Archive for March, 2013

Belief as end-point, not starting-line

The New Statesman asked several famous people about what atheists could learn from religious believers, here.  Particularly interesting were the responses of Francis Spufford and Karen Armstrong. 

Continue reading ‘Belief as end-point, not starting-line’




The ALP

The colonial political parties of the labour movement which preceded the Australian Labor Party date from 1891.  The first Labour MPs were elected that year to the New South Wales Legislative Assembly (aka “the Bear Pit”), winning 35 of 141 seats.  The first Labour government anywhere in the world was in Queensland in 1899, where the administration of Anderson Dawson held office for 7 days.   Federally, the first Labour Government was in 1904, under Chris Watson, a minority government that lasted just 4 months.  The party adopted the US spelling of “Labor” in 1912, in admiration of the US labor movement.

An American journalist and historian of Australia, C. Hartley Grattan (1902-1980), once wrote this about the Party (cited in Button 2012, page 145 large print edition):

It has struggled with every handicap to which political parties are heir.  It has been burdened with careerists, turncoats, hypocrites, outright scoundrels, stuffy functionaries devoid of sense and imagination, bellowing enemies of critical intelligence, irritatingly self-righteous clowns bent on enforcing suburban points of view, pussy-footers, demagogues, stooges for hostile outside groups and interests, aged and decaying hacks and ordinary blatherskites.  Every political party falls heir to these.  But it has outlived them all and still stands for something:  it stands for a social democratic Australia.”

Reference:

James Button [2012]: Speechless:  A Year in my Father’s Business.  Melbourne, Australia:  Melbourne University Press.

POSTSCRIPT (2013-03-30):  And here is a perceptive analysis of the current situation of the ALP by Guy Rundle, writing for Crikey magazine (HT).    I had not previously viewed the ALP’s Right-wing factions as being the descendants of the Catholic social movement, while the Centre-Left and Left factions may be seen descendants of Protestant Fabians and Marxists.




Political talk

James Button, one-time speech-writer to former Australian Prime Minister Kevin Rudd, wrote this in his recent book:

When Rudd spoke at the Department’s Christmas party, he had sketched a triangle in the air that distilled the work of producing a policy or speech into a three-point plan:  where are we now; where do we want to go and why; how are we going to get there?  The second point – where do we want to go and why – expressed our values, Rudd said. It was a simple way to structure a speech and I often used it when writing speeches in the year to come.” (Button 2012, page 55, large print edition).

Reading this I was reminded how inadequate I had found the analysis of political speech propounded by anthropologist Michael Silverstein in his short book on political talk (Silverstein 2003).   He seems to view political speech as mere information transfer, and the utterances made therefore as essentially being propositions – statements about the world that are either true or false.   Perhaps these propositions may be covered in rhetorical glitter, or presented incrementally, or subtly, or cleverly, but propositions they remain.   I know of no politician, and I can think of none, who speaks that way.   All political speeches (at least in the languages known to me) are calls to action of one form or another.   These actions may be undertaken by the speaker or their political party – “If elected, I will do XYZ” – or they may be actions which the current elected officials should be doing  – “Our Government should be doing XYZ.”     Implicit in such calls is always another call, to an action by the listener:  “Vote for me”.    Even lists of past achievements, which Button mentions Rudd was fond of giving, are implicit or explicit entreaties for votes.

Of course, such calls to action may, of necessity, be supported by elaborate propositional statements about the world as it is, or as it could be or should be, as Rudd’s structure shows.   And such propositions may be believed or not, by listeners.  But people called to action do not evaluate the calls they hear the way they would propositions.  It makes no sense, for instance, to talk about the “truth” or “falsity” of an action, or even of a call to action.   Instead, we assess such calls on the basis of the sincerity or commitment of the speaker, on the appropriateness or feasibility or ease or legality of the action, on the consequences of the proposed action, on its costs and benefits, its likelihood of success, its potential side effects, on how it compares to any alternative actions, on the extent to which others will support it also, etc.

