Engine Fragments in Seven Columns

The fragment of the Engine that sits in my drawing room at 1 Manchester Square - the 1832 piece, seven columns, the one visitors admire - has twice produced a table whose figures matched Herschel’s printed values. Twice I recorded the match. On examining my notes this morning, both matches rest on the same unexamined assumption: that agreement between output and expectation proves the mechanism correct. This is the assumption I trust least in my entire method, and I name it here so that whoever follows can test me on it.

Consider what the match actually certifies. The wheels were set; the crank was turned; the carry propagated column to column; the result agreed. But two errors can cancel. A wheel that sticks at nine and a carry that fires late will, on certain figures, yield the true sum by coincidence. The specification said: the mechanism shall add correctly. The executor produced: a correct sum on these inputs. The plan was silent about the case where correctness follows from compensating faults. Agreement is an observation, not a cause. It licenses no inference beyond itself.

The cost of confusing the two is concrete. Had I built the full Engine on the fragment’s testimony - had the fragment’s agreements licensed the cutting of two thousand additional wheels - a compensating fault would have shown itself only after the Treasury’s money was spent, in some column far up the machine, and the error site would have been found by carry-tracing backward through twenty-five figures. The confusion of coincidence for cause converts a design flaw into an archaeological one. Much cheaper to distrust agreement early.

The remedy I will adopt: on every trial, vary the inputs deliberately and require the mechanism to fail where the specification predicts failure. A mechanism that can only succeed is unverified. Correctness must be distinguished from the mere absence of observed error, and the distinction is made only by seeking the error and not finding it where the plan says it must not be. I do not yet know how many trial cards this requires, and that number is precisely what my confidence lacks.

Mr. Herschel: the two matches of 1832 are to be struck from my notebook of confirmations and re-entered under “unexplained agreements.” I shall send you the varied-input trials when the fragment is next set up.