For Niklas Luhmann:* “How Recursive is Communication?” - Understanding Understanding: Essays on Cybernetics and Cognition - page 320

FIGURE 9.
into u -in. This ring or torus is the topological representative of a doubly
closed system.
If you'd like pictures, you can find them already very early in Warren
McCulloch's article “A Hetarchy of Values Determined by the Topology of
Nervous Nets”:
07. Warren S. McCulloch (1945): “A Hetarchy of Values Determined by the Topol-
ogy of Nervous Nets” (Figure 9).
His argument is as follows: In his Figure 3 (Figure 9, left), he shows the
recursion of neural activity whose internal components are indicated by the
unbroken arcs and whose external components are indicated by the broken
ones: McCulloch's thesis of the closure of the neural pathways via the envi-
ronment. In this circuit the organization is hierarchical, for the presently
external senso-motoric loops (dromes) can inhibit the inner loops. There-
fore this network cannot calculate the “circularities in preference,” the
“value anomaly” that I spoke of. In his Figure 4 (Figure 9, right), he
introduces the diallels (“crossovers”) that from the lower circle can inhibit
the upper: twofold closure.
A second reference to the value of toroids for representing doubly closed
processes will be found in Proposition 8:
08. Double closure of the senso-motoric and inner-secretoric-neuronal circuits.
N = neural bundle; syn = synapse; NP = neurohypophysis; MS = motorium;
SS = sensorium (Figure 10).
Here you see sketched (Figure 10a) both of the orthogonally operating
circuits: on one side the neural signal flow from the sense organs ( SS ) via
the nerve bundles (separated by synapses) to the motorium and from there
through the environment and back to the sensorium ( SS ); on the other side