Thinking and Computation - Thinking as Computation - page 4

not have felt the change that happened in your thinking when the word was changed
from small to big .)
Thinking is clearly a biological process, since we are biological creatures. Does this
mean that thinking is like digestion? Or like mitosis in cells? Or is it different still?
The central conjecture of this topic is this:
Thinking can be usefully understood as a computational process.
Thinking has perhaps more in common with multiplication or sorting a list of
numbers than with digestion or mitosis.
This conjecture is controversial . Not all philosophers, psychologists, evolutionary
biologists, and neuroscientists are lined up to support it. Some do, some don't, and
some struggle with the concept of thinking in the first place.
Nonetheless this is the conjecture that this topic pursues.

1.2 Computation

Computer science as a field of study has two branches: hardware and software.
Hardware is the concern of engineers who study and build the physical machines
(computers) themselves. Software is the written instructions—programs—specifying
what those machines should do. And what the machines do is computation , a certain
manipulation of symbols. Birds “produce” flight, musicians “produce” music, and
computers “produce” computation according to a program.
This topic focuses on computation itself as the primary subject of computer sci-
ence. What (or who) is performing the symbol manipulation is a secondary concern.
Modern electronic computers happen to provide a fast, cheap, and reliable way to do
this computation, but other devices can do it as well. (The Dutch computer scientist
Edsger Dijkstra once said that computer science is no more about the computers than
astronomy is about telescopes.)

1.2.1 Symbols and symbolic structures

In their simplest form, symbols are just characters from some alphabet, like the

following:
digits: 3 , 7 , V (the last one is a Roman numeral)

letters: x , R , (the last one is a Greek letter)

β

operators: + , ≤ , ∩