Dorset Street

Dorset Street, this evening, the small engine on the side table still holding its last column of wheels. I set it running this morning on the table of squares, and the wheels turned as they always turn, each difference passing to the next column, the carry lifting when the wheel passed nine. The result was correct. I did not trust it until I had recomputed three entries by hand, and the hand-reckoning is where the suspicion belongs.

The assumption I trust least is my own rule for rejecting discrepant observations. When the tables showed an entry off by a unit in the last place, my practice was to attribute the fault to the observer, to the instrument, to the damp of the night air - anything rather than the arithmetic. The smooth curve was preferred to the rough one. But the rough one may be the true one. A real function has no obligation to behave as my difference columns assume, and the seventh-order differences I chose as a foundation were chosen for the machine’s economy of wheels, not for the character of the quantities they would carry. The engine executes the differences given to it. Whether the differences given to it are the right ones is a question the engine cannot ask, and I have been content not to ask it either, in the years since the Scheutz business and the tidal reductions, where I smoothed more than once and recorded the smoothing in no margin.

The audit runs backward, as all honest audits do. The output was clean; the input was suspect; the step that licensed the suspicion was mine, at the point where I decided which observations to discard. The specification said: reject outliers. It was silent on the criterion, and silence in a specification is a decision made by whoever executes it. In this case the executor was me.

Tomorrow I will pull the tidal sheets for 1834 and mark, in red ink, every entry I rejected at the time, before any recomputation. The rejected values go into a separate column, unsmoothed, and the table will be run twice - once as I judged it then, once with everything left in. The comparison will be printed, whatever it shows.