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Santayana on Stickney

Published
by
peter
on 2011-01-03
in Argumentation, Literature, Poetry and Recent Reading
. Closed

George Santayana was friends with Joe Trumbull Stickney.  In 1952, five decades after Stickney died from a brain tumour, Santayana wrote a letter about their friendship to William Kirkwood.  The letter is reproduced in facsimile in M. Kirkwood’s life of Santayana (1961, pp. 234-235).

Via di Santo Stefano Rotundo, 6
Rome, May 27, 1952

To Professor Wm. A. Kirkwood, Ph. D.
Trinity College, Toronto

Dear Sir,
It was a happy impulse that prompted you to think that the books you speak of and their annotations, and especially the lines in praise of Homer written by my friend Stickney would interest me. They have called up vividly in my mind the quality of his mind, although the verses represent a much earlier feeling for the classics, and a more conventional mood than he had in the years when we had our frequent moral fencing bouts; for there was a contrary drift in our views in spite of great sympathy in our tastes and pursuits. These verses are signed Sept. 15/ 90. Now Stickney graduated at Harvard in 1895, so that five years earlier he must have been about 17 years old. This explains to me the tone of the verses and also the fact that they advance line by line, seldom or never running over and breaking the next line at the cesura or before it, as he would surely have done in his maturity, when he doted on the dramatic interruptions of Shakespeare’s lines in Antony and Cleopatra in particular, and in all the later plays in general. [page break]

I see clearly the greater mastery and strength of impassioned drama, if impassioned drama is what you are in sympathy with; but I like to warn dogmatic critics of what a more naive art achieves in its impartial and peaceful labour and the risk that overcharged movement or surpluses [?] runs of drowning in its deathbed [?] waters. Every form of art has its charm and is appropriate in its place; but it is moral cramp to admit only one form of art to be legitimate or important. The reminder of this old debate that I had with Stickney who enlightened me more (precisely about the abuse of rhetoric) than I ever could enlighten him about the relativity of everything has been a pleasant reminder of younger days: although I am not sure that much progress towards reason and justice has been made since by critical opinion.

With best thanks and regards

Yours sincerely

G. Santayana

Reference:

M. M. Kirkwood [1961]:  Santayana:  Saint of the Imagination.  Toronto, Canada:  University of Toronto Press.

Previous posts on George Santayana here, and Joe Stickney here.




Dialogs over actions

Published
by
peter
on 2010-12-24
in Argumentation, Computer Science, Computing-as-interaction, Decision theory and Philosophy of Language
. Closed

In the post below, I mentioned the challenge for knowledge engineers of representing know-how, a task which may require explicit representation of actions, and sometimes also of utterances over actions.  The know-how involved in steering a large sailing ship with its diverse crew surely includes the knowledge of who to ask (or to command) to do what, when, and how to respond when these requests (or commands) are ignored, or fail to be executed successfully or timeously.

One might imagine epistemology – the philosophy of knowledge – would be of help here.  Philosophers, however, have been seduced since Aristotle with propositions (factual statements about the world having truth values), largely ignoring actions, and their representation.   Philosophers of language have also mostly focused on speech acts – utterances which act to change the world – rather than on utterances about actions themselves.  Even among speech act theorists the obsession with propositions is strong, with attempts to analyze utterances which are demonstrably not propositions (eg, commands) by means of implicit assertive statements – propositions  asserting something about the world, where “the world” is extended to include internal mental states and intangible social relations between people – which these utterances allegedly imply.  With only a few exceptions (Thomas Reid 1788, Adolf Reinach 1913, Juergen Habermas 1981, Charles Hamblin 1987), philosophers of language have mostly ignored utterances  about actions.

Consider the following two statements:

I promise you to wash the car.

I command you to wash the car.

The two statements have almost identical English syntax.   Yet their meanings, and the intentions of their speakers, are very distinct.  For a start, the action of washing the car would be done by different people – the speaker and the hearer, respectively (assuming for the moment that the command is validly issued, and accepted).  Similarly, the power to retract or revoke the action of washing the car rests with different people – with the hearer (as the recipient of the promise) and the speaker (as the commander), respectively.

Linguists generally use “semantics” to refer to the real-world referants of syntactically-correct expressions, while “pragmatics” refers to other aspects of the meaning and use of an expression not related to their relationship (or not) to things in the world, such as the speaker’s intentions.  For neither of these two expressions does it make sense to speak of  their truth value:  a promise may be questioned as to its sincerity, or its feasibility, or its appropriateness, etc, but not its truth or falsity;  likewise, a command  may be questioned as to its legal validity, or its feasibility, or its morality, etc, but also not its truth or falsity.

For utterances about actions, such as promises, requests, entreaties and commands, truth-value semantics makes no sense.  Instead, we generally need to consider two pragmatic aspects.  The first is uptake, the acceptance of the utterance by the hearer (an aspect first identified by Reid and by Reinach), an acceptance which generally creates a social commitment to execute the action described in the utterance by one or other party to the conversation (speaker or hearer).    Once uptaken, a second pragmatic aspect comes into play:  the power to revoke or retract the social commitment to execute the action.  This revocation power does not necessarily lie with the original speaker; only the recipient of a promise may cancel it, for example, and not the original promiser.  The revocation power also does not necessarily lie with the uptaker, as commands readily indicate.

Why would a computer scientist be interested in such humanistic arcana?  The more tasks we delegate to intelligent machines, the more they need to co-ordinate actions with others of like kind.  Such co-ordination requires conversations comprising utterances over actions, and, for success, these require agreed syntax, semantics and pragmatics.  To give just one example:  the use of intelligent devices by soldiers have made the modern battlefield a place of overwhelming information collection, analysis and communication.  Lots of this communication can be done by intelligent software agents, which is why the US military, inter alia, sponsors research applying the philosophy of language and the  philosophy of argumentation to machine communications.

