Q.E.D.
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Q.E.D.

Mathematicians We Should Know More About: Ada Lovelace

Born of Lord Byron (sort of a Kardashian in his time-poet, rake, lightning rod for controversy), and lucky enough to get a proper education in science and mathematics, which wasn’t too common for young women at the time, Ada Lovelace is considered perhaps the first computer programmer.

Her part in computer science and mathematics history begins when she meets Charles Babbage at 17, then working on his Difference Engine, a machine for doing calculations. Mechanical calculation was only a dream at the time, although Pascal and others had tried.

We have always sought to free ourselves from the tedium and monotony of calculations. To this day, many mathematicians see calculation as having little to do with the actual doing of mathematics.

As James Essinger says in his biography of Lovelace:

“…if a machine is carrying them out, their monotony does not matter.”

Babbage at that time was part of the London high society, host of Saturday night parties for the who’s who of the scene, including Dickens. He was a dreamer, and may have been a mad scientist type. He remained a good friend of Ada for her whole life, although he may not have appreciated her true brilliance.

The Difference Engine was a money pit of a project, and never finished, but it did lead to Babbage’s Analytical Engine, and Ada’s place in history.

The loom, it might surprise you to know, led to the ideas about automation that led to the modern computer. Woven designs from the loom were the pixel art of their time, and were coveted as wall hangings by the wealthy. Babbage observed loom innovation in France (the Jacquard loom), specifically automation of different colours, and pulled the idea into his Analytical Engine. The mechanical world inspired the ideas that would create the digital world.

Ada, for her part, was desperate to learn science and mathematics. Here restless and curious mind needed excitement:

“I find that nothing but very close & intense application to subjects of a scientific nature now seems at all to keep my imagination from running wild, or to stop up the void which seems to be left in my mind from a want of excitement.”

Ada’s legacy to the world is her translation of Menabrea’s paper on the Analytical Engine. It is here that we see her vision of the future digital world.

As she says:

“We may say, most aptly, that the Analytical Engine weaves algebraical patterns just as the Jacquard loom weaves flowers and leaves.”

She perceived things that Babbage did not. She recognized that the potential of the machine was far beyond mere calculation, but went into the world of abstraction. She was interested in how the punch cards used to program the machine allowed for the abstraction of variables to be used. The previous Difference Engine was quite primitive by comparison, carrying out calculations simply by means of interlocking cogwheels.

Essinger powerfully praises what came to be known as Ada’s Notes.

“Ada is the complete mistress of her thought-domain; which could be described as the domain of the intellectual prehistory of the computer.”

There is debate over whether Lovelace wrote the first computer program. Regardless of whether she did or not, she laid the foundations for algorithmic thinking. She was far more than Babbage’s sidekick, and there is evidence that Babbage did not realize how brilliant Ada was.

Here is section from Ada’s Notes so you can see for yourself how she though about computing:

It is desirable to guard against the possibility of exaggerated ideas that might arise as to the powers of the Analytical Engine. In considering any new subject, there is frequently a tendency, first, to overrate what we find to be already interesting or remarkable; and, secondly, by a sort of natural reaction, to undervalue the true state of the case, when we do discover that our notions have surpassed those that were really tenable.

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. This it is calculated to effect primarily and chiefly of course, through its executive faculties; but it is likely to exert an indirect and reciprocal influence on science itself in another manner. For, in so distributing and combining the truths and the formulæ of analysis, that they may become most easily and rapidly amenable to the mechanical combinations of the engine, the relations and the nature of many subjects in that science are necessarily thrown into new lights, and more profoundly investigated. This is a decidedly indirect, and a somewhat speculative, consequence of such an invention. It is however pretty evident, on general principles, that in devising for mathematical truths a new form in which to record and throw themselves out for actual use, views are likely to be induced, which should again react on the more theoretical phase of the subject. There are in all extensions of human power, or additions to human knowledge, various collateral influences, besides the main and primary object attained.

In a time of seemingly unrestrained optimism about computing, we should note that Ada was skeptical about the power of machines. They can only do what we tell them to do, and it is only now, 160 years later, that machine learning is seeing machines do things without our help.

Machines calculate, and we analyze. We think. Machines are “extensions of human power”. We are thinkers, and machines are extensions of our thought, if we program them through the power of our thought.

Ada Lovelace is part of the rich history of mathematics, and of computer science. Underappreciated in her time, she is the spiritual mother of the computer, and may have created the first algorithm.

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