  The machinery of the human brain -- analog, probabilistic, embodied -- can be
characterized computationally, but what machinery confers what computational
powers? Any such system can be abstractly cast in terms of two computational
components: a finite state machine carrying out computational steps, whether
via currents, chemistry, or mechanics; plus a set of allowable memory
operations, typically formulated in terms of an information store that can be
read from and written to, whether via synaptic change, state transition, or
recurrent activity. Probing these mechanisms for their information content, we
can capture the difference in computational power that various systems are
capable of. Most human cognitive abilities, from perception to action to
memory, are shared with other species; we seek to characterize those (few)
capabilities that are ubiquitously present among humans and absent from other
species. Three realms of formidable constraints -- a) measurable human
cognitive abilities, b) measurable allometric anatomic brain characteristics,
and c) measurable features of specific automata and formal grammars --
illustrate remarkably sharp restrictions on human abilities, unexpectedly
confining human cognition to a specific class of automata ("nested stack"),
which are markedly below Turing machines.
