Cladists need education in linear algebra

When we discuss reality, we partition it into entities and states of these entities. The fundamental question in physics is what states are. There are only two possibilities: 1. a set (as in set theory) or 2. a vector space.

Classical physics assumes that they are a set, which, however, Bertrand Russell about a hundred years ago showed leads to paradox, called Russell's paradox. Quantum physics, however, later clarified that states actually are a vector space, called the Hilbert space, of complex numbers. This finding influences our comprehension of reality profoundly by interpreting it as a matter of probabilities for states rather than as states themselves. Entities thus have probabilities to have states rather than states per se.

This fact ambiguates the German Nazi entomologist Willi Hennig's methodology to reconstruct relationships by meaning that it leads to paradox. It simply assumes that reality can be pinpointed in terms of states of entities, when fact is the other way around, that is, that reality can't be pinpointed in terms of states of entities. It thus assumes that an erroneous comprehension of reality is correct, and thus that a correct comprehension of reality is erroneous.

Vector spaces are dealt with by linear algebra. Biological systematists (especially cladists) thus need education in linear algebra.