Dear Peter,
I read with interest your depth analytical essay in the spirit of Cartesian doubt and new ideas. I fully agree: "But show the trickery is not the fault of maths but from misuse due to our poor initial conceptual understanding and analysis of empirical findings and thus valid formalisms. We propose more focus on teaching well developed methods of improving conceptual analytical and visualization skills, and also identify the importance of countering increasing 'compartmentalization' of physics by wide research and an open mind."
The problem of the ontological justification (basification) of fundamental sign systems, Mathematics and Physics - is the main task of knowledge. Ontological revolution Planck-Einstein must be completed. John Wheeler left physicists good covenant: "Philosophy is too important to be left to the philosophers". But how many people follow this covenant? What is needed is a synthesis of all knowledge accumulated by mankind. This problem is well formulated Edmund Husserl in "Origin of Geometry»: "Only to the extent, to which in case of idealization, the general content of spatio-temporal sphere is apodictically taken into account, which is invariant in all imaginable variations, ideal formation may arise, that will be clear in any future for all generations and in such form will be transferable by the tradition and reproducible in identical intersubjective sense."
Kind regards,
Vladimir