Modularity, Abstraction, and Modelling

Whether proving a theorem by creating up from lemmas to simple basic theorems to more accurate results, or designing a circuit by creating up from elements to modules to complex processors, or designing a software system by making up from generic functions to classes to class libraries, humans operates  with  complexity by exploiting the power of modularity and abstraction. Without such functions, a single person could be overwhelmed by the complexity of a machine, as there is only so much information that a one person can consciously manage at a time.

Modularity is the concept  of creating components that  may be re-used; and  abstraction is the concept that  after  preparing a module,  most  of the  information  of the module construction may be ignored and  a simpler description given  for module communication.

Given  simple  modules, one  may move  up  a level  of abstraction and  create a new  module by having together various  previously-create modules, thinking only  of their  abstract information, and  not their  implementations. And, of course, this function may be repeated over several stages. This function provides one the ability to construct machine with complexity far beyond what would be possible if it were important to understand every element in detail.

Any module may be defined in a large number of types.   We might illustrate the circuitry in a digital watch in parts of how it works as a clock and a stopwatch, or in terms of currents and voltages within the circuit, or in terms of the heat given at different types of the circuitry. Each of these is a different kind of model of the watch.  Different models will be important for different tasks: there is no single correct operation.  Rather, every model exposes different dimensions of the machine, allowing us to explore different aspects of the design space of a machine, and to sell off different factors in the performance of a machine.