Strategic Progamming

Over the last 40-odd years, a branch of Artificial Intelligence called AI Planning has developed.  One way to view Planning is as automated computer programming: 

  • Write a program that takes as input an initial state, a final state (“a goal”), and a collection of possible atomic actions, and  produces as output another computer programme comprising a combination of the actions (“a plan”) guaranteed to take us from the initial state to the final state. 

A prototypical example is robot motion:  Given an initial position (e.g., here), a means of locomotion (e.g., the robot can walk), and a desired end-position (e.g., over there), AI Planning seeks to empower the robot to develop a plan to walk from here to over there.   If some or all the actions are non-deterministic, or if there are other possibly intervening effects in the world, then the “guaranteed” modality may be replaced by a “likely” modality. 
Another way to view Planning is in contrast to Scheduling:

  • Scheduling is the orderly arrangement of a collection of tasks guranteed to achieve some goal from some initial state, when we know in advance the initial state, the goal state, and the tasks.
  • Planning is the identification and orderly arrangement of tasks guranteed to achieve some goal from some initial state, when we know in advance the initial state, the goal state, but we don’t yet know the tasks;  we only know in advance the atomic actions from which tasks may be constructed.

Relating these ideas to my business experience, I realized that a large swathe of complex planning activities in large companies involves something at a higher level of abstraction.  Henry Mintzberg called these activities “Strategic Programming”

  • Strategic Programming is the identification and priorization of a finite collection of programs or plans, given an initial state, a set of desirable end-states or objectives (possibly conflicting).  A program comprises an ordered collection of tasks, and these tasks and their ordering we may or may not know in advance.

Examples abound in complex business domains.   You wake up one morning to find yourself the owner of a national mobile telecommunications licence, and with funds to launch a network.  You have to buy the necessary equipment and deploy and connect it, in order to provide your new mobile network.   Your first decision is where to provide coverage:  you could aim to provide nationwide coverage, and not open your service to the public until the network has been installed and connected nationwide.  This is the strategy Orange adopted when launching PCS services in mainland Britain in 1994.   One downside of waiting till you’ve covered the nation before selling any service to customers is that revenues are delayed. 
Another downside is that a competitor may launch service before you, and that happened to Orange:  Mercury One2One (as it then was) offered service to the public in 1993, when they had only covered the area around London.   The upside of that strategy for One2One was early revenues.  The downside was that customers could not use their phones outside the island of coverage, essentially inside the M25 ring-road.   For some customer segments, wide-area or nationwide coverage may not be very important, so an early launch may be appropriate if those customer segments are being targeted.  But an early launch won’t help customers who need wider-area coverage, and – unless marketing communications are handled carefully – the early launch may position the network operator in the minds of such customers as permanently providing inadequate service.   The expectations of both current target customers and customers who are not currently targets need to be explicitly managed to avoid such mis-perceptions.
In this example, the different coverage rollout strategies ended up at the same place eventually, with both networks providing nationwide coverage.  But the two operators took different paths to that same end-state.   How to identify, compare, prioritize, and select-between these different paths is the very stuff of marketing and business strategy, ie, of strategic programming.  It is why business decision-making is often very complex and often intellectually very demanding.   Let no one say (as academics are wont to do) that decision-making in business is a doddle.   Everything is always more complicated than it looks from outside, and identifying and choosing-between alternative programs is among the most complex of decision-making activities.

