The magnetic behaviour is pure spherical rotation. Consequently magnetism propagates through space through rotation mechanisms of interaction.
Translation is by rolling the space in which magnetic field is exhibited. Shear propagation is by rolling neighbouring Space by contact or intersectional interactions. These types of magnetic propagation have vastly different velocities, and modes of propagation., and strain profiles . While this propagation is independent of electric field propagation, electric field propagation is entirely dependent on magnetic field propagation.
Lord Kelvinn and Gibbs introduced an algebra that was frankly not fit for the job! Grassmann and Hamilton both had deep algebras that were , but both were sidelined . Consequently thermo dynamics, fluid dynamics and it's derivative electromagnetism were in adequately modelled by theoreticians.
Maxwell was older, by the time Hamilton published his eagerly awaited Quaternions. Maxwell loved them, but later was forced to recant by Kelvin who pressurised him to rewrite his equations in he " modern" form espoused by Gibbs! Maxwell had no choice if he wanted to be published! Consequently his equations became a meaningless jumble, that only Heaviside saw through! Heviside redacted the work of Maxwell and reintroduced his own quaternion based calculus. In he Meantime Stinmetz had worked out the application of Quaternions to Electromagnetism. Being canny, as well as small, he kept his secret to himself, obscuring the link to Quaternions. In fact he could also use Grassmanns Algrbra to simplify evn the quaternion foms.
Today Clifford algebras are the general TEM for Grassmann Hamilton Clifford algebras. It is in these terms tht fluid dynamics nd electromagnetism will be successfully modelled mathematically..
The mathematical model will always be a mnemonic structure to the philosophical apprehension of empirical observation.