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We’ve all heard the phrase, but I think most people use it without understanding it or knowing where it came from, so I decided to dig a bit. According to A Dictionary of Modern English Usage (now a century old...), the preferred meaning is that the exception demonstrates that a rule exists – ie, that the fact that there is an exception proves that there is a rule. That seems consistent with modern usage, but doesn’t make a lot of sense... unless you accept the suggestion that it is based on a Latin phrase “exceptio probat regulam in casubus non exceptis”. This can be roughly translated as “the exception demonstrates [the existence of a] rule, in cases [which otherwise] have no exceptions”, and the latter parts of common quotes and phrases frequently dropped off over time, in common usage.
Interesting, and plausible. Is that how it happened, though? Maybe.
Another sense is that the presence of an exceptional case suggests or highlights that a rule exists. This seems close enough to the “standard” meaning that we could argue that this can be explained simply as “drift” from the original meaning.
So, what exception? What rule?
I would say that, for centuries, women have been the session musicians of the scientific world.
Bear with me – I think I can get there...
Consider session musicians, who are hired to perform in a recording session or live performance – often to “fill out” the sound of a band, or play instruments that the band members cannot. Some of the greatest musicians of the past century have been unsung heroes that most of us never hear about. They are often extraordinarily talented, and in high demand, but never “make it big” because they are not “members” of a popular band.
Take, as an example, Chester Thompson. He is a truly extraordinary musician, and has played for some of the biggest acts in the world (Genesis, Frank Zappa, Santana, and dozens of others), but relatively few people have heard of him because he’s “just” a touring / session musician, rather than a member of the band.
Now consider women in science. While they have been vital to many scientific advances through the centuries, few people can name more than “Marie Curie”. Why is this? Most often, the answer is that women needed a man (often a father, brother, or husband) to present discoveries in order for their work to be taken seriously by the scientific “establishment” (usually entirely male). As one example, Chien-Shiung Wu made a scientific breakthrough (the Wu experiment), for which her male colleagues were awarded a Nobel Prize.
This has been changing over the past few decades, but not enough, and not quickly enough. Until the release of the film Hidden Figures, for example, I would guess that most people had no idea of the existence of people like Katherine Johnson, Mary Jackson, or Dorothy Vaughan. I certainly hadn’t heard of them, and it makes me angry that we so seldom celebrate the accomplishments made by people in minority groups, particularly since they were all the more extraordinary because they were made in spite of systemic discrimination. How much more could they have accomplished if we, as a society, actually learned from past mistakes and took steps to fix them? (I know that the book came first, and that the film is a dramatic adaptation, but more people will have heard of and seen the film.)
Sigh.
This all brings me to Ada Lovelace, another exception that proves the rule.
Augusta Ada King, Countess of Lovelace, was the only legitimate child of the poet Lord Byron. Though she never really knew him, he appears to have had an enormous impact on her life. Ada’s mother was concerned that Lord Byron was “insane”, and attempted to protect Ada by pushing her toward an education focusing on mathematics and logic. Are we to presume from this that Lady Byron thought that an interest in poetry led to madness?
If so, it is interesting that Ada described her approach as “poetical science”, and herself as an “Analyst & Metaphysician”. In any case, her undeniable mathematical talents led to her work with Charles Babbage, and to her own immortality. Sadly, Ada suffered from ill-health throughout her life, and died at the age of 36 years.
Ada Lovelace is frequently described as being the first computer programmer. What does this mean, and how can we prove it?
Charles Babbage is known for the Difference Engine and the Analytical Engine. The Difference Engine is most easily thought of in terms of versions. Difference Engine 0 was a small version, completed in 1822 as a proof of concept.
Work on Difference Engine 1 ran from 1822 to 1833, at which point it was abandoned, apparently due to a combination of expense and conflicts between Babbage and the chief engineer. This first unit would have had about 25,000 parts, weigh 4 tons, and operate on 20-digit numbers by sixth-order differences, which means that it would have been able to solve polynomial equations with powers up to X6.
Between 1846 and 1849, Babbage used what he had learned from Difference Engine 1 and Analytical Engine to design Difference Engine 2. This was not built during his lifetime, but a working version was completed in 2002, having 8,000 parts, weighing about 5 tons, and operating on 31-digit numbers by seventh-order differences.
Ada Lovelace met Charles Babbage in 1833, when she was eighteen, around the time he was starting to work on the Analytical Engine. It appears that, while working on the special-purpose Difference Engine 1, he realized that a more general design was possible.
The Analytical Engine was envisioned as an enormous, steam-powered machine, consisting of a “store” (memory) of 1000 50-digit decimal numbers, a “mill” (CPU / Central Processing Unit), a printer, and punched-card feeders (based on the Jacquard machine) for “operation cards” (programs), “variable cards” (memory addressing), and “number cards” (input), along with “barrel controllers” dedicated to specific tasks. In fact, the Analytical Engine would have been Turing complete, which was not even a concept until a century later.
So, while Babbage designed the hardware, and envisioned the ability to create programs, he does not appear to have actually written any of significance. That distinction goes to Ada when, in 1842-1843, she translated an article by the Italian mathematician Luigi Menabrea on the Analytical Engine. Along with the translation, Ada added a set of notes, much longer than the translation, in which she discusses the machine in terms that suggest she may have understood the implications of the tool in a way that even Babbage did not.
The First Computer Program provides a number of quotes which suggest that Ada thoroughly understood the implications of Analytical Engine, and a walkthrough of the famous Note G, which is essentially a program for calculating Bernoulli numbers.
As examples of Ada’s foresight, she noted the risk of programmer error, whereby the cards might give wrong orders to the Analytical Engine. She also realized the potential of the Analytical Engine to act on abstract symbols, so long as they could be expressed as numbers or operations, and gives music as an example:
“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.”
Sadly, the Analytical Engine was never built, but Ada’s contributions are at least acknowledged by modern computer programmers, including having a programming language named after her.
We can only guess at what could have happened if Babbage had managed to build the Difference Engine or the Analytical Engine (and some have tried), or what could have happened if Ada had lived longer or had enjoyed better health, but it seems clear that Ada was far ahead of her time.
Cheers!
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