Jeff and Mike, Those are important points.
JBD
In a broad sense, Sir William Rowan Hamilton anticipated Einstein's idea that space and time can be conceived as parts of a four dimensional continuum. In fact, he used the algebra of quaternions to articulate a formal framework for conceiving of such physical relations as part of a four dimensional field.
Peirce was familiar with Hamilton's work. And when he was editing the second edition of his father's book _Linear Algebra_, he added some important theorems to it. In particular, he proved that the only N-dimensional algebras that had division were the real line (1D), the complex field (2D), quaternions (4D), and octonions (8D). MB
One of my favorite Peirce quotes... "space does for different subjects of one predicate precisely what time does for different predicates of the same subject." (CP 1.501)
He also discussed non-Euclidean geometry. While he was still at the US C&GS, he proposed a project to determine whether the sum of the angles of triangles at astronomical distances was exactly 180 degrees. Simon Newcomb rejected that project. John
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