Ada Lovelace: Enchantress of Number

Innovative geniuses often have some unique combination of genetic predisposition, education, and opportunities that allow them to go where no one has gone before.  Such is the case with Augusta Ada King, Countess of Lovelace, more often known as Ada Lovelace.  Ada is recognized today as the first person to conceptualize the modern digital computer.  What is remarkable is that she did this in the mid-19^th century, almost 100 years before the first computer was actually built, in a society where woman were expected to marry, raise children, and leave the thinking to the men.    But Ada had that unusual combination of nature, nuture, and opportunity which put her in a position to come up with an idea that was truly remarkable and way ahead of its time.

Ada Lovelace was born in London, England on December 10^th, 1815, the only legitimate child of Lord Byron, England’s foremost poet of his day. Lord Byron lived the romantic, cavalier life of the heroes of his poetry.  His lavish lifestyle of gambling and sexual escapades (including with his half-sister) often left him in scandal and dire financial straits.  He married Annabella Milbanke, daughter of a wealthy provincial family, in an attempt to inject some stability into his life.  Nevertheless, just short of a year after they were married, Anna left Lord Byron and fled to her parent’s estate with their five-week-old baby girl.  Ada would never know father.  As Ada grew, Anna worried that her emotional, highly-strung daughter had inherited her father’s wild temperament.  To tame these dangerous predilections, Anna prescribed a rigorous education in mathematics which Ada took to with relish. 

Charles Babbage

At the age of 16, Ada was presented at court, a rite of passage for young ladies of the aristocracy that was necessary to enter London society and find a suitable husband.  Ada was less than thrilled with the occasion.  A few weeks later, however, she was invited to attend the salon of Charles Babbage, London’s eminent mathematician and writer on industry and machinery.  At the salon, Babbage showed off the demonstration piece of his “Difference Engine”, a remarkable mechanical contraption that, when completed, could solve polynomial equations with the turn of a crank.  The importance of such a machine becomes clear when you consider that, back then, complex equations were calculated by hand and one mistake could render the result meaningless, or worse, dangerous.  While the demonstration was a great parlor trick for most participants of Babbage’s party, Ada was enthralled with the mathematical beauty of the invention.  Despite the difference in their ages (24 years) and social standing, they struck up a friendship that would last the rest of her life.  Kindled by her interest in Babbage’s calculating machine, she dedicated her studies to an assiduous pursuit of mathematics.

A fully operational Difference Engine at the Computer History Museum in Mountain View, California

Babbage would never complete the Difference Engine partly due to lack of funds but more importantly because he had envisioned something even grander.  Rather than making one calculation at a time, as with the Difference engine, what if you could give a machine a series of instructions in a reliable and reproducible way?  The complexity of the mathematical problems that could be solved would be far greater, perhaps greater than could ever by achieved by hand.  In essence, his proposed “Analytical Engine” would be a general-purpose computer that could perform a variety of mathematical tasks based on the programmed instructions it was given.  As a practical matter, it would have to be enormous, roughly the size of a steam locomotive with over 20,000 cogwheels.   To “input” the instructions, Babbage proposed to use the punched card system of the Jacquard loom.  The Jacquard loom had revolutionized the weaving industry by encoding the pattern of each pass of the shuttle on punched cards.  By feeding a long chain of cards into the loom, intricate patterns could be realized…and reliably reproduced.  Babbage’s idea was that the steps of a long series of calculations would be fed into his analytical engine using a similar device.  Babbage was so taken with the genius of the Jacquard loom that he purchased an exquisite, woven portrait of Jacquard himself and challenged his guests to guess how it was made.

At the age of 19, Ada married William King-Noel, Earl of Lovelace.  Three children soon followed.  William proved to be a fairly aimless man, spending most of his time supervising the construction of tunnels on Ashley Combe, their estate in Somerset, and their country homes.  While managing her homes and family, Ada worked with Babbage on his Analytical Engine.  Babbage would often visit Ashley Combe.  In deep discussion, the two would walk on the terrace they called the “Philosopher’s Walk”.

Ashley Combe, home of Ada, Countess of Lovelace, in the 1950's.
The house fell into disrepair and was demolished in 1974.

