The hardware - The Computing Universe: A Journey through a Revolution - page 24

twenty-year-old graduate from the University of Michigan, applied and got the
position. Although the Differential Analyzer was a mechanical machine with
many spinning discs and rods, there was, as Shannon said later, also “a com-
plicated control circuit with relays.” 4 A relay is just a mechanical switch that
can be opened or closed by an electromagnet, so that it is always in one of two
states: either on or off, just like a light switch. Bush suggested that a study of
the logical organization of these relays could be a good topic for a master's
thesis. Shannon agreed, and drawing on his undergraduate studies in symbolic
logic, he began trying to understand the best way to design complicated relay
circuits with hundreds of relays. Commenting on the importance of symbolic
logic in this endeavor, Shannon later said that “this branch of mathematics,
now called Boolean algebra, was very closely related to what happens in a
switching circuit.” 5 Let's see how this comes about.
George Boole ( B.2.2 ) was a nineteenth-century, self-taught mathematician
whose best-known work is a topic called An Investigation of the Laws of Thought .
In this topic, Boole tried to reduce the logic of human thought to a series of
mathematical operations in which decisions are predicated on determining
whether any given logical statement is true or false. It was the Greek philoso-
pher Aristotle who introduced what is now called propositional logic. This was
a form of reasoning that enabled him to deduce new conclusions by combining
true propositions in a “syllogism” of the form:

B.2.1. Claude Shannon (1916-2001)
is often referred to as the father of
information technology. He is cred-
ited with two groundbreaking ideas:
the application of Boolean algebra to
logical circuit design and digitization
of information. In this photograph,
he is holding a mechanical mouse
that can learn from experience as it
moves around the complicated maze.

Every Greek is human.
Every human is mortal.
Therefore, every Greek is mortal.

Boole devised a language for describing and manipulating such logical state-
ments and for determining whether more complex statements are true or
false. Equations involving such statements can be written down using the log-
ical operations AND, OR, and NOT. For example, we can write an equation to
express the obvious fact that if neither statement A nor statement B is true,
then both statements A and B must be false:

NOT (A OR B) = (NOT A) AND (NOT B)

This equation is actually known as De Morgan's theorem, after Boole's col-
league, Augustus De Morgan ( B.2.3 ). It is a simple, (but as we shall see) pow-
erful expression of Boolean logic. In this way, Boolean algebra allows much
more complex logical statements to be analyzed.
Shannon realized that relays combined in circuits were equivalent to
combining assertions in Boolean algebra. For example, if we connect two
relays, A and B, in series and apply a voltage to the ends, current can only
flow if both relays are closed ( Fig. 2.2 ). If we take the closed state of a relay
as corresponding to “true,” then this simple connection of two relays cor-
responds to an AND operation: both relays must be closed - both true - for
current to flow. Similarly, if we connect up the two relays in parallel, this cir-
cuit performs an OR operation, since current will flow if either relay A or B is
closed or true ( Fig. 2.3 ).
Shannon's master's thesis, “A Symbolic Analysis of Relay and Switching
Circuits,” showed how to build electrical circuits that were equivalent to

B.2.2. George Boole (1815-64)
invented the algebra of 0s and 1s by
introducing the rules and notation
for describing logic. He was a self-
taught mathematician and at the
age of thirty-four became a professor
of mathematics at Queens College
in Cork, Ireland. Boole was widely
recognized for his work aiming
to combine algebra and logic. De
Morgan, the leading logician of the
time wrote: “Boole's system of logic
is but one of many proofs of genius
and patience combined.” B1