Philosophy Through Video Games by Jon Cogburn & Mark Silcox

Author:Jon Cogburn & Mark Silcox [Cogburn, Jon & Silcox, Mark]
Language: eng
Format: epub
Tags: Philosophy
Published: 2011-01-20T06:00:00+00:00

The Metaphysics of Interactive Art 103

4- Since the counter reads 1, move L

(0 0 1 1 1 0 0 0 0), and go to state 4.

4- Since the counter reads 0, move R

(0 0 1 1 1 0 0 0 0).

With the example of these machines in mind, we can define a Turing-computable function as all those functions that can be computed by a Turing machine. A function can be computed by a Turing machine if there exists a Turing machine program such that any tape starting in canonical starting position (with the function’s inputs separated by one space and the counter on the beginning of the leftmost input) will, after running the program, halt with that function’s output on the tape and with the counter at the leftmost edge of that output. Program 1 computes the zero place function “is equal to three.”

To better see how this works, consider the simple Turing machine for the two-placed addition function. Just to make this as simple as possible, we will only consider adding positive natural numbers (and so not have to worry about adding zero) (see Program 2).

If in state

and the counter reads

then write/move

and then go to state

1

0

1

2

1

1

R

1

2

0

L

3

2

1

R

2

3

0

L

4

3

1

0

3

4

0

R

4

1

L

4

Program 2: standard Turing machine that adds two positive natural numbers.

To see this in action, consider the tape in the canonical starting position with the inputs being the numerals two and three, and then run the program.

(0 0 1 1 0 1 1 1 0) Go to state 1.

1- Since the counter reads 1, move R

(0 0 1 1 0 1 1 1 0), and go to state 1.

1- Since the counter reads 1, move R

(0 0 1 1 0 1 1 1 0), and go to state 1.

2- Since the counter reads 0, write 1

(0 0 1 1 1 1 1 1 0), and go to state 2.

2- Since the counter reads 1, move R

(0 0 1 1 1 1 1 1 0), and go to state 2.

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