Mind, Body, World- Foundations of Cognitive Science, 2013a

input, output, and manipulation processes were all designed for quantities represented
as Roman numerals (Pierce, 1993). Given that they were designed to work
with different number systems, it would be surprising to find many architectural
similarities between the architectures of THROBACK, the difference engine, and
the Victor electronic machines.
A third approach to explaining various calculators would be to describe the
procedures or algorithms that these devices use to accomplish their computations.
For instance, what internal procedures are used by the various machines to manipulate
numerical quantities? Algorithmic accounts could also describe more external
elements, such as the activities that a user must engage in to instruct a machine to
perform an operation of interest. Different electronic calculators may require different
sequences of key presses to compute the same equation.
For example, my own experience with pocket calculators involves typing in an
arithmetic expression by entering symbols in the same order in which they would be
written down in a mathematical expression. For instance, to subtract 2 from 4, I would
enter “4 – 2 =” and expect to see 2 on display as the result. However, when I tested to
see if the Victor 1800 that I found in my lab still worked, I couldn’t type that equation
in and get a proper response. This is because this 1971 machine was designed to be
easily used by people who were more familiar with mechanical adding machines. To
subtract 2 from 4, the following expression had to be entered: “4 + 2 –”. Apparently the
“=” button is only used for multiplication and division on this machine!
More dramatic procedural differences become evident when comparing devices
based on radically different architectures. A machine such as the Victor 1800 adds
two numbers together by using its logic gates to combine two memory registers that
represent digits in binary format. In contrast, Babbage’s difference engine represents
numbers in decimal format, where each digit in a number is represented by a
geared column. Calculations are carried out by setting up columns to represent the
desired numbers, and then by turning a crank that rotates gears. The turning of the
crank activates a set of levers and racks that raise and lower and rotate the numerical
columns. Even the algorithm for processing columns proceeds in a counterintuitive
fashion. During addition, the difference engine first adds the odd-numbered
columns to the even-numbered columns, and then adds the even-numbered columns
to the odd-numbered ones (Swade, 1993).
A fourth approach to explaining the different calculators would be to describe
them in terms of the relation between their inputs and outputs. Consider two of
our example calculating devices, the Victor 1800 and Babbage’s difference engine.
We have already noted that they differ physically, architecturally, and procedurally.
Given these differences, what would classify both of these machines as calculating
devices? The answer is that they are both calculators in the sense that they generate
the same input-output pairings. Indeed, all of the different devices that have been
Multiple Levels of Investigation 39