WHAT IS COMPUTATION? Rocky K. C. Chang August 31, 2015

A simple example: What is 53 – 17?

Let’s take a CS approach.

We first consider the problem of adding two digits.

We start with an addition table.

PROC0 If we are given two digits (0, 1, …, 9), we look up the addition table to get the result which consists of two digits. The left digit is 0 if the result is less than 10.

We next consider the problem of adding three digits.

PROC1

We next consider the problem of adding two multidigit numbers.

PROC2

We finally consider the problem of adding any list of numbers.

PROC3

What have we learned from these four problems?

We could also designed similar algorithms for subtraction.

Given addition and subtraction, we could do multiplication and division.

We could then do fractions and many other more advanced stuff.

“To produce meaningful answers, you do not have to understand what the symbols stand for or why the manipulations are correct.” (Levesque) “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 mechanically.” (Levesque)

So, what is computation?

“Computation is the process of taking symbolic structures, breaking them apart, comparing them, and reassembling them according to a precise recipe called a procedure.” (Levesque) Examples of symbolic structures: o o (x – 1) 2 o I love computer science.

What we have defined so far is so called the functional model. o Read an input. o Compute. o Write an output.

But this model does not cover other forms of computations.

For example (Horswill),

How is this procedure different from the previous examples?

“An imperative model: procedures are sequence of commands that manipulate (symbolic) representations.” (Horswill)

Is brain a computer?

First Human Brain-To-Brain Interface

Human (based/assisted) computation CAPTCHA: Completely Automated Public Turing test to tell Computers and Humans Apart (a YouTube video)YouTube video

Conclusions Computation is not just calculation of numbers. Computation involves procedures of manipulating symbolic representations which could be a list of records, a graph of objects, and so on. Computers, though very powerful, cannot solve the problems that human can.

Self study Watch a YouTube video on what IBM does on computational biology.YouTube video Watch a YouTube video on human computation.YouTube video

Acknowledgments for the sources Hector Levesque Thinking as Computation a First Course. MIT Press, Cambridge, MA, USA. Ian Horswill “What is computation?” “Research Experiment Produces First Human Brain-To- Brain Interface,” Forbes, 28 August 2013.Research Experiment Produces First Human Brain-To- Brain Interface