Two Simple Examples of DifferentiationThe process by which one initial cell replicates over and over, giving rise to
a myriad of differentiated cells with specialized functions, can be likened to
the spread of a chain letter from person to person, in which each new
participant is asked to propagate the message faithfully, but also to add
some extra personal touch. Eventually, there will be letters which are
tremendously different from each other.
Another illustration of the ideas of differentiation is provided by this
extremely simple computer analogue of a differentiating self-rep. Consider
a very short program which is controlled by an up-down switch, and which
has an internal parameter N -a natural number. This program can run in
two modes-the up-mode, and the down-mode. When it runs in the up-
mode, it self-replicates into an adjacent part of the computer's memory-
except it makes the internal parameter N of its "daughter" one greater
than in itself. When it runs in the down-mode, it does not self-rep, but
instead calculates the number(-I)NI(2N + 1)
and adds it to a running total.
Well, suppose that at the beginning, there is one copy of the program
in memory, N = 0, and the mode is up. Then the program will copy itself
next door in memory, with N = l. Repeating the process, the new pro-
gram will self-rep next door to itself, with a copy having N = 2. And over
and over again ... What happens is that a very large program is growing
inside memory. When memory is full, the process quits. Now all of memory
can be looked upon as being filled with one big program, composed of
many similar, but differentiated, modules-or "cells". Now suppose we
switch the mode to down, and run this big program. What happens? The
first "cell" runs, and calculates 1/1. The second "cell" runs, calculating
-1/3, and adding it to the previous result. The third "cell" runs, calculating
+ 1/5 and adding it on ... The end result is that the whole "organism"-the
big program-calculates the sum1 -1/3 + 1/5 -1/7 + 1/9 -·1/11 + 1/13 -1/15 +
to a large number of terms (as many terms as· "cells" can fit inside memory).
And since this series converges (albeit slowly) to 'TT14, we have a "phenotype"
whose function is to calculate the value of a famous mathematical constant.Level Mixing in the CellI hope that the descriptions of processes such as labeling, self-assembly,
differentiation, morphogenesis, as well as transcription and translation,
have helped to convey some notion of the immensely complex system
which is a cell-an information-processing system with some strikingly546 Self-Ref and Self-Rep