Vacuum cleaners generating hot air

Apparently, British inventor James Dyson has argued that more people should study engineering and fewer “French lesbian poetry”.    Assuming he is correctly quoted, there are a couple of things one could say in response.
First, all Mr Dyson need do is pay engineers more than the going market rates, and he will attract more people  into the profession.   Likewise, he could give students scholarships to study engineering.   He, unlike most of the rest of us, has it in his direct personal power to achieve this goal.   I think it ill-behooves someone who moved his manufacturing operations off-shore to bemoan any lack of home-grown talents.
Second, no matter how wonderful the engineering technology or novelty of the latest, jet-propelled, wind-turbine-bladed vacuum cleaner, the technology will not sell itself.   For that, even the vacuum cleaners of the famous Mr Dyson need marketing and advertising.  And, marketing needs people who can understand and predict customer attitudes and behaviours, people who have studied psychology and sociology and anthropology and economics.  Marketing needs people who can analyze data, increasingly in large quantities and in real-time, people who have studied mathematics and statistics and computer science and econometrics.  Marketing needs people who can strategize, people who have studied game theory and military strategy and political science and history, and can emphathize with customers and competitors.   As Australian advertising man Philip Adams once noted, Marxists and ex-Marxists are often the best marketing strategists, because they think dialectically about the long term.
And advertising needs people who can manipulate images, people who have usually studied art or art history or graphic design or architecture.  Advertising needs people who can take photos and use movie cameras and direct films, people who have studied photography and cinematography and lighting and film and theatre studies and acting.  Advertising needs people who can write jingles and advertising scores, and play the music required, people who have studied music and song and musical instruments.   Advertising needs people who can build sets, acquire props, and obtain costumes, people who are good with their hands or who have studied fashion.   And, finally, advertising needs people who can write ad copy and scripts – often people have studied history and journalism and languages and literature and poetry – even, at times, I would guess, the poetry of French lesbians.
One reason Britain is a such a world leader in marketing and advertising, despite the long-term decline and poor management of its manufacturing industry,  is because of its many leading art colleges and universities teaching the humanities and social sciences.  The name of Dyson would not be known to households across the country and beyond without the contributions of many, many professionals who did not study engineering.
 
UPDATE (2012-12-01):  And if you are still wondering why more people studying engineering would not be sufficient for business success, consider this from Grant McCracken:

Culture is the sea in which business swims. We can’t do good innovation without it. We can’t do good marketing without it. And we can’t build a good corporate culture without it.”

 

Markets as feedback mechanisms

I just posted after hearing a talk by economic journalist Tim Harford at LSE.  At the end of that post, I linked to a critical review of Harford’s latest book,  Adapt – Why Success Always Starts with Failure, by Whimsley.  This review quotes Harford talking about markets as feedback mechanisms:

To identify successful strategies, Harford argues that “we should not try to design a better world. We should make better feedback loops” (140) so that failures can be identified and successes capitalized on. Harford just asserts that “a market provides a short, strong feedback loop” (141), because “If one cafe is ordering a better combination of service, range of food, prices, decor, coffee blend, and so on, then more customers will congregate there than at the cafe next door“, but everyday small-scale examples like this have little to do with markets for credit default swaps or with any other large-scale operation.

Yes, indeed.  The lead-time between undertaking initial business planning in order to raise early capital investments and the launching of services to the  public for  global satellite communications networks is in the order of 10 years (since satellites, satellite networks and user devices need to be designed, manufactured, approved by regulators, deployed, and connected before they can provide service).  The time between initial business planning and the final decommissioning of an international gas or oil pipeline is about 50 years.  The time between initial business planning and the final decommissioning of an international undersea telecommunications cable may be as long as 100 years.   As I remarked once previously, the design of Transmission Control Protocol (TCP) packets, the primary engine of communication in the 21st century Internet, is closely modeled on the design of telegrams first sent in the middle of the 19th century.  Some markets, if they work at all, only work over the long run, but as Keynes famously said, in the long run we are all dead.
I have experience of trying to design telecoms services for satellite networks (among others), knowing that any accurate feedback for design decisions may come late or not at all, and when it comes may be vague and ambiguous, or even misleading.   Moreover, the success or failure of the selected marketing strategy may not ever be clear, since its success may depend on the quality of execution of the strategy, so that it may be impossible to determine what precisely led to the outcome.   I have talked about this issue before, both regarding military strategies and regarding complex decisions in general.  If the quality of execution also influences success (as it does), then just who or what is the market giving feedback to?
In other words, these coffees are not always short and strong (in Harford’s words), but may be cold, weak, very very slow in arriving, and even their very nature contested.   I’ve not yet read Harford’s book, but if he thinks all business is as simple as providing fmc (fast-moving consumer) services, his book is not worth reading.
Once again, an economist argues by anecdote and example.  And once again, I wonder at the world:  That economists have a reputation for talking about reality, when most of them evidently know so little about it, or reduce its messy complexities to homilies based on the operation of suburban coffee shops.

