A World Where Mathematics Is Invalid

Every child imagines of a world where he or she creates a world in their mind which only abides by their rules and can meander around with no care or responsibility whatsoever. They can imagine a place where they can be a house with infinite rooms or travel great distances within a speck amount of time. This peak of imagination which exists within a child starts to dwindle away when they grow older. In our world the foundation of mathematics is built on the work of Euclid but what if we could simulate a Universe where his laws are completely baseless and false? Let's find out!

Non-Euclidean Geometry

'The Elements' book which is the 2nd most published book in history after The Bible, has an unsatisfactory 5th postulate hence deemed independent of the other four. It has been found that a system of geometry can be built on the false statement of the 5th postulate. Hence that system of Mathematics has been named as Non-Euclidean Geometry. The 5th postulate is important for the world as it leads us to define what we know as parallel lines in our school books.

Most of the creative pursuit in art, theoretical architecture and objects gain inspiration from ideas based on Non-Euclidean Geometry as early as from the time of the Byzantine Empire.

Mechanics of The Theoretical World

One of the most famous coders in GitHub has created his own Game Engine which does not follow the basic laws of Euclid Geometry. He programmed a world where the rendered objects had unusual properties from the perspective of a non-mathematician. Take for this case a tunnel which looks long from the outside but when we travel through the tunnel, we travel it in a shorter time than expected. This idea can be easily explained if you imagine a paper with two points which later has been folded into each other and a hole made through the two.

This famous explanation in popular culture is in the Oscar-winning movie known as Interstellar (2014). It talks about the distance between two points, far away in space which can be travelled in a much faster time given that we travel through the hypothetical tunnel. Non-Euclidean Geometry has found it's application in both programming as well as in Theoretical Physics which can prove whether wormholes exist or not. It already has applications for imagining higher dimensions than space. In the Game Engine, the programmer boasts about his ability to fit infinite rooms in a finite space with the help of Non-Euclidean Geometry.

Bottom Line

Wizards like The Sorcerer Supreme A.K.A Doctor Strange or Cobb from Christopher Nolan's Inception (2010) can make Non-Euclidean worlds just with the thought of their minds but non- fictional human beings like us have a long way to go if we want to disprove Euclid completely and pave way for building the foundations of Mathematics on Non-Euclidean Geometry.