As indicated, this post is on the dialect of mathematics in exposing the deep reality of the universe—physical and dynamic. Voice of mathematics helps us understand this world, starting with simple algorithmic functions, and ceaselessly unfolding to rather complex and abstract hidden truths.
Mathematics is the language we employ to make sense of the physical universe, so much so that to whatever level, and however precise, we see the reality of the universe only in the window of mathematics. Both blatantly outward and deeply abstract nature of reality is captured in the words of mathematics. Take for example distance travelled by time spent allow us to seize the sense of speed: 60 miles/hr. Or at a sophisticated level, picturing the structure of space-time in the illustrious E = mc2, snapped by Einstein. Mathematical principles automatically come into play as soon as we urge to define, give a structure, or establish a relation. It’s not always this plain however. Complex behaviors of reality that involve lots of variables unfold exceedingly intricate numerical systematizations, but the glancing of reality, however deep, stretches all the way in the form of mathematics. This is only part of the whole story though.
The play of mathematics inseparably connects to the dynamics of the universe, so much so that one seemingly reflects the nature of the other.1,2 The expressions of mathematics and universe recite in identical tone—of an order that in one way or another imprints a cast of symmetry. From simple arithmetic to complex advanced algebra, from clear-cut cosmos to intricate quantum realm, the dictum of symmetry always palpates. Mass against energy, space against time, time versus movement, matter for antimatter, weaving fractals, growth patterns of plants, weather and stock market are all shades of symmetry other than the blatant ones we encounter in nature everyday. Physical laws governing the continuum of space-time too embody the plan of symmetry. The examples are endless, seen in myriad both forthrightly plain and mysteriously abstract ways.3 More often than not, symmetry is first seen in the mathematical articulation, and then at the physical level. Architectural and dynamic voices of mathematics are instructional, surfacing often to the amazement of unsuspecting mathematicians. The discovery of antimatter is a renowned such example where it first became manifest in the mathematical rendering, which was then authenticated physically.
At the surface or in its deep roots, every way we turn to we find a code of sorts gaping at us to be translated in the language of symmetry, so much so that we have gotten used to lookout for a motif in anything mathematical, at times just for its pure inspiration. The quandary arises when the helter-skelter seems to be the code. We find ourselves in the landscape of prime numbers.
In its utterly plain definition of being cut only by one or itself, the prime numbers have mesmerizingly incited the toughest of conjectures and trickiest of equations. Both its structuring mechanism and sprouting in number landscape eludes any systematic order that mathematics otherwise forthrightly displays in all forms—from plain number depictions to its intricate advanced molds. Prime numbers elude a pattern. Should they? Steep advancements, and shrewd insights unfurl prevailing of a conformity—subtle (very!) but robust—in the landscape of prime numbers.
Underneath the uncoordinated display, the prime numbers incite well-structured tones—of mathematics and the universe in their finest resolutions.
To comprehend this (its logic and beauty) we will have to dig deeper into some of the advancements of mathematics, and of physics—the storyline of the following post.
Will be back shortly,
- Mario Livio, Is God a Mathematician, Simon and Schuster, 2010
- Neeti Sinha, Physical Laws of the Mathematical Universe: Who Are We? Archway Publishing, 2016
- Dave Goldberg, The Universe in the Rearview Mirror, How Hidden Symmetries Shape Reality, A Plume Book, 2014