G. 't Hooft discusses the implications of reconciling gravitational collapse with quantum mechanics, suggesting that at the Planck scale, our world is not 3+1 dimensional but rather described by Boolean variables on a two-dimensional lattice. This dimensional reduction implies severe constraints on models of quantum gravity, making it challenging to construct consistent mathematical models of quantum black holes. The author argues that the number of degrees of freedom in a black hole is finite and can be estimated using thermodynamics and scattering experiments, leading to the conclusion that the entropy of a black hole is directly related to the area of its horizon. This suggests that the physical degrees of freedom in three-space are infinitely correlated and can be described by a topological quantum field theory. The paper also explores the challenges of implementing Lorentz invariance and coordinate reparametrization invariance in cellular automaton models, highlighting the need for commuting evolution laws and the difficulty in finding non-trivial solutions. Despite these challenges, 't Hooft advocates for further exploration of this approach to quantum gravity.G. 't Hooft discusses the implications of reconciling gravitational collapse with quantum mechanics, suggesting that at the Planck scale, our world is not 3+1 dimensional but rather described by Boolean variables on a two-dimensional lattice. This dimensional reduction implies severe constraints on models of quantum gravity, making it challenging to construct consistent mathematical models of quantum black holes. The author argues that the number of degrees of freedom in a black hole is finite and can be estimated using thermodynamics and scattering experiments, leading to the conclusion that the entropy of a black hole is directly related to the area of its horizon. This suggests that the physical degrees of freedom in three-space are infinitely correlated and can be described by a topological quantum field theory. The paper also explores the challenges of implementing Lorentz invariance and coordinate reparametrization invariance in cellular automaton models, highlighting the need for commuting evolution laws and the difficulty in finding non-trivial solutions. Despite these challenges, 't Hooft advocates for further exploration of this approach to quantum gravity.