Formulating a philosophical observation in math

Question

I am trying to describe an observation using mathematical formula however, I am not sure, if I am using the proper math language.

I am aiming to describe an analogy to the fourth dimension as following. Every object is described by O three coordinates, x, y, z along with c as color.

The c is summation of a function on human (F(h) that interacts with Object O in order of its color c (G(c). It is intuitive as every sensory is an interaction of human and object.

Therefore, I have formulated every sensory experience as following

$S = \int^{\infty}_{-\infty} f(h)O^{g(c)}df(h)d(g)$

However, S is in fact the fourth dimension of O. So my question is how I can modify or write down this expression/forumula in mathematical language. I understand this formula might not have any physical implication, rather philosophical/artistic - but it is important to me to write it down mathematically.

Answer 1

Can you give us concrete examples of what it means "function of human"? Does it map every pair (human, object) into a colour? Then you need to use formalism for functions of two variables $F(h, o)$.

Also, can colours be added/averaged, and how?

Possibly you want to say something like:

$$S(o)=\int_{H}F(h, o)dh$$

where $H$ is the set of all humans, with some defined measure (https://en.wikipedia.org/wiki/Measure_(mathematics) ) $dh$, and then you "add"/"integrate" the colours across all the humans for the given object $o$ to get you a one-variable function $S$ (the "true colour" of the object)? (Which then you can add as a "fourth co-ordinate" for the object?)

If that is where you are going, the above may be a way to write it "mathematically". One would still expect you to provide:

• The precise definition of the measure $dh$: are all humans treated equally, or do some humans carry more "weight" in terms of deciding colours for objects?
• How are colours modelled mathematically? In computing technology we already use three co-ordinates to determine colour (on your monitor, three separate numbers are associated to the strength of Red, Green and Blue colour that are mixed to create the illusion of colour). In nature, the spectrum of colours is infinitely-dimensional. So really you don't end up with four but with a lot more dimensions.
• Some motivation why this whole undertaking is useful.

As for the last point: if I was a curious young soul trying to understand the fourth dimension, I am not convinced that this mathematical language would help. It would put me off. So please, we (math teachers, parents of math students etc.) have enough trouble to convince young people that mathematics is a logical and useful tool, worth studying - let's not make things worse. Let's not use it as a way to add weight to otherwise weak arguments ("it's got math in it, it must be right").

Mind you, though, Euler once (allegedly) got away with it: Euler Vs. Diderot