Claude Shannon's 1938 thesis, "A Symbolic Analysis of Relay and Switching Circuits," demonstrated how to build logic circuits from relay switches.
His work was based in part on a treatise published in 1854 by the mathematician George Boole entitled An Investigation of the Laws of
Thought, which he encountered as the student of American logician Charles Sanders Pierce. Shannon's knowledge of relay switches and electrical
engineering working under the supervision of Vannevar Bush inspired the second part of his work. Shannon applied Boole's themes in a very
practical sense to design the reasoning machine that was fully realized in the EDVAC.
The main idea that Shannon picked up from Boole was that all human rational processes could be reduced to the three operative descriptors
(now called Boolean Operators) 'and', 'or' and 'not'. Boole argued that our rational processes depend primarily of grouping together things by,
for example, saying 'this thing and that thing'. Similarly, we make decisions based on
'this thing or that thing', and to make more specific selections, we say 'this thing not that thing'. This model of thought
conceives of a pool of all possible choices, from which specific categories of things are chosen. For example, a person may choose all the
candies with the descriptor 'red' from a bowl of assorted coloured candy mixed with chocolates. In this case, the rational process includes the
descriptions 'candy' and 'red'. By bringing together these two descriptors, only red candies may be selected from the container. If the
person wants more than just red candy, they may choose the categories !'candy' and
'red' or 'orange', thus describing all the possible candies in the bowl they want. Conversely, if they don't want a specific kind of
candy, but want all the rest, they may choose, for example, 'candy' not 'green'. This will give them everything in the bowl that is classified
non-green candy. This distinction is important, because there is also
something described as 'chocolate' in the bowl, which will also be excluded by default from their description, since it is a different
category of thing.
This very basic description of how Boolean categorization works is meant to describe the workings within a closed environment, meaning the possible
choices are limited by what is contained in the bowl. It should be noted here that Boole and Leibniz (on whose premises Boole built his philosophy)
were concerned with universals, not closed sources of information. This means they would have considered it necessary to specify which bowl of
candy was being searched as a category on its own, or it would be taken that all candy in the infinite universe was being searched through.
Shannon was not concerned with the philosophical issues raised by tangible things, instead focusing his energies entirely on abstract mathematical
values.
Kurt Godel had shown previously how, by assigning a whole number to each signifier comprising a numerical concept, all numeric values (for example,
negative numbers) and mathematical operation signs (such as a '+' or '^' sign) could be converted to
'natural' numbers (or digital integers). His proposition was to assign a whole number to represent each symbol, thereby
allowing all mathematical operations to be written as strings of numeric code. Turing developed this idea to create the
'Turing machine'. Turing believed he had observed that when performing a calculation, a human being
methodically performs one task at a time. Individual instructions could be given codes the same way the numbers and operations could be coded. A
string of code could be produced in real numbers that describe in sequence how to work with the desired data. Turing even theoretically showed how
to make this code in binary form, which is how it was done in the EDVAC. Godel's and Turing's ideas theoretically mean that, when combined with
Boolean operations, all human thought processes can be represented by a series of gates reflecting the above operations. Of course, this assumes
that Boole's postulates are accepted as the truth about human thought. I will not argue with Boole here, but rather move on with the understanding
that his is the mathematically expressed logic by which our dominating information storage medium operates, and quickly look at Shannon's
application of his work to electrical engineering.
The main mechanical function Shannon was concerned with was representing the
'and', 'or' and 'not' functions of Boolean algebra in terms of
electrical circuitry. This was accomplished by configuring relay switches to pass current or not according to what kind of signals were input. For
example, a simple 'and' switch requires a charge on both of its inputs to output a charge. If only one or the other input (or neither) receives a
stimulus, the relay will not forward a signal to the next level of relays. An 'or' switch requires a stimulus on either of its inputs, but not both,
to output a signal. Finally, a 'not' switch will output a signal only if nothing is input. Though several other configurations of switches are
possible, combinations of these basic three configurations into 'adders' can actually represent all possible outcomes that might be desired for the
function of the machine. Creating adders out of the above relays - or 'gates' as they are also
called - allows the design of a machine that is capable of any mathematical function. For example, Appendix E illustrates an addition circuit,
demonstrating the equation '1 + 1'. Since the sum of the equation performed is two, there must be provision to carry the one to the next
binary digit place. In this case, the carried digit will act as a signal
stimulus for the next half-adder. A full-adder contains half-adders, and is designed to accept a bit carried forward from a previous calculation,
itself outputting a sum and a value to carry to the next adder. As one might observe, the number of switches needed to build the types of
circuits that perform complex calculations, such as square roots, proliferates quite rapidly. Nevertheless, history has proven the
expression of Boolean algebra through electronic relays, and powered by binary coded electrical pulses, creates an efficient computing machine.
Shannon's engineering and theoretical work went far beyond designing Boolean switching arrays.
Directly related to his engineering work was his invention of digitization. Shannon's idea of sampling information from a given source
at a stable rate and converting that information into a "bit stream" of binary code that could be processed by the computer is the basis of the
digital revolution.
Every photo that is scanned, every voice that is digitally recorded, or any other type of computer-mediated information is either originated as or
converted into a "bit-stream" - the string of electrical pulses that are the binary text. Shannon devoted much of his efforts to maximizing the
accuracy and message carrying potential of digital circuitry, founding the field of Information Theory with his co-author Warren Weaver. Their book
The Mathematical Theory of Communication in 1949 outlined what would quickly become important theoretical issues in communication, not just
technically, but also socially.
Perhaps best known in the social sciences for designing the 'transmissive model' of communication, Weaver and Shannon were interested only in the
direct effects of communication. They defined communication as "all the procedures by which one mind may affect another", and were very aware of
the arbitrariness of their decision to focus only on encoding, transmission, and decoding. Their 1949 work was concerned only with the
accuracy of transmission, trying to make the received message resemble the sent message as accurately as possible. In so doing, they were careful to
point out that they were working at the level of information, not at the level of meaning, which requires interpretation of the sent and received
information. Meaning is culturally influenced, and Shannon and Weaver were really only concerned with making a better functioning machine.