  The Giroux correspondence and the notion of a near force-free magnetic field
are used to topologically characterize near force-free magnetic fields which
describe a variety of physical processes, including plasma equilibrium. As a
byproduct, the topological characterization of force-free magnetic fields
associated with current-carrying links, as conjectured by Crager and Kotiuga,
is shown to be necessary and conditions for sufficiency are given. Along the
way a paradox is exposed: The seemingly unintuitive mathematical tools, often
associated to higher dimensional topology, have their origins in three
dimensional contexts but in the hands of late-onset visually impaired
topologists. This paradox was previously exposed in the context of algorithms
for the visualization of three-dimensional magnetic fields. For this reason,
the paper concludes by developing connections between mathematics and cognitive
science in this specific context.
