Poor Euclid

I am currently reading “Is God a Mathematician” by Mario Livio, a book that my brother sent me over the holidays. First, I need to say that 98% of the book has absolutely nothing to do with god or religion in any way. There is about 5% that has to do with philosophy, but it is basically a straight forward history of mathematics. I would bet that the name of the book and subsequent references to God where added after the book was already written. It was a marketing ploy through and through.

I just finished the section on non-Euclidian geometry and it was just silly. Let me explain, for thousands of years, geometry was the basis for much of math and logic. Euclidian geometry is the math we all learn in school. By stating several undeniable “truths” or axioms, people are able to extrapolate more complex concept and truths. These truths were used as the basis for all other mathematical adventures. They include things like: if you have a triangle the sum of all the angles inside the triangle is 180. You can make any triangle you want and it will always match that truth. Another one is: the shortest distance between two points in a straight line. Seems simple, right? Than along came some smart-ass mathematician who said, “well, what if reality only existed on the surface of sphere.” Under this premise, Euclidian geometry falls apart. Triangles will have more than 180 degrees and the quickest way between two points in a curve. People have dedicated their careers to what the math would look like on such a circular reality. In fact, people just kept creating new ways that reality could be shaped and researched the math in their new world. This includes realities shaped like saddles, cones, lines, ellipses, and countless other shapes or functions.

Now there is some utility in concepts like this. A plane travelling from New York to Paris cannot travel in a straight line because that would mean it would have to go through the crust of the earth. The plane has to calculate the best possible curve to reach its destination. However, the curve is still not the shortest way, it is just the shortest way that we can realistically travel. The true shortest path is through the earth’s crust. Non-Euclidian geometry may be useful, but how can anyone consider it a way of describing a reality beyond the arbitrary rules it creates for itself.

Non-Euclidian also allows Mathematicians to do things like calculate the rules of geometry with more than three dimensions. So a cube would have length, width, height, and something else. What would be the math if this meta-physical fourth physical dimension (not time) existed. So they create this alternate reality and an alternate math and claim that the truths that exist in that world are true mathematical truths (which conflict with Euclidian geometry).

(Side note: It is this ridiculous logic that allowed physicists to add extra dimensions into their calculations in order to have their theories fit their observations. This is at the core of M-theory, which I do not even consider a scientific theory since it is based on evidence that can never be proven or disproven.)

Anyway, I am thinking about creating Lipka-Geometry. I will calculate a new math based on the concept of a reality that only exists on the surface of my face. What will a triangle look like? What is the shortest distance between my left ear and my right eyebrow? Uggg, poor Euclid.