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¹: Inquisitive points out an excellent example of this with the sphere. Applying these propositions to that example:  1. A (2 dimensional) circle is easier to understand than a (3 dimensional) sphere.  2. A (1 dimensional) line is easier to understand than a circle.  3. Beginning understanding with a point, then a line, then a circle and a sphere, the equations for each would build upon the most basic, shared elements of each: the center point and the radius. Therefore, more people know the formula for a circle than a sphere, because it's simpler, easier to understand, and has been a part of human knowledge for longer.

¹: Inquisitive points out an excellent example of this with the sphere. Applying these propositions to that example: 

1. A (2 dimensional) circle is easier to understand than a (3 dimensional) sphere. 
2. A (1 dimensional) line is easier to understand than a circle. 
3. Beginning understanding with a point, then a line, then a circle and a sphere, the equations for each would build upon the most basic, shared elements of each: the center point and the radius.
Therefore, more people know the formula for a circle than a sphere, because it's simpler, easier to understand, and has been a part of human knowledge for longer.

¹: Inquisitive points out an excellent example of this with the sphere. Applying these propositions to that example: 1. A (2 dimensional) circle is easier to understand than a (3 dimensional) sphere. 2. A (1 dimensional) line is easier to understand than a circle. 3. Beginning understanding with a point, then a line, then a circle and a sphere, the equations for each would build upon the most basic, shared elements of each: the center point and the radius. Therefore, more people know the formula for a circle than a sphere, because it's simpler, easier to understand, and has been a part of human knowledge for longer.

¹: Inquisitive points out an excellent example of this with the sphere. Applying these propositions to that example: 1. A (2 dimensional) circle is easier to understand than a (3 dimensional) sphere. 2. A (1 dimensional) line is easier to understand than a circle. 3. Beginning understanding with a point, then a line, then a circle and a sphere, the equations for each would build upon the most basic, shared elements of each: the center point and the radius. Therefore, more people know the formula for a circle than a sphere, because it's simpler, easier to understand, and has been a part of human knowledge for longer.

¹: Inquisitive points out an excellent example of this with the sphere. Applying these propositions to that example: 1. A (2 dimensional) circle is easier to understand than a (3 dimensional) sphere. 2. A (1 dimensional) line is easier to understand than a circle. 3. Beginning understanding with a point, then a line, then a circle and a sphere, the equations for each would build upon the most basic, shared elements of each: the center point and the radius.

I don't know what the equations in these fields look like. As Inquisitive demonstrates, you could probably find ways to express some or all of the equations in any field with non-integer exponents. However, if and when we arrive at 'the theory of everything,' I would wager the most popular form for the equations, the form that gets recorded in textbooks and taught in classrooms, will involve as many integer exponents as we can make fit.

¹: Inquisitive points out an excellent example of this with the sphere. Applying these propositions to that example: 1. A (2 dimensional) circle is easier to understand than a (3 dimensional) sphere. 2. A (1 dimensional) line is easier to understand than a circle. 3. Beginning understanding with a point, then a line, then a circle and a sphere, the equations for each would build upon the most basic, shared elements of each: the center point and the radius. Therefore, more people know the formula for a circle than a sphere, because it's simpler, easier to understand, and has been a part of human knowledge for longer.

I don't know what the equations in these fields look like. As Inquisitive demonstrates, you could probably find ways to express some or all of the equations in any field with non-integer exponents. However, if and when we arrive at 'the theory of everything,' I would wager the most popular form for the equations, the form that gets recorded in textbooks and taught in classrooms, will involve as many integer exponents as we can make fit.

A delicious example of this is Euler's formula, which describes trigonometric functions by means of an imaginary exponent: e^ix = cosx + isinx. Wikipedia summarizes it by saying "This formula can be interpreted as saying that the function e^ix is a unit complex number, i.e., traces out the unit circle in the complex plane as x ranges through the real numbers." In other words, while the simple, real circle is described with integer exponents, there is another circle describable with imaginary numbers. Who is to say which is more fundamental? Or which leads to more formulas or a broader description of physics and reality?