>From Holistic to Combinatorial Signals

Bart de Boer, Vrije Universiteit Brussel, bartb@arti.vub.ac.be
Willem Zuidema, University of Edinburgh, jelle@ling.ed.ac.uk


The signals that all human languages use are combinatorial. Languages
use a limited number of basic signals (depending on the theory these
can be phonemes or syllables) that can be combined into an enormous
number of possible complex signals. This is in contrast with holistic
signaling systems, such as common in animal communication, where the
signals cannot be analyzed as consisting of smaller units.

If holistically coded systems can contain a large number of signals,
and if a holistic system was the precursor of the combinatorial system
of human speech (which is likely given that primate call systems are
all holistic) the question arises of how an originally holistic call
system can evolve into a combinatorial system.  Existing explanations
for this transitions -- based on the intuition that, in principle,
combinatorics provides an efficient way to produce a large number of
signals -- are not entirely satisfactory.

For instance, it has been argued that combinatorial (phonemic) coding
results in more reliable communication than holistic coding.
However, such explanations for the emergence of phonemic coding do
not take into account that holistic signals can have a long duration
in time, and that a purely holistic system can thus contain many
individual signals.  Moreover, even if the possible fitness of a
combinatorial system is higher than that of a holistic system, that is
in itself not enough as an evolutionary explanation. Crucially, there
must be a path of ever increasing fitness from a holistic system
towards a combinatorial system. This is a serious constraint that can
not be ignored, and -- as combinatorial systems are qualitatively
different from holistic systems -- it is not trivial to imagine a
system that falls in between.

The hypothesis investigated here is that when one optimizes a holistic
system of signals for distinctiveness under noise, the resulting
system can be analyzed as a combinatorial system.  We used a computer
simulation, in which a repertoire of sounds of a fixed duration is
modelled.  Sounds are (almost) continuous trajectories in an abstract
acoustic space.  We maximize the total acoustic distance between the
trajectories in order to make them as distinctive as possible.  After
optimization, the resulting systems of trajectories appear to be coded
combinatorially, i.e. a small set of points of the space is re-used as
start- and endpoints of all trajectories.  Crucially, the phonemic
coding we observe in these simulation is superficial, and can not be
used productively by the system, i.e. the system cannot create novel
combination of existing building blocks.

The results do, however, suggest a novel evolutionary pathway from a
holistic system to a combinatorial system.  We assume an ancestral
population with a small number of signals, that are randomly arranged
in the available signal space and that cannot be analyzed as
consisting of a smaller number of building blocks. When the number of
signals increases, and they are optimized for distinctiveness under
noise, the way they are arranged in the signal space becomes less
random: the signals can now in principle be analyzed as being built-up
from a number of smaller building blocks. For an outside observer, the
signals are combinatorial. However, the "agents" that use these signals
do not yet make use of their combinatorial nature. They just learn and
reproduce these signals as if they were completely holistic.

The final step, which goes beyond the results of our simulation, would
be for the agents to start making use of the combinatorics of the
signals. Instead of learning the signals as holistic units, they learn
the basic building blocks and the combinations. This requires less
learning effort, and would allow these agents to produce new signals
more easily. Hence, agents that make use of the combinatorial nature
of the signals would have an evolutionary advantage. However, a small
set of these signals would also be perfectly usable by agents that can
only use holistic signals, thus ensuring evolutionary continuity and
continuously increasing fitness.