  Animals build Bayesian 3D models of their surroundings, to control their
movements. There is strong selection pressure to make these models as precise
as possible, given their sense data. A previous paper has described how a
precise 3D model of space can be built by object tracking. This only works if
3D locations are stored with high spatial precision. Neural models of 3D
spatial memory have large random errors; too large to support the tracking
model. An alternative is described, in which neurons couple to a wave
excitation in the brain, representing 3-D space. This can give high spatial
precision, fast response, and other benefits. Three lines of evidence support
the wave hypothesis: (1) it has better precision and speed than neural spatial
memory, and is good enough to support object tracking; (2) the central body of
the insect brain, whose form is highly conserved across all insect species, is
well suited to hold a wave; and (3) the thalamus, whose round shape is
conserved across all mammal species, is well suited to hold a wave. These lines
of evidence strongly support the wave hypothesis.
