Santayana and chemistry

The philosopher George Santayana (1863-1952), whom I have written about before, was fortunate to have two families, one Spanish and one American.  His mother was a widow when she married his father, and his parents later preferred to live in different countries – the USA and Spain, respectively.  Santayana spent part of his childhood with each, and accordingly grew up knowing his Bostonian step-family and their cousins, relatives of his mother’s first husband, the American Sturgis family.   Among these relatives, his step-cousin Susan Sturgis (1846-1923)  is mentioned briefly in Santayana’s 1944 autobiography (page 80). (See Footnote #1 below.)

Susan Sturgis was married twice, the second time in 1876 to Henry Bigelow Williams (1844-1912), a widower and property developer.   In 1890, Williams commissioned a stained glass window from Louis Tiffany for the All Souls Unitarian Church in Roxbury, Massachusetts (pictured below), to commemorate his first wife, Sarah Louisa Frothingham (1851-1871).

The first marriage of Susan Sturgis was in 1867, to Henry Horton McBurney (1843-1875).  McBurney’s younger brother, Charles Heber McBurney (1845-1913) went on to fame as a surgeon, developer of the procedure for diagnosis of appendicitis and removal of the appendix.  The normal place of incision for an appendectomy is known to every medical student still as McBurney’s Point.    The portrait below of Charles Heber McBurney was painted in 1911 by Ellen Emmet Rand (1875-1941), and is still in the possession of the McBurney family.  (The painting is copyright Gerard McBurney 2013.   As Ellen Emmet married William Blanchard Rand in 1911, this is possibly the first painting she signed with her married name.)
McBurney-Charles-Heber-1911-Ellen-Emmet-Rand-jpg
Charles H. McBurney was also a member of the medical team which treated US President William McKinley following his assassination.  He and his wife, Margaret Willoughby Weston (1846-1909), had two sons, Henry and Malcolm,  and a daughter, Alice.    The younger son, Malcolm, also became a doctor and married, having a daughter, but he died young.   Alice McBurney married Austen Fox Riggs (1876-1940), a protege of her father, Charles, and a pioneer of psychiatry.  He founded what is now the Austen Riggs Centre in Stockbridge, MA, in 1907.   They had two children,  one of whom, Benjamin Riggs (c.1914-1992), was also a distinguished psychiatrist, as well as a musician, sailor, and boat builder.

The elder son of Charles and Margaret, Henry McBurney (1874-1956), was an engineer whose own son, Charles Brian Montagu McBurney (1914-1979), became a famous Cambridge University archaeologist.  CBM’s children are the composer Gerard McBurney, the actor/director Simon McBurney OBE, and the art-historian, Henrietta Ryan FLS, FSA.   CBM’s sister, Daphne (1912-1997), married Richard Farmer.  Their four children were Angela Farmer, a yoga specialist, David Farmer FRS, a distinguished oceanographer, whose daughter Delphine Farmer, is a chemist,  Michael Farmer, painting conservator, and Henry Farmer, an IT specialist, whose son, Olivier Farmer, is a psychiatrist.

Henry H. and Charles H. had three sisters, Jane McBurney (born 1835 or 1836), Mary McBurney (1839- ), Almeria McBurney (who died young), and another brother, John Wayland McBurney (1848-1885).  They were born in Roxbury, MA, to Charles McBurney and Rosina Horton; Charles senior (1803 Ireland – Boston 1880) was initially a saddler and harness maker in Tremont Row, Boston  – the image above shows a label from a trunk he made.  Later, he was a pioneer of the rubber industry, for example, receiving a patent in 1858 for elastic pipe, and was a partner in the Boston Belting Company.    It is perhaps not a coincidence that Charles junior pioneered the use of rubber gloves by medical staff during surgery.

All three boys graduated from Harvard (Henry in 1862, Charles in 1866, and John in 1869). John married Louisa Eldridge in 1878, and they had a daughter, May (or Mary) Ruth McBurney (1879-1947).  May married William Howard Gardiner Jr. (1875-1952) in 1918, and on her death left an endowment to Harvard University to establish the Gardiner Professor in Oceanic History and Affairs to honour her husband.  John worked for his father’s company and later in his own brokerage firm, Barnes, McBurney & Co;  he died of tuberculosis.

Mary (or Mamie) McBurney married Dr Barthold Schlesinger (1828-1905), who was born in Germany of a Jewish ethnic background, and immigrated to the USA possibly in 1840, becoming a citizen in 1858.  For many years, from at least 1855, he was a director of a steel company, Naylor and Co, the US subsidiary of leading steel firm Naylor Vickers, of Sheffield, UK.    Barthold’s brother, Sebastian Benson Schlesinger (1837-1917), was also a director of Naylor & Co from 1855 to at least 1885; he was also a composer, mostly it seems of lieder and piano music; some of his music has been performed at the London Proms.  At the time, Naylor Vickers were renowned for their manufacture of church bells, but in the 20th century, under the name of Vickers, they became a leading British aerospace and defence engineering firm;  the last independent part of Vickers was bought by Rolls-Royce in 1999.

Mary and Barthold Schlesinger appear to have had at least five children, Mary (1859- , married in 1894 to Arthur Perrin, 1857- ), Barthold (1873- ), Helen (1874- , married in 1901 to James Alfred Parker, 1869- ), Leonora (1878- , married in 1902 to James Lovell Little, c. 1875- ), and Marion (1880- , married in 1905 to Jasper Whiting, 1868- ).   The Schlesingers owned an estate of 28 acres at Brookline, Boston, called Southwood.   In 1879, they commissioned landscape architect Frederick Law Olmstead (1822-1903), the designer of Central Park in New York and Prospect Park in Brooklyn, to design the gardens of Southwood;    some 19 acres of this estate now comprises the Holy Transfiguration Monastery, of the Greek Orthodox Church of North America.   The Schlesingers were lovers of art and music, and kept a house in Paris for many years.  An 1873 portrait of Barthold Schlesinger by William Morris Hunt (1824-1879) hangs in the Museum of Fine Arts in Boston.

