Biology Reference
In-Depth Information
EMERGENCE, TRAP-DOOR PROCESSES AND THE DANGERS
OF POST-HOC REASONING
Emergence often involves processes that are analogous to the 'trap-door' algorithms
beloved of cryptographers. Trap-door algorithms are those that cannot be reversed unambig-
uously. This concept can be illustrated with a simple arithmetic example: if one is told that the
multiplication product of two numbers is 12, one cannot deduce what those numbers were.
They may have been 1 and 12, or 2 and 6, or 3 and 4, or
4, or 1/3rd and 36, or an
infinite number of other possibilities.
)
Multiplication is a 'trap door' because, once a pair of
numbers has fallen through the process, some information about them is lost. Rule-based
emergent systems such as the Game of Life also involve trap-door functions: knowing that
the result of running a game is a particular arrangement of cells gives no indication of the
original layout of cells (
Figure 2.4
). This illustrates a very important point in the vastly
more complex emergent systems that constitute real developing embryos:
morphogenetic
processes cannot be deduced from final form
. Of course hypotheses can be proposed, especially
when a related developmental system is already understood, but these hypotheses must
always be tested by observing and experimenting on the system as it develops. A concrete
example of this is provided by the elongation of tissues, which is described in detail in later
chapters of this topic. Some elongation events are driven directly by elongation of cells as the
tissue elongates, some are driven by the rearrangement of cells without any elongation of the
cells themselves, and some involve flattening of cells before tissue elongation takes place, fol-
lowed by a return of cells to their normal shape as the tissue elongates. Simply observing that
a tissue becomes longer does not, therefore, lead one directly to the mechanism. Similar ambi-
guities are seen at the molecular level.
This point is stressed because drawing conclusions from post-hoc reasoning has been
a long and dangerous tradition in morphogenetic research. Since the early decades of the
last century, long before the advent of computers, attempts have been to model possible
mechanisms of development mathematically. If the model produced the correct shapes,
the modeller tended to accept the reality of the proposed mechanism. This tendency has
become more marked as computers have become more available. Used properly, in conjunc-
tion with experimental observation, computer modelling is a very important tool for inves-
tigation of morphogenesis (and is discussed in more detail in Chapters 25 and 26). The fact
that a mechanismworks on a computer is not, however, itself strong evidence that it works in
life; usually, many possible mechanisms will produce the 'correct' result and only observa-
tion of the real embryo will indicate which is used. Even now, there seem to be far too
many mathematically inclined researchers, usually entering biology from outside, who
miss or ignore this point.
3 and
FEEDBACK
, SELF-ASSEMBLY AND ADAPTIVE SELF-ORGA
NIZATION
The development of complex structures is not unique to the biological world. Purely phys-
ical systems can generate rich patterns that range from the sub-millimeter scales of crystals,
)
Infinite because, for any integer,
n
, multiplying 12
n
by 1/
n
will yield the result 12.
