Chapter 1: The Connection Between Mathematics and the Supernatural

Is there a mathematical basis for the existence of ghosts? Various viewpoints suggest that this might depend on how we perceive dimensions and perspectives.

My Mathematical Ghost!

This discussion can be linked to Edwin A. Abbott's 1884 novella, Flatland. In this story, our protagonist, Square, who embodies a square, ventures beyond his 2-dimensional world of Flatland to explore Spaceland (3 dimensions), Lineland (1 dimension), and Pointland (0 dimensions). Throughout his travels, he illustrates how perspective can profoundly alter our understanding of the shapes around us.

Before we delve deeper, let’s clarify a couple of terms. We will define “ghost” to encompass spirits, mediums, phantoms, and other related entities. For the sake of visualization, when we refer to the shadow of an object, we mean its (perpendicular) projection onto a lower dimension. In simpler terms, envision the silhouette formed if you were to compress an object down to eliminate its height. For instance:

• A sphere and a cylinder would both project as circles.
• A cuboid and a square-based pyramid would both project as squares.
• All two-dimensional shapes would shrink into lines of different lengths.
• All lines would reduce to points.

While this definition may seem insufficient, it suffices for our discussion as long as the imagery is clear.

#### Section 1.1: Shadows and Perceptions

We can easily distinguish between a sphere and a cylinder, but if we only had their shadows—both appearing as circles—we would be unable to differentiate them. The takeaway here is that if we were inhabitants of Flatland, the shadows of the sphere and cylinder would only present as circles to us, obscuring their true nature as 3-dimensional objects, which would be beyond our comprehension. One could even propose that these shadows might seem incorporeal, unlike the usual solid shapes in our realm.

Could it be, then, that what we term as ghosts are merely the fleeting shadows of 4-dimensional entities intersecting our 3-dimensional world? Much like how the shadow of a ball soaring above Flatland would momentarily look like a circle to its residents.

This intriguing concept is explored in the video titled "David Deutsch's 'The Fabric of Reality' Chapter 10 'The Nature of Mathematics' Part 2," which delves into the intersections of mathematics and philosophical ideas.

Section 1.2: Dimensions Beyond Our Understanding

This argument is admittedly not robust or precisely articulated, but it can certainly be further developed with more precise terminology and time. The goal here is not to present a well-structured argument, but rather to provide a thought-provoking idea for discussion—something to ponder over dinner, perhaps.

One question that arises is: how do ghosts acquire height based on our shadow definition? The straightforward answer is that they do not. According to our definition, these ghosts would remain flat. Consider what alterations would be needed to endow them with height.

Furthermore, for those who propose that we exist in a 4-dimensional world where time is the fourth dimension, it could be posited that these beings might be 5-dimensional or, intriguingly, exist in a 4-dimensional realm with a different dimensional framework than ours.

As a parting thought, I recall a student once asking, “Is that why some people refer to ghosts as shadows?” Perhaps that is a valid insight!

Thank you for taking the time to read this piece. If you enjoy my writing, consider following my publication, Y(Math), to help share these ideas with a broader audience.

Chapter 2: Can Science Validate the Existence of Ghosts?

As we continue this exploration, we must also consider the scientific perspective on the existence of ghosts.

The second video, "Can Science Prove Whether Ghosts Are Real or Not?" investigates the scientific inquiries and evidence surrounding the phenomenon of ghosts.