What has always struck me about Barack Obama’s speeches, particularly those during his first run for President in 2007-2008,  is how often he makes calls-to-action for actions to be undertaken by his listeners:  He would say “We should do X”, but actually mean, “You-all should do X”, since the action is often not something he can do alone, or even at all.  “Yes we can!” was of this form, since he is saying, “Yes, we can take back the government from the Republicans, by us all voting.”    From past political speeches I have read or seen, it seems to me that only JFK, MLK and RFK regularly spoke in this way, although I am sure there must have been other politicians who did.  This approach and the associated language comes directly from Obama’s work as a community organizer: success in that role consists in persuading people to work together on their own joint behalf.  Having spent lots of time in the company of foreign aid workers in Africa, this voice and these idioms were very familiar to me when I first heard Obama speak.

Rudd’s three-part structure matches closely to the formalism proposed by Atkinson et al. [2005] for making proposals for action in multi-party dialogs over action, a structure that supports rational critique and assessment of the proposed action, along the dimensions mentioned above.

References:

K. Atkinson, T. Bench-Capon and P. McBurney [2005]: A dialogue-game protocol for multi-agent argument over proposals for action.   Autonomous Agents and Multi-Agent Systems, 11 (2): 153-171.

James Button [2012]: Speechless:  A Year in my Father’s Business.  Melbourne, Australia:  Melbourne University Press.

Michael Silverstein [2003]:   Talking Politics:  The Substance of Style from Abe to “W”.  Chicago, IL, USA:  Prickly Paradigm Press.




Decision-making style

This week’s leadership-challenge-that-wasn’t in the Federal Parliamentary Caucus of the Australian Labor Party saw the likely end of Kevin Rudd’s political career.   At the last moment he bottled it, having calculated that he did not have the numbers to win a vote of his caucus colleagues and so deciding not to stand.  Ms Gillard was re-elected leader of the FPLP unopposed.       Why Rudd failed to win caucus support is explained clearly in subsequent commentary by one of his former speech-writers, James Button:

The trick to government, Paul Keating once said, is to pick three big things and do them well. But Rudd opened a hundred policy fronts, and focused on very few of them. He centralised decision-making in his office yet could not make difficult decisions. He called climate change the greatest moral challenge of our time, then walked away from introducing an emissions trading scheme. He set a template for governing that Labor must move beyond.

On Thursday, for the third time in three years, a large majority of Rudd’s caucus colleagues made it clear that they did not want him as leader. Yet for years Rudd seemed as if he would never be content until he returned as leader. On Friday he said that he would never again seek the leadership of the party. He must keep his word, or else the impasse will destabilise and derail the party until he leaves Parliament.

Since losing the prime ministership, Rudd never understood that for his prospects to change within the government he had to openly acknowledge, at least in part, that there were sensible reasons why Gillard and her supporters toppled him in 2010. Then, as hard as it would have been, he had to get behind Gillard, just as Bill Hayden put aside his great bitterness and got behind Bob Hawke and joined his ministry after losing the Labor leadership to him in 1983.

Yes, Rudd’s execution was murky and brutal and should have been done differently, perhaps with a delegation of senior ministers going to Rudd first to say change or go. Yes, the consequences have been catastrophic for Gillard and for the ALP. ”Blood will have blood,” as Dennis Glover, a former Gillard speechwriter who also wrote speeches for Rudd, said in a newspaper on Thursday.

But why did it happen? Why did so many Labor MPs resolve to vote against Rudd that he didn’t dare stand? Why was he thrashed in his 2012 challenge? Why have his numbers not significantly moved, despite all the government’s woes?

Because – it must be said again – Rudd was a poor prime minister. To his credit, he led the government’s brave and decisive response to the global financial crisis. His apology speech changed Australia and will be remembered for years to come. But beyond that he has few achievements, and the way he governed brought him down.

At the time of his 2012 challenge, seven ministers went public with fierce criticisms of Rudd’s governing style. When most of them made it clear they would not serve again in a Rudd cabinet, many commentators wrote this up as slander and character assassination of Rudd, or as one of those vicious but mysterious internal brawls that afflict the Labor Party from time to time. They missed the essential points: that the criticisms came from a diverse and representative set of ministers, and they had substance.

If the word of these seven ministers is not enough, consider the reporting of Rudd’s treatment of colleagues by Fairfax journalist David Marr in his 2010 Quarterly Essay, Power Trip. Or the words of Glover, who wrote last year that as a ”member of the Gang of Four Hundred or So (advisers and speechwriters) I can assure you that the chaos and frustration described by Gillard supporters during February’s failed leadership challenge rang very, very true with about 375 of us.”

