Most people, if they think about the topic at all, probably imagine computer science involves the programming of computers. But what are computers? In most cases, these are just machines of one form or another. And what is programming? Well, it is the issuing of instructions (“commands” in the programming jargon) for the machine to do something or other, or to achieve some state or other. Thus, I view Computer Science as nothing more or less than the science of delegation.
When delegating a task to another person, we are likely to be more effective (as the delegator or commander) the more we know about the skills and capabilities and curent commitments and attitudes of that person (the delegatee or commandee). So too with delegating to machines. Accordingly, a large part of theoretical computer science is concerned with exploring the properties of machines, or rather, the deductive properties of mathematical models of machines. Other parts of the discipline concern the properties of languages for commanding machines, including their meaning (their semantics) – this is programming language theory. Because the vast majority of lines of program code nowadays are written by teams of programmers, not individuals, then much of computer science – part of the branch known as software engineering – is concerned with how to best organize and manage and evaluate the work of teams of people. Because most machines are controlled by humans and act in concert for or with or to humans, then another, related branch of this science of delegation deals with the study of human-machine interactions. In both these branches, computer science reveals itself to have a side which connects directly with the human and social sciences, something not true of the other sciences often grouped with Computer Science: pure mathematics, physics, or chemistry.
And from its modern beginnings 70 years ago, computer science has been concerned with trying to automate whatever can be automated – in other words, with delegating the task of delegating. This is the branch known as Artificial Intelligence. We have intelligent machines which can command other machines, and manage and control them in the same way that humans could. But not all bilateral relationships between machines are those of commander-and-subordinate. More often, in distributed networks machines are peers of one another, intelligent and autonomous (to varying degrees). Thus, commanding is useless – persuasion is what is needed for one intelligent machine to ensure that another machine does what the first desires. And so, as one would expect in a science of delegation, computational argumentation arises as an important area of study.
Monthly Archives: April 2013
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.
What we're thinking
Christopher Weyant’s cartoon in The New Yorker (HT: SP).
PKOM at the Wigmore
This week, I was lucky to catch the first half of a concert by Finnish violinist Pekka Kuusisto and pianist/composer Olli Mustonen at London’s Wigmore Hall. I heard them play Beethoven’s Violin Sonata in A (Op. 30, #1) and Mustonen’s Sonata for Violin and Piano, which was a world premiere.
As always with PK, the playing was superb and full of energy. What he lacks in physical height, he more than makes up for in enthusiasm and pizzaz. He is an extraordinarily talented violinist, and I try not to miss opportunities to hear him play. (I have also heard him play piano, but the part was not a testing one.)
In the main, Beethoven’s violin sonatas do not impress me – our Ludwig couldn’t play the instrument nearly as well as he could play the piano, and this shows in his writing for the respective instruments. I view these sonatas as really being piano sonatas with violin commentaries. And, as so often with Beethoven, the music at some point comes to a stop, or nearly so, mid-way through the develoment section, like a clock winding down, and has to be re-started again. What underlying psychological thing is going on here, I wonder, that this happens so often in B’s music? After a while it becomes annoying, like a friend asking you the same unpleasant question every time you meet, and you end up wantIng to avoid talking with that person.
Mustonen’s Sonata was superb. The programme notes warned us that he began as a composer of “Busonian neo-classicism”. I thought this piece was not at all neo-classical, but also certainly not in the category of up-town modernist complexity. The first part comprised an ever-present walking treble line of odd intervals by the violin, sequences of uneven lengths and different intervals not quite repeated exactly, with various waves of piano arising and decaying around this. The particular odd intervals – tritones, sevenths – brought immediately to my mind some music of Australian composer Larry Sitsky, who studied with Egon Petri (1881-1962), who in turn was a student of Ferruccio Busoni (1866-1924). The emotional waves of this first part were very stark. Would I have thought of Sibelius and the forests of the North if I had not known the composer was Finnish? I don’t know.
The transition between the second and third parts was slow and beautiful, and very moving, and the effects PK produced were simply stunning. At one point, low trembling notes on the G string sounded like a breathy flute being played. And a series of repeated patterns combining trills and vibrata on different fingers of the left hand, was very impressive. Not at all clear how these effects were produced, but the independent but co-ordinated action of the left-hand fingers would have required long practice to achieve. Perhaps the effect was partly due to rapid changes of speed and pressure on the bow, also.
It was a privilege to be in the presence of such superb music played by these two virtuosos.
Here is another review of the same concert, by an anonymous blogger. Following the review, the blogger cites PK’s recording of Vivalid’s Four Seasons, as “restrained”. I wonder if he or she was actually listening! We’ve had 60 years of elegant, effete and twee recordings of The Seasons, so we know what restrained with regard to this music means. PK’s treatment is rustic and earthy and full-blooded, as if the entire ensemble had been taken outside and roughed-up in the mud of the farmyard, and the complete opposite of restrained! A simply superb interpretation, original, fresh and compelling. Your milage certainly can vary, as people say.
