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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.

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
Term
Wherever
Magnitude
Become
Powers
Shifting
Also
Complicated
Frequently
Indices
Together
Independent
Reasoning
Falsified
Figures
Sets
Numerical
Terms
Consideration
Secondly
Meaning
Operations
Considerations
Results
Symbols
Liable

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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.
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In considering any new subject, there is frequently a tendency, first, to overrate what we find to be already interesting or remarkable and, secondly, by a sort of natural reaction, to undervalue the true state of the case, when we do discover that our notions have surpassed those that were really tenable
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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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The more I study, the more insatiable do I feel my genius for it to be.
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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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In enabling mechanism to combine together general symbols in successions of unlimited variety and extent, a uniting link is established between the operations of matter and the abstract mental processes of the most abstract branch of mathematical science.
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The intellectual, the moral, the religious seem to me all naturally bound up and interlinked together in one great and harmonious whole.
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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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It must be evident how multifarious and how mutually complicated are the considerations which the working of such an engine involve. There are frequently several distinct sets of effects going on simultaneously all in a manner independent of each other, and yet to a greater or less degree exercising a mutual influence.
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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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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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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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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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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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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.
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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.
Ada Lovelace
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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. It can follow analysis but it has no power of anticipating any analytical relations or truths. Its province is to assist us to making available what we are already acquainted with.
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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.
Ada Lovelace
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That brain of mine is something more than merely mortal as time will show.
Ada Lovelace
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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.
Ada Lovelace