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