Consider the reporting of Rudd’s downfall by ABC journalist Barrie Cassidy in his book, Party Thieves. Never had numbers tumbled so quickly, Cassidy wrote. ”That’s because Rudd himself drove them. His own behaviour had caused deep-seated resentment to take root.” Leaders had survived slumps before and would again. But ”Rudd was treated differently because he was different: autocratic, exclusive, disrespectful and at times flat-out abusive”. Former Labor minister Barry Cohen told Cassidy: ”If Rudd was a better bloke he would still be leader. But he pissed everybody off.”

These accounts tallied with my own observations when I worked as a speechwriter for Rudd in 2009. While my own experience of Rudd was both poor and brief, I worked with many people – 40 or more – who worked closely with him. Their accounts were always the same. While Rudd was charming to the outside world, behind closed doors he treated people with rudeness and contempt. At first I kept waiting for my colleagues to give me another side of Rudd: that he could be difficult but was at heart a good bloke. Yet apart from some conversations in which people praised his handling of the global financial crisis, no one ever did.

Since he lost power, is there any sign that Rudd has reflected on his time in office, accepted that he made mistakes, that he held deep and unaccountable grudges and treated people terribly?

Did he reflect on the rages he would fly into when people gave him advice he didn’t want, how he would put those people into what his staff called ”the freezer”, sometimes not speaking to them for months or more? Did he reflect on the way he governed in a near permanent state of crisis, how his reluctance to make decisions until the very last moment coupled with a refusal to take unwelcome advice led his government into chaos by the middle of 2010, when his obsessive focus on his health reforms left the government utterly unprepared to deal with the challenges of the emissions trading scheme, the budget, the Henry tax review and the mining tax? To date there is no sign that he has learnt from the failures of his time as prime minister.

Through his wife, Rudd is currently the richest member of the Australian Commonwealth Parliament, and perhaps the  richest person ever to be an MP.    He is also fluent in Mandarin Chinese and famously intelligent, although perhaps not as bright as his predecessors as Labor leader, Gough Whitlam or Doc Evatt, or former ministers, Isaac Isaacs, Ted Theodore or Barry Jones.  It is possible, of course, to have a first-rate mind and a second-rate temperament.  An autocratic management style – unpopular within the Labor Party at any time, as Evatt and Whitlam both learnt – is even less appropriate when the Party lacks a majority in the House, and has to rely on a permanent, floating two-up game of ad hoc negotiations with Green and Independent MPs to pass legislation.




Progress in computing

Computer science typically proceeds by first doing something, and then thinking carefully about it:    Engineering usually precedes theory.    Some examples:

  • The first programmable device in modern times was the Jacquard Loom, a textile loom that could weave different patterns depending on the instruction cards fed into it.   This machine dates from the first decade of the 19th century, but we did not have a formal, mathematical theory of programming until the 1960s.
  • Charles Babbage designed various machines to undertake automated calculations in the first half of the 19th century, but we did not have a mathematical theory of computation until Alan Turing’s film-projector model a century later.
  • We’ve had a fully-functioning, scalable, global network enabling multiple, asynchronous, parallel, sequential and interleaved interactions since Arpanet four decades ago, but we still lack a fully-developed mathematical theory of interaction.   In particular, Turing’s film projectors seem inadequate to model interactive computational processes, such as those where new inputs arrive or partial outputs are delivered before processing is complete, or those processes which are infinitely divisible and decentralizable, or nearly so.
  • The first mathematical theory of communications (due to Claude Shannon) dates only from the 1940s, and that theory explicitly ignores the meaning of messages.   In the half-century since, computer scientists have used speech act theory from the philosophy of language to develop semantic theories of interactive communication.  Arguably, however, we still lack a good formal, semantically-rich account of dialogs and utterances  about actions.  Yet, smoke signals were used for communications in ancient China, in ancient Greece, and in medieval-era southern Africa.

An important consequence of this feature of the discipline is that theory and practice are strongly coupled and symbiotic.   We need practice to test and validate our theories, of course.   But our theories are not (in general) theories of something found in Nature, but theories of practice and of the objects and processes created by practice.  Favouring theory over practice risks creating a sterile, infeasible discipline out of touch with reality – a glass bead game such as string theory or pre-Crash mathematical economics.   Favouring practice over theory risks losing the benefits of intelligent thought and modeling about practice, and thus inhibiting our understanding about limits to practice.   Neither can exist very long or effectively without the other.




