Hakka, Bukka and the Mystery of Math's Cosmic Game

A long time ago, Hakka and Bukka, two extra-terrestrial creatures from the deep Cosmos, landed on a mysterious Planet 150 million kilometres away from a young star which the Planet’s inhabitants call the Sun. 

The duo set out on a mission.

Mission Duration: 12 Revolutions of the Planet around the Sun.

Mission Location: a mysterious organization that the inhabitants call School. 

Twelve Revolutions later, today, Hakka and Bukka’s gruelling mission comes to an end. Seated on a bench on a rainy day, they muse about a rather mysterious idea they encountered in School.  

Hakka: Imaginary numbers, eh? 

Bukka: Hmm…imaginary indeed!

Hakka: Wait, you mean to say these Inhabitants made them up?

Bukka: Of course, they did, and I am not surprised! 

Hakka: What do you mean?

Bukka: Well, you tell me what the square root of -1 means. The whole idea is ridiculous I say! But that’s the trend these mysterious Inhabitants called Mathematicians follow, isn’t it? Their reckless curiosities motivate them to think of some crazy ideas, build them up using logic from axioms, and Bob’s your uncle, we have to learn that crazy idea as a theory in School. It’s all just a game. Just a conceptual playground. An abstract charade. 

Hakka: Backtrack a little. Axioms?

Bukka: Yes, axioms. Those fundamental statements that are taken to be true in Math. Think of them as rules of a game, as starting points. For instance, in Geometry, the Mathematicians seem to revere a rather famous Inhabitant called Euclid. This guy chose to call five arbitrary statements “axioms”: there exists only one straight line between two points, all right angles are equal, something about parallel lines…anyway, all cosmically boring stuff. 

Hakka: Whoa slow down! Arbitrary? Taken to be true? Rules of a game?You mean to say we can’t prove these axioms?

Bukka: Not with the other axioms, no. But we can prove other crazy ideas using these axioms. Euclid did the same. For instance, Euclid proved that the sum of angles   a shape made by three lines must be two right angles. All just a game!

Hakka: I don’t think so. 

Bukka: Excuse me?

Hakka: I don’t think it’s that trivial. If it’s all a game, how is it that every time I draw this mysterious shape, and measure the angles, they add up to two right angles? 

Bukka: Must be a coincidence - 

Hakka: Or consider this. The other mysterious group of Inhabitants called Physicists, who attempt to describe the Planet and the Cosmos, seem to be using Euclid’s crazy ideas. 

Bukka: Hmm…elaborate. 

Hakka: Well, for one, look: the way light from the Sun reflects off this puddle of water seems to obey Euclid’s ideas about triangles and angles. Surely, if our observations of the Planet and Cosmos are captured by Math, it’s not all just a game? It’s not all imaginary? Or else, there must exist some mysterious reason for the Mathematician’s seemingly random games and rules to end up describing the Cosmos. 

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Hakka’s and Bukka’s discussion is quite interesting in the context of mathematics and science. The question of what exactly math is, what physics is and the role of math in physics, is beautifully explained in Eugene Wigner’s essay, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”. As the title of the paper indicates, it is the particularly baffling success of math in describing the fabric of reality, and even beyond that, how the world around us seems to be coded in the language of math, that is examined. There are several ideas in math developed by mathematicians as completely curiosity-led intellectual pursuits that pop up in unexpected places in physics later. The topic of imaginary numbers which Hakka and Bukka discuss appears to fall under this category. What began as a strange and somewhat artificial device, introduced by mathematicians to solve algebraic equations, the square root of negative one later turned out to be indispensable in describing the deepest laws of quantum physics. Laws that predict the outcome of our experiments. 

I still think about this unreasonable effectiveness every day, with the intent of understanding the beautiful and uncanny interconnectedness between maths and physics. In this account between Hakka and Bukka, I hope to have captured a fraction of Eugene Wigner’s discussion here, wishing to kindle your curiosity to uncover the truths about math and physics. 

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