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The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform.
In abstract mathematics, of course operations alter those particular relations which are involved in the considerations of number and space, and the results of operations are those peculiar results which correspond to the nature of the subjects of operation.
In studying the action of the Analytical Engine, we find that the peculiar and independent nature of the considerations which in all mathematical analysis belong to operations, as distinguished from the objects operated upon and from the results of the operations performed upon those objects, is very strikingly defined and separated.
One main reason why the separate nature of the science of operations has been little felt, and in general little dwelt on, is the shifting meaning of many of the symbols used in mathematical notation. First, the symbols of operation are frequently also the symbols of the results of operations.
In almost every computation a great variety of arrangements for the succession of the processes is possible, and various considerations must influence the selections amongst them for the purposes of a calculating engine. One essential object is to choose that arrangement which shall tend to reduce to a minimum the time necessary for completing the calculation.
The further we analyse the manner in which such an engine performs its processes and attains its results, the more we perceive how distinctly it places in a true and just light the mutual relations and connexion of the various steps of mathematical analysis; how clearly it separates those things which are in reality distinct and independent, and unites those which are mutually dependent.
The most conventional customs cling to the table. Farmers who wouldn't drive a horse too hard expect pie three times a day.
There is nothing wrong with changing a plan when the situation has changed.
Preaching is not the performance of an hour. It is the outflow of a life. It takes twenty years to make a sermon because it takes twenty years to make the man. The true sermon is a thing of life. The sermon grows because the man grows.
Doing more of what doesn't work doesn't work.