32. Self-Counting
The afternoon light slanted through the tall windows of the mathematics wing. The lecture had ended, yet Professor Reichenstein lingered, his eyes fixed on the blackboard as though daring it to betray him.
„You admire cleverness too easily,“ he said at last. „You praise methods without asking what they accumulate.“
His gaze settled on Mihkel.
„You rely on rules,“ Reichenstein continued. „Procedures stacked upon procedures. Tell me—do you know how many?“
Mihkel hesitated.
„Rules, Professor?“
„Transitions. Steps. Whatever carries your reasoning forward,“ the professor replied. „Thoughts may wander. Systems may not.“
A few students laughed. Reichenstein did not.
„When a method grows too large to be counted,“ he said quietly, „it has already escaped its author.“
Mihkel left without speaking.
That night, in the workshop, he opened his notebook. Page after page of transition rules stared back at him— each precise, each once justified. Together, they formed something dense and unyielding.
How many are there?
For the first time, he did not give the Logic Mill a problem from the world. He gave it itself.
The tape bore his own instructions, flattened into symbols and separators, rules stripped of authority and awaiting judgment.
The Mill turned slowly, traversing not numbers or words, but the very steps by which it knew how to act.
Mihkel watched, uneasy. A system that could measure itself could also outgrow its maker.
On the input tape you’ll get your submitted transition rules (spaces are stripped and new lines are replaced with @).
Your task is to output the number of transition rules in unary representation.
So basically your solution has to process itself.
For example, if your solution has 4 transition rules the output tape should be ||||.
If it’s still not clear, try to submit some simple transition rule (e.g., INIT _ HALT | R) and see the result.