themselves. Sometimes, enzymes may be needed-but in such cases, they
are recruited from the host cell, and enslaved. This is what is meant by
self-assembly.
By contrast, the DNA of more complex viruses, such as the T-evens,
codes not only for the parts, but in addition for various enzymes which play
special roles in the assembly of the parts into wholes. Since the assembly
process is not spontaneous but requires "machines", such viruses are not
considered to be self-assembling. The essence of the distinction, then,
between self-assembling units and non-self-assembling units is that the
former get away with self-reproduction without telling the cell anything
about their construction, while the latter need to give instructions as to how
to assemble themselves.
Now the parallel to Henkin sentences, implicit and explicit, ought to be
quite clear. Implicit Henkin sentences are self-proving but do not tell
anything at all about their proofs-they are analogous to self-assembling
viruses; explicit Henkin sentences direct the construction of their own
proofs-they are analogous to more complex viruses which direct their
host cells in putting copies of themselves together.
The concept of self-assembling biological structures as complex as
viruses raises the possibility of complex self-assembling machines as well.
Imagine a set of parts which, when placed in the proper supporting
environment, spontaneously group themselves in such a way as to form a
complex machine. It seems unlikely, yet this is quite an accurate way to
describe the process of the tobacco mosaic virus' method of self-
reproduction via self-assembly. The information for the total conformation
of the organism (or machine) is spread about in its parts; it is not concen-
trated in some single place.
Now this concept can lead in some strange directions, as was shown in
the Edifying Thoughts of a Tobacco Smoker. There, we saw how the Crab used
the idea that information for self-assembly can be distributed around,
instead of being concentrated in a single place. His hope was that this
would prevent his new phonographs from succumbing to the Tortoise's
phonograph-crashing method. Unfortunately, just as with the most sophis-
ticated axiom schemata, once the system is all built and packaged into a
box, its well-definedness renders it vulnerable to a sufficiently clever
"Godelizer"; and that was the sad tale related by the Crab. Despite its
apparent absurdity, the fantastic scenario of that Dialogue is not so far
from reality, in the strange, surreal world of the cell.
Two Outstanding Problems:
Differentiation and MorphogenesisNow self-assembly may be the trick whereby certain subunits of cells are
constructed, and certain viruses-but what of the most complex macro-
scopic structures, such as the body of an elephant or a spider, or the shape
of a Venus's-flytrap? How are homing instincts built into the brain of a
Self-Ref and Self-Rep543