Einstein on Involutions in Projective Geometry

TL;DR

This paper explores Einstein's early geometric sketches, revealing their focus on involutions in projective geometry and suggesting a unified theme related to the infinite point, based on analysis of his notebooks.

Contribution

It uncovers the connection between Einstein's sketches from different periods, highlighting his focus on involutions in projective geometry and proposing a conjecture on their purpose.

Findings

Einstein's sketches from 1912 and Princeton are thematically linked.

The sketches focus on involution in projective geometry, especially at the infinite point.

A conjecture is proposed regarding the purpose of these geometric considerations.

Abstract

We discuss Einstein's knowledge of projective geometry. We show that two pages of Einstein's Scratch Notebook from around 1912 with geometrical sketches can directly be associated with similar sketches in manuscript pages dating from his Princeton years. By this correspondence, we show that the sketches are all related to a common theme, the discussion of involution in a projective geometry setting with particular emphasis on the infinite point. We offer a conjecture as to the probable purpose of these geometric considerations.