Charles Babbage

Without computers I wouldn't be writing this blog post, and you wouldn't be reading it.  Of course there are many other reasons why computers are important to us in this information age in which we live.  But we wouldn't have the technology that we have today and all that it provides us had it not been for the bright, curious, inventive people who went before us - people who dreamed dreams and worked hard to make them come true.  In the case of computers there is such a long line of dreamers from whom our technology sprung, people like John Napier, Blaise Pascal and Charles Babbage.

Mathematician Charles Babbage (1791-1871) is widely considered to be a father of the computer.  As well as being a mathematician he was an inventor, an engineer, and a philosopher - so basically a polymath.  The machine pictured above is his "Difference Engine," which was intended to automatically calculate values of polynomial functions using finite differences.

The model pictured at the top of this post and in the five pictures below is of his Difference Engine.  This one was built in the 1990s at the Science Museum in London.  Sadly it proved too costly to be built in Babbage's lifetime.  He poured his own fortune into it and also petitioned money from parliament, but eventually they got fed up with giving him more and more money and not seeing results.  Since it had not been built in his time, it was uncertain as to whether it would work, but this model and the other (which resides in Mountain View, California) do, indeed, work.  It even includes a printer!

The picture below is not part of the Difference Engine but rather part of another of Babbage's inventions, the Analytical Engine.  Whereas the Difference Engine was more of a calculating device, the idea behind the Analytical was that of more general computation, and that idea was a great leap forward.  It was a machine that could be programmed using punch cards.  What is displayed below is one small part of the machine that was completed by Babbage.  As far as I know a full Analytical Engine has never been built.

While it was Babbage who had the vision for constructing these machines, it was his "colleague" (for lack of a better term) Ada Byron Lovelace who had a broader vision for the use of such a machine.  Though it was not built, she wrote a program for it for calculating Bernoulli Numbers.  This is considered to be the first computer code.  It's quite something, given the views about women in math and science in the 19th century that it is a woman who wrote the first computer code!  I have a post on Ada from my previous sabbatical at this link.

Ada saw even beyond using this device for numerical calculation, however and wrote that the Analytical Engine "  .  .  .  might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine  .  .  .  Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent."

Ada died young, only 36, and Babbage grew old and crotchety.  He continued working on his plans until the end of his life, but after he died his work was mostly forgotten.  When programming began to be understood in the 1940s their work was rediscovered.  One of those who rediscovered them through their writings was Alan Turing, he of the Turing Test, Bletchley Park, and the Enigma Code - all of which you can read about at this link.

Though I did see the Difference Engine in the Science Museum during my last sabbatical, I chose to focus exclusively on Ada in writing about it.  This was in part because I had hoped to get to Babbage's grave-site in London at Kensal Green Cemetery, but I was running around so fast and furiously that this one site escaped me at that time (whereas I did get to see Ada's grave in Hucknall - next to that of her father Lord Byron).  This second sabbatical has given me a second chance, and I headed straight for Kensal Green Cemetery on the day I arrived in London in order to pay homage to this great and visionary man.  Here is the entrance to Kensal Green:

As I learned on my last sabbatical, it is very hard to find one specific grave in a large (old) cemetery - even when one has done one's research about its location and its features.

Looking  .  .  .  looking  .  .  .  looking  .  .  .

AHA!  This shape is familiar from images I've seen online.

Yes!  It is Babbage's grave!

Rest in peace - your work has lived on!  Your dream has changed the world!

Mathematical Gottingen

Mobius strip sculpture in front of Gottingen Observatory - once home to Gauss and then Dirichlet and then Riemann

Where to begin?!

Gottingen is absolutely bursting with mathematical history.  As I mentioned in my other post on Gottingen, it included the likes of Gauss, Dirichlet, Riemann, Clebsch, Klein, Hilbert, Minkowski, Noether, and Mobius.  It was THE most important place for mathematics in the world from the time of Hilbert and Klein in the last decades of the 1800s until just before 1933 (Hitler's advent as Chancelor of Germany - at which point he got rid of the Jews and the women from Gottingen University, so there was pretty much no one left to do mathematics).

Today (Friday, May 6, 2016) I had opportunity to meet with a professor from Gottingen,  Dr. Samuel James Patterson, to whom I am profoundly grateful for his having shown me around the Mathematisches Institut and its Collection of Mathematical Models and Instruments, of which he was previously curator.  I'm also grateful for all that he shared with me in conversation regarding the personalities of the famous mathematicians of Gottingen, the history of mathematics and physics in Gottingen, the history of the university and institute there, and for directing me toward points of interest that hadn't shown up in my research before I arrived.

Dr. Samuel James Patterson of the University of Gottingen

Mathematics Institute, Gottingen - from the front - the top of the "T" (Bunsenstrasse 3-5)

Mathematics Institute, Gottingen from the back

Aside - physicists as well as mathematicians were active in this building, and it was in this area out back where, through the conversations of these physicists, that quantum mechanics was born, so I felt it quite a stunning privilege to be here for multiple reasons!