What use are models?

What are models for?   Most developers and users of models, in my experience, seem to assume the answer to this question is obvious and thus never raise it.   In fact, modeling has many potential purposes, and some of these conflict with one another.   Some of the criticisms made of particular models arise from mis-understandings or mis-perceptions of the purposes of those models, and the modeling activities which led to them.
Liking cladistics as I do, I thought it useful to list all the potential purposes of models and modeling.   The only discussion that considers this topic that I know is a brief discussion by game theorist Ariel Rubinstein in an appendix to a book on modeling rational behaviour (Rubinstein 1998).  Rubinstein considers several alternative purposes for economic modeling, but ignores many others.   My list is as follows (to be expanded and annotated in due course):

  • 1. To better understand some real phenomena or existing system.   This is perhaps the most commonly perceived purpose of modeling, in the sciences and the social sciences.
  • 2. To predict (some properties of) some real phenomena or existing system.  A model aiming to predict some domain may be successful without aiding our understanding  of the domain at all.  Isaac Newton’s model of the motion of planets, for example, was predictive but not explanatory.   I understand that physicist David Deutsch argues that predictive ability is not an end of scientific modeling but a means, since it is how we assess and compare alternative models of the same phenomena.    This is wrong on both counts:  prediction IS an end of much modeling activity (especially in business strategy and public policy domains), and it not the only means we use to assess models.  Indeed, for many modeling activities, calibration and prediction are problematic, and so predictive capability may not even be  possible as a form of model assessment.
  • 3. To manage or control (some properties of) some real phenomena or existing system.
  • 4. To better understand a model of some real phenomena or existing system.  Arguably, most of economic theorizing and modeling falls into this category, and Rubinstein’s preferred purpose is this type.   Macro-economic models, if they are calibrated at all, are calibrated against artificial, human-defined, variables such as employment, GDP and inflation, variables which may themselves bear a tenuous and dynamic relationship to any underlying economic reality.   Micro-economic models, if they are calibrated at all, are often calibrated with stylized facts, abstractions and simplifications of reality which economists have come to regard as representative of the domain in question.    In other words, economic models are not not usually calibrated against reality directly, but against other models of reality.  Similarly, large parts of contemporary mathematical physics (such as string theory and brane theory) have no access to any physical phenomena other than via the mathematical model itself:  our only means of apprehension of vibrating strings in inaccessible dimensions beyond the four we live in, for instance, is through the mathematics of string theory.    In this light, it seems nonsense to talk about the effectiveness, reasonable or otherwise, of mathematics in modeling reality, since how we could tell?
  • 5. To predict (some properties of) a model of some real phenomena or existing system.
  • 6. To better understand, predict or manage some intended (not-yet-existing) artificial system, so to guide its design and development.   Understanding a system that does  not yet exist is qualitatively different to understanding an existing domain or system, because the possibility of calibration is often absent and because the model may act to define the limits and possibilities of subsequent design actions on the artificial system.  The use of speech act theory (a model of natural human language) for the design of artificial machine-to-machine languages, or the use of economic game theory (a mathematical model of a stylized conceptual model of particular micro-economic realities) for the design of online auction sites are examples here.   The modeling activity can even be performative, helping to create the reality it may purport to describe, as in the case of the Black-Scholes model of options pricing.
  • 7. To provide a locus for discussion between relevant stakeholders in some business or public policy domain.  Most large-scale business planning models have this purpose within companies, particularly when multiple partners are involved.  Likewise, models of major public policy issues, such as epidemics, have this function.  In many complex domains, such as those in public health, models provide a means to tame and domesticate the complexity of the domain.  This helps stakeholders to jointly consider concepts, data, dynamics, policy options, and assessment of potential consequences of policy options,  all of which may need to be socially constructed. 
  • 8. To provide a means for identification, articulation and potentially resolution of trade-offs and their consequences in some business or public policy domain.   This is the case, for example, with models of public health risk assessment of chemicals or new products by environmental protection agencies, and models of epidemics deployed by government health authorities.
  • 9. To enable rigorous and justified thinking about the assumptions and their relationships to one another in modeling some domain.   Business planning models usually serve this purpose.   They may be used to inform actions, both to eliminate or mitigate negative consequences and to enhance positive consequences, as in retroflexive decision making.
  • 10. To enable a means of assessment of managerial competencies of the people undertaking the modeling activity. Investors in start-ups know that the business plans of the company founders are likely to be out of date very quickly.  The function of such business plans is not to model reality accurately, but to force rigorous thinking about the domain, and to provide a means by which potential investors can challenge the assumptions and thinking of management as way of probing the managerial competence of those managers.    Business planning can thus be seen to be a form of epideictic argument, where arguments are assessed on their form rather than their content, as I have argued here.
  • 11. As a means of play, to enable the exercise of human intelligence, ingenuity and creativity, in developing and exploring the properties of models themselves.  This purpose is true of that human activity known as doing pure mathematics, and perhaps of most of that academic activity known as doing mathematical economics.   As I have argued before, mathematical economics is closer to theology than to the modeling undertaken in the natural sciences. I see nothing wrong with this being a purpose of modeling, although it would be nice if academic economists were honest enough to admit that their use of public funds was primarily in pursuit of private pleasures, and any wider social benefits from their modeling activities were incidental.

