Pray-Mister-Babbage problems

A famous exchange recorded in Charles Babbage’s Passages from the Life of a Philosopher (1864):

On two occasions I have been asked,— “Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?” … I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.

Often when explaining technical material I encounter questioners who raise what I have come to think of as “Pray-Mister-Babbage problems.”

However, it should be noted that many modern technologies — error-correcting codes, static analysis, spell-check, UX design — are essentially attempts to deal with specific Pray-Mister-Babbage problems in a legitimate and non-dismissive way!

In fact, Babbage’s own book continues:

I did, however, explain the following property, which might in some measure approach towards an answer to it.

It is possible to construct the Analytical Engine in such a manner that after the question is once communicated to the engine, it may be stopped at any turn of the handle and set on again as often as may be desired. At each stoppage every figure-wheel throughout the Engine, which is capable of being moved without breaking, may be moved on to any other digit. Yet after each of these apparent falsifications the engine will be found to make the next calculation with perfect truth.

(This is an early allusion to a kind of error-correcting code. Did you catch also Babbage’s early form of undefined behavior? The user may adjust any figure-wheel “which is capable of being moved without breaking.” If you force any other wheel, you’ll find yourself with a broken Analytical Engine. I hope the distinction between moveable and non-moveable figure-wheels was apparent to the novice!)

And Babbage concludes his chapter by resuming the curmudgeonly position:

The explanation is very simple, and the property itself useless. The whole of the mechanism ought of course to be enclosed in glass, and kept under lock and key, in which case the mechanism necessary to give it the property alluded to would be useless.

(This is an example of “seeing the rabbit-hole and refusing to go down it,” an action I take with disappointing infrequency.)

Posted 2018-09-26