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“The Analytical Engine might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine… Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.”

“The epithet beautiful is used by surgeons to describe operations which their patients describe as ghastly, by physicists to describe methods of measurement which leave sentimentalists cold, by lawyers to describe cases which ruin all the parties to them, and by lovers to describe the objects of their infatuation, however unattractive they may appear to the unaffected spectators.”

“Man is distinguished from the brute animals in proportion as thought prevails over sense: but in the healthy processes of the mind, a balance is constantly maintained between the impressions from outward objects and the inward operations of the intellect:--for if there be an overbalance in the contemplative faculty, man thereby becomes the creature of mere meditation, and loses his natural power of action.”

“The secondary Imagination I consider as an echo of the former, co-existing with the conscious will, yet still as identical with the primary in the kind of its agency, and differing only in degree, and in the mode of its operation. It dissolves, diffuses, dissipates, in order to recreate: or where this process is rendered impossible, yet still at all events it struggles to idealize and to unify. It is essentially vital, even as all objects (as objects) are essentially fixed and dead.”

“So far as the object of taxation is to raise a revenue for discharging the debts and defraying the expenses of the community, its operation should be adapted as much as possible to suit the burden with equal hand upon all in proportion with their ability of bearing it without oppression.”

“Responsibility, in order to be reasonable, must be limited to objects within the power of the responsible party, and in order to be effectual, must relate to operations of that power, of which a ready and proper judgment can be formed by the constituents.”

“To hold that Congress has general police power would be to hold that it may accomplish objects not intrusted to the general government, and to defeat the operation of the 10th Amendment, declaring that 'the powers not delegated to the United States by the Constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people.”

“Since we are dead in sin, a spiritual light and flame in the heart suitable to the nature of the object of our worship, cannot be raised in us without the operation of supernatural grace... such a worship God must have, whereby he is acknowledged to be the true sanctifier and quickener of the soul.”

“. . . the membership relation for sets can often be replaced by the composition operation for functions. This leads to an alternative foundation for Mathematics upon categories -- specifically, on the category of all functions. Now much of Mathematics is dynamic, in that it deals with morphisms of an object into another object of the same kind. Such morphisms (like functions) form categories, and so the approach via categories fits well with the objective of organizing and understanding Mathematics. That, in truth, should be the goal of a proper philosophy of Mathematics.”

“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.”