While a student at Harvard, Henry H. McBurney was a prominent rower.   After graduation, he spent 2 years in Europe, working in the laboratories of two of the 19th century’s greatest chemists: Adolphe Wurtz in Paris and Robert Bunsen in Heidelberg.   Presumably, even Harvard graduates did not get to spend time working with famous chemists without at least strong letters of recommendation from their professors, so Henry McBurney must have been better than average as a chemistry student.    He returned to Massachusetts to work in the then company, Boston Elastic Fabric Company, of his father, and then, from November 1866, as partner for another firm, Campbell, Whittier, and Co.  From what I can discover, this company was a leading engineering firm, building in 1866 the world’s first cog locomotive, for example, and, from 1867, manufacturing and selling an early commercial elevator.

Henry H. and Susan S. McBurney had three children: Mary McBurney (1867- , in 1889 married Frederick Parker), Thomas Curtis McBurney (1870-1874), and Margaret McBurney (1873-, in 1892 married Henry Remsen Whitehouse).  Mary McBurney and Frederick Parker had five children: Frederic Parker (1890-), Elizabeth Parker (1891-), Henry McBurney Parker (1893-), Thomas Parker (1898.04.20-1898.08.30), and Mary Parker (1899-).  Margaret McBurney and Henry Whitehouse had a daughter, Beatrix Whitehouse (1893-).  The name “Thomas” seems to have been ill-fated in this extended family.

HH died suddenly in Bournemouth, England, in 1875, after suffering from a lung disease.   As with any early death, I wonder what he could have achieved in life had he lived longer.

POSTSCRIPT (Added 2011-11-21): Henry H. McBurney’s visit to the Heidelberg chemistry lab of Robert Bunsen is mentioned in an account published in 1899 by American chemist, Henry Carrington Bolton, who also worked with Bunsen, and indeed with Wurtz.   Bolton refers to McBurney as “Harry McBurney, of Boston” (p. 869).

POSTSCRIPT 2 (Added 2012-10-09): According to the 1912 Harvard Class Report for the Class of 1862 (see Ware 1912), Henry H. McBurney spent the year from September 1862 in Paris with Wurtz and the following year in Heidelberg with Bunsen.  He therefore presumably just missed meeting Paul Mendelssohn-Bartholdy (1841-1880), son of composer Felix, who graduated in chemistry from Heidelberg in 1863.   PM-B went on to co-found the chemicals firm Agfa, an  acronym for Aktien-Gesellschaft für Anilin-Fabrikation.   I wonder if  Paul Mendelssohn-Bartholdy ever returned to visit Bunsen in the year that Henry McBurney was there.

POSTSCRIPT 3 (Added 2013-01-20):  I am most grateful to Gerard McBurney for the portrait of Charles H. McBurney, and for additional information on the family.  I am also grateful to Henrietta McBurney Ryan for information.  All mistakes and omissions, however, are my own.

NOTE:  If you know more about any of the people mentioned in this post or their families, I would welcome hearing from you.   Email:  peter [at] vukutu.com

References:

Henry Carrington Bolton [1899]: Reminiscences of Bunsen and the Heidelberg Laboratory, 1863-1865.  Science, New Series Volume X (259): 865-870. 15 December 1899.  Available here.

George Santayana [1944]:  Persons and Places:  The Background of My Life. (London, UK:  Constable.) (New York, USA:  Charles Scribner’s Sons.)

Charles Pickard Ware (Editor) [1912]:   1862 – Class Report – 1912.  Class of Sixty-Two.  Harvard University.  Fiftieth Anniversary.  Cambridge, MA, USA,  Available here.

Footnotes:
1. Santayana writes as follows about Susan Sturgis Williams (Santayana 1944, page 74 in the US edition):

Nothing withered, however, about their sister Susie, one of the five Susie Sturgises of that epoch, all handsome women, but none more agreeably handsome than this one, called Susie Mac-Burney and Susie Williams successively after her two husbands.  When I knew her best she was a woman between fifty and sixty, stout, placid, intelligent, without an affectation or a prejudice, adding a grain of malice to the Sturgis affability, without meaning or doing the least unkindness. I felt that she had something of the Spanish feeling, So Catholic or so Moorish, that nothing in this world is of terrible importance. Everything happens, and we had better take it all as easily or as resignedly as possible. But this without a shadow of religion. Morally, therefore,  she may not have been complete; but physically and socially she was completeness itself, and friendliness and understanding. She was not awed by Boston. Her first marriage was disapproved, her husband being an outsider and considered unreliable; but she weathered whatever domestic storms may have ensued, and didn’t mind. Her second husband was like her father, a man with a checkered business career; but he too survived all storms, and seemed the healthier and happier for them. They appeared to be well enough off. In her motherliness there was something queenly, she moved well, she spoke well, and her freedom from prejudice never descended to vulgarity or loss of dignity. Her mother’s modest solid nature had excluded in her the worst of her father’s foibles, while the Sturgis warmth and amiability had been added to make her a charming woman.”

POST MOST RECENTLY UPDATED:  2013-03-26.

