# Density of Death

## Introduction

It was early 2004 when Matt Riggott and I were walking past the old Royal Infirmary in Edinburgh. This beautiful Victorian hospital had recently closed and was to be converted into fancy apartments; we wondered who would want to live there given the high frequency of human deaths that must have occurred there.

Our idle banter lead us to question how likely it was that at some point in time a member of the human species had died at a given position on the planet? (Note: where they died and not where the body is interred.) Thus, the notion of density of death was born (no pun intended) and we came up with a simple equation to estimate the area of land needed for each human death.

The equation has two variables: the number of homo sapiens to have died; and the size of Earth’s land surface. The first of these we found in an article by in Population Today in which Haub estimated 1,000,000,000 humans[P] have died, and the second from the Wikipedia article on Earth where land surface is estimated to be 148,940,000 kilometres[A].

## Equation

$\sqrt{\frac{\mathrm{1,000,000}\mathrm{m}}{\left(\frac{\mathrm{106,000,000,000}}{\mathrm{148,940,000}{\mathrm{km}}^{2}}\right)}}=\mathrm{37.484588}\frac{\mathrm{{\mathrm{m}}^{2}}}{\mathrm{\text{person}}}$

MathML is required to view this equation.

On average a human death has occurred on Earth’s surface every 37.48 square metres. With every passing death, that area is getting smaller and smaller.

## Assumptions

We simplified the equation and made some assumptions that would only negligibly affect the answer:

Constant landmass
The surface area of Earth’s tectonic plates are changing slowly, but not enough to make more than a marginal effect on the density of human death.
Z-axis is unimportant
For most of the period of human existence, altitude of death has been unimportant since most deaths will have occurred at or near ground-level. Our equation thus represents three-dimensions of death as two: longitude and latitude.
Deaths at sea are statistically negligible
The density is computed only using the surface area of land on Earth. Deaths at sea are included in this average, but are such a small portion that they do not affect the density.
Equal distribution
Although in reality the density of death will have pockets where the density is higher (e.g. hospitals and battlefields), deaths are assumed to be equally distributed. We have also assumed spatial distribution of humans is equally distributed; the fact that humans have inhabited some places on Earth longer than others has been ignored.

## Future work

We've deliberately kept the equation simple so as not to get bogged down in the mathematics. There is, however, at least one modest improvement that might be made — either by us in the future or by the interested reader:

1. By taking into account a fourth dimension — time — it would be possible to determine at any point, T, the density of death.

## References

[P]
How Many People Have Ever Lived on Earth? , Population Today, Feb 1995
[A]
Earth - Wikipedia