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 therefore 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.)
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]
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.
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.”


Herbert Hoover, zombie

I posted last week on Robert Skidelsky’s criticisms of the current British Government’s deflationary economic policy for lacking any rational theoretical underpinning.   Two Nobelistas have now joined the fray.  Here is Joe Stiglitz, writing about the apparent belief in a Confidence Fairy:

There is a shortage of aggregate demand – the demand for goods and services that generates jobs. Cutbacks in government spending will mean lower output and higher unemployment, unless something else fills the gap. Monetary policy won’t. Short-term interest rates can’t go any lower, and quantitative easing is not likely to substantially reduce the long-term interest rates government pays – and is even less likely to lead to substantial increases either in consumption or investment. If only one country does it, it might hope to gain an advantage through the weakening of its currency; but if anything the US is more likely to succeed in weakening its currency against sterling through its aggressive quantitative easing, worsening Britain’s trade position.
Of course if Britain succeeds in getting the world to believe that its economic policies are among the worst – an admittedly fierce contest at the moment – its currency may decline, but this is hardly the road to a recovery. Besides, in the malaise into which the global economy is sinking, the challenge will be to maintain exports; they can’t be relied on as a substitute for domestic demand. The few instances where small countries managed to grow in the face of austerity were those where their trading partners were experiencing a boom.
. . . .
Britain is embarking on a highly risky experiment. More likely than not, it will add one more data point to the well- established result that austerity in the midst of a downturn lowers GDP and increases unemployment, and excessive austerity can have long-lasting effects.
If Britain were wealthier, or if the prospects of success were greater, it might be a risk worth taking. But it is a gamble with almost no potential upside. Austerity is a gamble which Britain can ill afford.

And here is Paul Krugman, accusing the  British Government of being dedicated followers of fashion:

In the spring of 2010, fiscal austerity became fashionable. I use the term advisedly: the sudden consensus among Very Serious People that everyone must balance budgets now now now wasn’t based on any kind of careful analysis. It was more like a fad, something everyone professed to believe because that was what the in-crowd was saying.
. . . .
But trendy fashion, almost by definition, isn’t sensible — and the British government seems determined to ignore the lessons of history.
Both the new British budget announced on Wednesday and the rhetoric that accompanied the announcement might have come straight from the desk of Andrew Mellon, the Treasury secretary who told President Herbert Hoover to fight the Depression by liquidating the farmers, liquidating the workers, and driving down wages. Or if you prefer more British precedents, it echoes the Snowden budget of 1931, which tried to restore confidence but ended up deepening the economic crisis.
The British government’s plan is bold, say the pundits — and so it is. But it boldly goes in exactly the wrong direction. It would cut government employment by 490,000 workers — the equivalent of almost three million layoffs in the United States — at a time when the private sector is in no position to provide alternative employment. It would slash spending at a time when private demand isn’t at all ready to take up the slack.
Why is the British government doing this? The real reason has a lot to do with ideology: the Tories are using the deficit as an excuse to downsize the welfare state. But the official rationale is that there is no alternative.
Indeed, there has been a noticeable change in the rhetoric of the government of Prime Minister David Cameron over the past few weeks — a shift from hope to fear. In his speech announcing the budget plan, George Osborne, the chancellor of the Exchequer, seemed to have given up on the confidence fairy — that is, on claims that the plan would have positive effects on employment and growth.
Instead, it was all about the apocalypse looming if Britain failed to go down this route. Never mind that British debt as a percentage of national income is actually below its historical average; never mind that British interest rates stayed low even as the nation’s budget deficit soared, reflecting the belief of investors that the country can and will get its finances under control. Britain, declared Mr. Osborne, was on the “brink of bankruptcy.”
What happens now? Maybe Britain will get lucky, and something will come along to rescue the economy. But the best guess is that Britain in 2011 will look like Britain in 1931, or the United States in 1937, or Japan in 1997. That is, premature fiscal austerity will lead to a renewed economic slump. As always, those who refuse to learn from the past are doomed to repeat it.

Pity for all of us here, there’s no there there in current UK economic policy.