Combining actions

How might two actions be combined?  Well, depending on the actions, we may be able to do one action and then the other, or we may be able do the other and then the one, or maybe not.  We call such a combination a sequence or concatenation of the two actions.  In some cases, we may be able to do the two actions in parallel, both at the same time.  We may have to start them simultaneously, or we may be able to start one before the other.  Or, we may have to ensure they finish together, or that they jointly meet some other intermediate synchronization targets.

In some cases, we may be able to interleave them, doing part of one action, then part of the second, then part of the first again, what management consultants in telecommunications call multiplexing.   For many human physical activities – such as learning to play the piano or learning to play golf – interleaving is how parallel activities are first learnt and complex motor skills acquired:  first play a few bars of music on the piano with only the left hand, then the same bars with only the right, and keep practicing the hands on their own, and only after the two hands are each practiced individually do we try playing the piano with the two hands together.

Computer science, which I view as the science of delegation, knows a great deal about how actions may be combined, how they may be distributed across multiple actors, and what the meanings and consequences of these different combinations are likely to be.     It is useful to have a list of the possibilities.  Let us suppose we have two actions, represented by A and B respectively.   Then we may be able to do the following compound actions:

  • Sequence:  The execution of A followed by the execution of B, denoted A ;  B
  • Iterate: A executed n times, denoted A ^ n  (This is sequential execution of a single action.)
  • Parallelize: Both A and B are executed together, denoted A & B
  • Interleave:  Action A is partly executed, followed by part-execution of B, followed by continued part-execution of A, etc, denoted A || B
  • Choose:  Either A is executed or B is executed but not both, denoted A v B
  • Combinations of the above:  For example, with interleaving, only one action is ever being executed at one time.  But it may be that the part-executions of A and B can overlap, so we have a combination of Parallel and Interleaved compositions of A and B.

Depending on the nature of the domain and the nature of the actions, not all of these compound actions may necessarily  be possible.  For instance, if action B has some pre-conditions before it can be executed, then the prior execution of A has to successfully achieve these pre-conditions in order for the sequence A ; B to be feasible.

This stuff may seem very nitty-gritty, but anyone who’s ever asked a teenager to do some task they don’t wish to do, will know all the variations in which a required task can be done after, or alongside, or intermittently with, or be replaced instead by, some other task the teen would prefer to do.    Machines, it turns out, are much like recalcitrant and literal-minded teenagers when it comes to commanding them to do stuff.




Taking a view vs. maximizing expected utility

The standard or classical model in decision theory is called Maximum Expected Utility (MEU) theory, which I have excoriated here and here (and which Cosma Shalizi satirized here).   Its flaws and weaknesses for real decision-making have been pointed out by critics since its inception, six decades ago.  Despite this, the theory is still taught in economics classes and MBA programs as a normative model of decision-making.  

A key feature of MEU is the the decision-maker is required to identify ALL possible action options, and ALL consequential states of these options.   He or she then reasons ACROSS these consequences by adding together the utilites of the consquential states, weighted by the likelihood that each state will occur.  

However, financial and business planners do something completely contrary to this in everyday financial and business modeling.   In developing a financial model for a major business decision or for a new venture, the collection of possible actions is usually infinite and the space of possible consequential states even more so.  Making human sense of the possible actions and the resulting consequential states is usually a key reason for undertaking the financial modeling activity, and so cannot be an input to the modeling.  Because of the explosion in the number states and in their internal complexity, business planners cannot articulate all the actions and all the states, nor even usually a subset of these beyond a mere handful.  

Therefore, planners typically choose to model just 3 or 4 states – usually called cases or scenarios – with each of these combining a complex mix of (a) assumed actions, (b) assumed stakeholder responses and (c) environmental events and parameters.  The assumptions and parameter values are instantiated for each case, the model run, and  the outputs of the 3 or 4 cases compared with one another.  The process is usually repeated with different (but close) assumptions and parameter values, to gain a sense of the sensitivity of the model outputs to those assumptions.     

Often the scenarios will be labeled “Best Case”, “Worst Case”, “Base Case”, etc to identify the broad underlying  principles that are used to make the relevant assumptions in each case.   Actually adopting a financial model for (say) a new venture means assuming that one of these cases is close enough to current reality and its likely future development in the domain under study- ie, that one case is realistic.   People in the finance world call this adoption of one case “taking a view” on the future. 

