Class began with Dr. Wagstaff telling us a bit more about herself. She grew up in a small town near Moab, Utah. Her undergraduate degree was in computer science at University of Utah; she followed that up with a graduate degree in computer science with a minor in Mars from Cornell University, and then worked in algorithm development for space programs at Johns Hopkins University Applied Physics Lab and finally JPL.

Dr. Wagstaff then directed us to the two following puzzles:
2, 6, 12, 20, 30, ?? = 42 = x^2+x
-3, 0, 15, 48, 105, ?? = 192 = x^3-4x

The easiest method to solve these puzzles was the one employed by Babbage’s Difference Engine No. 2: the first puzzle had a constant difference of differences (2) between each number, and the second puzzle had a constant difference of difference of differences (6). Each of these corresponded to a polynomial equation of the kind that the Difference Engine could solve. A crucial point was that in Babbage’s day, it was essential to have accurate tables of polynomials, logarithms and trigonometric functions for all kinds of calculations theoretical and practical, navigation, et cetera. This was the reason for Babbage including printing on paper and printing of plaster molds in his machine – so that the tables would never need to be copied by a human, and thus would remain reliable.

Another effect of Babbage’s desire for reliability was his demand for high quality machined parts. We discussed his disagreements with his engineer, Joseph Clement, and how most of the British government’s grant money likely ended up in the engineer’s pockets. Also mentioned was Babbage’s inability to be diplomatic, as related even in his autobiography – his funding dried up as he could not convince government officials such as the Chancellor of the Exchequer of the important of his machines. A side note to this was that a Swedish engineer, Per Georg Schultz, created a derivative Difference Engine for several governments – Sweden, England and eventually the United States. His engine was delivered over-budget but on time.

Babbage’s Difference Engine No. 2 was not fully completed until recently. We saw a video that detailed the course of his endeavors, from the first difference engine, and the analytical engine, to the complete and improved plans for the second difference engine. Most interestingly, this video featured many shots of the replica Difference Engine No. 2 in action.

Babbage’s Analytical Engine, however, has never been fully realized. The same video showed the ‘mill’ of the Analytical Engine, which Babbage’s son eventually completed. The mill was to be the area in which computations were done, as opposed to the ‘store’ of memory.

photo credit: http://www.zdnet.co.uk/i/z5/illo/nw/story_graphics/11mar/science-museum/science-museum-babbage.jpg

The Analytical Engine also incorporated three kinds of punched cards – operations, numbers, and variables (which were essentially addresses). This engine has never been completed, but a group at http://plan28.org/ is taking the first steps towards building it.

Class ended with a question to ponder: was Charles Babbage a success or a failure?