Impure mathematics at Cambridge

I have remarked before that the Mathematics Tripos at Cambridge, with its impure emphasis on the calculations needed for mathematical physics to the great detriment of pure mathematical thinking, understanding and rigor, had deleterious consequences across the globe more than a century later.  Even as late as the 1980s, there were few Australian university mathematics degree programs that did not require students to waste at least one year on the prehensile, brain-dead calculations needed for what is wrongly called Applied Mathematics.    I am still angered by this waste of effort.    Marx called traditions nothing more than the collected errors of past generations, and never was this statement more true.  What pure mathematician or statistician or computer scientist with integrity could stomach such nonsense?
I am not alone in my views. One of the earliest people who opposed Cambridge’s focus on impure, bottom-up, unprincipled mathematics – those three adjectives are each precisely judged – was Charles Babbage, later a computer pioneer and industrial organizer.  I mentioned his Analytical Society here, created while he was still an undergraduate.     Now, I have just seen an article by Harvey Becher [1995] which places Babbage’s campaign for Cambridge University to teach modern pure mathematics within its full radical political and nonconformist religious context.   A couple of nice excerpts from Becher’s article:

As the revolution and then Napoleon swept across Europe, French research mathematicians such as J. L. Lagrange and S. P. Laplace, and French textbook writers such as S. F. Lacroix, made it obvious that British mathematicians who adhered to the geometrically oriented fluxional mathematics and dot notation of Newton had become anachronisms.  The more powerful abstract and generalized analysis developed on the Continent had become the focus of mathematicians and the language of the physical sciences. This mathematical transmutation fused with social revolution.  ‘Lagrange’s treatises on the calculus were written in response to the educational needs of the Revolution’, recounts Ivor Grattan-Guinness, and Lagrange, Laplace and Lacroix were intimately involved with the educational and scientific reorganizations of the earlier revolutionaries and Napoleon.   Thus, French mathematics became associated with revolutionary France.
This confluence of social and mathematical revolution washed into the heart of Cambridge University because the main purpose of the Cambridge mathematics curriculum, as the core of a liberal education, Cambridge’s raison d’etre, was to produce [page-break] educated gentlemen for careers in the Church, the law and academe. With a student clientele such as this, few were disturbed that the Cambridge curriculum stuck to emphasizing Euclidean geometry, geometric optics and Newtonian fluxions, mechanics and astronomy. However, it was not the landed sons (who constituted the largest segment of the undergraduates), but the middle class and professional sons who, though a minority of the student body as a whole, made up the majority of the wranglers.   For them, especially those who might have an interest in mathematics as an end in itself rather than as merely a means to a comfortable career, the currency of the mathematics in the curriculum might be of concern.
Even though a Cambridge liberal education catered to a social/political elite, most nineteenth-century British mathematicians and mathematical physicists graduated from Cambridge University as wranglers. The Cambridge curriculum, therefore, contoured British mathematics, mathematical physics and other scientific fields. Early in the century, the mathematics curriculum underwent an ‘analytical revolution’ aimed at ending the isolation of Cambridge mathematics from continental mathematics by installing continental analytics in place of the traditional curriculum. Although the revolution began before the creation of the undergraduate constituted ‘Analytical Society’ in 1811, and though the revolution continued after the demise of that Society around 1817, the Analytical Society, its leaders – Charles Babbage, John Herschel and George Peacock – and their opponents, set the parameters within which the remodelling of the curriculum would take place.  This essay is an appraisal of their activities within the mathematical/social/political/religious environment of Cambridge.  The purpose is to reveal why the curriculum took the form it did, a form conducive to the education of a liberally educated elite and mathematical physicists, but not necessarily to the education of pure mathematicians.” [pages 405-406]

And later:

As Babbage and Herschel were radicals religiously and socially, they were radicals mathematically. They did not want to reform Cambridge mathematics; rather, they wanted [page-break] to reconstruct it. As young men, they had no interest in mixed mathematics, the focal point of Cambridge mathematics. In mixed mathematics, mathematics was creatively employed to achieve results for isolated, particular, sometimes trivial, physical problems. The mathematics created for a specific problem was intuitively derived from and applied to the problem, and its only mathematical relevance was that the ingenious techniques developed to solve one problem might be applicable to another. The test of mathematical rigour was to check results empirically. Correspondingly, mathematics was taught from ‘the bottom up’ by particular examples of applications.
Babbage’s and Herschel’s concerns lay not in mixed mathematics, but rather, as they put it in the introduction to the Memoirs, ‘exclusively with pure analytics’. In the Memoirs and other of their publications as young men, they devoted themselves to developing mathematics by means of the mechanical manipulation of symbols, a means purely abstract and general with no heuristic intuitive, physical, or geometric content. This Lagrangian formalism was what they conceived mathematics should be, and how it should be taught.  Indeed, they believed that Cambridge mathematicians could not read the more sophisticated French works because they had been taught analysis by means of its applications to the exclusion of general abstract operations. To overcome this, they wanted first to inculcate in the students general operations free of applications to get them to think in the abstract rather than intuitively.  On the theoretical level, they urged that the calculus ought not to be taught from an intuitive limit concept, to wit, as the derivative being generated by the vanishing sides of a triangle defined by two points on a curve approaching indefinitely close to one another; or by instantaneous velocity represented by the limit of time over distance as the quantities of time and distance vanished; or by force defined as the ultimate ratio of velocity to time. Rather, they urged that students start with derived functions of Lagrange, that is, successive coefficients of the expansion of a function in a Taylor Series being defined as the successive derivatives of the function. This was algebra, free of all limiting intuitive or physical encumbrances. It would condition the student to think in the abstract without intuitive crutches. And on the practical level, pure calculus, so defined, should be taught prior to any of its applications. To achieve this would have inverted the traditional Cambridge approach and revolutionized the curriculum, both intellectually and socially, for only a handful of abstract thinkers, pure mathematicians like Babbage and Herschel, could have successfully tackled it.   The established liberal education would have been a thing of the past.” [pages 411-412]

