


A crucial property of the action potential is that it is an allornone phenomenon, representing a nonlinear transformation of the summed graded potentials. The neuron converts continuously varying inputs into a response that is either on (action potential generated) or off (action potential not generated). This has been called the allornone law (Levitan & Kaczmarek, 1991). “The allornone law guarantees that once an action potential is generated it is always full size, minimizing the possibility that information will be lost along the way” (Levitan & Kaczmarek, 1991, p. 43). The allornone output of neurons is a nonlinear transformation of summed, continuously varying input, and is the reason that the brain can be described as digital in nature (von Neumann, 1958).
The allornone behavior of a neuron makes it logically equivalent to relays or switches. This logical interpretation was exploited in an early mathematical account of the neural information processing (McCulloch & Pitts, 1943). McCulloch and Pitts used the allornone law to justify describing neurons very abstractly as devices that made true or false logical assertions about input information. "The allornone law of nervous activity is sufficient to ensure that the activity of any neuron may be represented as a proposition. Physiological relations existing among nervous activities correspond, of course, to relations among the propositions; and the utility of the representation depends upon the identity of these relations with those of the logical propositions. To each reaction of any neuron there is a corresponding assertion of a simple proposition." (McCulloch & Pitts, 1943).
References:
 Levitan, I. B., & Kaczmarek, L. K. (1991). The Neuron: Cell And Molecular Biology. New York: Oxford University Press.
 McCulloch, W. S., & Pitts, W. (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 5, 115133.
 von Neumann, J. (1958). The Computer And The Brain. New Haven, CN: Yale University Press.



