Biology Reference
In-Depth Information
the four members of C in Fig. 7a must share 20 functions between them (four
to make B and 16 to make D), or that the two members of B in Fig. 7b share
16 functions between them. Whereas this option is not logically impossible, it
confronts us directly with an number of crucial questions: Is there by necessity
an increase in the degree of complication of fabricators as one goes up the
fabrication hierarchy? Intuitively, one would think so. Therefore, if yes, it is
possible for a 'simpler' fabricator to make a more complicated fabricator? In
fact, can a fabricator conceivably make itself?
It seems to be generally accepted that Von Neumann (1966, fifth Lecture)
showed that self-fabrication of a machine (autonomous turnover of self on
the basis of a supplied blueprint) and self-reproduction (making a copy of
self, including the blueprint) is in principle possible. Von Neumann's so-called
kinematic self-reproducing machine consists of a general purpose fabricator
P
+
X, which is an automaton consisting of two parts: A constructor P that
fabricates a machine X from spare parts according to X, the blueprint for X.
When supplied with its own blueprint P the constructor makes itself.
12
The incorporation of a general purpose fabricator such as P
X into
our factory solves the 'insufficient number of machines' dilemma sketched
above; in fact, I suspect this to be the only way to circumvent the problem.
In Fig. 8, I sketch a self-fabricating factory that shows how incorporating
the Von Neumann architecture makes Fig. 4e self-fabricating. The symbolism
used in this figure derives from Eqn. (4); the Von Neumann constructor P is
symbolised by r, while the blueprint X referred to above is now an element
i of the set of blueprints I; any element ri of the Cartesian product r
+
×
I is
A
f
r x I
C
=
{
r
,
f
}
B
Figure 8
An abstract self-fabricating factory that
incorporates the Von Neumann
architecture.
Raw materials A are converted into building blocks B for the fabricators in the factory. A Von
Neumann constructor r uses the information in the set of blueprints I to fabricate the set of
machines C. The fabricator ri
k
with i
k
∈
I can make itself directly when supplied with its own
blueprint i
k
=
i
r
. With i
k
=
i
r
it makes all the other machines f required by the factory.
12
To give the entire fabricator P
+
X the ability to make a copy of itself, von Neumann added a blueprint
copier Q and a controller R so that the fabricator becomes P
+
Q
+
R
+
X, which can make not only
X but also a copy of X. When supplied with its own blueprint, P
+
Q
+
R, it can make a copy
P
R of itself and of its blueprint, thereby ensuring self-fabrication of the full system.
However, for the purpose of analysing self-fabrication we do need to concern ourselves with replication of
the blueprint.
+
Q
+
R
+
P
+
Q
+
