 1968, Gabriele Veneziano discovered that such a formula was identical to the formula from 200 years ago, the Euler beta function. (Britanica).
Scientists wondered how could 200-year-old integral formula could perfectly explain the physics of particles in an atom’s nucleus. Among those were three scientists Leonard Susskind, Holger Nielsen, and Yoichiro Nambu, and they discovered something far greater.
As all functions can be geometrically expressed in form of a shape or graph, they sought for the geometric meaning of beta function and discovered that it expresses the form of elementary particles when it is assumed to exist as a one-dimensional form: a string. Upon such assumption that universe’s elementary unit exists in one dimension and more intangible dimensions exist beyond, stemmed String theory-competent candidate for the theory of everything. It holds the possibility to explain the four most fundamental forces-gravity, electronegativity, strong, weak nuclear force-in a singular framework and to mathematically incorporate the quantum physics-law of the microscopic world-and theory of relativity-law of the macroscopic world-which are otherwise incompatible.
Although string theory is yet to be completed and displays multiple contradictions, it still holds the potential to be the theory of everything that all scientists sought for and it is simply astounding that a function created 200 years ago could provide the basis to such potential.
Are We Chasing After the Mirage?
When comprehending the hints of absoluteness and ubiquity that above instances display, we are struck with wonder that math might be what Believers described as God. From such hope, mathematicians dedicated their days and nights to chase their one ultimate dream: solve the secrets of universe through their work. However, some discoveries claim that such dream might never be realized.
Newtonian mechanics long served as the fundamental framework, alleged as ‘laws’ that explain and predict physics in object’s motion and interactions. However, the laws were soon proved to be wrong by new framework-theory of relativity. Newly emerged theory refuted the integral premise in Newton’s laws that time and space is absolute. Although Newton’s laws yield fairly accurate approximates unless the speed of object approaches near light speed, it fails to ‘explain’ the dynamic outcomes. Additionally, in the quantum mechanics’ scope of microscopic world, either position or velocity is immeasurable, making Newton's laws inapplicable. Such demise of what have been believed as law discouraged mathematician’s dream as no universal framework has been discovered to have infinite range of application.
Moreover, some scholars argue that mathematics' potential as verities ended when Austrian mathematician Kurt Godel proved that “in any reasonable mathematical system there will always be true statement that cannot be proved” in his incompleteness theorem.
However, mathematics is still the most competent candidate for veritas in our era. If our scholars continue their dedicated pursuit for great cause to solve secret of universe, we will eventually discover the fate of mathematics, and through such process our understanding of world will undoubtedly expand.
References
Bristow, William. “Enlightenment.” Stanford Encyclopedia of Philosophy, Stanford University, 29 Aug. 2017, https://plato.stanford.edu/entries/enlightenment/.
“Newtonian Mechanics - University of British Columbia.” Columbia, 5 May 2019, https://phas.ubc.ca/~stamp/TEACHING/PHYS340/NOTES/FILES/Newton-Mechanics.pdf.
de Bruijne, Jos, et al. “Benfords' Law: Gaia Parallaxes and Distances.” NASA/ADS, https://ui.adsabs.harvard.edu/abs/2019gaia.confE..24D/abstract.
History.com Editors. “Enlightenment.” History.com, A&E Television Networks, 16 Dec. 2009, https://www.history.com/topics/british-history/enlightenment.
Moros, Viktor. The Riemann Zeta Function and Its Analytic Continuation | Request PDF. https://www.researchgate.net/publication/317493517_The_Riemann_Zeta_Function_and_Its_Analytic_Continuation.
“String Theory.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., https://www.britannica.com/science/string-theory.
Wolfram.Editors. “Benford's Law.” From Wolfram MathWorld, 20 May 2020, https://mathworld.wolfram.com/BenfordsLaw.html.
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