POSTSCRIPT (Added 2010-11-03):
I have just seen the short paper by David Forfar [1996], reporting on the subsequent careers of the Cambridge Tripos Wranglers.    The paper has two flaws.  First, he includes in his Tripos alumni Charles Babbage, someone who refused to sit the Tripos, and who actively and bravely campaigned for its reform.  Forfar does, it is true, mention Babbage’s non-sitting, but only a page later after first listing him, and then without reference to his principled opposition.  Second, Forfar presents overwhelming evidence for the failure of British pure mathematics in the 19th- and early 20th-centuries, listing just Cayley, Sylvester, Clifford, Hardy and Littlewood as world-class British pure mathematicians – I would add Babbage, Boole and De Morgan – against 14 world-class German and 17 world-class French mathematicians that he identifies.   But then, despite this pellucid evidence, Forfar can’t bring himself to admit the obvious cause of the phenomenon – the Tripos exam.  He concludes:  “The relative failure of British pure mathematics during this period in comparison with France and Germany remains something of a paradox.” No, Mr Forfar,  there is no paradox here; there is not even any mystery.    (En passant, I can’t imagine any pure mathematician using the word “paradox” in the way Forfar does here.)
Forfar says:  “While accepting these criticisms [of GH Hardy], it seems curious that those who became professional pure mathematicians apparently found difficulty in shaking off the legacy of the Tripos.” The years which Tripos students spent on the exam were those years generally judged most  productive for pure mathematicians – their late teens and early twenties.  To spend those years practising mindless tricks like some performing seal, instead of gaining a deep understanding of analysis or geometry, is why British pure mathematics was in the doldrums during the whole of the Georgian, Victorian and Edwardian eras, the whole of the long nineteenth century, from 1750 to 1914.
References:
Harvey W. Becher [1995]:  Radicals, Whigs and conservatives:  the middle and lower classes in the analytical revolution at Cambridge in the age of aristocracy.   British Journal for the History of Science, 28:  405-426.
David O. Forfar [1996]:  What  became of the Senior Wranglers?  Mathematical Spectrum, 29 (1).

In defence of secularism

Edmund Adamus, director of pastoral affairs at the Roman Catholic diocese of Westminster, London, is apparently upset at modern, liberal secular society, claiming (inter alia) that:

Our laws and lawmakers for over 50 years have been the most permissively anti-life and progressively anti-family and marriage, in essence one of the most anti-Catholic landscapes, culturally speaking – more than even those places where Catholics suffer open persecution.”

This is nonsense.  It was secularists – atheists, agnostics, non-believers, liberals, and anti-bigots – who led the campaign in Britain for Catholic emancipation, the right to vote, and the right to sit in Parliament, granted in 1829.   It was secularists who achieved the right for Jews to sit in Parliament from 1858 and the right to vote in 1867, something that the same political party currently ruling Britain stymied for a quarter century.  (The bill emancipating Jews passed the House of Commons in 1833, but was repeatedly blocked in the House of Lords by Conservative peers and bishops.  What reasonable person with knowledge of this history could belong to such a party?)  It was secularists, not the religious, who led the campaign which ended the deaths of women in illegal back-street abortions and gave equal rights to people regardless of their gender or colour or sexual orientation.  It was even  secularists who passed a law in 2001 – yes, 2001!  – that finally allowed Catholic priests and former priests to sit in the British Parliament.    If not for secularism and the progressive extension of political and social rights to all citizens, regardless of their religion or race or gender, Edmund Adamus would not even have the freedom of speech to voice his obnoxious opinions.
Few things make me angry.  Religious bigotry and racial prejudice are among them.  So too is this stupidity of religious conservatives, unable to see where there own self-interests lie.  Their interests are best served by a secular society and state which guarantees equal rights to all, not special rights to some on the basis of their religious beliefs or their gender or any other biological or social construct.  Britain is still not entirely there yet, with the fact of unelected, unrepresentative, and unaccountable Church of England Bishops still sitting in the House of Lords (and thus voting on legislation that impacts us all), and the country’s denial of religious freedom for the Head of State and his or her immediate family.  But the great progress in extending freedom to all that has been made these last 200 years is due to secularism and secularists, not to religious bigotry or obscurantism.

A computer pioneer

I have posted before about how the history of commercial computing is intimately linked with the British tea-shop, via LEO, a successful line of commercial computers developed by the Lyons tea-shop chain.  The first business application run on a Lyons computer was almost 60 years ago, in 1951.  Today’s Grauniad carries an obituary for John Aris (1934-2010), who had worked for LEO on the first stage of an illustrious career in commercial IT.  His career included a period as Chief Systems Engineer with British computer firm ICL (later part of Fujitsu).  Aris’ university education was in Classics, and he provides another example to show that the matherati represent a cast of mind, and not merely a collection of people educated in mathematics.

John’s career in computing began in 1958 when he was recruited to the Leo (Lyons Electronic Office) computer team by J Lyons, then the major food business in the UK, and initiators of the notion that the future of computers lay in their use as a business tool. At the time, the prevailing view was that work with computers required a trained mathematician. The Leo management thought otherwise and recruited using an aptitude test. John, an Oxford classics graduate, passed with flying colours, noting that “the great advantage of studying classics is that it does not fit you for anything specific”. “

Of course, LEO was not the first time that cafes had led to new information industries, as we noted here in a post about the intellectual and commercial consequences of the rise of coffee houses in Europe from the mid-17th century.  The new industries the first time round were newspapers, insurance, and fine art auctions (and through them, painting as a commercial activity aimed at non-aristocrat collectors); the new intellectual discipline was the formal modeling of uncertainty (then aka probability theory).

