Information Technology Reference
In-Depth Information
Going from here
Given a procedure that can do addition, it is not too hard to imagine doing subtraction
the same way. Given those two, one can define procedures that do multiplication and
division. Building on these, one can have a procedure to tell whether a number is
prime. One can use pairs of numbers to represent fractions (rational numbers) and
do arithmetic on them. One can arrange rational numbers into matrices and have
procedures that operate on them to solve systems of equations. One can use systems
of equations to model complex physical systems and have procedures that perform
numerical simulations of these systems.
And on it goes.
So starting with simple symbolic operations (such as table lookup, putting together
and taking apart sequences of symbols, comparing them, and so on), one can assem-
ble the operations into ever larger procedures and develop an extremely wide range
of behaviors as computational processes. This is what computer science is about.
1.2.4 The lesson
The key observation on these arithmetic procedures is this:
To produce meaningful answers, you do not have to understand what the symbols
stand for or why the manipulations are correct.
Although one can certainly understand the procedures as doing arithmetic, one does
not need this understanding to actually carry out the procedures.
Here is a simple thought experiment to support this claim. Imagine replacing the
symbols
0
through
9
everywhere by new symbols that do not look at all like digits, for
example, a heart shape for
0
, a star for
1
, an anchor shape for
2
, and so on. Now give
the procedures PROC0-PROC3, including the table for PROC0 with the new symbols,
to a friend without saying what these new symbols mean or what the procedures are
supposed to be doing. By following PROC2, the friend should still be able to do
addition: take as input two sequences of new symbols representing numbers, and
return as output the sequence of new symbols that represents their sum.
So symbols can be processed purely mechanically and still end up producing the
right results. This might be called the trick of computation:
Computers can perform a wide variety of impressive activities precisely because
those activities can be described as a type of symbol processing that can be carried
out purely mechanically.