Another view from the back - bottom of the "T"

The Collection of Mathematical Models and Instruments, which is housed on the second floor of the Mathematisches Institut, displays wonderfully the history of mathematical activity in Gottingen.  It stretches back to paper models of polyhedra and other mathematical shapes hand-made by Gauss's teacher in 1780 (paper being made differently then than now!) - continues through models made by Felix Klein (1849-1925) and into the mechanical calculator era - and all the way up to the present with a fractal clock and a screen showing computer-generated models!  A small sampling is given in the pictures below - beginning with the paper models of 1780.

The famous Mobius Strip

The next two images are of models that Klein himself made in order to visualize what he was studying.  These two images are followed by a video of these types of objects as they can be studied through today's technology.

The next two images are of Klein bottles - objects with interesting topological properties.  These do not date back to Klein but were donated to the collection somewhat recently by someone who noticed they did have a Klein bottle, which seemed to them a travesty!  

And let's just continue with a few more samples that I can't resist posting:

A Riemann Surface

Calculating Devices

This piece of the collection reminds me of my office!

The collection was begun by Felix Klein prior to the construction of the Mathematical Institute Building.  At that time it could be found in a corridor on the third floor of the Auditorienhaus, the center of mathematical activity at Gottingen at the time, where the famous mathematical library, the Lesezimmer, had been founded by Klein as well.  For more information and more pictures, see my post on David Hilbert.

Gottingen University Auditorienhaus

Back to the Mathematics Institute, there are pictures of famous Gottingen mathematicians lining the halls - 

Carl Friedrich Causs

Felix Klein

Bernhard Riemann

David Hilbert

Hermann Minkowski

Emmy Noether

 - as well as interesting posters outside offices of professors.

Do you know the story behind this?  Hint: it's located above a door.

As well as the Auditorienhaus and the Mathematisches Institut, another building in Gottingen associated with mathematics and mathematicians is the observatory.  It was home (successively) to Gauss, Dirichlet and Riemann. Each would have lived in rooms on the left as you face the front (the west side).

Observatory from the back (facing south)

Inside the back courtyard - facing southeast

Wing of the observatory where the living quarters would have been (west)

There were places relating to the history of mathematics wherever I looked in Gottingen.  The two images below are of the Gänseliesel, or "Little Goose Girl" fountain, which stands in front of the Rathaus (medieval town hall). It is a tradition of Gottingen University students to kiss her upon graduating with a Ph.D.

I found in my time in Gottingen that the mathematicians and physicists of the town are both highly honored and also taken a bit for granted.  Many Gottingen streets are named after mathematicians and physicists.  Homes where famous mathematicians lived bear plaques identifying them.  Other buildings also bear plaques in honor of mathematicians.  There are also statues and busts of famous mathematicians and physicists.  (Some of the pictures following, as well as others in the post, are repeated in other posts, but I want this to be complete, so I am including them more than once.  See posts on Hilbert and Gauss for more such pictures.)

Here are some examples of these items:

Home of Hermann Minkowski - colleague and best friend of David Hilbert

On the front of the Mathematics Institute

Yet for all the honor, they are also to some degree an everyday fact of life here.  First we see the bust of David Hilbert in the Mathematics Institute, as adorned by students studying nearby.  Then we see Gauss's grave, which I approached on pilgrimage, as if it were Mecca, and then found myself having to process the fact that people were picnicking in front of it!  I wish I could remember how Dr. Patterson put it exactly when I bemoaned this state of affairs to him - something along the lines of, "We always have Gauss with us."

Dr. Patterson explained to me that where Gauss is buried, which was once the Albani Cemetery is now part of a city park, Cheltenham-Park.  It is no longer used as a cemetery, and only the most prominent stone were left.

As you can imagine the town cemeteries are filled with famous mathematicians of the past.  Alfred Clebsh is buried in a small cemetery just north of the town center, not far from the Auditorienhaus.

And then there is the Stadtfriedhof or "city cemetery" just west of the town center, which contains the graves of many mathematicians and physicists and also contains a "Nobel Circle," an area honoring all the Nobel Prize winners associated with Gottingen.  I love how so many of the stones have formulas and equations on them!

If you know of a cemetery with more famous mathematicians, physicists and Nobel Prize winners, please let me know, because I'd love to visit it.  Here is the monument to the nobelists, the "Nobel Rondell":

I spent a lot of time in cemeteries during my travels - Greyfriars Kirkyard in Scotland, Highgate in London, Pere Lachaise in Paris, and many others - all were strikingly beautiful and profoundly interesting, but I found this one to be by far the most calming and peaceful to visit.

The "Nobel Rondell" is near this pond, and many of the nobelists are buried in this area.