UPDATE (2012-05-22):  The Telegraph of 2011-11-10 ran an article about the Lyons Tea Shop computer business, here, to celebrate the 60th anniversary of the LEO (1951-11-17).

The DDR and the invasion of Czechoslovakia in 1968

In a recent post, I briefly reviewed Hans Kundnani’s fascinating book about the German left, Utopia or Auschwitz:  Germany’s 1968 Generation and the Holocaust.  I said that he had overlooked that the army of the DDR joined the Warsaw Pact forces which invaded the Czechoslovak Socialist Republic in August 1968.    It turns out I was wrong.

My apologies to Mr Kundnani, to whom I also owe the knowledge of this correction.   Although forces of the army of the DDR, the National People’s Army (NVA), did assemble near the border ready to invade, at the last moment their action was stayed.  The decision to stay them seems to have been made in the Kremlin on the advice of senior Czech communists who were supporting the invasion, a fact only confirmed recently.  Interestingly, it seems that during and subsequent to the invasion, the SED Government of the DDR never corrected reports which said that they had participated.

It was not until 2008, at an international joint project on the ‘Prague Spring’, that researchers from the Austrian Ludwig Boltzmann Institute in Graz, from Russian institutes and archives [sic] from other research institutions were able to provide a clear answer.  In Moscow they found previously unknown documentary evidence that the decision for the non-participation of the NVA in the invasion was indeed made on short notice by Soviet Party leader Leonid Brezhnev following requests by high-ranking Czechoslovak opponents of Dubcek.”  (Wenzke, p. 155)

References:
Rudiger Wenzke [2010]:   The role and activities of the SED, the East German State and its military during the “Prague Spring” of 1968. pp. 137-164 in:  M. Mark Stolarik (Editor): The Prague Spring and the Warsaw Pact Invasion of Czechoslovakia, 1968:  Forty Years Later. Illinois, USA: Mundelein.
Hans Kundnani [2009]:  Utopia or Auschwitz:  Germany’s 1968 Generation and the Holocaust. London, UK:  Hurst and Company.

The Matherati

Howard Gardner’s theory of multiple intelligences includes an intelligence he called Logical-Mathematical Intelligence, the ability to reason about numbers, shapes and structure, to think logically and abstractly.   In truth, there are several different capabilities in this broad category of intelligence – being good at pure mathematics does not necessarily make you good at abstraction, and vice versa, and so the set of great mathematicians and the set of great computer programmers, for example, are not identical.
But there is definitely a cast of mind we might call mathmind.   As well as the usual suspects, such as Euclid, Newton and Einstein, there are many others with this cast of mind.  For example, Thomas Harriott (c. 1560-1621), inventor of the less-than symbol, and the first person to draw the  moon with a telescope was one.   Newton’s friend, Nicolas Fatio de Duiller (1664-1753), was another.   In the talented 18th-century family of Charles Burney, whose relatives and children included musicians, dancers, artists, and writers (and an admiral), Charles’ grandson, Alexander d’Arblay (1794-1837), the son of writer Fanny Burney, was 10th wrangler in the Mathematics Tripos at Cambridge in 1818, and played chess to a high standard.  He was friends with Charles Babbage, also a student at Cambridge at the time, and a member of the Analytical Society which Babbage had co-founded; this was an attempt to modernize the teaching of pure mathematics in Britain by importing the rigor and notation of continental analysis, which d’Arblay had already encountered as a school student in France.
And there are people with mathmind right up to the present day.   The Guardian a year ago carried an obituary, written by a family member, of Joan Burchardt, who was described as follows:

My aunt, Joan Burchardt, who has died aged 91, had a full and interesting life as an aircraft engineer, a teacher of physics and maths, an amateur astronomer, goat farmer and volunteer for Oxfam. If you had heard her talking over the gate of her smallholding near Sherborne, Dorset, you might have thought she was a figure from the past. In fact, if she represented anything, it was the modern, independent-minded energy and intelligence of England. In her 80s she mastered the latest computer software coding.”

Since language and text have dominated modern Western culture these last few centuries, our culture’s histories are mostly written in words.   These histories favor the literate, who naturally tend to write about each other.    Clive James’ book of a lifetime’s reading and thinking, Cultural Amnesia (2007), for instance, lists just 1 musician and 1 film-maker in his 126 profiles, and includes not a single mathematician or scientist.     It is testimony to text’s continuing dominance in our culture, despite our society’s deep-seated, long-standing reliance on sophisticated technology and engineering, that we do not celebrate more the matherati.
On this page you will find an index to Vukutu posts about the Matherati.
FOOTNOTE: The image above shows the equivalence classes of directed homotopy (or, dihomotopy) paths in 2-dimensional spaces with two holes (shown as the black and white boxes). The two diagrams model situations where there are two alternative courses of action (eg, two possible directions) represented respectively by the horizontal and vertical axes.  The paths on each diagram correspond to different choices of interleaving of these two types of actions.  The word directed is used because actions happen in sequence, represented by movement from the lower left of each diagram to the upper right.  The word homotopy refers to paths which can be smoothly deformed into one another without crossing one of the holes.  The upper diagram shows there are just two classes of dihomotopically-equivalent paths from lower-left to upper-right, while the lower diagram (where the holes are positioned differently) has three such dihomotopic equivalence classes.  Of course, depending on the precise definitions of action combinations, the upper diagram may in fact reveal four equivalence classes, if paths that first skirt above the black hole and then beneath the white one (or vice versa) are permitted.  Applications of these ideas occur in concurrency theory in computer science and in theoretical physics.

