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.

**Ada Lovelace**

i-never-am-really-satisfied-that-i-understand-anything-because-understand-it-well-as-i-may-my-comprehension-can-only-be-infinitesimal-fraction-all-i-ada-lovelace

With whomsoever or wheresoever may rest the present causes of difficulty that apparently exist towards either the completion of the old engine, or the commencement of the new one, we trust they will not ultimately result in this generation's being acquainted with these inventions through the medium of pen, ink and paper merely; and still more do we hope, that for the honour of our country's reputation in the future pages of history, these causes will not lead to the completion of the undertaking by some other nation or government.

**Ada Lovelace**

with-whomsoever-wheresoever-may-rest-present-causes-difficulty-that-apparently-exist-towards-either-completion-old-engine-commencement-new-ada-lovelace

whomsoever quoteswheresoever quotesrest quotespresent quotesdifficulty quotesapparently quotesexist quotescompletion quotesengine quotescommencement quotestrust quotesultimately quotesresult quotesgenerations quotesacquainted quotesinventions quotesmedium quotespen quotesink quotespaper quoteshope quoteshonour quotescountrys quotesreputation quotesfuture quotespages quoteshistory quoteslead quotesundertaking quotesnation quotesgovernment quotes

it-may-be-desirable-to-explain-that-by-word-operation-we-mean-any-process-which-alters-mutual-relation-two-more-things-be-this-relation-what-kind-ada-lovelace

understand-well-as-i-may-my-comprehension-can-only-be-infinitesimal-fraction-all-i-want-to-understand-ada-lovelace

but-science-operations-as-derived-from-mathematics-more-especially-is-science-itself-has-its-own-abstract-truth-value-just-as-logic-has-its-own-ada-lovelace

Indeed we may consider the engine as the material and mechanical representative of analysis, and that our actual working powers in this department of human study will be enabled more effectually than heretofore to keep pace with our theoretical knowledge of its principles and laws, through the complete control which the engine gives us over the executive manipulation of algebraical and numerical symbols.

**Ada Lovelace**

indeed-we-may-consider-engine-as-material-mechanical-representative-analysis-that-our-actual-working-powers-in-this-department-human-study-will-ada-lovelace

engine quotesmaterial quotesmechanical quotesrepresentative quotesanalysis quotesactual quotesworking quotespowers quotesdepartment quoteshuman quotesstudy quotesenabled quoteseffectually quotesheretofore quotespace quotestheoretical quotesknowledge quotesprinciples quoteslaws quotescomplete quotescontrol quotesexecutive quotesmanipulation quotesalgebraical quotesnumerical quotessymbols quotes

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

**Ada Lovelace**

in-considering-any-new-subject-there-is-frequently-tendency-first-to-overrate-what-we-find-to-be-already-interesting-remarkable-secondly-by-sort-ada-lovelace

that-brain-mine-is-something-more-than-merely-mortal-as-time-will-show-ada-lovelace

It were much to be desired, that when mathematical processes pass through the human brain instead of through the medium of inanimate mechanism, it were equally a necessity of things that the reasonings connected with operations should hold the same just place as a clear and well-defined branch of the subject of analysis, a fundamental but yet independent ingredient in the science, which they must do in studying the engine.

**Ada Lovelace**

it-were-much-to-be-desired-that-when-mathematical-processes-pass-through-human-brain-instead-through-medium-inanimate-mechanism-it-were-equally-ada-lovelace

desired quotesmathematical quotesprocesses quotespass quoteshuman quotesbrain quotesmedium quotesinanimate quotesmechanism quotesequally quotesnecessity quotesthings quotesreasonings quotesconnected quotesoperations quoteshold quotesplace quotesclear quoteswelldefined quotesbranch quotessubject quotesanalysis quotesfundamental quotesindependent quotesingredient quotesscience quotesstudying quotesengine quotes

Many persons who are not conversant with mathematical studies imagine that because the business of [Babbage's Analytical Engine] is to give its results in numerical notation, the nature of its processes must consequently be arithmetical and numerical, rather than algebraical and analytical. This is an error. The engine can arrange and combine its numerical quantities exactly as if they were letters or any other general symbols; and in fact it might bring out its results in algebraical notation, were provisions made accordingly.

