Survival time of Princess Kaguya in an air-tight bamboo chamber

TL;DR

This paper investigates how long Princess Kaguya could have survived in a sealed bamboo chamber by analyzing geometric and biological factors affecting oxygen availability and consumption.

Contribution

It introduces a geometric model linking chamber volume, body size, and surface area to survival time, revealing a scaling relation in biological quantities.

Findings

Survival time depends on chamber volume, body volume, and surface area.

A scaling relation between biological quantities is identified.

The model provides insights into oxygen consumption in confined spaces.

Abstract

Princess Kaguya is a heroine of a famous folk tale, as every Japanese knows. She was assumed to be confined in a bamboo cavity with cylindrical shape, and then fortuitously discovered by an elderly man in the forest. Here, we pose a question as to how long she could have survived in an enclosed space such as the bamboo chamber, which had no external oxygen supply at all. We demonstrate that the survival time should be determined by three geometric quantities: the inner volume of the bamboo chamber, the volumetric size of her body, and her body's total surface area that governs the rate of oxygen consumption in the body. We also emphasize that this geometric problem shed light on an interesting scaling relation between biological quantities for living organisms.