You will notice in the 
diagram how common 
divergence and convergence 
are: how almost as a rule the 
axon from a cell in a given stage 
splits on arriving at the next 
stage and ends on several or 
many cells, and conversely, a 
cell at any stage except the first 
receives synaptic inputs from a 
few or many cells in the 
previous stage.

    We obviously need to amend 
and qualify this simplified 
diagram, but at least we have a 
model to qualify. We must first 
recognize that at the input end 
we have not just one but many 
sensory systems--vision, 
touch, taste, smell, and 
hearing--and that each system 
has its own sets of stages in the 
brain. When and where in the 
brain the various sets of stages 
are brought together, if indeed 
they are brought together, is 
still not clear.

    In tracing one system such 
as the visual or auditory from 
the receptors further into the 
brain, we may find that it splits 
into separate subdivisions. In 
the case of vision, these 
subsystems might deal 
separately with eye movements, 
pupillary constriction, form, 
movement, depth, or color. 
Thus the whole system diverges 
into separate subpathways. 
Moreover, the subpaths may be 
many, and may differ widely in 
their lengths. On a gross scale, 
some paths have many 
structures along the way and 
others few. At a finer level, an 
axon from one stage may not go 
to the next stage in the series 
but instead may skip that stage 
and even the next; it may go all 
the way to the motor neuron. 
(You can think of the skipping 
of stages in neuroanatomy as 
analogous to what can happen 
in genealogy. The present 
English sovereign is not related 
to William the Conqueror by a 
unique number of generations: 
the number of "greats" 
modifying the grandfather is 
indeterminate because of 
intermarriage between 
nephews and aunts and even 
more questionable events.)

    When the path from input to 
output is very short, we call it a 
reflex. In the visual system, 
the constriction of the pupil in 
response to light is an example 
of a reflex, in which the 
number of synapses is probably 
about six. In the most extreme 
case, the axon from a receptor 
ends directly on a motor 
neuron, so that we have, from 
input to output, only three 
cells: receptor, motor neuron, 
and muscle fiber, and just two 
synapses, in what we call a 
monosynaptic reflex arc. 
(Perhaps the person who coined 
the term did not consider the 
nerve-muscle junction a real 
synapse, or could not count to 
two.) That short path is 
activated when the doctor taps 
your knee with a hammer and 
your knee jumps. John Nicholls 
used to tell his classes at 
Harvard Medical School that 
there are two reasons for 
testing this reflex: to stall for 
time, and to see if you have 
syphilis.