When describing a Riemannian geometry as a spectral triple, the algebra of functions on the geometry is infinite. But if we are looking at computer simulations, or physical measurements we will never be able to know the entire algebra and Dirac operator.
While recent work by Connes and van Suijlekom has shown that analytically a truncated spectral triple can be understood as an operator system, in the work I discuss here we started from the idea of truncated spectral triples and explore them in computer simulations.
In particular, we looked at simulations using the Heisenberg relation defined by Connes, Chamseddine, and Mukhanov, and then developed a code to recover an embedding of the geometry encoded in the spectral triple to understand in the hopes of understanding the unexpected results of our simulations.
This talk will be based on work with Abel Stern arXiv:1909.08054 and arXiv:1912.09227