Schicker's Calculating Machine
During the 16th to 19th century, people made great strides with mathematics, astronomy and engineering. We basically figured out during this period how to make machines that performed simple arithmetic. In 1623, Wilhelm Schickard invented what was the first calculator. This was used by Johannes Kepler to calculate orbital movements. I bet you didn’t know that!
Wilhelm Schickard

Gottfried Wilhelm von Leibniz
However, the first real calculating machines are credited to Gottfried Wilhelm Leibnitz
Blaise Pascal
and Blaise Pascal. Leibnitz may have been the first Computer Scientist - he developed a form of arithmetic with a base of 2 - binary. You will see how this is important in a minute. You have to read of Pascal as he accomplished so much yet died at 39. He was the scientific Mozart. In fact, in the 20th century, there was a popular programming language named after him!
Johannes Kepler

So, at the end of the 17th century, we have mechanical calculators and new ways of counting, binary, octal (base 8). In the 18th century, the major event that will lead to today is the work on Electricity. But it was only seen as a phenomena, it was not harnessed until 100 years later. Largely, this was because in the early 19th century, steam engines were invented, leading to new forms of transportation, and changing the world with the advent of the Industrial Revolution. Factories were built, agriculture was mechanized, and the lowly calculating machines were relegated to the role of cash registers and accounting help.

George Boole was probably the first English mathematician since the time of John Wallis who had also written upon logic. Speculations concerning a calculus of reasoning had at different times occupied Boole's thoughts, but it was not till the spring of 1847 that he put his ideas into the pamphlet called "Mathematical Analysis of Logic". Boole afterwards regarded this as a hasty and imperfect exposition of his logical system, and he desired that his much larger work, "An Investigation of the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities ", should be considered as containing a mature statement of his views.

He did not regard logic as a branch of mathematics, as the title of his earlier pamphlet might be taken to imply, but he pointed out such a deep analogy between the symbols of algebra and those which can be made, in his opinion, to represent logical forms and syllogisms, that we can hardly help saying that (especially his) formal logic is mathematics restricted to the two quantities, 0 and 1. (You can see where this is going?)

By unity Boole denoted the universe of thinkable objects; literal symbols, such as x, y, z, v, u, etc., were used with the elective meaning attaching to common adjectives and substantives. Thus, if x = horned and y = sheep, then the successive acts of election represented by x and y, if performed on unity, give the whole of the class horned sheep. Boole showed that elective symbols of this kind obey the same primary laws of combination as algebraic symbols, whence it followed that they could be added, subtracted, multiplied and even divided, almost exactly in the same manner as numbers. Thus, (1 – x) would represent the operation of selecting all things in the world except horned things, that is, all not horned things, and (1 – x) (1 – y) would give us all things neither horned nor sheep. By the use of such symbols propositions could be reduced to the form of equations, and the syllogistic conclusion from two premises was obtained by eliminating the middle term according to ordinary algebraic rules.

Still more original and remarkable, however, was that part of his system, fully stated in his Laws of Thought, formed a general symbolic method of logical inference. Given any propositions involving any number of terms, Boole showed how, by the purely symbolic treatment of the premises, to draw any conclusion logically contained in those premises. The second part of the Laws of Thought contained a corresponding attempt to discover a general method in probabilities, which should enable us from the given probabilities of any system of events to determine the consequent probability of any other event logically connected with the given events.

Boole's work (as well as that of his intellectual progeny) was relatively obscure, except among logicians. At the time, it appeared to have no practical uses. However, approximately seventy years after Boole's death, Claude Shannon attended a philosophy class at the University of Michigan which introduced him to Boole's studies. Shannon recognised that Boole's work could form the basis of mechanisms and processes in the real world, and it was therefore highly relevant. Shannon went on to write a master's thesis at the Massachusetts Institute of Technology, in which he showed how Boolean algebra could optimize the design of systems of electromechanical relays then used in telephone routing switches. He also proved that circuits with relays could solve Boolean algebra problems. Employing the properties of electrical switches to process logic is the basic concept that underlies all modern electronic digital computers. Victor Shestakov at Moscow State University (1907–1987) proposed a theory of electric switches based on Boolean logic even earlier than Claude Shannon in 1935 (but its acceptance was delayed due to certification of Soviet logicians and mathematicians). Hence Boolean algebra became the foundation of practical digital circuit design; and Boole, via Shannon and Shestakov, provided the theoretical grounding for the Digital Age.

The crater Boole on the Moon is named in his honour.

Charles Babbage
Charles Babbage along with Ada Lovelace were the most formative people in information technology in the 19th century. Babbage was born in London Dec. 26, 1791, in London. Babbage attended Trinity College, Cambridge where he knew Lagrange, Leibniz, Lacroix, but he was seriously disappointed about the math programs available at Cambridge. So he, with John Herschel and other friends, decided to form the Analytical Society.

First Design of Computers

In Babbage's time, there was a really high error rate in the calculation of math tables, and Babbage wanted to find a new mechanical method to remove the human error factor. He was heavily inspired from existing work on calculating machines produced by Schickard, Pascal, and Leibniz. Babbage presented something that he called "difference engine" to the
Royal Astronomical Society on Jun 14, 1822 in a paper entitled "Notes on the application of machinery to the computation of astronomical and mathematical tables."

It was able to calculate
polynomials by using a numerical method called the differences method.

