Careful consideration of the issues raised by Pezard
and colleagues (in this issue of Psychophysiology)
allows for the conclusion that spatial embedding may
be valid as a method of dynamical reconstruction. However,
two problems with the technique cannot be ignored. First,
spatial embedding of EEG invariably involves linear cross-correlation
among channels, which distorts the dynamical reconstruction
due to compression toward the main state-space diagonal.
Further, before spatially embedding across a set of channels,
one must first check for at least “similar”
dynamics among them, using, for example, a measure such
as estimated mutual dimension. Measuring a “whole
cortex” state via spatial embedding may also be possible
in principle, except for the nontrivial obstacle of separating
local dynamics that are heterogeneous across the cortex
from activity reflecting the “unified field”
of the cortex as a whole.