AI's first millenium: prepare to celebrate

A search algorithm is a computational procedure (an algorithm) for finding a particular object or objects in a larger collection of objects. Typically, these algorithms search for objects with desired properties whose identities are otherwise not yet known.   Search algorithms (and search generally) has been an integral part of artificial intelligence and computer science this last half-century, since the first working AI program, designed to play checkers, was written in 1951-2 by Christopher Strachey. At each round, that program evaluated the alternative board positions that resulted from potential next moves, thereby searching for the “best” next move for that round.

The first search algorithm in modern times apparently dates from 1895:  a depth-first search algorithm to solve a maze, due to amateur French mathematician Gaston Tarry (1843-1913).  Now, in a recent paper by logician Wilfrid Hodges, the date for the first search algorithm has been pushed back much further: to the third decade of the second millenium, the 1020s, a thousand years ago. Hodges translates and analyzes a logic text of Persian Islamic philosopher and mathematician, Ibn Sina (aka Avicenna, c. 980 – 1037) on methods for finding a proof of a syllogistic claim when some premises of the syllogism are missing.

Representation of domain knowledge using formal logic and automated reasoning over these logical representations (ie, logic programming) has become a key way in which intelligence is inserted into modern machines; searching for proofs of claims (“potential theorems”) is how such intelligent machines determine what they know or can deduce. It is nice to think that automated theorem-proving is almost 990 years old.

References:

B. Jack Copeland [2000]:  What is Artificial Intelligence?

Wilfrid Hodges [2010]: Ibn Sina on analysis: 1. Proof search. or: abstract state machines as a tool for history of logic.  pp. 354-404, in: A. Blass, N. Dershowitz and W. Reisig (Editors):  Fields of Logic and Computation. Lecture Notes in Computer Science, volume 6300.  Berlin, Germany:  Springer.   A version of the paper is available from Hodges’ website, here.

Gaston Tarry [1895]: La problem des labyrinths. Nouvelles Annales de Mathématiques, 14: 187-190.

The long after-life of design decisions

Reading Natasha Vargas-Cooper’s lively romp through the 1960s culture referenced in the TV series Mad Men, I came across Tim Siedell’s discussion of a witty, early 1960s advert by Doyle Dane Bernbach for Western Union telegrams, displayed here

Seeing a telegram for the first time in about, oh, 35 years*, I looked at the structure.   Note the header, with information about the company, as well as meta-information about the message.   That structure immediately brought to mind the structure of a TCP packet.

The Transmission Control Protocol (TCP) is the work-horse protocol of the Internet, and was developed by Vince Cerf and Bob Kahn in 1974.   Their division of the packet contents into a header-part (the control information) and a data part (the payload) no doubt derived from earlier work on the design of packets for packet-switched networks.   Later packets (eg, for IP, the Internet Protocol) were simpler, but still retained this two-part structure.  This two-part division is also found in voice telecommunications at the time, for example in Common Channel Signalling Systems, which separated message content from information about the message (control information).   Such systems were adopted internationally by the ITU for voice communications from Signalling System #6 (SS6) in 1975 onwards.  In case the packet design seems obvious, it is worth considering some alternatives:  the meta-information could be in a footer rather than in a header, or enmeshed in the data itself (as, for example, HTML tags are enmeshed in the content they modify).  Or, the meta-data could be sent in a separate packet, perhaps ahead of the data packet, as happens with control information in Signalling System #7 (SS7), adopted from 1980.  There are technical reasons why some of these design possibilities are not feasible or not elegant, and perhaps the same reasons apply to transmission of telegrams (which is, after all, a communications medium using packets).
The first commercial electrical telegraph networks date from 1837, and the Western Union company itself dates from 1855 (although created from the merger of earlier companies).  I don’t know when the two-part structure for telegrams was adopted, but it was certainly long before Vannevar Bush predicted the Internet in 1945, and long before packet-switched communications networks were first conceived in the early 1960s.   It is interesting that the two-part structure of the telegramlives on in the structure of internet packets.
* Footnote: As I recall, I sent my first email in 1979.
Reference:
Tim Siedell [2010]: “Western Union:  What makes a great ad?” pp. 15-17 of:  Natasha Vargas-Cooper [2010]:  Mad Men Unbuttoned. New York, NY:  HarperCollins.