Babbage's Difference Engine
The Society approved the idea, and the government granted him £1500 to construct it, in 1823. Babbage converted one of the rooms in his home to a workshop and hired Joseph Clement to oversee construction of the engine. Every part had to be formed by hand using custom machine tools, many of which Babbage himself designed. He took extensive tours of industry to better understand manufacturing processes. Based on these trips and his experience with the difference engine, Babbage published “On the Economy of Machinery and Manufacture” in 1832. It was the first publication on what we would now call Operations Research.

The death of Georgiana, Babbage's father, and an infant son interrupted construction in 1827. Work had already taxed Babbage heavily and he was on the edge of a breakdown. Herschel and several other friends convinced Babbage to take a trip to Europe to recuperate. He passed through the Netherlands, Belgium, Germany, and Italy visiting universities and manufacturing facilities.

The difference engine project had come under fire during Babbage's absence. Rumours had spread that Babbage had wasted the government's money; that the machine did not work; and that it had no practical value if it did. Herschel and the Royal Society publicly defended the engine. The government continued its support, advancing £1500 on April 29, 1829, £3000 on December 3, and £3000 on February 24, 1830. Work continued, but Babbage would have continual difficulty getting money from the treasury.

Babbage's problems with the treasury coincided with numerous disagreements with Clement. Babbage had built a two-story, 50 foot long workshop behind his house. It had a glass roof for lighting, and a fireproof, dust-free room to contain the machine. Clement refused to move his operations to the new workshop and demanded more money for the difficulty of travelling across town to oversee construction. In response, Babbage suggested that Clement draw his pay directly from the treasury. Before then, Babbage would get money from the government that he would use to pay Clement. He often had to pay Clement out of his own pocket when the bureaucracy lagged behind Clement's pay schedule. Clement refused the request and stopped working.

Clement further refused to turn over the drawings and tools used to build the difference engine. After an investment of £23,000, including £6000 of Babbage's own money, work on the unfinished machine ceased in 1834. Charles wrote, "The drawings and parts of the Engine are at length in a place of safety. I am almost worn out with disgust and annoyance at the whole affair." In 1842 the government officially abandoned the project.

The Analytical Engine

While he was separated from the difference engine, Babbage began to think about an improved calculating engine. Between 1833 and 1842 he tried to build a machine that would be programmable to do any kind of calculation, not just ones relating to polynomial equations. The first breakthrough came when he redirected the machine's output to the input for further equations. He described this as the machine "eating its own tail". It did not take much longer for him to define the main points of his analytical engine.

The mature analytical engine used punched cards adapted from the Jacquard loom to specify input and the calculations to perform. The engine consisted of two parts: the mill and the store. The mill, analogous to a modern computer's CPU, executed the operations on values retrieved from the store, which we would consider memory. It was the world's first general-purpose computer.

A design for this emerged by 1835. The scale of the work was truly incredible. Babbage and a handful of assistants created 500 large design drawings, 1000 sheets of mechanical notation, and 7000 sheets of scribbles. The completed mill would measure 15 feet tall and 6 feet in diameter. The 100 digit store would stretch to 25 feet long. Babbage constructed only small test parts for his new engine; a full engine was never completed. In 1842, following repeated failures to obtain funding from the First Lord of the Treasury, Babbage approached Sir Robert Peel for funding. Peel refused, and offered Babbage a knighthood instead. Babbage refused. He would continue modifying and improving the design for many years to come.

Ada Lovelace.

Who said all Programmers were geeks?
In October 1842, Federico Luigi, Conte Menabrea, an Italian general and mathematician, published a paper on the analytical engine. The young Augusta Ada King, Countess of Lovelace, known to everyone as Ada, (and was Lord Byron’s daughter -- you know, the poet), who was a longtime friend of Babbage, translated the paper into English. Charles suggested that she added notes to accompany the paper.

In a series of letters between 1842 and 1843, the pair collaborated on seven notes, the combined length of which was three times longer than the actual paper. In one note Ada prepared a table of execution for a program that Babbage wrote to calculate the Bernoulli numbers.

The Geek's Babe!!
In another paper, she wrote about a generalized algebra engine that could perform operations on symbols as well as numbers. Lovelace was perhaps the first to grasp the more general goals of Babbage’s machine, and some consider her the world's first computer programmer. She began work on a book describing the analytical engine in more detail, but it was never finished. She died of uterine cancer at 36 years old. She was the first Computer Programmer.“ Ada” was coined by the US Military Industrial Complex in the 1970s as a secretive programming language.

Second Difference Engine.

Between October 1846 and March 1849 Babbage started designing a second difference engine using knowledge gained from the analytical engine. It used only about 8000 parts, three times fewer than the first. It was a marvel of mechanical engineering.

The Difference Engine 2 Unlike the analytical engine that he continually tweaked and modified, he did not try to improve the second difference engine after completing the initial design. Babbage made no attempt to actually construct the machine.

The 24 schematics remained in the Science Museum archives until a full-size replica was built between 1985-1991 to celebrate the 200th anniversary of Babbage’s birth. It measured 11 feet long, 7 feet high and 18 inches deep, and weighted 2.6 tonnes. The limits of precision were restricted to those achievable by Babbage. Remarkably, it functioned perfectly.

Parts of Babbage's uncompleted mechanisms are available for visits in the
London Science Museum.