- Perl, Teri.
*The Ladies Diary*or*Woman's Almanac*, 1704-1841,**Historica Mathematica 6**(1979): 36-53 - Wallis, Ruth and Peter.
*Female Philomaths*,**Historica Mathematica 7**, (1980), 57-64.

"There were indeed women in mid-century England who signed their names to
mathematical articles in popular journals, and there were influential
periodicals, such as the *Edinburgh Review*, that lent intellectual women
psychological support.... Although the *Ladies Diary* ... , the most
popular of the mathematical periodicals, encouraged women to join wit
with beauty, it attracted serious amateurs of both sexes... [it] was
a respectable place to pose mathematical problems and sustain
debate... since there were few science periodicals in England until the
1830s, technical articles often appeared in general periodicals like the
*Ladies Diary*. It may have been something similar that originally
sparked Mrs. Somerville's interest in mathematics. At a tea party one
afternoon, she recalled years later, young Mary Fairfax had been given a
ladies' fashion magazine that contained a puzzle, the answer to which was
given in strange symbols. These symbols turned out to be algebra. And
that magazine became her introduction to the world of Euclidean geometry
and number."

**Baum, p. 35**

*Submitted by Linda Talisman*

Notes annotated in collaboration with Colonel Rick Gross, USAF. ``Ada, The Enchantress of Numbers'' can be purchased from Strawberry Press P.O. Box 452 Sausalito, CA 94966 for $29.95.

All quotations and page numbers refer to the original Memoir which was
printed in *Scientific Memoirs, Selections from The Transactions of Foreign
Academies and Learned Societies and from Foreign Journals*, edited by Richard
Taylor, F.S.A.,Vol III London: 1843, Article XXIX. Sketch of the Analytical
Engine invented by Charles Babbage Esq. By L. F. Menabrea, of Turin, Officer
of the Military Engineers. [From the Bibliothque Universelle de Gnve, No. 82
October 1842].

*Submitted by Betty Alexandra Toole Ed.D.*

The first step is to see how Ada went about her task and what follows is a few pages from my book ``Ada, The Enchantress of Numbers.''

To start with, Ada added a footnote to her translation of Menabrea's article. She emphasized the difference between Pascal's machine, which can be compared to a calculator, and Babbage's Analytical Engine, which can be compared to a modern day computer. Ada translated what Menabrea wrote: RFor instance, the much-admired machine of Pascal is now simply an object of curiosity, which, whilst it displays the powerful intellect of its inventor, is yet of little utility in itself. Its power extended no further than the execution of the first four operations . . .S Ada augments Menabrea's statement and clearly defines the boundaries of Babbage's Analytical Engine.

Ada emphasized the fundamentally different capability of the Analytical Engine, that is, to be able to store a program (a sequence of operations or instructions) as well as data (informational values themselves). At this point, she began to recognize and to amplify the increased responsibility this new capability placed upon the machine's user, to specify the stored program both precisely and in complete accordance with the user's interest. Her recognition of this increased responsibility is a remarkable insight, in that the magnitude of this specification task (a task we refer to today as software development) is only now being appreciated.

It is accordingly most fitting, and most honouring to her insight, that the programming language Ada, developed in the early 1980's by the U.S. Department of Defense, provides the most precise facilities for this software development (specification) task of any general-purpose software language for large-scale problems existing today. In the following passage, Ada explained the difficulty of the software development task, that is, the difficulty of communicating to the machine what it is we expect it to do. But note that in so doing, she also, in effect, extolled the power of mathematical language when it is precise. Thus, a software language capable of great precision in specification (like the Ada language) also provides great power.

Ada exhibited the principle that power comes from disciplined creativity.

Once Ada had made the distinction between numbers and the operations to be performed, it was not difficult for her to project further how the Analytical Engine would then be capable of giving two types of results; numerical and symbolic, (eg algebraic). In effect, an Analytical Engine could generate new programs as well as numbers. As a result the Analytical Engine opened up a vast new territory for the analysis of information. Here again, the Ada software language contains somewhat unique facilities corresponding in a sense to Ada's insight. One such Ada facility is the generic subprogram, a template for future software generation. Having defined a generic subprogram for data of one type, the Ada software developer can create new copies automatically tailored to data of other types.

In addition to Ada's prescient comments linking the Analytical Engine to its potential use for sound and graphics she provided what might be justly called "the first computer program", a plan for the Analytical Engine to calculate Bernoulli numbers, a very complicated chore. This table is also found in this chapter.

However, of all the material in the translation, the following Note has probably engendered the most controversy today in light of its denial of the possibility of creating original knowledge through so-called ``Artificial Intelligence.''