The Bott clock can be understood by considering the problem of Clifford algebra extensions. Near an interface between two inequivalent bulk materials, the Hamiltonian approaches a gap closing. To lowest order expansion in momentum slightly away from the gap closing, the Hamiltonian takes the form of a Dirac Hamiltonian H Dirac ( k → → ) = ∑ ∑ j = 1 d Γ Γ j v j k j + m Γ Γ 0 . Here, Γ Γ 1 , Γ Γ 2 , … … , Γ Γ d are a representation of the Clifford Algebra { Γ Γ i , Γ Γ j } = 2 δ δ i j , while m Γ Γ 0 is an added "mass term" that and anticommutes with the rest of the Hamiltonian and vanishes at the interface (thus giving the interface a gapless edge mode at k = 0 ). The m Γ Γ 0 term for the Hamiltonian on one side of the interface cannot be continuously deformed into the m Γ Γ 0 term for the Hamiltonian on the other side of the interface. Thus (letting m be an arbitrary positive scalar) the problem of classifying topological invariants reduces to the problem of classifying all possible inequivalent choices of Γ Γ 0 to extend the Clifford algebra to one higher dimension, while maintaining the symmetry constraints.