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We compare two alternative representations of quantum mechanics: PolymerQuantum Mechanics (PQM), which presents features similar to Loop QuantumGravity and Loop Quantum Cosmology, and the Generalized Uncertainty Principle(GUP) representation, that through a modified Algebra yields an alternativeuncertainty principle similar to those derived in String Theories and BraneCosmology. These formalisms can be recast to apparently look similar, but whilethe GUP yields an absolute minimal uncertainty on position, PQM implements somekind of ultraviolet cut-off through a lattice and does not have a minimaluncertainty. Then we implement them on the anisotropic Bianchi I model inMisner-like variables on a semiclassical level: PQM always implies a removal ofthe singularities, while the GUP fails to do so, highlighting once again howthe two representations are fundamentally incompatible.

PQM and the GUP: Implications of Lattice Dynamics and Minimal Uncertainties in Quantum Mechanics and Cosmology