Molecular Ethology, An Immodest Proposal for Semantic Clarification - Understanding Understanding: Essays on Cybernetics and Cognition - page 159

ji

() ∫ () =- yi yi ( 1 ) + a f x

i

() (56)

Using the suggested recursion [compare with Eq. (14)]:

() = () + () + ( ) yi a f x

i

a

i - 1

f x * a

i - 2

f x ** ...

or

i

Â

( )

() =

()

yi a

ik -

f x

k *

(57)

k = 0

and

ym () ∫ ( m , m a )

The function f is, of course, computed by the ribosome which reads the
codon x , and synthesizes the amino acids which, in turn, are linked together
by the recursion to a connected polypeptide chain.
Visualizing the whole process as the operations of a sequential finite state
machine was probably more than just a clue in “breaking the genetic code”
and identifying as the input state to this machine the triplet ( u , v , w ) of adja-
cent symbols in the

- -number representation of the messenger RNA.
A method for computing

-numbers of molecular sequences directly
from properties of the generated structure was suggested by Pattee (1961).
He used the concept of a sequential “shift register,” i.e., in principle that of
an autonomous tile. For computing periodic sequences in growing helical
molecules, the computation for the next element to be attached to the helix
is solely determined by the present and some earlier building block. No
extraneous computing system is required.
If on a higher level of the hierarchical organization the neuron is taken
as a functional unit, the examples are numerous in which it is seen as a
recursive function computer. Depending on what is taken to be the “signal,”
a single pulse, an average frequency code, a latency code, a probability code
(Bullock, 1968), etc., the neuron becomes an “all or nothing” device for
computing logical functions (McCulloch and Pitts, 1943), a linear element
(Sherrington, 1906), a logarithmic element, etc., by changing in essence only
a single parameter characteristic for that neuron (Von Foerster, 1967b). The
same is true for neural nets in which the recursion is achieved by loops or
sometimes directly through recurring fibers. The “reverberating” neural net
is a typical example of a finite state machine in its dynamic equilibrium.
In the face of perhaps a whole library filled with recorded instances in
which the concept of the finite state machine proved useful, it may come
as a surprise that on purely physical grounds these systems are absurd. In
order to keep going they must be nothing less than perpetual motion
machines. While this is easily accomplished by a mathematical object, it is
impossible for an object of reality. Of course, from a heuristical point of
view it is irrelevant whether or not a model is physically realizable, as long
as it is self-consistent and an intellectual stimulus for further investigations.