Gödel, Escher, Bach An Eternal Golden Braid by Douglas R. Hofstadter

and see how the enzyme acts on the strand. It so happens that the enzyme

binds to G only. Let us bind to the middle G and begin. Search rightwards

for a purine (viz., A or G). We (the enzyme) skip over TCC and land on A.

Insert a C. Now we have

TAGATCCAGTCCACTCGA

+

where the arrow points to the unit to which the enzyme is bound. Set Copy

mode. This puts an upside-down G above the C. Move right, move left,

then switch to the other strand. Here's what we have so far:

+

r:JV

TAGATCCAGTCCACTCGA

Let's turn it upside down, so that the enzyme is attached to the lower

strand:

Vr:JJIJVJJlr:JVJJlVr:JVl

AG

Now we search leftwards for a purine, • and find A. Copy mode is on, but the

complementary bases are already there, so nothing is added. Finally, we

insert a T (in Copy mode), and quit:

Vr:JJ IVJVJJ 1 r:JVJJ 1 Vr:JV 1

ATG

Our final product is thus two stJnds:

ATG, and TAGATCCAGTCCACATCGA

The old one is of course gone.

Translation and the Typogenetic Code

Now you might be wondering where the enzymes and strands come from,
and how to tell the initial binding-preference of a given enzyme. One way
might be just to throw some random strands and some random enzymes
together, and see what happens when those enzymes act on those strands
and their progeny. This has a similar flavor to the MU-puzzle, where there
were some given rules of inference and an axiom, and you just began. The
only difference is that here, every time a strand is acted on, its original form
is gone forever. In the MU-puzzle, acting on Ml to make MlU didn't destroy
Ml.
But in Typogenetics, as in real genetics, the scheme is quite a bit
trickier. We do begin with some arbitrary strand, somewhat like an axiom
in a formal system. But we have, initially, no "rules of inference"-that is,
no enzymes. However, we can translate each strand into one or more
enzymes! Thus, the strands themselves will dictate the operations which
will be performed upon them, and those operations will in turn produce

Self-Ref and Self-Rep^509