POSTSCRIPT (Added 2011-06-17):  I have just seen Joshua Epstein’s 2008 discussion of the purposes of modeling in science and social science.   Epstein lists 17 reasons to build explicit models (in his words, although I have added the label “0” to his first reason):

0. Prediction
1. Explain (very different from predict)
2. Guide data collection
3. Illuminate core dynamics
4. Suggest dynamical analogies
5. Discover new questions
6. Promote a scientific habit of mind
7. Bound (bracket) outcomes to plausible ranges
8. Illuminate core uncertainties
9. Offer crisis options in near-real time. [Presumably, Epstein means “crisis-response options” here.]
10. Demonstrate tradeoffe/ suggest efficiencies
11. Challenge the robustness of prevailing theory through peturbations
12. Expose prevailing wisdom as imcompatible with available data
13. Train practitioners
14. Discipline the policy dialog
15. Educate the general public
16. Reveal the apparently simple (complex) to be complex (simple).

These are at a lower level than my list, and I believe some of his items are the consequences of purposes rather than purposes themselves, at least for honest modelers (eg, #11, #12, #16).
References:
Joshua M Epstein [2008]: Why model? Keynote address to the Second World Congress on Social Simulation, George Mason University, USA.  Available here (PDF).
Robert E Marks [2007]:  Validating simulation models: a general framework and four applied examples. Computational Economics, 30 (3): 265-290.
David F Midgley, Robert E Marks and D Kunchamwar [2007]:  The building and assurance of agent-based models: an example and challenge to the field. Journal of Business Research, 60 (8): 884-893.
Robert Rosen [1985]: Anticipatory Systems. Pergamon Press.
Ariel Rubinstein [1998]: Modeling Bounded Rationality. Cambridge, MA, USA: MIT Press.  Zeuthen Lecture Book Series.
Ariel Rubinstein [2006]: Dilemmas of an economic theorist. Econometrica, 74 (4): 865-883.