Mathematics in Britain
From the music critic of The Times, writing in 1952 (issue of 2 May 1952, page 8, column 6, review of The Background of Music, by H. Lowery, published in 1952 by Hutchinson):
At Redbrick [University] they treat mathematics as an instrument of technology; at Cambridge they regard it as an ally of physics and an approach to philosophy; at Oxford they think of it as an art in itself having affinities with counterpoint and dancing.”
Quoted (incorrectly) by Ida Winifred Busbridge, in a 1974 history of mathematics at Oxford University, here. (Note that Busbridge writes “music” instead of “counterpoint”.)
Oxford University was a strong supporter of Catholicism in Elizabeth I’s time (eg, it was home to Thomas Campion), while Cambridge and the Fens, due to their proximity to the Netherlands, was the centre for an extreme Protestant sect, called the Family of Love, or the Familists. Elizabeth I’s religious policy often sought to find a middle ground between these two extremes. These religious differences persisted, so that Oxford was again, in the mid 19th-century, a centre of Catholic, and, within the Anglican Church, Anglo-Catholic (“High Church”) ideas. The Redbrick Universities (Liverpool, Birmingham, Leeds, Victoria University of Manchester, etc), mostly founded in the North and Midlands of England in the late 19th century or early 20th century, were the result of money-raising campaigns by local business people and civic worthies, who were often of a Nonconformist or Jewish religious background. The name Redbrick arose from novels written by a professor of Spanish at the University of Liverpool, Edgar Peers, about a fictional northern university modeled on Liverpool.
I don’t think the distinct differences between Nonconformist, Protestant and Catholic world views could be better expressed than those here between the philosophies of mathematics of Redbrick, Cambridge and Oxford: Nonconformism as pragmatic utilitarianism; Protestantism as serious reflection on life’s higher ends; and Catholicism as enjoyment of life and its pleasures!
Letter from Finchley
The influence of Mrs Margaret Thatcher on British economic and cultural life is shown now, at her death, by the pages and pages and pages of newsprint devoted to her in every British newspaper, all day every day since her death. Even the Gruaniard has joined in the chorus, although sometimes singing from the hymnal of another denomination, but still with pages and pages of text and images. It is like the mass media psychosis that hit Britain the week after the death of Princess Diana in 1997.
The praise heaped on Saint Margaret has stretched credulity to the limit. Like some modern-day Bolivar, she apparently single-handedly liberated Eastern Europe from Communism, which if true would surely be news to the Central Committee of the Communist Party of the USSR (1989 membership), the Central Committee of the CzechoSlovak Communist Party (April 1968 membership), the Central Committee of the United Workers Party of Poland (1956 and 1989 memberships), and the millions of brave citizens of Berlin, Leipzig, Budapest, Gdansk, Prague, Warsaw, Bucharest, Moscow, and throughout the region, who actually did, through argument and protest and strike and resistance, liberate their countries from tyranny. Part of the justification given for her role in the freedom of Eastern Europe is the fact of her early meeting with Mikhail Gorbachev, before his elevation to the General Secretary-ship of the CPSU, after which meeting she proclaimed that she could do business with him. But why would this endorsement have helped him rise? Surely such a public statement from one of the nation’s nuclear-armed enemies potentially lost him votes in the race to be General Secretary.
And, by a certain class of people, she was then, and still is, seen as the Simon Bolivar of Britain. Yes, like all politicians, she represented a particular economic class and indeed she represented their interests very effectively. (It was not, by the way, the class of her parents or of her upbringing, but it was the class of her husband.) But statesmanship requires a politician to decide in the national interest, not in the interests of a particular class. With just one possible exception, I cannot think of a single major decision she took in which she decided in favour of the nation against the interests of her own sectional base. The one exception was the decision to defend the Falkland Islands following invasion by the Argentinian military junta in 1982.
One could – and she did – defend such sectional decision-making on ideological grounds, for example, using the so-called theories of trickle-down economics, of metaphysical entities (eg, invisible hands), and of magical thinking and psychokinesis (eg, frictionless adjustment to free trade) that constitute the parallel, reality-free, universe that is neoclassical economics. In other words, she argued that although the decisions she took seemed to favour one group over another, in reality all would benefit, although perhaps not all would benefit immediately. But all economic policies have both winners and losers. Mrs Thatcher rarely evinced any public sympathy for the losers of her policies, and her contempt for those who lost was always obvious.
