Simple Matroids and Alfred North Whitehead's theory of dimension (1906)
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915961110528000 |
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| author | Hales, Thomas |
| author_facet | Hales, Thomas |
| contents | We give a correspondence between simple matroids and a reconstruction of Alfred North Whitehead's theory of dimension, as developed in "On Mathematical Concepts of the Material World" (1906). In brief, if a geometrical system in the generalized sense of Whitehead has finite ground set and is phi-maximal, then it is a simple matroid. Here "generalized" means that Whitehead's three-dimensional axiom is replaced by finite-dimensionality. Conversely, every simple matroid is a phi-maximal geometrical system in the generalized sense of Whitehead. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24699 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Simple Matroids and Alfred North Whitehead's theory of dimension (1906) Hales, Thomas Combinatorics History and Overview 05B35 (Primary) 01A60 (Secondary) We give a correspondence between simple matroids and a reconstruction of Alfred North Whitehead's theory of dimension, as developed in "On Mathematical Concepts of the Material World" (1906). In brief, if a geometrical system in the generalized sense of Whitehead has finite ground set and is phi-maximal, then it is a simple matroid. Here "generalized" means that Whitehead's three-dimensional axiom is replaced by finite-dimensionality. Conversely, every simple matroid is a phi-maximal geometrical system in the generalized sense of Whitehead. |
| title | Simple Matroids and Alfred North Whitehead's theory of dimension (1906) |
| topic | Combinatorics History and Overview 05B35 (Primary) 01A60 (Secondary) |
| url | https://arxiv.org/abs/2604.24699 |