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TABLE 2. The number of effective internal states
Z
,the
number of possible driving functions
N
D
, and the
number of effective state functions
N
S
for machines with
one two-valued output and with from one to four two-
valued inputs
n
Z
N
D
N
S
1
4
256
65 536
2
16
2.10
19
6.10
76
300.10
4.10
3
3
256
10
600
300.10
4.10
3
1600.10
7.10
4
4
65 536
Since the total number of driving functions
f
y
(
x
,
z
) is
N
D
=
Y
XZ
,
(20)
its largest value is:
X
N
D
=
Y
XY
(21)
Similarly, for the number of state functions
f
z
(
z
,
x
) we have
N
S
=
Z
Y
◊
Z
(22)
whose largest effective value is
X
X
=
[]
XXY
◊
(23)
N
=
Y
N
s
D
These numbers grow very quickly into meta-astronomical magnitudes
even for machines with most modest aspirations.
Let a machine have only one two-valued output (
n
y
= 1;
v
y
= 2;
y
= {0; 1};
Y
= 2) and
n
two-valued inputs (
n
x
=
n
;
v
x
= 2;
x
= {0; 1};
X
= 2
n
). Table 2
gives the number of effective internal states, the number of possible driving
functions, and the number of effective state functions for machines with
from one to four “afferents” according to the equations
Z
= 2
2
n
N
D
= 2
2
2
n
+
n
N
S
= 2
2
2
n
+2
n
These fast-rising numbers suggest that already on the molecular level
without much ado a computational variety can be met which defies imagi-
nation. Apparently, the large variety of results of genetic computation, as
manifest in the variety of living forms even within a single species, suggests
such possibilities. However, the discussion of these possibilities will be
reserved for the next section.
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