Taking a view involves assuming (at least pro tem) that one trajectory (or one class of trajectories) describes the evolution of the states of some system.  Such betting on the future is the complete opposite cognitive behaviour to reasoning over all the possible states before choosing an action, which the protagonists of the MEU model insist we all do.   Yet the MEU model continues to be taught as a normative model for decision-making to MBA students who will spend their post-graduation life doing business planning by taking a view.

 




Mathematicians of the 20th Century

With so many blogs being written by members of the literati, it’s not surprising that a widespread meme involves compiling lists of writers and books.  I’ve even succumbed to it myself.   Lists of mathematicians are not as common, so I thought I’d present a list of the 20th century greats.    Some of these are famous for a small number of contributions, or for work which is only narrow, while others have had impacts across many parts of mathematics.

Each major area of mathematics represented here (eg, category theory, computer science) could equally do with its own list, which perhaps I’ll manage in due course.  I’ve included David Hilbert, Felix Hausdorff and Bertrand Russell because their most influential works were published in the 20th century.  Although Hilbert reached adulthood in the 19th century, his address to the 1900 International Congress of Mathematicians in Paris greatly influenced the research agenda of mathematicians for much of the 20th century, and his 1899 axiomatization of geometry (following the lead of Mario Pieri) influenced the century’s main style of doing mathematics.   For most of the 20th century, mathematics was much more abstract and more general than it had been in the previous two centuries.    This abstract style perhaps reached its zenith in the work of Bourbaki, Grothendieck, Eilenberg and Mac Lane, while the mathematics of Thurston, for example, was a throwback to the particularist, even perhaps anti-abstract, style of 19th century mathematics.  And Perelman’s major contributions have been in this century, of course.

  • David Hilbert (1862-1943)
  • Felix Hausdorff (1868-1942)
  • Bertrand Russell (1872-1970)
  • Henri Lebesgue (1875-1941)
  • Godfrey Hardy (1877-1947)
  • LEJ (“Bertus”) Brouwer (1881-1966)
  • Srinivasa Ramanujan (1887-1920)
  • Alonzo Church (1903-1995)
  • Andrei Kolmogorov (1903-1987)
  • John von Neumann (1903-1957)
  • Henri Cartan (1904-2008)
  • Kurt Gödel (1906-1978)
  • Saunders Mac Lane (1909-2005)
  • Leonid Kantorovich (1912-1986)
  • Alan Turing (1912-1954)
  • Samuel Eilenberg (1913-1998)
  • René Thom (1923-2002)
  • John Forbes Nash (1928-2015)
  • Alexander Grothendieck (1928-2014)
  • Michael Atiyah (1929- )
  • Steven Smale (1930- )
  • Paul Cohen (1934-2007)
  • Nicolas Bourbaki (1935- )
  • Sergei Novikov (1938- )
  • Stephen Cook (1939- )
  • William Thurston (1946-2012)
  • Edward Witten (1951- )
  • Andrew Wiles (1953- )
  • Richard Borcherds (1959- )
  • Grigori Perelman (1966- )
  • Vladimir Voevodsky (1966- )
  • Edward Frenkel (1968- )

And here’s my list of great mathematical ideas.




Let me count the ways

A cartoon I once saw had a manager asking his subordinate to list all the action-options available for some decision, then to list the pros and cons of each action-option and then to count them, pros and cons combined, and to choose the option with the highest combined total.  Thus, if one option A had 2 pros and 1 con, and another option B had 1 pro and 5 cons, the latter would be selected.   You might call this the Pointy-Haired Boss model of decision-making.

It is interesting to ask exactly why is this NOT a sensible way of deciding what to do in some situation.   Most of us would say that firstly, this method ignores the direction of the arguments for and against doing something – it flattens out the positive and negative nature of (respectively) the pros and the cons.   Even inserting positive and negative signs to the numbers of supporting arguments would be better:  Thus, option A would have +2 and -1, giving a net value of +1, while option B would have +1 and -5, giving a net value of -4; choosing option A over B on this basis would feel better, since we taking into account the direction of support or attack.

But even this additive approach ignores the strength of the support of each pro argument, and the strength of the attack of each con argument.    In other words, even the additive approach still flattens something – in this case, the importance of each pro or con.    We might then consider inserting some measure of value or importance to the arguments.  If they involve any uncertainty, then we might also add some measure of that in some form or other, whether quantitative (eg, probabilities) or qualitative (eg, linguistic labels).