**Ada Lovelace**

many-persons-who-are-not-conversant-with-mathematical-studies-imagine-that-because-business-babbages-analytical-engine-is-to-give-its-results-in-ada-lovelace

persons quotesconversant quotesmathematical quotesstudies quotesimagine quotesbusiness quotesbabbages quotesanalytical quotesengine quotesgive quotesresults quotesnumerical quotesnotation quotesnature quotesprocesses quotesarithmetical quotesnumerical quotesalgebraical quotesanalytical quoteserror quotesengine quotesarrange quotescombine quotesquantities quotesletters quotesgeneral quotessymbols quotesfact quotesbring quotesprovisions quotesmade quotes

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.

**Ada Lovelace**

in-almost-every-computation-great-variety-arrangements-for-succession-processes-is-possible-various-considerations-must-influence-selections-ada-lovelace

computation quotesgreat quotesvariety quotesarrangements quotessuccession quotesprocesses quotesconsiderations quotesinfluence quotesselections quotespurposes quotescalculating quotesengine quotesessential quotesobject quoteschoose quotesarrangement quotestend quotesreduce quotesminimum quotestime quotescompleting quotescalculation quotes

in-enabling-mechanism-to-combine-together-general-symbols-in-successions-unlimited-variety-extent-uniting-link-is-established-between-operations-ada-lovelace

the-object-engine-is-in-fact-to-give-utmost-practical-efficiency-to-resources-numerical-interpretations-higher-science-analysis-while-it-uses-ada-lovelace

The Difference Engine can in reality (as has been already partly explained) do nothing but add; and any other processes, not excepting those of simple subtraction, multiplication and division, can be performed by it only just to that extent in which it is possible, by judicious mathematical arrangement and artifices, to reduce them to a series of additions.

**Ada Lovelace**

the-difference-engine-can-in-reality-as-has-been-already-partly-explained-do-nothing-but-add-any-other-processes-not-excepting-those-simple-ada-lovelace

difference quotesengine quotesreality quotespartly quotesexplained quotesadd quotesprocesses quotesexcepting quotessimple quotessubtraction quotesmultiplication quotesdivision quotesperformed quotesextent quotesjudicious quotesmathematical quotesarrangement quotesartifices quotesreduce quotesseries quotesadditions quotes

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.

**Ada Lovelace**

the-further-we-analyse-manner-in-which-such-engine-performs-its-processes-attains-its-results-more-we-perceive-how-distinctly-it-places-in-true-ada-lovelace

analyse quotesmanner quotesengine quotesperforms quotesprocesses quotesattains quotesresults quotesperceive quotesdistinctly quotesplaces quotestrue quoteslight quotesmutual quotesrelations quotesconnexion quotessteps quotesmathematical quotesanalysis quotesseparates quotesthings quotesreality quotesdistinct quotesindependent quotesunites quotesmutually quotesdependent quotes

thus-not-only-mental-material-but-theoretical-practical-in-mathematical-world-are-brought-into-more-intimate-effective-connection-with-each-ada-lovelace

We might even invent laws for series or formula in an arbitrary manner, and set the engine to work upon them, and thus deduce numerical results which we might not otherwise have thought of obtaining; but this would hardly perhaps in any instance be productive of any great practical utility, or calculated to rank higher than as a philosophical amusement.

**Ada Lovelace**

we-might-even-invent-laws-for-series-formula-in-arbitrary-manner-set-engine-to-work-upon-them-thus-deduce-numerical-results-which-we-might-not-ada-lovelace

invent quoteslaws quotesseries quotesformula quotesarbitrary quotesmanner quotesset quotesengine quoteswork quotesdeduce quotesnumerical quotesresults quotesthought quotesobtaining quotesinstance quotesproductive quotesgreat quotespractical quotesutility quotescalculated quotesrank quoteshigher quotesphilosophical quotesamusement quotes

The method of differences is, in fact, a method of additions; and as it includes within its means a larger number of results attainable by addition simply, than any other mathematical principle, it was very appropriately selected as the basis on which to construct an Adding Machine, so as to give to the powers of such a machine the widest possible range.

