A bit on the side.

One of the joys of the world of blogging is the guest post. The Renaissance Mathematicus has provided cyberspace to a couple of excellent guest posts in the past and hopes to attract some more in the future.

As many readers will know, because I keep repeating it, I actually guest blogged at the excellent Evolving Thoughts blog of John Wilkins (@john_s_wilkins) the Albino Aussie Anthropoid^TM as well as the equally excellent Ether Wave Propaganda of Will Thomas (@GWilliamThomas) before I started up this little endeavour. Later I did a series of guest posts on the guest blog of the Scientopia collective.

Now my wandering eye has struck again and I have indulged in a little tickle on the side with a guest post at the fascinating Recipes Project blog (@historecipes). If you are dying to know how to differentiate between Mucardinus avellanarius and Glis glis and how to stuff the latter the Roman way then wander on over and take a look.

Out to Lunch!

Hurricane force winds allowing I shall be making a flying visit to England on the coming weekend. On Monday 19^th December I shall be in London for the day on my way back to Germany and I will be lunching with Rebekah “Becky” Higgitt  and possibly her colleague Richard Dunn in Greenwich. Any readers of the Renaissance Mathematicus who are in London and who have time would be very welcome to join us; if you want to come leave a message in the comments or send me an email.

Multiplying the Renaissance way

At the always excellent Ptak Science Books blog John Ptak has a nice post about Renaissance multiplication 9876 X 6789 = 67048164 in which he was unable to work out the algorithm used to carry out the multiplication. In the following I show the example from John’s blog as it was displayed followed by the correct form with working method.

Multiplication the Diamond

9876

6789

81

484948

4242

54565654

7272

636463

36

67048164

The Diamond done correctly:

9876

6789

36

4242

484948

54565654

636463

7272

81

67048164

From left to right lower row L1,L2,L3,L4

From left to right upper row U1,U2,U3,U4

Method:

Row 1: L1 X U4

Row 2: L1 X U3, L2 X U4

Row 3: L1 X U2, L2 X U3, L3 X U4

Row 4: L1 X U1, L2 X U2, L3 X U3, L4 X U4

Row 5: L2 X U1, L3 X U2, L4 X U3

Row 6: L3 X U1, L4 X U2

Row 7: L4 X U1

Then sum vertically from right to left

Write 4

8+5+3=16 write 6 carry 1

1+2+4+6+6+2=21 write 1 carry 2

2+6+4+9+5+4+7+1=38 write 8 carry 3

3+3+2+4+6+6+2+8=34 write 4 carry 3

3+4+8+5+3+7=30 write 0 carry 3

3+4+4+6=17 write 7 carry 1

1+5=6 write 6

Added 11/11: Also motivated by John Ptak, Ray Girvan at Journal of a Southern Book Reader has a really good poston the subject of these Renaissance multiplication algorithms, definitely recommended reading.

History Blog Carnival: The All Saints Eclectic Edition.

Today the Renaissance Mathematicus is breaking out of its shell, at least temporarily, to explore new horizons outside of the narrow boundaries of the history of science in the wide-open waters of general history. A historian of science must of course be, in the first instance, a historian and I had a deep passion for history long before I had ever heard of the history of science. I also worked for a number of years as a professional field archaeologist so it is with great pleasure that I am hosting the latest edition of the History Blog Carnival. Eclecticism is the guiding principle of all aspects of my life and so I have strived to put together an as widely eclectic edition as possible.

We come out of the starting gate with Natalie Bennett of Philobiblon who shares with us her views on Women fighting political, scientific and literary exclusion.  Staying with women for the moment we travel to The Cotswolds where Nell Darby introduces us to the birth of triplets to a farmers wife in 1735. Returning to women’s politics, this time in 19^th century America, as The Thoroughly Anglophile Journal takes us to Seneca Falls and the First Women’s Rights Convention from 1848. It’s about Time offers us Artist Joseph Blackburn’s view of 18^th century American women. Written in Bone at the Smithsonian helps us to identify a 17^th century American women who was Buried in a Lead Coffin. Rebecca Price at Chick History introduces us to the Female Mystic who Inadvertently wrote the First English Autobiography!

Pausing in the 19^th century Building 19^th century Ireland offers us some thoughts on the encroaching Dickens bicentennial “Please, Sir, I want some more.” Going back a century Georgian Gentleman introduces us to the London of Mr Downing and his street. We stay in London for London Historians’ account of the 1814 London Beer Flood. One of my favourite blogs The Quack Doctor takes on a tour of Mr Rackstrow’s Museum in Fleet Street in the 18^th century. After beer floods, museums and Downing Street we are now treated to a brief history of the pineapple in London by the always excellent Lucie Inglis at The Food Bugle.

