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Ada Lovelace - Quotes

The purpose which that engine has been specially intended and adapted to fulfil, is the computation of nautical and astronomical tables.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

The Analytical Engine, on the contrary, is not merely adapted for tabulating the results of one particular function and of no other, but for developing and tabulating any function whatever. In fact the engine may be described as being the material expression of any indefinite function of any degree of generality and complexity...
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

In this, which we may call the neutral or zero state of the engine, it is ready to receive at any moment, by means of cards constituting a portion of its mechanism (and applied on the principle of those used in the Jacquard-loom), the impress of whatever special function we may desire to develope or to tabulate.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

...the particular numerical data and the numerical results are determined by means and by portions of the mechanism which act quite independently of those that regulate the operations.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

...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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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 reasonings and results are frequently falsified.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

The Analytical Engine is an embodying of the science of operations, constructed with peculiar reference to abstract number as the subject of those operations.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

Those who view mathematical science, not merely as a vast body of abstract and immutable truths, whose intrinsic beauty, symmetry and logical completeness, when regarded in their connexion together as a whole, entitle them to a prominent place in the interest of all profound and logical minds, but as possessing a yet deeper interest for the human race, when it is remembered that this science constitutes the language through which alone we can adequately express the great facts of the natural world, and those unceasing changes of mutual relationship which, visibly or invisibly, consciously or unconsciously to our immediate physical perceptions, are interminably going on in the agencies of the creation we live amidst: those who thus think on mathematical truth as the instrument through which the weak mind of man can most effectually read his Creator's works, will regard with especial interest all that can tend to facilitate the translation of its principles into explicit practical forms.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

We may say most aptly, that the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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 connexion with each other.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

One essential object is to choose that arrangement which shall tend to reduce to a minimum the time necessary for completing the calculation.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

We already know that there are functions whose numerical value it is of importance for the purposes both of abstract and of practical science to ascertain, but whose determination requires processes so lengthy and so complicated, that, although it is possible to arrive at them through great expenditure of time, labour and money, it is yet on these accounts practically almost unattainable; and we can conceive there being some results which it may be absolutely impossible in practice to attain with any accuracy, and whose precise determination it may prove highly important for some of the future wants of science, in its manifold, complicated and rapidly-developing fields of inquiry, to arrive at.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

We might even invent laws for series or formulæ 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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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 in making available what we are already acquainted with.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.