Quantum Harmonic Oscillator Coherence Versus Quantum Random Fluctuations

If we submit ourselves to the mathematical description chosen by Heisenberg, et al, to represent so-called quantum processes, we are in essence submitting to a dogma of irrationality. The choice of  a matrix algebra of eigenstates based upon statistical probability is doubly unfortunate in this regard. Ah but the critic will respond that this choice of mathematics works. Actually, if one delves into the descriptive functions that are spliced in an ad hoc fashion time and time again in order to save the mathematical edifice from crumbling such as "operators" as an example, the fact is there is no necessity for embedding the fallacies of statistics and Grassmanian reductionism into the study of quantum physics. Rather, it is quite possible to envisage a wonderful coherence along the lines that Leibniz limns in his Monadology in the kind of superpositions that quantum systems evince. This, I believe, is quite the opposite to the gratuitous importing of the absurd into science which bled over into so much of the oeuvre of the "intellengentsia" during the twentieth century. Take Schopenhauer (please!) for instance.