Chapter 1: The Life of Charles Babbage

Charles Babbage, an English mathematician and mechanical engineer born in Devonshire in 1792, was the son of a banker named Benjamin Babbage. Due to health issues in his childhood, he was educated privately until entering Cambridge in 1810. His passion for mathematics, which he largely taught himself, left him frustrated when he realized he was more knowledgeable than his instructor.

While at university, Babbage formed close friendships with John Herschel and George Peacock, both of whom shared his enthusiasm for mathematics and astronomy. Together with Edward Bromhead, they established the Analytical Society, aiming to modernize mathematical education and promote the adoption of European calculus methods.

In his twenties, Babbage gained recognition as a mathematician and became a Fellow of the Royal Society in 1816. He played a pivotal role in founding the Astronomical Society, later known as the Royal Astronomical Society, in 1820. Collaborating with Herschel, he worked on correcting astronomical tables that had been computed by human 'computers', who manually performed calculations following set procedures. Babbage grew frustrated with the slow process and famously wished for the calculations to be done by steam power.

Babbage's idea for a mechanical device to compute mathematical tables emerged around 1812, and this concept would shape his future endeavors.

Numerous attempts had been made to create calculating machines over the years. In the 1640s, French mathematician Blaise Pascal invented a mechanical calculator capable of addition and subtraction, which was patented and sold. Thirty years later, German mathematician Gottfried Leibniz sought to enhance Pascal's invention to include multiplication and division but failed to produce a reliable version.

Babbage, aware of Pascal and Leibniz's work, aimed to create a mechanical method for tabulating logarithms, inspired by French mathematician Gaspard de Prony. De Prony simplified operations for generating trigonometric tables into basic steps involving just addition and subtraction.

In 1822, Babbage devised the 'Difference Engine', a machine designed to calculate polynomial function values. Securing funding from the British Government, he enlisted Joseph Clement to help realize his vision.

After inheriting a fortune from his father, Babbage hosted gatherings at his home attended by intellectuals, industrialists, and scientists. A highlight of these events was his demonstration of a model of the Difference Engine, where he would crank the handle to showcase how different coded instructions altered the output. Guests interested in the machine were taken to the stables where the full-scale model was under construction.

Ada Lovelace, the daughter of Lord Byron, inherited her father's romantic spirit, which her mother sought to temper through mathematics lessons. Unlike her father, Ada found harmony between the Romantic and Industrial eras. At one of Babbage's gatherings, she impressed him with her interest in his machine.

In the mid-1830s, while continuing work on the Difference Engine, Babbage conceptualized the 'Analytical Engine', a programmable mechanical digital computer capable of executing any calculation through four fundamental arithmetic operations. The machine was to be powered by steam and comprised four components: the mill (akin to a modern CPU), the store (analogous to memory and storage), the reader (input device), and the printer (output device). Unfortunately, the Analytical Engine was never constructed, as its complexity exceeded the technological capabilities of the time.

Lovelace recognized the potential of Babbage's vision and sought to inspire others to appreciate it as well. While seeking support for his ideas, Babbage agreed to present at the Congress of Italian Scientists in Turin. Among the attendees was a young engineer, Captain Luigi Menabrea, who later became Italy's prime minister. In 1842, Menabrea published a French account of the machine's workings.

Encouraged by her peers, Lovelace translated Menabrea's article for 'Scientific Memoirs', a scientific publication. This opportunity allowed her to assist Babbage and showcase her abilities.

Upon completing the translation, she informed Babbage, who suggested she enhance it with additional notes. Lovelace's 'Notes by the Translator' ultimately became twice as extensive as the original article.

These notes gained significant recognition, establishing Lovelace as a vital figure in computing history.

In her notes, Lovelace explored several key concepts:

The first was distinguishing the Difference Engine from the Analytical Engine. While the former was designed for computing nautical tables, the latter was intended to perform any function, resembling modern general-purpose computers.

Secondly, Lovelace understood that the machine's operations could extend beyond mere numbers to encompass symbols like words and musical notes. This foundational idea for the digital age proposed that any content—be it data, music, text, images, or video—could be expressed and processed digitally. While Babbage focused on numerical calculations, Lovelace made the leap to broader computational concepts.

Her third insight involved detailing what we now refer to as computer programming or algorithms. She crafted a program to compute Bernoulli numbers, outlining a sequence of operations and a chart for coding each operation into the machine. This program included subroutines and recursive loops, all made possible through punch cards.

Lastly, Lovelace pondered the question of whether machines could think. Her conclusion was no: “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.”

Babbage's plans for the Analytical Engine remained obscured until the discovery of his notebooks in 1937. In 1991, the London Science Museum constructed a working model of Babbage's Difference Engine No. 2, incorporating improvements he envisioned while developing the Analytical Engine.

The first video titled "Babbage's Analytical Engine - Computerphile" provides an insightful overview of Babbage's revolutionary machine and its significance in the history of computing.

The second video, "Charles Babbage and Ada Lovelace: Early Computing | Heroes of Progress | Ep. 49," dives into the contributions of both Babbage and Lovelace in shaping the early landscape of computing.