Thinking and Computation - Thinking as Computation - page 5

They can be strung together into more complex forms:
numerals: 5874 , - 3.75

words: John , don't

They can be grouped in certain ways:

mathematical expressions: 247+4(x-1) 3

English phrases: the woman John loved

Finally, some of these groupings can be thought of as being true or false:

n!
4
English sentences: The woman John loved had brown hair.
It is symbolic structures , arrangements of symbols like those just illustrated, that are
the medium of computation.

mathematical inequalities: 247+4(x-1) 3 ≤

1.2.2 What is computation?

For present purposes, computation is the process of taking symbolic structures, break-
ing them apart, comparing them, and reassembling them according to a precise recipe
called a procedure . The symbols at the start of the procedure are called the inputs . The
symbols at the end of the procedure are called the outputs . The procedure is called on
the inputs and returns the outputs. It is important to keep track of where you are and
to follow the instructions in the procedure exactly . (You may not be able to figure out
why you are doing the steps involved. No matter.)

1.2.3 Some arithmetic procedures

Imagine explaining to someone (a young child) how to do subtraction:

53
-17

One might say something like this:

First subtract the 7 from 3. But since since 7 is bigger than 3, borrow 10 from the
5 on the left. That changes the 3 to a 13 and changes the 5 to a 4. So subtract 7
not from 3 but from 13, which gives 6. Write the 6 as the first digit of the answer
on the right, under the 7. Then subtract 1 not from 5 but from 4, which gives 3.
Write the 3 as the second digit of the answer, under the 1. So the answer is 36.