The Simple Topology of Nature
The Shape of Nature
Simple Object Topology provides an easy way to model the shape of real objects. The necessary basic concepts to understand shape are simple and few and we introduce them here.
We begin by postulating a self evident truth:
All objects are round!
What do we mean by round? Physically examine or mentally consider a free object. A free object is not attached to, or part of, something else. Consider a baseball, a pencil, or an ‘irregular’ rock, any convenient object will do. Pick it up, rotate it, and examine the whole object. We quickly discover, what is essentially available for our direct examination is the surface of the object. The surface is closed with a physical extension we call area. Empirically evident surface closure is what makes all objects topologically, and physically, round.The surface is the self-connected physical boundary between what is inside and what is outside. What is inside – including the surface area – is a physical extension we call volume. What is outside or beyond the surface area is everything else, a physical extension which we call environment.
Topological Properties of Objects
The surface and volume of an object have intuitive topological properties. A topological property is an intuitive property that cannot be removed and remains with the physical surface area and volume of the object during transformation procedures. Some intuitive topological properties of surfaces and volumes are:
Area, volume, and environment are physical whole quantities
There is no such thing as an object with a half area, two volumes, or two environments. We are allowed to compare different objects with each other, and say that one has twice the area or one half the volume of the other, but the two areas and volumes being compared remain physically unique and individually complete. The environment can change but always remains whole.
No matter what is done with an object its surface(s) and volume will remain a physical whole quantity
Consider a wooden ball the size of a baseball and mentally cut it in half without loss of material. What results is two objects and two complete surfaces. Each object has one half of the original physical volume. The two surfaces are still closed, and we are still on the outside. Now take the same two objects and “glue” them back together. The two complete surfaces now become one complete surface again. Whatever the number of pieces the ball is cut into, the total physical volume remains constant.
Closure, connectedness, and completeness, are topologically whole properties. There is no such thing as a somewhat connected, incomplete, or partially closed surface
Similarly, homogeneity is a topological property of volume. No matter how much it is subdivided a homogenous volume is always “smooth”, never “grainy.”
The Two Types of Surfaces
There are only two types of surfaces in nature:
- Type 1 – convex ball surface
- Type 2 – concave hollow surface
- S2 surfaces of the neutron and neucleonic membranes
- S3 surface of the electron membrane hollow
There are no types of “flat” surfaces in nature.