The otherness of the other

In previous posts (eg, here and here), I have talked about the difficulty of assessing the intentions of others, whether for marketing or for computer network design or for national security. The standard English phrase speaks of “putting ourselves in the other person’s shoes”.  But this is usually not sufficient:  we have to put them into their shoes, with their beliefs, their history, their desires, and their constraints, not ourselves, in order to understand their goals and intentions, and to anticipate their likely strategies and actions.    In a fine political thriller by Henry Porter, I come across this statement (page 220):

‘Motive is always difficult to read,’ he replied.  ‘We make a rational assumption about someone’s behaviour based on what we would, or would not, do in the same circumstances, ignoring the otherness of the other. We consider only influences that make us what we are and impose those beliefs on them.  It is the classic mistake of intelligence analysis.’  “

Reference:
Henry Porter [2009]: The Dying Light. London, UK:  Orion Books.
Obscure fact:  Porter (born 1953) is the grand-nephew of novelist Howard Sturgis (1855-1920), step-cousin to George Santayana (1863-1952).

In defence of futures thinking

Norm at Normblog has a post defending theology as a legitimate area of academic inquiry, after an attack on theology by Oliver Kamm.  (Since OK’s post is behind a paywall, I have not read it, so my comments here may be awry with respect to that post.)  Norm argues, very correctly, that it is legitimate for theology, considered as a branch of philosophy to, inter alia, reflect on the properties of entities whose existence has not yet been proven.  In strong support of Norm, let me add:  Not just in philosophy!
In business strategy, good decision-making requires consideration of the consequences of potential actions, which in turn requires the consideration of the potential actions of other actors and stakeholders in response to the first set of actions.  These actors may include entities whose existence is not yet known or even suspected, for example, future competitors to a product whose launch creates a new product category.   Why, there’s even a whole branch of strategy analysis, devoted to scenario planning, a discipline that began in the military analysis of alternative post-nuclear worlds, and whose very essence involves the creation of imagined futures (for forecasting and prognosis) and/or imagined pasts (for diagnosis and analysis).   Every good air-crash investigation, medical diagnosis, and police homicide investigation, for instance, involves the creation of imagined alternative pasts, and often the creation of imaginary entities in those imagined pasts, whose fictional attributes we may explore at length.   Arguably, in one widespread view of the philosophy of mathematics, pure mathematicians do nothing but explore the attributes of entities without material existence.
And not just in business, medicine, the military, and the professions.   In computer software engineering, no new software system development is complete without due and rigorous consideration of the likely actions of users or other actors with and on the system, for example.   Users and actors here include those who are the intended target users of the system, as well as malevolent or whimsical or poorly-behaved or bug-ridden others, both human and virtual, not all of whom may even exist when the system is first developed or put into production.      If creative articulation and manipulation of imaginary futures (possible or impossible) is to be outlawed, not only would we have no literary fiction or much poetry, we’d also have few working software systems either.

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.

