In its simplest definition, a tesseract (or “hypercube”) is the 3-dimensional shadow of a cube in the fourth dimension.

You and I can only consciously perceive 3 dimensions (consisting of height, length and width) with our senses, but mathematics and physics shows us that there are many possible dimensions. Four dimensions are required to explain how gravity works. Theoretical 4-D structures can be plotted on 4 axes: x, y, z and t where t=time. Physicists call this fourth dimension space-time.

I can’t remember the first time I became aware of the concept of a tesseract. It was probably after reading Robert Heinlein’s novel Have Spacesuit, Will Travel (the best science fiction writers are really philosophers, I think). In it, he described how a cube, moving through the t=time axis could appear as a cube getting smaller and smaller until it seemed to disappear into nothingness (i.e. a singularity). Basically, any 3-dimensional platonic solid (e.g. tetrahedron, sphere etc.) has a theoretical correlate in 4-dimensions, but it seems that a cube is the easiest one for us to understand. Indeed, it is often used in university-level physics and mathematics courses in order to teach the concept of the fourth dimension.

This has been my way of introducing the following premises upon which my subsequent posts in this series are based, namely:

• The fourth dimension (space-time) exists.
• Understanding what a tesseract is will help you to “visualize” what the fourth dimension “looks” like.
• An understanding of the fourth dimension is vital to comprehending how Jung’s theories of psyche, matter and consciousness are internally consistent.

I invite you to click on the links above, as well as the ones in the External links section of the Tesseract Wikipedia page, in order to “get” the idea of how a tesseract is the best way of comprehending the fourth dimension.