Tag Archives: Ada Lovelace

Ada Lovelace – The Enchantress of Numbers

Women in Mathematics

Reading about Sophie Germain’s contributions to the world of mathematics ignited my curiosity about the role of other women in contributing to the advancement of math throughout history. Women have made some incredible contributions to mathematics, and I was more than pleasantly surprised (as a Computer Science major) to read the story of Ada Lovelace – the only legitimate daughter of the romantic poet Lord Byron, and the woman often called the world’s first “computer programmer” – her collaboration with British Mathematician Charles Babbage began around the middle of the 19th century.

History

Ada Lovelace was born to Lord Byron and Anne Isabelle Milbanke in 1815, though she never met her famous father – he was reportedly disappointed at not having a boy, and left both mother and child when Ada was only one month old. Lord Byron passed away when she was only eight years old (Ada herself was buried next to her father after she succumbed to uterine  cancer at only 37). Her mother saw to it that Ada did not take seek her father’s “artful” pursuits, and made sure that the girl was tutored in mathematics, science and music. While not unusual for someone of her family’s elite noble class, it was unusual for a woman to study math and science in that time. These intellectual pursuits led Ada to communicate with the circle of “gentlemanly scientists” of that era (though the term scientist was not actually coined until 1836, the description applies), and it was in this circle that she met her lifelong friend, British Mathematician Charles Babbage, the inventor of the Difference Engine (the machine itself never made it past the prototype stage). They wrote extensive correspondences back and forth on mathematics and logic, among other topics. Babbage was impressed by Lovelace’s intelligence and analytical skill, referring to her as the Enchantress of Numbers.

Ada_Lovelace_portrait

Watercolor portrait of Ada King, Countess of Lovelace (Ada Lovelace) by Alfred Edward Chalon. Alfred Edward Chalon [Public domain], via Wikimedia Commons

Babbage and the Analytical Machine

In the 19th century, complicated mathematical computations had to be done by hand, or using the shortcut of published tables, which also had to be written by hand and were prone errors themselves. In 1834, Babbage began work on a new kind of calculating machine, the Analytical Engine – a machine that would automate calculations of addition, subtraction, multiplication and division. In 1842, Lovelace was enlisted by Babbage to translate from French the work of Italian mathematician Luigi (or Louis) Menabrae. Her work in this translation, and her copious notes written during the process, are responsible for her enduring fame.

Her contribution

Lovelace’s notes on Menabrae’s work were larger than the translation itself, and in them she describes how the Analytical Engine itself works, as well as an algorithm, or what she called a “plan”, for using the Analytical Engine to compute Bernoulli numbers. This is said to be the first algorithm specifically suited for a computational machine to carry out a series of instructions, using the “specific ability of a calculating device to make control decisions based on the data”. In her work, she also noted the grand potential of the Analytical Engine to solve problems of any complexity, and even projected that this type of machine could be used to “compose elaborate and scientific pieces of music”.

There is some controversy about the extent of Lovelace’s contribution. However, in their article published in Scientific American (issue 280, p 71-75), Eugene Eric Kim and Betty Alexander Toole noted that while Babbage wrote several small programs, none of his approached the complexity of Lovelace’s Bernoulli numbers program, and that this program was her idea; it also cannot be disputed that her vision for the potential of such machines to extend functionality beyond simple value computations was visionary, especially for the 19th century.

Conclusion

Women have contributed extensively to the advancement of mathematics and computer science (please read any biography you can get your hands on about the incomparable Admiral Grace Hopper, and look for my upcoming third blog post all about this amazing woman!), and it is important for these contributions to be recognized. This is not only to give credit where it is due, but also to give the many girls and women thinking about a future in the sciences and mathematics role models to look up to. Ada Lovelace is recognized in a number of ways: a day in early to mid October (the actual date varies) is celebrated now as Ada Lovelace day, a day to celebrate the achievements of women in science, technology, engineering and mathematics (STEM), and the computer programming language Ada was created by the Department of Defense around 1980, named in her honor.

Sources:

https://www.sdsc.edu/ScienceWomen/lovelace.html

http://womenshistory.about.com/cs/sciencemath1/a/bio_lovelace.htm

http://mathworld.wolfram.com/FermatsLastTheorem.html

http://en.wikipedia.org/wiki/Ada_Lovelace

http://findingada.com/

http://www.linuxvoice.com/history-of-computing-part-1/

http://www.conservapedia.com/Ada_Lovelace

 

A Glimpse into Female Mathematicians of the Past

After our discussion in class about the work of Sophie Germain, I was interested in learning more about other prominent women in mathematics. I’m sure we will go over some of them in class, but here is what I discovered about some very smart women.

One of the earliest known female mathematicians was Hypatia. She lived in the time period of approximately 350-416 C.E. She was excellent at mathematics, astronomy and philosophy. No doubt this is because her father was Theon, one of the last members of the library of Alexandria. Unfortunately for us, we do not know many of her contributions to science. She is more well known for her brutal death. She was riding in her carriage, when she was forcefully removed, stripped, beaten to death, and then her body was burned. Not a nice way to go. Regardless, of that cruelty, she is one of the first well known women mathematicians, and in her time that was quite an accomplishment.

