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

2.6 Multiple Levels of Investigation and Explanation
Imagine bringing several different calculating devices into a class, with the goal of
explaining how they work. How would you explain those devices? The topics that
have been covered in the preceding pages indicate that several different approaches
could—and likely should—be taken.
One approach would be to explain what was going on at a physical or implementational
level. For instance, if one of the devices was an old electronic calculator,
then you would feel comfortable in taking it apart to expose its internal workings.
You would likely see an internal integrated circuit. You might explain how such
circuits work by talking about the properties of semiconductors and how different
layers of a silicon semiconductor can be doped with elements like arsenic or boron
to manipulate conductivity (Reid, 2001) in order to create components like transistors
and resistors.
Interestingly, the physical account of one calculator will not necessarily apply to
another. Charles Babbage’s difference engine was an automatic calculator, but was
built from a set of geared columns (Swade, 1993). Slide rules were the dominant
method of calculation prior to the 1970s (Stoll, 2006) and involved aligning rulers
that represented different number scales. The abacus is a set of moveable beads
mounted on vertical bars and can be used by experts to perform arithmetic calculations
extremely quickly (Kojima, 1954). The physical accounts of each of these
three calculating devices would be quite different from the physical account of any
electronic calculator.
A second approach to explaining a calculating device would be to describe its
basic architecture, which might be similar for two different calculators that have
obvious physical differences. For example, consider two different machines manufactured
by Victor. One, the modern 908 pocket calculator, is a solar-powered
device that is approximately 3" × 4" × ½" in size and uses a liquid crystal display. The
other is the 1800 desk machine, which was introduced in 1971 with the much larger
dimensions of 9" × 11" × 4½". One reason for the 1800’s larger size is the nature of
its power supply and display: it plugged into a wall socket, and it had to be large
enough to enclose two very large (inches-high!) capacitors and a transformer. It also
used a gas discharge display panel instead of liquid crystals. In spite of such striking
physical differences between the 1800 and the 908, the “brains” of each calculator
are integrated circuits that apply arithmetic operations to numbers represented
in binary format. As a result, it would not be surprising to find many similarities
between the architectures of these two devices.
Of course, there can be radical differences between the architectures of different
calculators. The difference engine did not use binary numbers, instead representing
values in base 10 (Swade, 1993). Claude Shannon’s THROBACK computer’s
38 Chapter 2