10. Shapes & Space

Shapes & Space

Geometry is one of the oldest branches of mathematics. Originally developed to model the physical world, it has applications in almost all sciences, as well as in art, architecture, and design.

Geometry encompasses two major components: shapes and space.

A shape is the geometrical description of an object: its form, outline, or external surface, as opposed to other properties such as colour, texture, or material.

The concept of shape is deeply interconnected with the one of space, whether zero-dimensional – such as a point; unidimensional – such as a line; bidimensional – such as a triangle; or three dimensional – such as a cube.

The dimension is an intrinsic property of an object, in the sense that it is independent of the dimension of the space in which the object exists in.

While modern mathematics uses many types of spaces (Euclidean, linear, topological, etc.), it does not define the notion of space itself. Yet, we all experience space: our bodies know how to move in it and our minds can generate its thought, to the point of being able to measure it. 

The space we live in is a 3D world, but many other dimensions exist in geometry and topology. If we consider time as a fourth dimension, we are projected in a 4D space, where time itself can be stopped, or transformed into a direction we could move along. This seemingly impossible experience becomes possible by letting ourselves be hypnotized by mind-bending visual experiences.