**Ada Lovelace**

the-method-differences-is-in-fact-method-additions-as-it-includes-within-its-means-larger-number-results-attainable-by-addition-simply-than-any-ada-lovelace

method quotesdifferences quotesfact quotesadditions quotesincludes quotesmeans quoteslarger quotesnumber quotesresults quotesattainable quotesaddition quotessimply quotesmathematical quotesprinciple quotesappropriately quotesselected quotesbasis quotesconstruct quotesadding quotesmachine quotesgive quotespowers quotesmachine quoteswidest quotesrange quotes

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.

**Ada Lovelace**

the-analytical-engine-might-act-upon-other-things-besides-number-were-objects-found-whose-mutual-fundamental-relations-could-be-expressed-by-those-ada-lovelace

analytical quotesengine quotesact quotesthings quotesnumber quotesobjects quotesfound quotesmutual quotesfundamental quotesrelations quotesexpressed quotesabstract quotesscience quotesoperations quotessusceptible quotesadaptations quotesaction quotesoperating quotesnotation quotesmechanism quotesengine quotessupposing quotesinstance quotespitched quotessounds quotesharmony quotesmusical quotescomposition quotesexpression quotesadaptations quotesengine quotescompose quoteselaborate quotesscientific quotespieces quotesmusic quotesdegree quotescomplexity quotesextent quotes

it-is-however-pretty-evident-on-general-principles-that-in-devising-for-mathematical-truths-new-form-in-which-to-record-throw-themselves-out-for-ada-lovelace

Imagination is the Discovering Faculty, pre-eminently ... It is that which feels & discovers what is, the REAL which we see not, which exists not for our senses... Mathematical science shows what is. It is the language of unseen relations between things... Imagination too shows what is ... Hence she is or should be especially cultivated by the truly Scientific, those who wish to enter into the worlds around us!

**Ada Lovelace**

imagination-is-discovering-faculty-preeminently-it-is-that-which-feels-discovers-what-is-real-which-we-see-not-which-exists-not-for-our-senses-ada-lovelace

this-one-fact-implies-everything-it-is-scarcely-necessary-to-point-out-for-instance-that-while-difference-engine-can-merely-tabulate-is-incapable-ada-lovelace

The confusion, the difficulties, the contradictions which, in consequence of a want of accurate distinctions in this particular, have up to even a recent period encumbered mathematics in all those branches involving the consideration of negative and impossible quantities, will at once occur to the reader who is at all versed in this science, and would alone suffice to justify dwelling somewhat on the point, in connexion with any subject so peculiarly fitted to give forcible illustration of it as the Analytical Engine.

**Ada Lovelace**

the-confusion-difficulties-contradictions-which-in-consequence-want-accurate-distinctions-in-this-particular-have-up-to-even-recent-period-ada-lovelace

confusion quotesdifficulties quotescontradictions quotesconsequence quotesaccurate quotesdistinctions quotesrecent quotesperiod quotesencumbered quotesmathematics quotesbranches quotesinvolving quotesconsideration quotesnegative quotesimpossible quotesquantities quotesoccur quotesreader quotesversed quotesscience quotessuffice quotesjustify quotesdwelling quotespoint quotesconnexion quotessubject quotespeculiarly quotesfitted quotesgive quotesforcible quotesillustration quotesanalytical quotesengine quotes

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.