Metrosexual competition

Writing about the macho world of pure mathematics (at least, in my experience, in analysis and group theory, less so in category theory and number theory, for example), led me to think that some academic disciplines seem hyper-competitive:  physics, philosophy, and mainstream economics come to mind.  A problem for economics is that the domain of the discipline includes the study of competition, and the macho, hyper-competitive nature of academic economists has led them, I believe, astray in their thinking about the marketplace competition they claim to be studying.  They have assumed that their own nasty, bullying, dog-eat-dog world is a good model for the world of business.
If business were truly the self-interested, take-no-prisoners world of competition described in economics textbooks and assumed in mainstream economics, our lives would all be very different.  Fortunately, our world is mostly not like this.   One example is in telecommunications where companies compete and collaborate with each other at the same time, and often through the same business units.  For instance, British Telecommunications and Vodafone are competitors (both directly in the same product categories and indirectly through partial substitutes such as fixed and mobile services), and collaborators, through the legally-required and commercially-sensible inter-connections of their respective networks.  Indeed, for many years, each company was the other company’s largest customer, since the inter-connection of their networks means each company completes calls that originate on the other’s network; thus each company receives payments from the other.  Do you seek to drive your main competitor out of business when that competitor is also your largest customer?   Would you do this, as stupid as it seems, knowing that your competitor could retaliate (perhaps pre-emptively!) by disconnecting your network or reducing the quality of your calls that interconnect?  No rational business manager would do this, although perhaps an economist might.
Nor would you destroy your competitors when you and they are sharing physical infrastructure  – co-locating switches in each other’s buildings, for example, or sharing rural cellular base stations, both of which are common in telecommunications.   And, to complicate matters, large corporate customers of telecommunications companies increasingly want direct access to the telco’s own switches, leading to very porous boundaries between companies and their suppliers.   Doctrines of nuclear warfare, such as mutually-assured destruction or iterated prisoners’ dilemma, are better models for this marketplace than the mainstream one-shot utility-maximizing models, in my opinion.
You might protest that telecommunications is a special case, since the product is a networked good – that is, one where a customer’s utility from a particular service may depend on the numbers of other customers also using the service.    However, even for non-networked goods, the fact that business usually involves repeated interactions with the same group of people (and is decidely not a one-shot interaction) leads to more co-operation than is found in an economist’s philosophy.   The empirical studies of hedge funds undertaken by sociologist Donald MacKenzie, for example, showed the great extent to which hedge fund managers rely in their investment decisions on information they receive from their competitors.  Because everyone hopes to come to work tomorrow and the day after, as well as today, there are strong incentives on people not to  mis-use these networks through, for instance, disseminating false or explicitly-self-serving information.
It’s a dog-help-dog world out there!
Reference:
Iain Hardie and Donald MacKenzie [2007]:  Assembling an economic actor: the agencement of a hedge fund. The Sociological Review, 55 (1): 57-80.

Thinkers of renown

The recent death of mathematician Jim Wiegold (1934-2009), whom I once knew, has led me to ponder the nature of intellectual influence.  Written matter – initially, hand-copied books, then printed books, and now the Web – has been the main conduit of influence.   For those of us with a formal education, lectures and tutorials are another means of influence, more direct than written materials.   Yet despite these broadcast methods, we still seek out individual contact with others.  Speaking for myself, it is almost never the knowledge or facts of others, per se, that I have sought or seek in making personal contact, but rather their various different ways of looking at the world.   In mathematical terminology, the ideas that have influenced me have not been the solutions that certain people have for particular problems, but rather the methods and perspectives they use for approaching and tackling problems, even when these methods are not always successful.

To express my gratitude, I thought I would list some of the people whose ideas have influenced me, either directly through their lectures, or indirectly through their books and other writings.   In the second category, I have not included those whose ideas have come to me mediated through the books or lectures of others, which therefore excludes many mathematicians whose work has influenced me (in particular:  Newton, Leibniz, Cauchy, Weierstrauss, Cantor, Frege, Poincare, Pieri, Hilbert, Lebesque, Kolmogorov, and Godel).  I have also not included the many writers of poetry, fiction, history and biography whose work has had great impact on me.  These two categories also exclude people whose intellectual influence has been manifest in non-verbal forms, such as through visual arts or music, or via working together, since those categories need posts of their own.