An Extraordinary Incident brings us a contemporary account of the death of Nelson at Trafalgar. The V&A Museum blog delivers a fascinating account of the history of kimono design. You need a fan to go with that kimono? Susan at Life Takes Lemons takes us on a tour of Ringling Museum Ladys’ Fans. With a swift change of topic and venue John Ptak of the scientific bookshop talks about the history of Blank Empty and Missing Things as displayed in one of my favourite books the Nuremberg Chronicles from 1493. Romeo Vitelli at Providentia presents The Strange Case of Phineas Gage whilst Anthony Vaver at Early American Crime tells the tale of Owen Syllavan’s Bunker. Art historian Hasan Niyazi at Three Pipe Problem investigates La Belle Jardinère – A Raphael case study. Mageret Makepeace of British Library Untold Lives visits Napoleon on St Helena in Napoleon-du pain, du vin… Jason at Executed Today offers the sombre topic of the 1964 execution of the 17-year-old Vietnamese communist Nguyen Van Troi for the attempted assassination of Robert McNamara. XBradTC at Bring the Heat gives a running commentary on the Battle of Agincourt from Oct 25 1415. A more modern war in France is presented by Fiona Robinson from Ghosts of 1914 with her post Teatime in the Trenches. K Meyers at Bones Don’t Lie brings Skeletal Evidence of a War in Peru. M. H. Beals at Demography and the Imperial Public Sphere before Victoria offers his thoughts on Stealing from the Provincial Press. John Levin from Alsatia takes us far a field with his post Sanctury outside England: Iran. The History Reporter Tiffany Dziurman Stozicki introduces us to the Russian pianist Ossip Gabrilowitsch and his wife Clara in early 20^th century Detroit. Judith Weingarten at Zenobia: Empress of the East presents A Muscular Christian in Palmyra. Lindsey Fitzharris the fascinatingly gruesome Chirurgeon’s Apprentice delivers The Final Indignity: Dissecting the Criminal Body. Natalie Bennett at Philobiblon having opened the month’s nominations almost closes it with her An alternative world history, with the nation state on the outside.

For those who prefer their history in pictures we have a Photo Essay: History of the Travelling Circus. The Yale Law Library serves up a pictorial digest of Justice as a Sign of the Law.

A History Blog Carnival on the 1^st of November must include something on Halloween and Jane Winters at IHR History puzzles over the rarity of Halloween in the historical documentation in Invisible Halloween. For Halloween Michelle Ziegler at Heaven Field dug Ireland 896 Vermin Invasion out of her archives. The Halloween contribution of An Extraordinary Incident has the intriguing title A small matter of being possessed of blood imbibing vampires.  Sir Thopas of Pure Medievalry closes this edition of the History Blog Carnival by wishing us a Happy Halloween with a medieval ghost story in original Middle English! (with translation )

I hope you have enjoyed our romp through the history blog posts of the last month and I’m sure you will find enough to read until I find time to post something new myself. But as you are here you’re are welcome to take a look around and see if you can find anything to your tastes amongst my scribblings.

Christie’s Law

I think we need a new rule for Internet discussions on the history of science.

I present Christie’s Law:

In any Internet history of science discussion on the relationship between religion and science the first person to invoke the Galileo Affair has lost.

Lynch‘s Corollary:

Anyone who compares themselves (or others) to Galileo or Bruno in said debate should be burnt at the stake.

Ich bin ein Gastblogger II: The wrong question

I’m an alien

I’m a legal alien

I’m an Englishman in Nürnberg

Being an English historian of mathematics resident in Germany I have been often asked, over the years, by people who know a little about the history of mathematics, “Who invented the calculus, Newton or Leibniz?” This is probably the most famous argument about priority of discovery and possible plagiarism in the history of science and still able to provoke nationalist sensibilities 300 years after the fact. Now as I mentioned in my first post this was the first theme in the history of mathematics that caught my attention and over the years I have devoted a considerable amount of time and effort to investigating the subject. There are two possible answers to the question….

Where I am at this moment.

Jerry the Builder from the Waterfall

Today we don’t have an obscure Renaissance mathematician but rather an obscure Renaissance physician. Now on this blog this usually means that we are either in Leiden or Padua and today it’s the later. It’s an oft-repeated fact that Andreas Vesalius published his De fabrica in the same year as Copernicus his De revolutionibus leading many people to consider that year, 1543, to be the start of the so-called scientific revolution. Whatever the case maybe, Vesalius’ book marks the beginning of the Paduan school of anatomy an institution that over more than 100 years contributed immensely to the development of the life sciences in general and medicine in particular. Called to the post of personal Imperial physician shortly after the publication of his groundbreaking work Vesalius was succeeded by Realdo Colombo who achieved fame by criticising Vesalius in the same way as Vesalius had criticised Galen finding and correcting many errors in the De fabrica. He did not stay long in Padua moving first to Pisa and then to the Sapienza in Rome where he stayed in bitter enmity to Vesalius till his death. His successor in Padua was the physician Gabriella Falloppia who continued Colombo’s improvements on the work of Vesalius and who is most notable in the history of medicine for his description of the uterine tubes, which bear his name.

