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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.

Ada Lovelace

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Ada Lovelace
Age: 36 †
Born: 1815
Born: December 10
Died: 1852
Died: November 27
Computer Scientist
Countess Of Lovelace
Engineer
Inventor
Mathematician
Poet
Programmer
Translator
Writer
London
England
Augusta Ada Byron
Lady Ada
Augusta Ada King
Countess of Lovelace
Ada Byron
Augusta Ada King
Ada King
Augusta Ada King-Noel
Countess of Lovelace
Upon
Mathematical
Engine
Action
Belong
Separated
Nature
Analysis
Distinguished
Find
Defined
Studying
Strikingly
Independent
Engines
Operated
Objects
Peculiar
Analytical
Results
Consideration
Considerations
Study
Operations
Performed

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Thus not only the mental and the material, but the theoretical and the practical in the mathematical world, are brought into more intimate and effective connection with each other.
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That brain of mine is something more than merely mortal as time will show.
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It is however pretty evident, on general principles, that in devising for mathematical truths a new form in which to record and throw themselves out for actual use, views are likely to be induced, which should again react on the more theoretical phase of the subject.
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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.
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I never am really satisfied that I understand anything because, understand it well as I may, my comprehension can only be an infinitesimal fraction of all I want to understand about the many connections and relations which occur to me, how the matter in question was first thought of or arrived at, etc., etc.
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One essential object is to choose that arrangement which shall tend to reduce to a minimum the time necessary for completing the calculation.
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The object of the engine is in fact to give the utmost practical efficiency to the resources of numerical interpretations of the higher science of analysis, while it uses the processes and combinations of this latter.
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The Analytical Engine, on the contrary, can either add, subtract, multiply or divide with equal facility and performs each of these four operations in a direct manner, without the aid of any of the other three.
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But the science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value just as logic has its own peculiar truth and value, independently of the subjects to which we may apply its reasonings and processes.
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The more I study, the more insatiable do I feel my genius for it to be.
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Secondly, figures, the symbols of numerical magnitude, are frequently also the symbols of operations, as when they are the indices of powers. Wherever terms have a shifting meaning, independent sets of considerations are liable to become complicated together, and reasoning and results are frequently falsified.
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Understand well as I may, my comprehension can only be an infinitesimal fraction of all I want to understand.
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A new, a vast, and a powerful language is developed for the future use of analysis, in which to wield its truths so that these may become of more speedy and accurate practical application for the purposes of mankind than the means hitherto in our possession have rendered possible.
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We cannot forbear suggesting one practical result which it appears to us must be greatly facilitated by the independent manner in which the engine orders and combines its operations: we allude to the attainment of those combinations into which imaginary quantities enter.
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This one fact implies everything and it is scarcely necessary to point out, for instance, that while the Difference Engine can merely tabulate, and is incapable of developing, the Analytical Engine can either tabulate or develope.
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It may be desirable to explain, that by the word operation, we mean any process which alters the mutual relation of two or more things, be this relation of what kind it may. This is the most general definition, and would include all subjects in the universe.
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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.
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If you can't give me poetry, can't you give me poetical science?
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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.
Ada Lovelace
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The Analytical Engine is an embodying of the science of operations, constructed with peculiar reference to abstract number as the subject of those operations.
Ada Lovelace