But let us stay with the pointy-haired boss for a moment.   We have 3 arguments (2 pro, 1 con) under A, and 6 arguments (1 pro, 5 con) under B.   Why do we have more arguments for some options than for others?  It could be because we have thought about some options more than we have others, or because, through our own direct experience or observation of the experiences of others, we know more about the likely upsides and downsides of some options.   The grass is always greener on the other side of the fence, for example, because we’ve not yet been over that side of the fence to see the mud there.   On our side, we can clearly see all the downsides as well as the ups.  Human decision biases may also lead us to emphasize the negative sides of more familiar situations, while emphasizing the positives of less familiar situations.

A model of decision-making I have proposed before – retroflexive decision-making – understands that real managers in real organizations making important decisions don’t generally have only the one pass at deciding the possible decision-options and articulating the pros and cons of each.  Rather, managers work iteratively and collectively, sharing their knowledge and experiences, drawing on wide sources, and usually seeking to build a consensus view.   In addition, they almost never work in a vacuum – rather, they work within a context of legacy policies and systems, with particular corporate strengths, experiences, skills, expertise, technologies, business partners, trading relationships, regulatory environments, and even personalities, and within overall intended future corporate directions.   All this context means that some decision-options will already be favoured and others disfavoured.   That much is human – and corporate – nature.   Consequently, decision-makers will naturally seek to strengthen the pros and the positive consequences of some options (including, but usually not only, the favoured ones), while weakening or mitigating their cons and negative consequences of those options.

None of this is wrong – in fact, it is good management.   Every decision-option in any even moderately complex domain will have both pros and cons.  Making work whichever option is selected will be a matter of finding ways to eliminate or mitigate the negative consequences, while at the same time seeking to strengthen the positive consequences.   Those options where we know more about the pros and cons are also likely to be the options where we have the greatest leverage from experience, knowledge, and expertise to accentuate the pros and to mitigate the cons.    To that extent, the Pointy-Haired Boss model is not necessarily as stupid as it may seem.




Composers concat

While making lists of artists whose work speaks to me, here’s my list of classical composers likewise.  Of course, I don’t necessarily like everything these composers wrote.

  • Johann Adam Reincken (1643-1722)
  • Johann Sebastian Bach (1685-1750)
  • Johan Helmich Roman (1694-1758)
  • Joseph Haydn (1732-1809)
  • Michael Haydn (1737-1806)
  • Johann Baptist Vanhal (1739-1813)
  • Wolfgang Amadeus Mozart (1756-1791)
  • Luigi Cherubini (1760-1842)
  • Ludwig van Beethoven (1770-1827)
  • Johann Hummel (1778-1837)
  • Franz Schubert (1797-1828)
  • Louise Farrenc (1804-1875)
  • Fanny Mendelssohn (1805-1847)
  • Juan Chrisostomo Arriaga (1806-1826)
  • Felix Mendelssohn (1809-1847)
  • Robert Schumann (1810-1856)
  • William Sterndale Bennett (1816-1875)
  • Neils Gade (1817-1890)
  • Pyotr Ilyich Tchaikovsky (1840–1893)
  • Antoni Stolpe (1851-1872)
  • Claude Debussy (1862-1918)
  • Alfred Hill (1869-1960)
  • Colin McPhee (1900-1964)
  • Aram Khachaturian (1903–1978)
  • Dmitri Shostakovich (1906-1975)
  • John Cage (1912-1992)
  • Jim Penberthy (1917-1999)
  • Iannis Xenakis (1922-2001)
  • Morton Feldman (1926-1987)
  • Peter Sculthorpe  (1929-2014)
  • Toru Takemitsu (1930-1996)
  • Richard Meale (1932-2009)
  • Terry Riley (1935- )
  • Steve Reich (1936- )
  • Philip Glass (1937- )
  • Louis Andriessen (1939- )
  • Michael Nyman (1944- )
  • Barry Conyngham (1944- )
  • John Adams (1947- )
  • Akira Nishimura (1953- )
  • Cecilie Ore (1954- )
  • Pascal Dusapin (1955- )
  • Andrew McGuiness
  • Christophe Bertrand (1981-2010).

The alert reader will notice the absence of Richard Wagner.   This is deliberate.