Her last major enacted policy – towards the end of her 11 years in power – was the Poll Tax, which punished society’s losers with a most unfair and regressive tax, at the same time as giving manifest and immediate benefit to her sectional base. This was not a policy of someone governing in the national interest. This was not a policy of someone having personal compassion for the downtrodden, the ill, the unlucky, the old, and the unfortunate in our society. This was not policy – and her dogged insistence on maintaining it against all evidence that it was not working epideictically reinforces this – that showed her approaching the challenges of governing in a reasoned or pragmatic way, with an open and rational mind, intent on balancing competing interests, or of finding the best solution for the country as a whole.
Norm is correct to castigate those who have publicly rejoiced at her death. Such rejoicing is quite understandable, even though wrong. Mrs Thatcher’s condescension, contempt, and antipathy for those who suffered from her policies or from life in general was evident to everyone, all along. She herself said there was no such thing as society. She herself said that anyone using public transport over the age of 35 was a failure in life. It is no wonder that the worst riots in Britain in the 20th century happened under Mrs Thatcher. It is no wonder that her party has no longer any support to speak of in Scotland (ground zero for the Poll Tax), and no wonder that support for Scottish independence is now so strong. It is no wonder that punk and reggae developed in overt opposition to her. Linton Kwesi Johnson named his famous song for her, conflating her with Inglan. It is no wonder that people are organizing street parties in the cities of Britain to celebrate her departure.
In contrast to most of the reporting engulfing us now, here are two responses to show the historians of the future that not all of us alive at this moment welcome the sudden attempt at canonization. The first is from a Guardian editorial on Tuesday 9 April 2013:
In the last analysis, though, her stock in trade was division. By instinct, inclination and effect she was a polariser. She glorified both individualism and the nation state, but lacked much feeling for the communities and bonds that knit them together. When she spoke, as she often did, about “our people”, she did not mean the people of Britain; she meant people who thought like her and shared her prejudices. She abhorred disorder, decadence and bad behaviour but she was the empress ruler of a process of social and cultural atomism that has fostered all of them, and still does.”
The second is an impassioned speech from Glenda Jackson MP, given in the House of Commons yesterday, about the pain Mrs Thatcher’s policies wrought. The speech was given against and over the top of much noise and shouting from the Yahoo Henrys who still, apparently, sit on the Conservative Party Benches. I say thee, Yay, Ms. Jackson, Yay!
Brass in Perth
Brisbane Excelsior Brass Band have won the 2013 A-Grade Australian National Band Championships, held in Perth, WA, last week. Congratulations to all!
According to this band contest archive, Excelsior have previously won the national championship in 2005, 2006, 2007, 2008 and 2010. Some members of the band performed last year in a concert in Tyalgum, NSW, which I reported here, and in a concert two years ago in Bundamba to celebrate 125 years of the Salvation Army in Ipswich, Qld.
What do mathematicians do?
Over at the AMS Graduate Student Blog, Jean Joseph wonders what it is that mathematicians do, asking if what they do is to solve problems:
After I heard someone ask about what a mathematician does, I myself wonder what it means to do mathematics if all what one can answer is that mathematicians do mathematics. Solving problems have been considered by some as the main activity of a mathematician, which might then be the answer to the question. But, could reading and writing about mathematics or crafting a new theory be considered as serious mathematical activities or mere extracurricular activities?”
Not all mathematics is problem-solving, as we’ve discussed here before, and I think it would be a great shame if the idea were to take hold that all that mathematicians did was to solve problems. As Joseph says, this view does not account for lots of activities that we know mathematicians engage in which are not anywhere near to problem-solving, such as creating theories, defining concepts, writing expositions, teaching, etc.
I view mathematics (and the related disciplines in the pure mathematical universe) as the rigorous study of structure and relationship. What mathematicians do, then, is to rigorously study structure and relationship. They do this by creating, sharing and jointly manipulating abstract mental models, seeking always to understand the properties and inter-relations of these models.
Some of these models may arise from, or be applied to, particular domains or particular problems, but mathematicians (at least, pure mathematicians) are typically chiefly interested in the abstract models themselves and their formal properties, rather than the applications. In some parts of mathematics (eg, algebra) written documents such as research papers and textbooks provide accurate descriptions of these mental models. In other parts (eg, geometry), the written documents can only approximate the mental models. As mathematician William Thurston once said:
There were published theorems that were generally known to be false, or where the proofs were generally known to be incomplete. Mathematical knowledge and understanding were embedded in the minds and in the social fabric of the community of people thinking about a particular topic. This knowledge was supported by written documents, but the written documents were not really primary.
I think this pattern varies quite a bit from field to field. I was interested in geometric areas of mathematics, where it is often pretty hard to have a document that reflects well the way people actually think. In more algebraic or symbolic fields, this is not necessarily so, and I have the impression that in some areas documents are much closer to carrying the life of the field. But in any field, there is a strong social standard of validity and truth.
. . .
When people are doing mathematics, the flow of ideas and the social standard of validity is much more reliable than formal documents. People are usually not very good in checking formal correctness of proofs, but they are quite good at detecting potential weaknesses or flaws in proofs.”