Homoloidal Webs, Space Cremona Transformations and the Dimensionality and Signature of Macro-Spacetime

3. Conclusion

The concept of Cremonian spacetimes represents a very interesting and fruitful generalization of the pencil concept of spacetime by simply raising the dimensionality of its projective setting from two to three. When compared with its two-dimensional sibling, this extended, three-dimensional framework brings much fresh air into old pressing issues concerning the structure of spacetime, and allows us to look at the latter in novel, in some cases completely unexpected ways. Firstly, and of greatest importance, this framework offers a natural qualitative elucidation of the observed dimensionality and signature of macro-spacetime, based on the sound algebro-geometrical principles. Secondly, it sheds substantial light at and provides us with a promising conceptual basis for the eventual reconciliation between the two extreme views of spacetime, namely physical and perceptual. Thirdly, it gives a significant boost to the idea already indicated by the planar model that the multiplicity of spatial dimensions and the generic structure of time are intimately linked to each other. Finally, being found to be formally on a similar philosophical track as the fractal Cantorian approach, it grants the latter further credibility.