IEEE Technology and Society Magazine - December 2016 - 48

was her birthright allowed for a particular liberation
of thought, enabling her to make one of the most significant contributions that humankind has ever seen?
Let us begin at the beginning. A paradoxical statement is one that, despite relying on sound reasoning,
leads to a seemingly senseless or (at least) incongruous
conclusion. Let us examine one facet of Ada's intellectual life - her interest in Babbage's Analytical Engine.
Never having been completely built, the engine has
been the topic of discussion in the field of Computer
Science for years. A great deal of that discussion
revolves around the question of whether the Analytical
Engine can be called a computer. Gandy [1] makes the
case that the Analytical Engine fulfills all the requirements of a Turing machine and is therefore a computer.
The concept of a Turing machine was first introduced by the British mathematician, Alan Turing. Essentially, it is a mathematical abstraction describing a
simple but highly effective computational model. Turing
asked us to consider a system made up of an infinite
number of storage locations accessible in a line, each
capable of holding a symbol understood to be part of a
language's grammar. The machine is capable of examining and modifying only a single symbol at a time using
a set of internal rules. The rules are informed by the
symbol itself, but not by any other symbols that might
be stored in other locations. In other words, a Turing
machine is ideal for the process of modifying individual
items in a sequence of other items and forms the basis
for computability theory.
A problem is considered computable if it can be
solved by some means. Some problems are solvable
(what are the integers greater than zero but less than
10?) others are not (what is the last digit of Pi?) For the
most part, the computability of a solution to a problem
is related to our ability to come up with a plan to
solve it - commonly referred to as an "algorithm" and
formally described as a "computational function." The
instantiation of one form of computational function is a
computer program. A computer program is simply a
means of describing an algorithm to a computer. In
other words, a computer is a Turing machine in so much
as it is able to run programs.
Robin Gandy's analysis of Babbage's Analytical Engine
[1] makes the argument that it is a Turing machine in the
sense that it has all the features necessary to describe
such a machine: 1) having a set of operations (+, - and x),
2) that multiple operations can be treated as a single
operation (allowing the extension of operations), and 3)
that iteration is possible (repeatedly executing the same
operations as long as a condition is met). Based on Gandy's analysis, most computer scientists concede that the
Analytical Engine is an example of a Turing machine and
cite him as the source of this revelation.

However, in her footnotes to her translation of the
work of the Italian mathematician, Menabrea [2] describing the Analytical Engine, Ada Lovelace expounds upon
certain features of the Engine in a very similar manner
to Gandy. She fulfills the first Turing machine requirement by arguing that, "It may be desirable to explain,
that by the word operation, we mean any process which
alters the mutual relation of two or more things, be this
relation of what kind it may. This is the most general
definition, and would include all subjects in the universe." And that, "... it [the Analytical Engine] might act
upon other things besides number, were objects found
whose mutual fundamental relations could be
expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and
mechanism of the engine" [2, p. 693].
Ada Lovelace makes an argument supporting the
second requirement by observing, "... whenever numbers meaning operations and not quantities (such as
indices of powers), are inscribed on any column or set
of columns, those columns immediately act in a wholly
separate and independent manner." Finally, Lovelace
indirectly satisfies the third requirement by observing
that, "Supposing, for instance, that the fundamental
relations of pitched sounds in the science of harmony
and of musical composition were susceptible of such
expression and adaptations, the engine might compose
elaborate and scientific pieces of music of any degree of
complexity or extent" [2, p. 694]. Arguably, musical
composition could not be possible if some form of repetition were not supported by the Analytical Engine.
In essence, Ada Lovelace successfully argued that,
the Analytical Engine is a Turing Machine. The paradox
lies in the fact that Alan Turing wasn't born until Jun 23,
1912, and Robin Gandy on Sept 22, 1919, 59 and 66
years, respectively, after Ada Lovelace died (Nov. 27,
1852). Turing is often considered to be the father of the
field of Computer Science. If this is true, Ada Lovelace is
most certainly its mother.

Women in Science, Technology,
Engineering and Math Today
There is rich irony in the concept that Ada Lovelace contributed to one of the greatest achievements by humankind because she was less constrained by the
conventions of the time due to circumstance and accident
of birth, and that she was forced to pursue her education
and interests independently of the educational structures
of the time because of exclusion and prejudice. We propose that possibly an unintended consequence of the
exclusion, prejudice, and stereotyping was that an intellectually curious girl became "a smart, sophisticated person, with a clear, logical mind." Wolfram [5] suggests

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