Falloppia was succeeded by his own pupil the splendidly named Hieronymus Fabricius ab Aquapendende the Latinised version of his Italian name Girolamo Fabrizi d’Aquapendente, which can be roughly translated as Jerry the Builder from the Waterfall. Born in the 20^th May 1537 in the town of Aquapendente Fabricius, a neo-Aristotelian, is notable in the history of the life sciences for several reasons. Firstly he changed the style of illustration in his work from the highly artistic style favoured by Vesalius and his followers to a neutral, sober scientific style. Secondly he was the first of the ‘modern’ anatomist to move away from a pure human medicine to a comparative anatomy thereby laying the foundations for the development of zoology as a modern discipline. In his work he produced the first systematic study of the development of embryos, working on chicken embryos. In human medicine he gave the first scientific investigation and description the ‘valves’ in the interior of veins. However Fabricius was eclipsed in his work by his most famous pupil William Harvey.  Harvey took up and extended his teachers work on the development of the embryo and most famously incorporated Fabricius’ work on the vein valves into his epochal work on the blood circulation. Like his teacher Harvey was a neo-Aristotelian putting a lie to the myth that the scientific revolution was a result of scientists rejecting the influence of Aristotle.

If somebody asks you why the blood doesn’t flow backwards in your veins then you can tell them that your veins are lined with small valves whose working was first described in the 17^th century by Jerry the Builder from the Waterfall.

A Life on the Ocean Waves.

The latest edition of The Giant’s Shoulders has emerged above the waves at Deep-Sea News under the special edition title of Leviathan’s Shoulders. Swim over and dive in.

Bertie’s Dream

Today’s birthday boy is a mathematician but he is not from the Renaissance and anything but obscure, he is Betrand Arthur William 3^rd Earl Russell known to the world of academia as Mr Russell and to his friends as Bertie. An intellectual giant who straddled the 20^th century, he was born 18^th May 1870 and died aged 97 2^nd February 1970. His Wikipedia article lists him as philosopher, logician, mathematician, historian, socialist, pacifist and social critic missing out popular author and educationalist; Russell left an intellectual heritage that touched almost areas of human existence. To produce a potted biography of Russell here would be literally impossible and I don’t intend to try I will just make a few remarks about Russell the logician.

I paid my dues as a historian of science working in a research project on the history of formal logic and Russell, of course, loomed large on the horizon no matter in which direction one looked as a logic historian. A mathematical graduate of Cambridge University Russell was inspired by a meeting with the Italian mathematician Giuseppe Peano at the International Philosophy Conference in Paris in 1900 and set out deduce the whole of mathematics from the axiom of formal logic in order to avoid the foundational crises into which mathematics had been plunged by the set theoretical antinomies generated by Cantorian set theory. Unbeknown to Russell at that point the German mathematician Gottlob Frege was already engaged in the same project. Unfortunately Russell torpedoed both his own and Frege’s efforts with the discovery of the so-called Russell’s paradox in 1901. Russell’s own presentation of the paradox in simple language is the question, ‘in a village where the barber shaves all of those who do not shave themselves who shaves the barber?’ If the barber shaves himself then he doesn’t shave himself however if he doesn’t shave himself then he as the barber must shave himself. Applied to infinite set theory the paradox torpedoes all attempts to define numbers in terms of sets, the basis of both Russell’s and Frege’s work. Russell’s solution to the problem was type theory just one of the monuments that he raised to himself in his long and fruitful life.

Russell presented his logically founded mathematics together with Alfred North Whitehead, who was actually the principle author, in the three volume Principia Mathematica (1910, 1912, 1913). The Cambridge University Press was convinced that the book would be a financial flop and set the price accordingly and only printed 750 copies. However the first edition sold out and they actually made a profit on what is probably the most unreadable ‘best seller’ of all times. A second edition was issued in 1925. Although probably inferior to Frege’s own Grundgesetze der Arithmetik PM set the standard for symbolic mathematical logic because Frege’s two-dimensional Begriffschrift was regarded as incomprehensible by most readers.

Somewhere in his autobiographical writings Russell tells the following story about PM. He has a recurring dream that takes place at some undefined point in the future. He is in a library and a librarian is walking along the stacks selecting books from the selves that are to be deleted and throwing them into a bucket. As Russell watches he reaches the last copy of PM in the world and stops, at this point Russell wakes from his dream…

All fame is transitory.