Recent reading 4: Achtundsechziger


While elements of the left turned to revolutionary violence in most countries of the West at the end of the 1960s, three countries experienced this turn to a much greater extent than any other:  Germany, Italy, and Japan.  This fact has always intrigued me.   Why these three?     What facts of history or culture link the three?  All three endured fascist totalitarian regimes before WW II, but so too did, say, Poland, Hungary, Greece, Portugal, and Spain.  The countries of Eastern Europe, however, met the 1960s still under the Soviet imperium, and so opportunities for violent resistance were few, and in any case were unlikely to come from the left.   Spain and Portugal and, for a time, Greece, were still under fascism in the post-war period, so opposition tended to aim at enlarging democracy, not at violent resistance.   Perhaps that history is a partial explanation, with (some of) the first post-war generation, the 68ers (in German, achtundsechziger) seeking by their armed resistance to absolve their shame at the perceived lack of resistance to fascism of their parents’ generation.  Certainly the writings of the Red Army Fraction (RAF), the Red Brigades, and the Japanese Red Army give this as a justification for their turn to violence.
I have always thought that another causal factor in common between these three countries was the absence of alternating left and right governments.  With a succession of right-wing and centre-right regimes in Italy and Japan, and right-wing and grand-coalition (right-and-left-together) regimes in Germany, how were views in favour of socialist change able to be represented and heard?  Indeed, in the German Federal Republic, the communist party had been declared illegal in 1956, and remained so until its reformation (under a new name) until 1968.   And even the USA may not be an exception to this heuristic:  In 1968, the candidate of the major party of the left, Hubert Humphrey, was a protagonist for the war in Vietnam (at least in public, and during the election campaign).  And while the candidate of the major party of the right, Richard Nixon, had promised during the campaign to end the war, once in office he intensified and extended it.   For anyone opposed to the war in Vietnam, the democratic political system appeared to have failed;  indeed, one of those who had most publicly opposed the war, Robert Kennedy, had been assassinated. It is interesting in this regard to note that the Weather Underground only adopted armed resistance as a strategy in December 1969, a year after Nixon’s election.   In Chantal Mouffe’s agonistic pluralism view of democracy, a key role of political argument and verbal conflict is to bring everyone into the political tent.  If some voices, or some views, are excluded by definition or silenced by assassination, we should not then be surprised that those excluded try to burn down the tent.
And perhaps because I like the idea of acting according to (an empirically-grounded) theory of history, I always found the primary argument of the RAF very intriguing:  That by engaging in armed resistance to the capitalist state, the revolutionary left would force the state to reveal its essential fascist character, and that this revelation would awaken the consciousness of the proletariat, leading to the revolutionary overthrow of the state. Although intrigued by it, I never found this argument quite compelling:  First, it could be argued that a democratic state only has a fascist character in response to, and to the extent of, armed resistance to it.  So predictions of its fascist tendencies become self-fulfilling.   Second, the history of countries ruled by fascism in the 20th century surely shows that life under totalitarian rule makes organizing and engaging in dissident activities, particularly group-oriented dissident activities, less not more feasible.     Third, I believe strongly that not only do ends not usually justify means, but often means vitiate ends.     This is the case here:  suppose the violent left’s violent resistance had indeed worked in overthrowing the governments they were directed at.  What sort of society would have resulted?   What we know of the personalities of Andreas Baader and Ulrike Meinhof and their revolutionary colleagues leads me to think that a Cambodia under the Khmer Rouges, rather than a Sweden under Olof Palme, would be a more likely description for life in a West Germany led by the RAF.  Thank our stars they failed.
These thoughts are provoked by some recent reading on the subject of leftist urban terrorism in the West, both fiction and non-fiction.  The fiction concerns the psychology and consequences of life underground, long after any thrill of plotting and executing armed resistance has passed.
First,  a novel about the Angry Brigade (AB), the lite, British version of the Red Army Fraction:  Hari Kunzru’s “My Revolutions”.   This is a gripping first-person account by someone who had participated in AB actions, and now, 30 years later, is living under an assumed name.  His past comes back to him, through some not-fully-explained, but dirty, tricks that British intelligence agencies seem to be running.  These dirty actions are (or rather, appear to be) targeted against those who were on the edges of the violent left, but not part of it, who have now risen to prominence in Government (Joschka Fischer comes to mind), and the narrator is used by the shadowy intelligence forces to blackmail or destroy the career of the target of the action.  The writing is fluent and plausible, and the tale engrossing.  Only occasionally does Kunzru trip:  Who ever uses “recurrent” (page 4) in ordinary speech?  (Some people may say “recurring”.)    Precisely how does the sun beat down like a drummer? (page 10).   But most of the novel reads as the words of the protagonist, and not the words of the novelist, indicating that a realistic character has been created by the author’s words.
The same cannot be said for Dana Spiotta’s “Eat the Document”.   Although this book too is riveting, it is not nearly as well-written as Kunzru’s book.   The story also concerns the later after-life of some formerly violent leftists, presumably once members of the Weather Underground, now living in hiding in the USA, incognito.   The story is told through the purported words of multiple narrators, a technique which enables the events to be described from diverse and interesting perspectives.  I say “purported” because too often the words and tone of different narrators sound the same.  In addition, often a narrator uses expressions which seem quite implausible for that particular narrator, as when the teenage boy Jason speaks of “recondite” personalities in suburbia (page 74):  these are not Jason’s words but those of the author.
These works of fiction are partly engrossing to me because I once unwittingly knew a former violent leftist on the lam – the Symbionese Liberation Army’s James Kilgore,  whom I knew as John Pape.  I wish I could say I’d always suspected him, but that is not the case.  Indeed, if anything, I suspected him of being a secret religious believer.  He was serious, always intense, and softly-spoken, and ideologically pure to the point of having no sense of humour. The Struggle was all, and life seemed to be all gravitas, with no levitas (at least in my interactions with him.  I have no idea how much of this serious demeanor  is or was his true self.)  Adopting a position as a committed revolutionary is certainly an interesting strategy for a cover;  one does not expect underground weathermen to be regular attenders at Trotskyist reading circles, but Pape was.  (And he did the homework!) But perhaps someone with a sense of humour does not join a movement of revolutionary violence in the first place, at least not in a democracy.
In the non-fiction category is Susan Braudy’s history of the Boudin family, one of whose members, Kathy Boudin, was a member of the Weather Underground.   As with Kunzru’s and Spiotta’s novels, this non-fictional account is also riveting.   It is, however, appallingly badly written. For instance, for a history, the book is very fuzzy about dates – when did Jean Boudin die, for example?  And much of the text reads like third-hand family anecdotes, perhaps interesting or amusing to the family but not to anyone else.  (Aunty Merle always was partial to rhubarb and once asked for it in a restaurant.)    And lots of very relevant information is simply not provided, for instance the prison sentences given to Kathy Boudin’s fellow-accused in 1981.   As a history book, this is certainly a book.
Finally, a quick report on Hans Kundnani’s superb analysis of the extreme German left, Utopia or AuschwitzGermany’s 1968 Generation and the Holocaust.  Kundnani argues that there were competing strains within the violent German left in the 1960s and 1970s:  one strain engaged in struggle (against capitalist and western imperialist injustice) as a form of remedy for the failure – or at least, the perceived failure – of their parents’ generation to resist Nazism, and other strains comprising German-nationalist and, suprisingly, even anti-semitic tendencies.    The presence of such tendencies at least explains how some on the far left in the 1960s ended up on the neo-Nazi right thirty years later.  Kundnani’s book is superb – interesting, well-written, humane, engrossing, and tightly-argued.  I had only one small quibble, which is perhaps a typo or an oversight:  On page 252, Kundnani refers to German military participation in a NATO-led attack on Serbian forces on 24 March 1999 as the “first time since 1945, Germany was at war.”  Well, the Federal Republic of Germany perhaps.   The DDR sent troups to join the Warsaw Pact invasion of the Czechoslovak Socialist Republic in August 1968.   If I was a former citizen of the DDR, regardless of my opposition to that invasion, I would be annoyed that my nation’s history seems to have been forgotten by people writing after unification on German history.
UPDATE (2010-08-25): My remark about participation by the DDR military in the Warsaw Pact invasion of the CSSR in 1968 is wrong.   The forces of the DDR were, at the last moment, stayed, as I explain here.    Thanks to Hans Kundnani for correcting me on this (see comment below).
References:
Bill Ayers [2001]:  Fugitive Days:  A Memoir. Boston, MA, USA:  Beacon Press.
Dan Berger [2006]:  Outlaws of America: The Weather Underground and the Politics of Solidarity. Oakland, CA, USA:  AK Press.
Susan Braudy [2003]:  Family Circle:  The Boudins and the Aristocracy of the Left. New York, NY, USA;  Anchor Books.
Uli Edel [Director, 2008]: Der Baader-Meinhof Komplex.  Germany.
Ron Jacob [1997]: The Way the Wind Blew:  A History of the Weather Underground. London, UK:  Verso.
Hans Kundnani[2009]:  Utopia or Auschwitz:  Germany’s 1968 Generation and the Holocaust. London, UK:  Hurst and Company.
Hari Kunzru[2007]:  My Revolutions.  London, UK:  Penguin.
Chantal Mouffe[1993]: The Return of the Political.  London, UK: Verso.
Dana Spiotta[2006]:  Eat the Document.  New York: Scribner/London, UK: Picador.
Tom Vague [1988/2005]:  The Red Army Faction Story 1963-1993.  San Francisco:  AK Press.
Jeremy Varon [2004]:  Bringing the War Home:  The Weather Underground, the Red Army Faction, and Revolutionary Violence in the Sixties and Seventies. Berkeley, CA, USA:  University of California Press.
Some previous thoughts on beating terrorism here.  Past entries in the Recent Reading series are here.