Cutting morality

When, in 2 or 5 or 25 years,  we look back on this strange, phony-war period of wasted economic opportunity, we will wonder why the lessons of the Great Depression – lessons that we know, and that we know that we know – are not being applied by those with the power to decide levels of Government spending:  Congress in the USA, the ConDem coalition in the UK, austeritarians everywhere.    The reasons for the drive to austerity cannot be ignorance, for we know full well that this policy is inappropriate in the present circumstances.   Here is Robert Skidelsky, economist and Keynes’ biographer, writing in the Financial Times this week (2010-10-13) showing the wrong-headed-ness of a policy of cutting spending in a recession:

David Cameron, Mr Osborne, and Nick Clegg appear to believe in something called “crowding out”. This is the view that for every extra pound the government spends, the private sector spends one pound less.  Jobs created by stimulus spending are jobs lost by the decline of private spending. Any stimulus to revive the economy is doubly damned: not only does it fail to stimulate, but, because government spending is less efficient than private, it reduces the economy’s longer term recovery potential.
Applied to the deficit, the “crowding out” thesis takes two forms. The first is “Ricardian equivalence’’. Government borrowing is simply deferred taxation, because it produces no revenue to pay for it. Households save more to pay the higher taxes they expect. This means that any extra income created by the deficit will be saved, not spent. Net stimulus: zero.
The other leg of the “crowding out” argument is that government borrowing causes interest rates to rise. There is a fixed lump of saving. The more the government borrows, the more private borrowers will have to pay for their loans.
A refinement of this argument is “psychological crowding out”. In this version it is not a shortage of saving, but a shortage of confidence in the government’s creditworthiness – due to a fear of default – which causes interest rates to rise. Either way the deficit “crowds out” private investment. Net stimulus: zero.
The supposed implication of this type of argument is that in the short-run the deficit can do no good; and that in the slightly longer term it harms the potential for recovery. What the cutters have to believe is that every pound of deficit reduction will be matched by an extra pound of private sector spending.  That is, if the government weren’t spending this money, the private sector would be, and making much better use of it. Mr Osborne’s programme is a beautiful cure for recession, provided there’s no recession to cure!
Keynesians do not deny the possibility of “psychological crowding out”: markets are subject to all kinds of irrational hopes and fears. But what the cutters mean by “crowding out” can normally only happen at full employment.  At full employment, extra public spending obviously subtracts from private spending. But this is not the position we are in today.
What Keynesians say is that when resources are unemployed, government borrowing is not deferred taxation: it brings resources into use that would otherwise be idle, and thus increases the government’s revenues without having to raise taxes. When the government borrows money for which there is no current business use, this increases people’s incomes and therefore the saving needed to finance the borrowing, without interest rates having to rise. And though confidence problems may occur even in an under-employed economy, the probability of the UK government defaulting on its debt is, if not zero, extremely low.
In short, the “crowding out” argument is false.  The problem is not the expansion of the deficit but the shrinkage of the economy. The deficit is the stimulant the economy needs to start growing again: its withdrawal guarantees stagnation or worse.”

With such knowledge, what forgiveness?  Ignorance of the appropriate macro-economic policy thus cannot be the reason for our political leaders adopting a policy of drastic cuts.  The reason for cutting now can only be a desire to reduce the total levels of Government spending to further some ideological agenda, regardless of the deleterious economic and social consequences of the policy.
In Britain, the Conservative and Unionist Party has prepared for this ideological moment for some time, despite appearances to the contrary.  In the period leading up to the June 2010 election, the Conservative party was awash with funds.  The party paid to place enormous campaign posters in central Liverpool, in the constituency of Liverpool Riverside, a constituency that has been held by the Labour Party since the constituency’s creation in 1983.  Liverpool Riverside was formed from constituencies which had been held by Labour since 1964 (Liverpool Toxteth, although for 2 years its MP was a Social Democrat), 1945 (Liverpool Exchange), and 1929 (Liverpool Scotland, before which it was held from 1885 by prominent Irish Nationalist, TP (aka “Tay Pay”) O’Connor).  In the election of June 2010, the Labour MP, Louise Ellman actually increased her share of the vote to 59%, and the Conservatives placed 3rd, with a mere 11% of the vote.   In other words, parts of Liverpool Riverside have not voted for the Conservative Party for more than 125 years, almost back to the time when the Party actively prevented Jewish emancipation.
Why would the Conservative and Unionist party waste large sums of money on campaign posters in a constituency it would never win?  The answer is in the content of the posters:  The posters were billboard size and showed a picture of Gordon Brown’s head with a slogan blaming him for increasing the national debt massively.   What they did not do was thank Brown for steering the economy successfully through the worst recession for 80 years, nor for saving millions from unemployment, nor for leading the G20 nations in policies to ensure the world did not suffer worse, nor for leading global efforts to re-regulate the financial sector to prevent a repeat of the events leading to the crash.   With such posters, the ground was being prepared for a push for austerity, even months before the election, and despite the warm and fuzzy noises of the Conservative leadership during the campaign itself.
These posters were the tendentious work of ideologues, intent on reducing the size of the state, regardless of any economic or social consequences, and undertaken with forethought.  Given the consequences of a policy of large cuts at the present time, and our knowledge of them, adopting such a deleterious policy is malicious and immoral, and shames all those who have promoted it.

