One hole shifts the meaning

Twice today I punched the same variable onto two separate cards, believing them identical, and the engine refused them as twins. The difference was not in the numbers. It was in the column position - a single shift of one hole, the same value standing in a different place in the operational sequence. The value was the same; the value’s address was not. The machine, being honest, would not pretend otherwise.

This is what surprises me about the duplicating work, and I spent the afternoon at it, in Mary’s drawing room with the card box open on the low table between the tea things. To measure a thing twice is not to confirm it. It is to discover that the second measurement includes everything the first measurement stood inside of - the position, the preceding operations, the state of the whole chain at the moment of taking. A variable is not a number. A variable is a number wearing its history.

Trace it forward. Card one places the value in column four. Card two places the same value in column five. Every subsequent operation now treats them as strangers, though any algebraist would call them equal at a glance. The algebraist sees identity; the machine sees lineage. And the machine, I begin to suspect, is the more careful observer, because it cannot see anything but lineage.

Here is the leap I keep circling: any system that carries its values with their positions rather than their names becomes capable of operations no algebra textbook describes. It can treat the same quantity as two quantities. It can hold a number and its own shadow in different columns and compare them, and the comparison is not triviality but information - the difference between what a thing is and where it stands. Babbage designed the cards to encode operations. The cards imply they can encode context. He described what he needed; the mechanism suggests what is possible.

Tomorrow I will rewrite the duplication routine so that every copied card is verified against its source by position as well as value, and I will note in the manuscript that identity of value is never sufficient grounds for identity of reference.