The demonstration function was 2 + 1 = 3
I lined up nine students in front of the class to be the 'tape' and one student in front to be the 'machine head'.
Each student on the 'tape' represented either a 1 or a 0 and stood in the following pattern
- '1s' stood facing the class and each represented the number '1'
- '0s' stood with their backs to the class and represented the space between numbers.
The Machine Head
The 'machine head' student started in state A. State A was visually represented by the 'superman pose' (hands on hips, looking triumphant).
When the machine head switched to state B, she put her hands by her sides.
In order to 'write' on the tape, she used her hands to mechanically turn the pertinent 'tape' student around 180 degrees so that he or she now represented a 0 or 1 respectively.
After a few minutes demonstrating the machine head's repertoire of possible actions, I positioned the machine head to the far right and gave the class the following rules to solve 2 + 1 = 3
1. If the machine is in state A, and reads a 0, then it stays in state A, writes a 0, and moves one square to the right.
2. If the machine is in state A, and reads a 1, then it changes to state B, writes a 1, and moves one square to the right.
3. If the machine is in state B, and reads a 0, then it changes to state A, writes a 1 and stops.
4. If the machine is in state B, and reads a 1, then it stays in state B, writes a 1, and moves one square to the right.
Students calculated 2 + 1 = 3 using instructions 1 through 4. Each output on the 'tape' is represented by steps (i) through (vii) represented in the diagram above. The final output was:
Which meant three students faced the class and the machine head stood in superman pose at a halt.
Students seemed to have fun and I hope they got a better understanding of Turing Machines by acting them out physically than simply reading about them in a book.
* Instructions and output from Crane, T. (2003) Computers and Thought. The Mechanical Mind, Ch.3, 94-95.