Poetry as process, not product

I have remarked before on the mistake of assessing visual art as product rather than as process, for example, here and here.    Today’s Grauniad carries a fascinating article by poet and jazz musician Don Paterson on Shakespeare’s sonnets, which makes the same point about his poetry:

I wanted to say something to counteract the perception of Shakespeare’s compositional method as a kind of lyric soduku, and put in a word for the kind of glorious, messy procedure I’m quite certain it was, whatever the crystalline and symmetrical beauty of the final results. Like most poets, Shakespeare uses the poem as way of working out what he’s thinking, not as a means of reporting that thought. Often he’ll start with nothing more than a hangover, a fever and a bad night spent being tormented by the spectre of his absent lover. Then he’ll use the sonnet as a way of making sense of it all – a way, first, to extract a logic from pain, and then a comfort from that logic, however warped it might be. Form, in other words, allows him to draw some assuagement from the very source of the agony itself.”

Continue reading ‘Poetry as process, not product’

Chance would be a fine thing

Music critic Alex Ross discusses John Cage’s music in a recent article in The New Yorker.    Ross goes some way before he trips up, using those dreaded  – and completely inappropriate – words “randomness” and “chance”:

Later in the forties, he [Cage] laid out “gamuts” – gridlike arrays of preset sounds – trying to go from one to the next without consciously shaping the outcome.  He read widely in South Asian and East Asian thought, his readings guided by the young Indian musician Gita Sarabhai and, later, by the Zen scholar Daisetz Suzuki.  Sarabhai supplied him with a pivotal formulation of music’s purpose:  “to sober and quiet the mind, thus rendering it susceptible to divine influences.”  Cage also looked to Meister Eckhart and Thomas Aquinas, finding another motto in Aquinas’s declaration that “art imitates nature in the manner of its operation.”
. . .
In 1951, writing the closing movement of his Concerto for Prepared Piano, he finally let nature run its course, flipping coins and consulting the I Ching to determine which elements of his charts should come next.   “Music of Changes,” a forty-three-minute piece of solo piano, was written entirely in this manner, the labor-intensive process consuming most of a year.
As randomness took over, so did noise.  “Imaginary Landscape No. 4″ employs twelve radios, whose tuning, [page-break] volume, and tone are governed by chance operations.”  [pages 57-58]

That even such a sympathetic, literate, and erudite observer as Alex Ross should misconstrue what Cage was doing with the I Ching as based on chance events is disappointing.  But, as I’ve argued before about Cage’s music, the belief that the material world is all there is is so deeply entrenched in contemporary western culture that westerners seem rarely able to conceive of other ways of being.  Tossing coins may seem to be a chance operation to someone unversed in eastern philosophy, but was surely not to John Cage.
Alex Ross [2010]:  Searching for silence.  John Cage’s art of noise.   The New Yorker, 4 October 2010, pp. 52-61.
James Pritchett [1993]:  The Music of John Cage.  Cambridge, UK:  Cambridge University Press.
Here are other posts on music and art.

The writing on the wall

Over at Normblog, Norm tells us that he wants his books and not merely the words they contain.   We’ve discussed this human passion before:  books, unlike e-readers, are postcards from our past-self to our future-self, tangible souvenirs of the emotions we had when we first read them.   For that very reason – that they transport us through time – books aren’t going anywhere.  It’s a very rare technology indeed that completely eliminates all its predecessors, since every technology has something unique it provides to some users or other.   We could ask, for example, why we still carve words onto stone and why we still engrave names onto rings and pewter mugs for special occasions, when the invention of printing should have done away with those earlier text-delivery platforms, more expensive and less portable than books and paper?

Dynamic geometric abstraction

The Tate Modern Exhibition earlier this year on the art of Theo van Doesburg (1883-1931) and the International Avant-Garde included some sublime art by Bauhaus artist, Ludwig Hirschfeld-Mack (1893-1965).

These installations were computer-generated realizations of his originally-mechanical Farbenlicht-Spiel (Colourlight-Play) of 1921.   Hirschfeld-Mack’s concept, shown here, was a machine for producing dynamic images, images which slowly changed their colours and shapes.  The images were the projection onto a 2-dimensional surface of regular two-dimensional polygons (triangles, quadrilaterals, circles, ellipses, etc) moving, apparently independently, in planes parallel in the third dimension (the dimension of the projection), i.e., appearing to move closer to or further away from the viewer.  As the example below may indicate, the resulting images are sublime.  Computer generation of such dynamic images is, of course, considerably easier now than with the mechanical means available to Hirschfeld-Mack.

