Almost all cells in the 
nervous system receive inputs 
from more than one other cell. 
This is called convergence. 
Almost all cells have axons that 
split many times and supply a 
large number of other nerve 
cells--perhaps hundreds or 
thousands. We call this 
divergence. You can easily see 
that without convergence and 
divergence the nervous system 
would not be worth much: an 
excitatory synapse that 
slavishly passed every impulse 
along to the next cell would 
serve no function, and an 
inhibitory synapse that 
provided the only input to a cell 
would have nothing to inhibit, 
unless the postsynaptic cell 
had some special mechanism to 
cause it to fire spontaneously.

    I should make a final 
comment about the signals that 
nerve fibers transmit. Although 
most axons carry all-or-none 
impulses, some exceptions 
exist. If local depolarization of 
a nerve is subthreshold--that 
is, if it is insufficient to start 
up an explosive, all-or-none 
propagated impulse--it will 
nevertheless tend to spread 
along the fiber, declining with 
time and with distance from the 
place where it began. (In a 
propagated nerve impulse, this 
local spread is what brings the 
potential in the next, resting 
section of nerve membrane to 
the threshold level of 
depolarization, at which 
regeneration occurs.) Some 
axons are so short that no 
propagated impulse is needed; 
by passive spread, 
depolarization at the cell body 
or dendrites can produce 
enough depolarization at the 
synaptic terminals to cause a 
release of transmitter. In 
mammals, the cases in which 
information is known to be 
transmitted without impulses 
are few but important. In our 
retinas, two or three of the five 
nerve-cell types function 
without impulses.

    An important way in which 
these passively conducted 
signals differ from impulses--
besides their small and 
progressively diminishing 
amplitude--is that their size 
varies depending on the 
strength of the stimulus. They 
are therefore often referred to 
as graded signals. The bigger the 
signal, the more depolarization 
at the terminals, and the more 
transmitter released. You will 
remember that impulses, on the 
contrary, do not increase in 
size as the stimulus increases; 
instead, their repetition rate 
increases. And the faster an 
impulse fires, the more 
transmitter is released at the 
terminals. So the final result is 
not very different. It is popular 
to say that graded potentials 
represent an example of analog 
signals, and that impulse 
conduction, being all or none, 
is digital. I find this 
misleading, because the exact 
position of each impulse in a 
train is not in most cases of any 
significance. What matters is 
the average rate in a given time 
interval, not the fine details. 
Both kinds of signals are thus 
essentially analog.