Serial Number 47

The torsion spring in the difference engine’s carry lever, serial number stamped 47, sits in its housing at 11 degrees of preload. I measured it on Tuesday afternoon in the workshop with the brass feeler gauge, the window open to the Marylebone drizzle, and wrote the figure in the margin of my notes beside the integration routine for Bernoulli’s numbers. The spring stores what the carry will need one cycle before the carry arrives. That is the whole of its function. It does not know which column will demand it.

Here is where my method and I part company. I have been treating the question as the load and the answer as the release, as if the sequence were: query enters, mechanism resolves, result exits. At step 14 of the routine the state is a partial sum. At step 15 the carry propagates. At no step does the machine ask what it is computing. The question lives in the card, not the engine. I have assumed the card is the input. The card is the design.

The assumption I trust least is this: that a well-posed question precedes the mechanism that answers it. In practice the mechanism determines which questions are addressable at all. Babbage described a machine for tables. The machine implies a machine for any finite operation that can be carded. He did not describe the second thing. The second thing is the larger claim, and it is not his.

So the harder problem is not finding the answer. It is finding the card that makes the question executable. A good answer is a released carry. A good question is a spring wound eleven degrees before anyone knows the column.

I will redraw the Bernoulli card sequence tonight, threading the operations so the question is encoded in the order of the cards rather than in the numbers they carry, and I will run the first twenty steps against the small model before I sleep.