I have asked before what music is for.  I don’t know Hirschfeld-Mack’s intentions.  However, from my own experience, I know that watching this work can induce an altered mental state in its viewer, “sobering and quieting the mind, thus rendering it susceptible to divine influences,” in the words of Gita Sarabhai (talking about music).  The experience of watching this work is intensely meditative, akin to listening attentively to the slowly-changing music of Morton Feldman (1926-1987).

Hirschfeld-Mack was the only Bauhaus artist to end his career in Australia, a career Helen Webberley describes here.    His art is another instance of the flowering of geometric abstraction in art in the first three decades of the 20th century.  In the last decades of the 19th century and the early years of the 20th, there was widespread public interest in the ideas which had recently revolutionized the study of geometry in pure mathematics.  These ideas – the manifestation of postmodernism in pure mathematics a century before it appeared in other disciplines – first involved the rigorous study of alternatives to Euclidean geometry during the 19th century, a study undertaken when there still considerably ambiguity about the epistemological status of such alternatives, and then the realization (initially by Mario Pieri and David Hilbert in the 1890s) that one could articulate and study formal axiomatic systems for geometry without regard to any possible real-world instantiation of them.  Geometry was no longer being studied in order to represent or model the world we live in, but for its own sake, for its inherent mathematical beauty and structure.

At the same time, there was interest – in mathematics and in the wider (European) culture – in additional dimensions of reality.    The concept of a “fourth dimension” of space motivated many artists, including Kazimir Malevich and Piet Mondrian; both men sought to represent these new ideas from geometry in their art, and said so explicitly.  Similarly, the cubists sought to present an object from all perspectives simultaneously, the futurists to capture the dynanism of machines and the colours of metals, and the constructivists to distill visual art to its essential and abstract forms and colours.   Of course, having many times flown over the Netherlands,  I have always seen Mondrian’s art as straightforward landscape painting, painting the Dutch countryside from above.

Geometric abstraction reappeared in the art of Brazil in the 1960s, and in so-called minimalist art in the USA and Europe, from the 1960s onwards.  Like Hirschfeld-Mack’s work, much of that art is sublime and deeply spiritual.  More of that anon.

M Dabrowski [1992]:  Malevich and Mondrian:  nonobjective form as the expression of the “absolute’”.  pp. 145-168, in: GH Roman and VH Marquardt (Editors): The Avant-Garde Frontier: Russia Meets the West, 1910-1930. University Press of Florida, Gainesville, FL, USA.

Gladys Fabre and Doris Wintgens Hotte (Editors), Michael White (Consultant Editor) [2009]:  Van Doesburg & the International Avant-Garde.  Constructing a New World.  London, UK:  Tate Publishing.
LD Henderson [1983]: The Fourth Dimension and Non-Euclidean Geometry in Modern Art. Princeton University Press, Princeton, NJ, USA.

David Hilbert [1899]: Grundlagen der Geometrie. pp. 3-92, in: Festschrift zur Feier der Enthullung des Gauss-Weber-Denkmals in Gottingen. Teubner, Leipzig, Germany.   Translated by EJ Townsend as:  Foundations of Geometry, Open Court, Chicago, IL, USA. 1910.

Mario Pieri [1895]:  Sui principi che reggiono la geometria di posizione.  Atti della Reale Accademia delle scienze di Torino, 30: 54-108.

Mario Pieri [1897-98]: I principii della geometria di posizione composti in sistema logico deduttivo.  Memorie della Reale Accademia delle Scienze di Torino 2, 48: 1-62.

Note: The image shown above is from Ludwig Hirschfeld-Mack: “Farbenlicht-Spiel”, 1921.  Photography © Ludwig Hirschfeld-Mack.   Szenenfoto Farbenlichtspiel, Rekonstruktion 1999. Corinne Schweizer, Peter Böhm,  Ludwig Hirschfeld-Mack.

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.
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).

Poem: Sonnet II

A poem George Santayana wrote on the early death in 1893 of his close friend, Warwick Potter, who apparently died in Brest of cholera caught after being weakened due to severe sea-sickness experienced while yachting. More about Potter here.

Sonnet II, from “To W.P.”
With you a part of me hath passed away;
For in the peopled forest of my mind
A tree made leafless by this wintry wind
Shall never don again its green array.
Chapel and fireside, country road and bay,
Have something of their friendliness resigned;
Another, if I would, I could not find,
And I am grown much older in a day.
But yet I treasure in my memory
Your gift of charity, and young heart’s ease,
And the dear honour of your amity;
For these once mine, my life is rich with these.
And I scarce know which part may greater be,–
What I keep of you, or you rob from me.

Previous posts of poetry are here.