In the normal state of the high temperature superconductors Bi(2)Sr(2)CaCu(2)O(8+delta) and La2(-x)Sr(x)CuO4, and in the related "stripe ordered" material, La(1.25)Nd(0.6)Sr(0.15)CuO4, there is sharp structure in the measured single hole spectral function, A<(k-->,omega), considered as a function of k--> at fixed small binding energy omega. At the same time, as a function of omega at fixed k--> on much of the putative Fermi surface, any structure in A<(k-->,omega), other than the Fermi cutoff, is very broad. This is characteristic of the situation in which there are no stable excitations with the quantum numbers of the electron, as is the case in the one-dimensional electron gas.