PTIByrne

You are right. By itself, an underlying zero dimensional expanse would lack any kind of geometry because it would lack space and time. As with Stephen Hawking's no boundary proposal, 'Imaginary' time shows up in physics equations involving time, and in relation to black holes & singularities, etc. As I understand it, imaginary time can be seen as being infinite and timeless -- just as a dimensionless void would be infinite and timeless. And an interaction of 'imaginary time' and 'real time' to form 'complex' time, would cause a warping of time, and would be a part of the warping of space-time. At the extreme state of singularities, the presence of basically 100% imaginary time would be timeless and lack time asymmetry -- just as an underlying non dimensional expanse would be timeless and lack time asymmetry. So, non dimensionality could already be represented in physics equations in the guise of imaginary time -- and as interacting with space-time in the guise of complex time. By itself an underlying non dimensionality would lack geometry. But interacting with space-time, it could be seen as a warped space-time geometry -- revealing its presence as a hybrid combination of dimensionality (time) & non dimensionality (zero time) ... in what we perceive as curved space-time or gravity.

Vlatko Vedral has said that we need to understand reality ultimately as having a basis in spaceless/timeless-ness -- which could be called a basis of zero dimensionality. Perhaps such a zero-dimensional basis is 'revealed' in black hole singularities -- where a spaceless / timeless-ness occurs as an underlying basis of reality, rather than an infinite curvature of space-time. At the very least, this would enable the 'transfer' of such infinities outside of space-time. So -- is there some way that the equation of general relativity could include a basis of zero-dimensions, while still dealing with curvatures in space & time.?