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January 4, 2016 AT 12:00 am

Mathematical winters: Ada Lovelace, 200 years on #WomenInSTEM

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Via The Conversation. Thanks to Michiel for sending this in!

Christmas 1840, cold and crisp. The fashionable and wealthy Lovelace family are learning to skate, the four year-old Byron (junior, the grandson of Lord Byron) pushing a chair along the ice to keep his balance. Driven inside by the cold, his mother retires to her study and her lessons in advanced calculus. She writes to her tutor: “This is very mathematical weather. When one cannot exercise one’s muscles out of doors, one is peculiarly inclined to exercise one’s brains in-doors.” Then she plunges into a detailed discussion of the convergence of series.

Her name is Ada, Countess of Lovelace. Her teacher was Augustus De Morgan, one of the foremost mathematicians of the day. She is studying the material he taught his advanced class at the then all-male University College London: he writes of her power of thinking as “utterly out of the common way”, capable of grasping the “real difficulties of first principles”.

This grounding in advanced mathematics was essential for Ada Lovelace’s most famous work, a paper published in 1843, which translated and considerably extended a work by please by Luigi Menabrea about a general-purpose mechanical computer designed by Charles Babbage, his unbuilt analytical engine. The substantial appendices written by Ada Lovelace contain an account of the principles of the machine and a table often described as “the first computer programme”. Lovelace presents the machine, not in terms of ironmongery, but as what we would now call an “abstract machine”, describing the functions of memory, CPU, registers, loops and so on.

What is truly remarkable to the modern computer scientist is her high-level view. She understands the complexity of programming, the difficulty of checking correctness and the need for programme optimisation. She reflects on the power of abstraction, how the machine might “weave algebraical patterns”, how it might work with quantities other than number and its potential for creativity. In what Turing later described as “Lady Lovelace’s objection” to whether machines can think, she observed that: “The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform.”

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