Another leading lady in mathematics was Ada Lovelace. She lived from 1815-1852 as the daughter of well known writer, Lord Byron. She never met her father, and her mother advocated her to study fields that were different from language and poems. Essentially, anything different from what her father was well known for. It must have been a bad break up. Thus, math and science it was. Turns out, she is credited with being the world’s first programmer. But before that achievement, she demonstrated ingenuity as a child. She set her mind toward the daunting task of flying, at the young age of twelve. She researched materials, how to build wings, and even wanted to incorporated steam! Being curious from a young age really inspired her to continue her study of the sciences.

Because of the strict laws against the education of women she had to study mathematics with a tutor, she could not technically enroll in university.  She met Charles Babbage later in life and their friendship encouraged her studies. They continued their correspondence even after her marriage to the Earl of Lovelace. At the time Babbage was working on a theoretical machine called the Analytical Engine. The idea was that the Engine could store numbers, and it could do long cycles and loops without the help of people. She wrote to Babbage about including Bernoulli numbers and how such implicit functions could be solved by the Engine. According to Wolfram Alpha, “The Bernoulli numbers are a sequence of signed rational numbers that can be defined by the exponential generating function. x/(e^x-1)=sum_(n=0)^infty(B_nx^n)/(n!).  These numbers arise in the series expansions of trigonometric functions, and are extremely important in number theory and analysis.” In order to calculate Bernoulli numbers, there must be a lot of operations involved. To top it off, they anticipated that the Analytical Engine could perform this task. Below I have pictured one of Ada’s tables on how she envisioned the Engine could compute this. Remarkably enough, Lady Lovelace once said, “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.” She understood that the machine is only as good as the people who are using it. It cannot come up with new ideas, or understand why it is doing computation, it can only do said computation. If this machine were to have been made, it would have been an incredible invention. However, the fact that it was never brought to production, does not in any way reduce all of the work both Ada and Charles did.

Ada Lovelace's plan to generate Bernoulli numbers.

Ada Lovelace’s plan to generate Bernoulli numbers. Image: Betty Toole.

Unfortunately, there has been speculation that Ada did not contribute in the mathematical sense, but was merely a notetaker for Babbage. This is baffling because in his autobiography, Babbage gives her credit for all of the theoretical math she did for his Analytical Engine. I could continue this post with a commentary about women in science even today, but I’d better move onto the final female mathematician I wish to recognize.

The final female mathematician I wish to discuss is Emmy Noether. Emmy was born in Germany in the late 1800’s. She was denied a lot of formal education because she was a woman. She began her studies with piano and languages, but soon discovered a passion for math, like her father, and her brother.  Universities in Germany were hesitant to let her become a professor, although, she did get the status of Associate Professor eventually. This title was taken away however, when the Nazi’s came to power because she was Jewish. Despite all of this, she had many notable accomplishments. So much so, that Albert Einstein once referred to her as “the most significant creative mathematical genius thus far produced since the higher education of women began.” This is high praise, especially coming from a man our society reveres as the most intelligent man ever known.

She was behind a revolutionary theorem, called Noether’s Theorem. This theorem states that: “Each symmetry of a system leads to a physically conserved quantity. Symmetry under translation corresponds to conservation of momentum, symmetry under rotation to conservation of angular momentum, symmetry in time to conservation of energy, etc.” And when I first read this, I was quite confused. However, with some help from my sources, I was able to wrap my mind around it to a certain extent. Noether is telling us that when we find symmetrical things, in nature or otherwise, there is some sort of conservation force that goes with it. One example of this, that is referenced in the New York Times article, is the relationship between time and energy. To paraphrase, if a person throws a ball up in the air right now, or throws it the same way sometime in the future, the time does not affect the trajectory of the ball. This means that the symmetry of time is related to the conservation of energy. This is crucial to how we think about physics today, and I could definitely relate this to my old physics teacher being like a broken record and telling us energy cannot be created or destroyed, it only changes form. Emmy clearly made an impact on not only math, but the way we think about certain concepts today. She even developed some of the mathematical formulas that Einstein used for his Theory of Relativity.

It seems to me that Emmy deserves much more recognition than she is receiving. Truthfully, I had not even heard of her until I began research for this blog post. I know this is not a class about how our society can improve, but one way would be to get more women in math and science. It is interesting to think about how limited women once were. I am optimistic about the progress we have made in that regard, but just think about how much further along we could possibly be in terms of figuring out the mysteries of the world if we had help from every person, from every demographic, and every gender. I do not know if this is possible, but inclusion is a nice thought. These ladies kicked butt in their time, and I hope that the women of the present and the future follow their example and continue to do the same.

I have recently learned that October 14th was Ada Lovelace Day! Ada Lovelace Day celebrates women in all areas of science. And because of that, I would like to dedicate this post to all the amazing ladies out there making leaps and bounds in the sciences. You are an inspiration to me, but all young women of the world.

Works Cited:

  • Angier, Natalie. “The Mighty Mathematician You’ve Never Heard Of.” The New York Times. N.p., 26 Mar. 2012. Web. 29 Sept. 2014. <www.nytimes.com%2F2012%2F03%2F27%2Fscience%2Femmy-noether-the-most-significant-mathematician-youve-never-heard-of.html%3Fpagewanted%3D1%26_r%3D0>.
  • “Bernoulli Number.” — from Wolfram MathWorld. N.p., n.d. Web. 10 Oct. 2014.
  • Boyer, Carl B., and Uta C. Merzbach. A History of Mathematics. 3rd ed. Hoboken, NJ: Jon Wiley and Sons, 2010. Print.