Teachers & lecturers I have had who have influenced my thinking includeLeo Birsen (1902-1992), Sr. Claver Butler RSM (ca. 1930-2009), Burgess Cameron (1922-2020), Sr. Clare Castle RSM (ca. 1920- ca. 2000), John Coates (1945-2022), Dot Crowe, James Cutt, Bro. Clive Davis FMS, Tom Donaldson (1945-2006), Aleksandr Doronin, Gary Dunbier, Sol Encel (1925-2010), Felix Fabryczny de Leiris, Claudio Forcada, Richard Gill (1941-2018), Myrtle Hanley (1909-1984), Sr. Jennifer Hartley RSM, Chip Heathcote (1931-2016),  Hope Hewitt (1915-2011), Alec Hope (1907-2000),  John Hutchinson, Marg Keetles, Joe Lynch, Robert Marks, John McBurney (1932-1998), David Midgley, Lindsay Morley, Leopoldo Mugnai, Terry O’Neill, Jim Penberthy* (1917-1999), Malcolm Rennie (1940-1980), John Roberts, Gisela Soares, Brian Stacey (1946-1996), James Taylor, Frank Torpie (1934-1989),  Neil Trudinger, David Urquhart-Jones, Frederick Wedd (1890-1972), Gary Whale (1943-2019), Ted Wheelwright (1921-2007), John Woods and Alkiviadis Zalavras.

People whose writings have influenced my thinking includeJohn Baez, Ole Barndorff-Nielsen (1935-2022), Charlotte Joko Beck (1917-2011), Johan van Bentham, Mark Evan Bonds, John Cage (1912-1992), Albert Camus (1913-1960), Nikolai Chentsov (1930-1992), John Miller Chernoff, Stewart Copeland, Sam Eilenberg (1913-1998), Paul Feyerabend (1924-1994), George Fowler (1929-2000), Kyle Gann, Alfred Gell (1945-1997), Herb Gintis, Jurgen Habermas, Charles Hamblin (1922-1985), Vaclav Havel (1936-2011), Lafcadio Hearn (1850-1904), Jaakko Hintikka (1929-2015), Eric von Hippel, Wilfrid Hodges, Christmas Humphreys (1901-1983), Jon Kabat-Zinn, Herman Kahn (1922-1983), John Maynard Keynes (1883-1946), Andrey Kolmogorov (1903-1987), Paul Krugman, Imre Lakatos (1922-1974), Trevor Leggett (1914-2000), George Leonard (1923-2010), Brad de Long, Donald MacKenzie,  Saunders Mac Lane (1909-2005), Karl Marx (1818-1883), Grant McCracken, Henry Mintzberg, Philip Mirowski, Michel de Montaigne (1533-1592), Michael Porter, Charles Reich (1928-2019), Jean-Francois Revel (1924-2006), Daniel Rose, Bertrand Russell (1872-1970), Pierre Ryckmans (aka Simon Leys) (1935-2014), Oliver Sacks (1933-2015), Gunther Schuller (1925-2015), George Shackle (1903-1992), Cosma Shalizi, Rupert Sheldrake, Raymond Smullyan (1919-2017), Rory Stewart, Anne Sweeney (d. 2007), Nassim Taleb, Henry David Thoreau (1817-1862), Stephen Toulmin (1922-2009), Scott Turner, Roy Weintraub, Geoffrey Vickers VC (1894-1982), and Richard Wilson.

FOOTNOTES:
* Which makes me a grand-pupil of Nadia Boulanger (1887-1979).
** Of course, this being the World-Wide-Web, I need to explicitly say that nothing in what I have written here should be taken to mean that I agree with anything in particular which any of the people mentioned here have said or written.
A more complete list of teachers is here.

Class struggles at the check-out

Newcomers to Britain usually notice the pervasiveness of the nation’s class system.  This is a country which even has two classes of stamps!  The British supermarket chains have long been a battleground of the class struggle, with some offering mainly own-label, discounted products, and others offering mainly own-label, premium-priced products!   I can recall an elderly neighbour once asking me which of the several nearby supermarkets I shopped at, and then saying, “I’m so pleased!” when I gave an answer which she thought demonstrated that we were in the same social class.
Now there is news that some of the chains are heading down-market, in order to take advantage of the recession.   But how to do this without losing your current market-position image, nor those customers still able and willing to pay premium prices?