**Ada Lovelace**

one-main-reason-why-separate-nature-science-operations-has-been-little-felt-in-general-little-dwelt-on-is-shifting-meaning-many-symbols-used-ada-lovelace

in-abstract-mathematics-course-operations-alter-those-particular-relations-which-are-involved-in-considerations-number-space-results-operations-ada-lovelace

the-analytical-engine-is-embodying-science-operations-constructed-with-peculiar-reference-to-abstract-number-as-subject-those-operations-ada-lovelace

forget-this-world-all-its-troubles-if-possible-its-multitudinous-charlatans-everything-in-short-but-enchantress-numbers-ada-lovelace

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**

secondly-figures-symbols-numerical-magnitude-are-frequently-also-symbols-operations-as-when-they-are-indices-powers-wherever-terms-have-ada-lovelace

the-analytical-engine-on-contrary-can-either-add-subtract-multiply-divide-with-equal-facility-performs-each-these-four-operations-in-direct-ada-lovelace

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.

**Ada Lovelace**

it-must-be-evident-how-multifarious-how-mutually-complicated-are-considerations-which-working-such-engine-involve-there-are-frequently-several-ada-lovelace

evident quotesmultifarious quotesmutually quotescomplicated quotesconsiderations quotesworking quotesengine quotesinvolve quotesfrequently quotesdistinct quotessets quoteseffects quotessimultaneously quotesmanner quotesindependent quotesgreater quotesdegree quotesexercising quotesmutual quotesinfluence quotes

the-more-i-study-more-insatiable-do-i-feel-my-genius-for-it-to-be-ada-lovelace

mathematical-science-shows-what-is-it-is-language-unseen-relations-between-things-but-to-use-apply-that-language-we-must-be-able-fully-to-appreciate-to-feel-to-seize-unseen-uncon

the-science-operations-as-derived-from-mathematics-more-especially-is-science-itself-has-its-own-abstract-truth-value

that-brain-mine-is-something-more-than-merely-mortal-as-time-will-show

imagination-is-discovering-faculty-pre-eminently-it-is-that-which-penetrates-into-unseen-worlds-around-us-worlds-science

as-soon-as-i-have-got-flying-to-perfection-i-have-got-scheme-about-steam-engine

those-who-have-learned-to-walk-on-threshold-unknown-worlds-by-means-what-are-commonly-termed-par-excellence-exact-sciences-may-then-with-fair-white-wings-imagination-hope-to-soar

i-am-much-pleased-to-find-how-well-i-stand-work-how-my-powers-attention-continued-effort-increase

the-analytical-engine-does-not-occupy-common-ground-with-mere-calculating-machines-it-holds-position-wholly-its-own-considerations-it-suggests-are-more-interesting-in-their-natur

we-may-say-most-aptly-that-analytical-engine-weaves-algebraical-patterns-just-as-jacquard-loom-weaves-flowers-leaves

i-was-rather-foolish-in-saying-that-i-did-not-like-arithmetic-to-learn-figures-when-i-did-i-was-not-thinking-quite-what-i-was-about-the-sums-can-be-done-better-if-i-tried-than-th

i-have-my-hopes-distinct-ones-too-one-day-getting-cerebral-phenomena-such-that-i-can-put-them-into-mathematical-equations-in-short-law-laws-for-mutual-actions-molecules-brain-equ

i-believe-myself-to-possess-most-singular-combination-qualities-exactly-fitted-to-make-me-pre-eminently-discoverer-hidden-realities-nature

i-think-i-am-more-determined-than-ever-in-my-future-plans-i-have-quite-made-up-my-mind-that-nothing-must-be-suffered-to-interfere-with-them-i-intend-to-make-such-arrangements-in-

i-have-got-scheme-to-make-thing-in-form-horse-with-steam-engine-in-inside-contrived-as-to-move-immense-pair-wings-fixed-on-outside-horse-in-such-manner-as-to-carry-it-up-into-air

i-am-never-happy-as-when-i-am-really-engaged-in-good-earnest-it-makes-me-must-wonderfully-cheerful-merry-at-other-times-which-is-curious-satisfactory

the-analytical-engine-has-no-pretensions-whatever-to-originate-anything-it-can-do-whatever-we-know-how-to-order-it-to-perform-but-it-is-likely-to-exert-indirect-reciprocal-influe