|The Golden Proportion is not just a mysterious number. The reason why this proportion is aesthetically pleasing has been known for ages. It mathematically unites objects into a grid and clarifies to the mind the object's mass and distance.|
Very simple mathematical reasoning allows us to see how the golden mean lets us know whether objects are far away or small. An environment that conforms to the golden mean helps the brain figure this out quicker.
Mass and Distance have a Linear Relationship
Imagine you are looking at two telephone poles on the skyline. You can't tell how far away they are but it looks like they are the same size. So you jump really high in the air and take a look at them from a different point of view. You realize that one of them is much farther away than the other one, but it is also much larger so that made it look closer.
Things look bigger when they are closer to you. This simple fact provides the basis for relationships of all objects in space. Mass=1/distance. The greater the distance to an object, the smaller the mass of the object appears.
But we can't tell whether a singular object is far away or if it just small. From our point of view it is the same thing. We need a third object to reference and judge against. Maybe a line of telephone poles that are the same size.
With enough objects in space that relate to each others' masses and distances, we can know how mass and distance relate- mass gets smaller as distance gets greater. Each pole's top and bottom are parallel and converge on a vanishing point. It is a linear relationship
The perceived distance between poles is D=x-1 where x is the length of the previous distance between the closer poles. The Length of the entire perceived row of poles is the sum of each space: L=∑(x+1)/i where i is the distance between you and the first pole.
Harmonic Series Gives Form
Now let's keep throwing telephone poles in there at random. After a while there are so many telephone poles that you can't see through to the other side, all you see is telephone poles. The point at which this happens is the very instant these telephone poles become an object, a single unit in space.
At what point does this occur? It depends on the distance between poles and the size of the poles.
The harmonic series tells you at what rate you can add smaller pieces of a pie to make the entire pie. The poles get smaller at a linear rate, remember, as they get farther away. With the harmonic series, all the poles a distance of 1 away from you will add up to a mass of 1/4; all the poles a distance of 2 will add up to a mass of 1/9; and so forth. If you keep going, all the poles together will add up to a mass of 1.
It is a very simple rate: 1/k². This is also the rate at which light gets dimmer through space.
Harmic Series and Linear Series Prove Golden Mean
What happens when we make these two equations equal to each other: 1/x² = 1/(x+1)?
The rate at which mass gets smaller in distance is equal to the rate at which smaller parts make up a whole. There is only one number that x can equal: 1.618 or the golden mean.
The golden mean gives a relationship between distance and mass that lets the viewer determine if objects are either small or far away. If the objects fit into this proportion there is no question.
This can also be demonstrated geometrically. If the viewer is a distance of 1 away from the first telephone pole and the pole is 1 in size, all you need to do is space the second pole 1.618 away and it will appear to you 1/1.618 in size. Or you can make the second pole 1.618 in size, space it 1 away, and it will appear 1 in size.
Golden Mean Allows Quantum Physics
The Quantum theory states that there is a definite size that relates all energy in the universe. Energy and matter can be broken down to a basic size and no further.
Our original problem of things getting smaller as distance gets greater therefore isn't such a big problem. On a quantum level the golden mean can let us know the distance between everything, as all energy is made up of the same units. Furthermore, we know that there is a finite distance that can be reached between two objects in space.
Think of the telephone poles as quantum units of energy and distance as the momentum that separates those energies from the observer.
Parmenides contended that space doesn't really exist if there is nothing in it and that motion or multiplicity therefore doesn't exist. The ability of energy to travel between states is what gives us what looks like space. The golden mean is a standard that the space appears as, according to the mass of the energies being perceived.
Copyright Benjamin Blankenbehler