There isnt that much freedom it seems...and INFINITY

[Poffo]

This light of love was made to have in its occurrences of being certain characteristics, among them the infinite whole paradoxically described by the straight line, as you would call it. This paradox is responsible for the shape of the various physical illusion entities you call solar systems, galaxies, and planets of revolving and tending towards the lenticular.

Would anyone like to tackle the above paragraph about the infinite whole described by a straight line??

*raises hand*

Here's my interpretation, as imperfect as it may be:

len·tic·u·lar
   /lɛnˈtɪkyələr/ Show Spelled[len-tik-yuh-ler]

–adjective
1. of or pertaining to a lens.
2. biconvex; convexo-convex.
3. resembling the seed of a lentil in form; lentil-shaped.

Planets/galaxies/solar systems tend to be round and the ultimate symbol of roundness is the perfect circle, though such perfection is rare in the universe with elliptical orbits and imperfect spheres as planets, but Ra did say, "the shape...revolving and tending towards the lenticular", which for the most part is circular.

The circle is simply a straight line segment that has been curved around so that each end touches the other. We can think of a circle as an infinitely sided regular polygon (regular meaning all sides are of the same length, like an equilateral triangle). This is because in succeeding regular polygons (triangle -> square -> pentagon -> hexagon -> etc.) the internal angles between any two adjacent sides becomes closer and closer towards being 180° which is a straight line; triangle = 60°, square = 90°, pentagon = 108°, ..., 137-gon = 177.37226277°..., 369-gon = 179.02439...°, 10000-gon = 179.964°, etc.
[For anyone who wants to calculate the internal angles of a polygon, use this simple formula: (n-2) × 180° / n, where n = the number of sides]

As you can see, the more sides to your polygon means the internal angle will get as close to 180° as possible but never actually reach it. After a certain point of increasing the number of sides, a regular polygon will look like just like a circle if one doesn't have a microscope handy to actually see the different sides close up. Even this 18 sided polygon is basically a circle, so would you really be able to tell a 10000-gon from a true circle?



This is why a circle is an infinitely sided regular polygon, because only one with infinite sides would actually reach 180°. This means that the circle is actually a straight line curved back on itself. This also means that an equilateral triangle, the simplest possible polygon, is a like a circle of 3 sides, as weird as that sounds. If you look at a circle, made by a compass say, and cover it up so that you can only see the tiniest little bit of a line, it is virtually straight, but you'd have to zoom in forever to not actually see the curve....paradoxical? Another fun thing to visualize is that if you could actually make a polygon with internal angles of 180° it would instantaneously flatten out to a straight line!

How does light relate to circles? Well, the light that we know of as electromagnetic waves/radiation is essentially an electric field and a magnetic field which are orthogonal (at right angles) to each other, and each takes on the shape of a sine wave:



For anyone who remembers their trigonometry from high school, the sine wave is generated by plotting points around a circle onto a 2D (x,y) graph.

[for an awesome animation of this process click the image!]

Assuming a vacuum clear of gravitationally significant bodies, light would travel in a straight line, but interestingly it is made of these two sine wave fields that move in and out of each other, and the waves can be described as the plot of points on a circle.

So, you could think of a circle as representing the infinite whole, in that it can be a container for ALL and also that there is no real beginning or ending point to it. We also could say that what we know of as white light contains all the colours of the visible light spectrum and is thus a unity of finite elements.

I hope this made some sense!

/:idea: