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Notes annotated in collaboration with Colonel Rick Gross, USAF. "Ada, The Enchantress of Numbers" can be purchasedfrom Strawberry Press P.O. Box 452 Sausalito, CA 94966 for $29.95.
All quotations and page numbers refer to the original Memoir which wasprinted inScientific Memoirs, Selections from The Transactions of ForeignAcademies and Learned Societies and from Foreign Journals, edited by RichardTaylor, F.S.A.,Vol III London: 1843, Article XXIX. Sketch of the AnalyticalEngine invented by Charles Babbage Esq. By L. F. Menabrea, of Turin, Officerof the Military Engineers. [From the Bibliothque Universelle de Gnve, No. 82October 1842].
Submitted by Betty Alexandra Toole Ed.D.
What captured my attention about Ada Byron, Lady Lovelace, in 1976 when Iwas getting my doctorate at the University of California at Berkeley, washow strange it was that the daughter of the famous poet Lord Byron wasconnected with the birth of the computer revolution. What expanded my senseof strangeness was when I was at Oxford working with Ada's letters from1984-1987, Iwould take a break at Blackwell's Bookstore and be overwhelmed by the tensof books on the shelves about "Ada" the programming language. In 1991 Iwrote an article for "Ada's Letters" entitled " Ada Byron, Lady Lovelace,Analyst and Metaphysician" and had the good fortune to have Colonel Grossreview the article. It was Ada's mind-set, her creative critical skillsthat not only laid the groundwork for her ability to write the firstcomputer program but correctly predict the future of computing. It doestake imagination, a leap of faith, to go from the structure of language,lines of code, to creative thinking, context and creativity, skills that Adaexhibited and I try to promote and had the expert help of Colonel Gross. AsAda programmers you might see other relationships between Ada's mind-set andthe nature and execution of Ada, the programming language.
The first step is to see how Ada went about her task and what follows is afew pages from my book "Ada, The Enchantress of Numbers."
To start with, Ada added a footnote to her translation of Menabrea'sarticle. She emphasized the difference between Pascal's machine, which canbe compared to a calculator, and Babbage's Analytical Engine, which can becompared to a modern day computer. Ada translated what Menabrea wrote: RForinstance, the much-admired machine of Pascal is now simply an object ofcuriosity, which, whilst it displays the powerful intellect of its inventor,is yet of little utility in itself. Its power extended no further than theexecution of the first four operations . . .S Ada augments Menabrea'sstatement and clearly defines the boundaries of Babbage's Analytical Engine.
Ada emphasized the fundamentally different capability of the AnalyticalEngine, that is, to be able to store a program (a sequence of operations orinstructions) as well as data (informational values themselves). At thispoint, she began to recognize and to amplify the increased responsibilitythis new capability placed upon the machine's user, to specify the storedprogram both precisely and in complete accordance with the user's interest.Her recognition of this increased responsibility is a remarkable insight, inthat the magnitude of this specification task (a task we refer to today assoftware development) is only now being appreciated.
It is accordingly most fitting, and most honouring to her insight, that theprogramming language Ada, developed in the early 1980's by the U.S.Department of Defense, provides the most precise facilities for thissoftware development (specification) task of any general-purpose softwarelanguage for large-scale problems existing today.In the following passage, Ada explained the difficulty of the softwaredevelopment task, that is, the difficulty of communicating to the machinewhat it is we expect it to do. But note that in so doing, she also, ineffect, extolled the power of mathematical language when it is precise.Thus, a software language capable of great precision in specification (likethe Ada language) also provides great power.
Ada exhibited the principle that power comes from disciplined creativity.
The confusion, the difficulties, the contradictions which, in consequence ofwant of accurate distinctions in this particular, have up to even a recentperiod encumbered mathematics . . . It may be desirable to explain, that bythe word operation, we mean any process which alters the mutual relation oftwo or more things, be this relation of what kind it may. This is the mostgeneral definition, and would include all subjects in the universe . . .They will also be aware that one main reason why the separate nature of thescience of operations has been little felt, and in general little dwelt on,is the shifting meaning of many of the symbols used in mathematicalnotation. First, the symbols of operation are frequently also the symbolsof the results of operations . . .Secondly, figures, the symbols of numerical magnitude, are frequently alsothe symbols of operations, as when they are the indices of powers [e.g., 2and 32] . . . [In] the Analytical Engine . . . whenever numbers meaningoperations and not quantities (such as indices of powers), are inscribed onany column or set of columns, those columns immediately act in a whollyseparate and independent manner . . .
Again, it [the Analytical Engine] might act upon other things besidesnumber, were objects found whose mutual fundamental relations could beexpressed by those of the abstract science of operations, and which shouldbe also susceptible of adaptations to the action of the operating notationand mechanism of the engine . . . Supposing, for instance, that thefundamental relations of pitched sounds in the science of harmony and ofmusical composition were susceptible of such expression and adaptations, theengine might compose elaborate and scientific pieces of music of any degreeof complexity or extent.
Once Ada had made the distinction between numbers and the operations to beperformed, it was not difficult for her to project further how theAnalytical Engine would then be capable of giving two types of results;numerical and symbolic, (eg algebraic). In effect, an Analytical Enginecould generate new programs as well as numbers. As a result the AnalyticalEngine opened up a vast new territory for the analysis of information.Here again, the Ada software language contains somewhat unique facilitiescorresponding in a sense to Ada's insight. One such Ada facility is thegeneric subprogram, a template for future software generation. Havingdefined a generic subprogram for data of one type, the Ada softwaredeveloper can create new copies automatically tailored to data of othertypes.
The distinctive characteristic of the Analytical Engine, and that which hasrendered it possible to endow mechanism with such extensive faculties as bidfair to make this engine the executive right-hand of abstract algebra, isthe introduction into it of the principle which Jacquard devised forregulating, by means of punched cards, the most complicated patterns in thefabrication of brocaded stuffs. It is in this that the distinction betweenthe two engines lies. Nothing of the sort exists in the Difference Engine.We may say most aptly that the Analytical Engine weaves algebraical patternsjust as the Jacquard-loom weaves flowers and leaves.
In addition to Ada's prescient comments linking the Analytical Engine to itspotential use for sound and graphics she provided what might be justlycalled "the first computer program", a plan for the Analytical Engine tocalculate Bernoulli numbers, a very complicated chore. This table is alsofound in this chapter.
However, of all the material in the translation, the following Note hasprobably engendered the most controversy today in light of its denial of thepossibility of creating original knowledge through so-called ``ArtificialIntelligence.''
It is desirable to guard against the possibility of exaggerated ideas thatmight arise as to the powers of the Analytical Engine. In considering anynew subject, there is frequently a tendency, first, to overrate what we findto be already interesting or remarkable; and, secondly, by a sort of naturalreaction, to undervalue the true state of the case, when we do discover thatour notions have surpassed those that were really tenable.The Analytical Engine has no pretensions whatever to originate any thing.It can do whatever we know how to order it to perform. It can followanalysis; but it has no power of anticipating any analytical relations ortruths. Its province is to assist us in making available what we arealready acquainted with. This it is calculated to effect primarily andchiefly of course, through its executive faculties; but it is likely toexert an indirect and reciprocal influence on science itself in anothermanner. For, in so distributing and combining the truths and the formula ofanalysis, that they may become most easily and rapidly amenable to themechanical combinations of the engine, the relations and the nature of manysubjects in that science are necessarily thrown into new lights, and moreprofoundly investigated.
Biography of Ada Bryon, Lady Lovelace
