The New Physician as Unwitting Quantum Mechanic: Is Adapting Dirac's Inference System Best Practice for Personalized Medicine, Genomics, and Proteomics?

Abstract

What is the Best Practice for automated inference in Medical Decision Support for personalized medicine? A known system already exists as Dirac's inference system from quantum mechanics (QM) using bra-kets <A | B> and bras <A| and kets |B> where A and B are states, events, or measurements representing, say, clinical and biomedical rules. Dirac's system should theoretically be the universal best practice for all inference, though QM is notorious as sometimes leading to bizarre conclusions that appear not to be applicable to the macroscopic world of everyday world human experience and medical practice. It is here argued that this apparent difficulty vanishes if QM is assigned one new multiplication function @, which conserves conditionality appropriately, making QM applicable to classical inference including a quantitative form of the predicate calculus. An alternative interpretation with the same consequences is if every i = radical-1 in Dirac's QM is replaced by h, an entity distinct from 1 and i and arguably a hidden root of 1 such that h2 = 1. With that exception, this paper is thus primarily a review of the application of Dirac's system, by application of linear algebra in the complex domain to help manipulate information about associations and ontology in complicated data. Any combined bra-ket <A | B> can be shown to be composed only of the sum of QM-like bra and ket weights c(<A|) and c(|B>), times an exponential function of Fano's mutual information measure I(A; B) about the association between A and B, that is, an association rule from data mining. With the weights and Fano measure re-expressed as expectations on finite data using Riemann's Incomplete (i.e., Generalized) Zeta Functions, actual counts of observations for real world sparse data can be readily utilized. Finally, the paper compares identical character, distinguishability of states events or measurements, correlation, mutual information, and orthogonal character, important issues in data mining and biomedical analytics, as in QM.