Theoretical Geometry

The Unbearable Lightness of Seeing

Note:
In this article, the fourth dimension is looked at, not as time, but as a fourth spatial axis—a direction we cannot point to, cannot see, and cannot imagine, but which mathematics insists is there.

From the instant you start your day by waking up and looking around till when you close your eyes to sleep at night, you see things only in three dimensions—length, width, and depth. Even simple, so-called ‘2-dimensional’ drawings on paper, or pixels on a screen, are on a 3D base.

Our life consists only of 3-dimensional elements. However, what would happen if this changed? What if a more complex, 4-D object appeared in our 3-D world?

The “Finger” Analogy

Before we delve into sensation, we must understand how the object would reach us. The thing is, it will already have been there.

Imagine hovering your 3D finger above a 2D drawing. You aren’t in the drawing’s world yet, but you exist. When you press down, you suddenly become a part of that plane. A 4-D object is similarly “above” our reality, waiting to intersect.

“The 4-D object would already have been there, just in the fourth dimension—one we simply cannot comprehend.”

Encountering the Hypercube

Take the object as a hypercube (tesseract). Just as squares form a cube, multiple cubes form this 4-dimensional figure. If one appeared, you’d first see a perfect cube floating in the air. Perfectly normal—until it begins to shift.

Geometric Metamorphosis

  • CUBE
  • RHOMBUS
  • HEXAGON
  • SMALLER CUBE

As the angle of view shifts, the figure violates the set laws of 3-D geometry, appearing as a shifting optical illusion because its depth is incomprehensible to us.

What’s worse, it would phase right through matter. Imagine a ghost-like shape floating towards you—it doesn’t walk around you; it “steps over” you in a direction you cannot grasp. To us, it would appear to teleport or phase through solid walls.

“Our brains will repeatedly try, and fail, to recognise or even understand the existence of the figure, possibly driving many mad.”

Ultimately, if a 4-dimensional shape appeared in our world, it would remain an unsolved mystery—a ghost of a dimension we are built to never truly see.