The paper Česnavičius and Scholze just posted on arXiv answers several longstanding open questions in fundamental algebraic geometry. It also introduces a new definition with energetic new terminology:
I don’t pretend to know which of the authors had the idea of returning to Latin roots in order to find the appropriate word to designate the objects that Lurie had chosen to call “spaces,” as well as their cognates in other settings. Scholze’s terminological innovations have been more than commonly successful up to now, but I predict that “animated sets” will be especially popular. A whole thesis in philosophy of mathematics — and a second thesis in theology of mathematics? — could be devoted to the last sentence above.
It turns out that the expression “soul of a space” has been popular for some time among interior designers and architects.
A room designed by architect Vipin Bakliwala
Bakliwala’s reply also deserves our attention:
As architects, it is our duty to induce emotions into a space and create an ambience that brings forth our hidden calm, positive and spiritual side. We strive to expand the brief given by the client and create a space that elevates and improves his life. We struggle to provide an environment which is an enhanced reflection of his thoughts. We call such places soul shelters. It is that space where the soul remains in its innate nature.
Do emotions inhere more spontaneously in “worldly” point-set “physical” topological spaces or in their animated “calm, positive, and spiritual” ghostly doubles? Descartes and Spinoza might help us sort this out.
UPDATE: T.G. pointed out that, if I had read past the introduction to the acknowledgments, I would have realized that
The terminology is due to Clausen, inspired by Beilinson; see the acknowledgements, and the first paragraph of section 5.1.
Here is a passage from Beilinson’s article Topological E-factors that sheds some light on his perception of the need for appropriate terminology, and about the desolation of ordinary category theory.
A. A. Beilinson, Topological E-factors, Pure and Applied Mathematics Quarterly 3, 357-391, (2007)
Beilinson, or my imagined recollection of him, expresses a rather different opinion of spaces on p. 202 of MWA.
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