Agonistic planning

One key feature of the Kennedy and Johnson administrations identified by David Halberstam in his superb account of the development of US policy on Vietnam, The Best and the Brightest, was groupthink:  the failure of White House national security, foreign policy and defense staff to propose or even countenance alternatives to the prevailing views on Vietnam, especially when these alternatives were in radical conflict with the prevailing wisdom.   Among the junior staffers working in those administrations was Richard Holbrooke, now the US Special Representative for Afghanistan and Pakistan in the Obama administration.  A New Yorker profile of Holbrooke last year included this statement by him, about the need for policy planning processes to incorporate agonism:

“You have to test your hypothesis against other theories,” Holbrooke said. “Certainty in the face of complex situations is very dangerous.” During Vietnam, he had seen officials such as McGeorge Bundy, Kennedy’s and Johnson’s national-security adviser, “cut people to ribbons because the views they were getting weren’t acceptable.” Washington promotes tactical brilliance framed by strategic conformity—the facility to outmaneuver one’s counterpart in a discussion, without questioning fundamental assumptions. A more farsighted wisdom is often unwelcome. In 1975, with Bundy in mind, Holbrooke published an essay in Harpers in which he wrote, “The smartest man in the room is not always right.” That was one of the lessons of Vietnam. Holbrooke described his method to me as “a form of democratic centralism, where you want open airing of views and opinions and suggestions upward, but once the policy’s decided you want rigorous, disciplined implementation of it. And very often in the government the exact opposite happens. People sit in a room, they don’t air their real differences, a false and sloppy consensus papers over those underlying differences, and they go back to their offices and continue to work at cross-purposes, even actively undermining each other.”  (page 47)
Of course, Holbrooke’s positing of policy development as distinct from policy implementation is itself a dangerous simplification of the reality for most complex policy, both private and public, where the relationship between the two is usually far messier.    The details of policy, for example, are often only decided, or even able to be decided, at implementation-time, not at policy design-time.    Do you sell your new hi-tech product via retail outlets, for instance?  The answer may depend on whether there are outlets available to collaborate with you (not tied to competitors) and technically capable of selling it, and these facts may not be known until you approach the outlets.  Moreover, if the stakeholders implementing (or constraining implementation) of a policy need to believe they have been adequately consulted in policy development for the policy to be executed effectively (as is the case with major military strategies in democracies, for example here), then a further complication to this reductive distinction exists.
 
 
UPDATE (2011-07-03):
British MP Rory Stewart recounts another instance of Holbrooke’s agonist approach to policy in this post-mortem tribute: Holbrooke, although disagreeing with Stewart on policy toward Afghanistan, insisted that Stewart present his case directly to US Secretary of State Hilary Clinton in a meeting that Holbrooke arranged.
 
References:

David Halberstam [1972]:  The Best and the Brightest.  New York, NY, USA: Random House.
George Packer [2009]:  The last mission: Richard Holbrooke’s plan to avoid the mistakes of Vietnam in AfghanistanThe New Yorker, 2009-09-28, pp. 38-55.