In the summer of 1840, Babbage presented his concept for the Analytical Engine at a meeting of Italian scientists in Turin, Italy.  Based on that presentation, a young mathematician named Luigi Menabrea published a “Sketch of The Analytical Engine Invented by Charles Babbage” in an obscure Swiss journal in 1842.  In the summer of 1843, Ada translated the article from French into English in the hope that its publication in a reputable English journal might raise interest in the Analytical Engine.  With Babbage’s encouragement and assistance, she also wrote “Notes by the Translator”, in which she expands on Menabrea’s discussion with ideas and examples of her own.  Ada’s notes are roughly three times longer than the original Menabrea article.  While much of the notes are highly technical mathematics, large sections focus on the significance and practical utility of the Analytical Engine.  By bringing together the artistic and poetic nature of her father, her knowledge of mathematics, and her fascination with Babbage’s invention, Ada makes several important conceptual leaps that effectively invent the modern digital computer. 

First, in Note A, she makes a clear distinction between the Difference Engine, which can calculate one specific function, with the Analytical Engine:

“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.”

This is achieved through the use of the Jacquard loom cards to program the machine.  The Analytical Engine can perform whatever calculations are required to solve the problem at hand.

“The distinctive characteristic of the Analytical Engine, and that which has rendered it possible to endow mechanism with such extensive faculties as bid fair to make this engine the executive right-hand of abstract algebra, is the introduction into it of the principle which Jacquard devised for regulating, by means of punched cards, the most complicated patterns in the fabrication of brocaded stuffs. It is in this that the distinction between the two engines lies. Nothing of the sort exists in the Difference Engine. We may say most aptly, that the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.” 

She is making a clear distinction between a one-purpose calculator and a general purpose computer, built to answer myriad questions.  But then she goes much further than even Babbage himself ever did.  While Babbage saw the Analytical Engine as a number cruncher, Ada wonders what other “objects”, i.e. data, might be subject to analysis.

“Again, it 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.”

From our 21^st century perspective, where music, text, video, and images have all been digitized, Ada’s  idea is absolutely stunning.  Twenty-five years ago, today’s digital world was unimaginable to most of us.  Ada Lovelace imagines it 175 years ago!  

In Note G, Ada writes a series of instructions for the Analytical Engine to calculate Bernoulli numbers.  It’s essentially the world’s first computer program, making her the world’s first computer programmer.  In the routine, she uses several concepts that today’s programmers would immediately recognize including subroutines, recursive loops, and conditional branching.  In his memoir, Babbage acknowledges that Ada caught a “grave mistake” that he had introduced into the program.  If this is true, Ada is the world’s first debugger as well!

Ada's Algorithm for the calculation of Bernoulli numbers from Note G.

Note G also contains Ada’s thoughts on whether or not computers can think, or what has come to be known as Lady Lovelace’s objection.

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. 

According to Alan Turing’s Imitation Game, if we cannot determine whether or not we are conversing with a human or a computer, then the computer could be said to be thinking.  IBM’s computer Watson sure sounded like he was thinking on Jeopardy!  Nonetheless, Lady Lovelace’s objection from 1848 still stands today.

The publication of her “Notes by the Translator” was the high point of Ada’s intellectual career.  The Countess of Lovelace had her children, husband, and three homes to attend to.  Ada and Charles Babbage would remain friends.  As he wrote in one letter to her, she was his “Enchantress of Number”.  After a long and painful illness, Ada died of uterine cancer at the age of 36.  Babbage, who never finished the Difference Engine, much less the Analytical Engine, apparently became such a petty, doddering old coot that Charles Dickens satirized him in All the Year Round.

And what of the Analytical Engine?  Did any of Babbage and Lovelace’s work contribute to the development of the computer, even if it did take 100 years?  Probably not.  There is little evidence that Ada’s concepts were directly involved in the invention of computers or the development of computer programming.  It’s only in retrospect that her achievements have been recognized.  Any history of the computer has to start with the pioneering insight of Augusta Ada Lovelace.

Walter Isaacson, The Innovators: How a Group of Hackers, Geniuses, and Geeks Created the Digital Revolution. Simon & Schuster, New York, NY, 2014.

James Essinger, Ada’s Algorithm: How Lord Byron’s Daughter Ada Lovelace Launched the Digital Age. Melville House, Brooklyn, NY, 2014.

L.F. Menabrea, Sketch of The Analytical Engine Invented by Charles Babbage.  Bibliotheque Universelle de Geneve, October, 1942, No. 82.  Notes by the Translator by Ada Augusta, Countess of Lovelace.