Representational consistency: a paradox of simultaneous representations of numbers

A paradox of simultaneous representation of numbers is presented. This is formu- lated as an algebraic notion of representational consistency. Possible examples come from geometric analysis of symmetric spaces and Hopf algebras, like spin groups, Clifford algebras, complex projective spaces and Grassmannians. There are un- solved problems and applications considering Oxygen metabolism and NMR/MRI; it is shown that representational consistency implies the BOLD effect.