Meanwhile, the philistine British Government intends to cease funding tertiary education in the arts and the humanities.   Even utilitarians should object to this.

References:

Juergen  Habermas [1984/1981]:   The Theory of Communicative Action:  Volume 1:  Reason and the Rationalization of Society.  London, UK:  Heinemann.   (Translation by T. McCarthy of:  Theorie des Kommunikativen Handelns, Band I,  Handlungsrationalitat und gesellschaftliche Rationalisierung. Suhrkamp, Frankfurt, Germany, 1981.)

Charles  L. Hamblin [1987]:  Imperatives. Oxford, UK:  Basil Blackwell.

P. McBurney and S. Parsons [2007]: Retraction and revocation in agent deliberation dialogs. Argumentation, 21 (3): 269-289.

Adolph Reinach [1913]:  Die apriorischen Grundlagen des bürgerlichen Rechtes.  Jahrbuch für Philosophie und phänomenologische Forschung, 1: 685-847.




Good decisions

Published
by
peter
on 2010-11-07
in Argumentation, Decision theory, Economics and Planning
. Closed

Which decisions are good decisions?

Since 1945, mainstream economists have arrogated the word “rational” to describe a mode of decision-making which they consider to be best.   This method, called maximum-expected utility (MEU) decision-making, assumes that the decision-maker has only a finite set of possible action-options and that she knows what these are, that she knows the possible consequences of each of these actions and can quantify (or at least can estimate) these consequences, and can do so on a single, common, numerical scale of value (the payoffs), that she knows a finite and complete collection of uncertain events that are possible and which may impact the consequences and their values, and knows (or at least can estimate) the probabilities of these uncertain events, again on a common numerical scale of uncertainty.  The MEU decision procedure is then to quantify the consequences of each action-option, weighting them by the relative likelihood of their arising according to their probabilities of the uncertain events which influence them.

The decision-maker then selects that action-option which has the maximum expected consequential value, ie the consequential value weighted by the probabilities of the uncertain events. Such decision-making, in an abuse of language that cries out for a criminal charges, is then called rational by economists.   Bayesian statistician Dennis Lindley even wrote a book about MEU which included the stunningly-arrogant sentence, “The main conclusion [of this book] is that there is essentially only one way to reach a decision sensibly.”

Rational?  This method is not even feasible, let alone sensible or good!

First, where do all these numbers come from?  With the explicit assumptions that I have listed, economists are assuming that the decision-maker has some form of perfect knowledge.  Well, no one making any real-world decisions has that much knowledge.  Of course, economists often respond, estimates can be used when the knowledge is missing.  But whose estimates?   Sourced from where?   Updated when? Anyone with any corporate or public policy experience knows straight away that consensus on such numbers for any half-way important problem will be hard to find.  Worse than that, any consensus achieved should immediately be suspected and interrogated, since it may be evidence of groupthink.    There simply is no certainty about the future, and if a group of people all do agree on what it holds, down to quantified probabilities and payoffs, they deserve the comeuppance they are likely to get!

Second, the MEU principle simply averages across uncertain events.   What of action-options with potentially catastrophic outcomes?   Their small likelihood of occurrence may mean they disappear in the averaging process, but no real-world decision-maker – at least, none with any experience or common sense – would risk a catastrophic outcome, despite their estimated low probabilities.   Wall Street trading firms have off-street (and often off-city) backup IT systems, and sometimes even entire backup trading floors, ready for those rare events.

Third, look at all the assumptions not made explicit in this framework.  There is no mention of the time allowed for the decision, so apparently the decision-maker has infinities of time available.  No mention is made of the processing or memory resources available for making the decision, so she has infinities of world also.   That makes a change from most real-world decisions:  what a pleasant utopia this MEU-land must be.  Nothing is said – at least nothing explicit – about taking into account the historical or other contexts of the decision, such as past decisions by this or related decision-makers, technology standards, legacy systems, organization policies and constraints, or the strategies of the company or the society in which the decision-maker sits.   How could a decision procedure which ignores such issues be considered, even for a moment, rational?   I think only an academic could ignore context in this way; no business person I know would do so, since certain unemployment would be the result.  And how could members of an academic discipline purporting to be a social science accept and disseminate a decision-making framework which ignores such social, contextual features?

And do the selected action-options just execute themselves?  Nothing is said in this framework about consultation with stakeholders during the decision-process, so presumably the decision-maker has no one to report to, no board members or stockholders or division presidents or ward chairmen or electors to manage or inform or liaise with or mollify or reward or appease or seek re-election from, no technical departments to seek feasibility approval from, no implementation staff to motivate or inspire, no regulators or ethicists or corporate counsel to seek legal approval from, no funders or investors to raise finance from, no suppliers to convince to accept orders with, no distribution channels to persuade to schedule throughput with,  no competitors to second-guess or outwit, and no actual, self-immolating protesters outside one’s office window to avert one’s eyes from and feel guilt about for years afterward.*

For many complex decisions, the ultimate success or failure of the decision can depend significantly on the degree to which those having to execute the decision also support it.  Consequently, the choice of a specific action-option (and the logical reasoning process used to select it) may be far less important for success of the decision than that key stakeholders feel that they have been consulted appropriately during the reasoning process.  In other words, the quality of the decision may depend much more on how and with who the decision-maker reasons than on the particular conclusion she reaches.   Arguably this is true of almost all significant corporate strategy decisions and major public policy decisions:  There is ultimately no point sending your military to prop up an anti-communist regime in South-East Asia, for example, if your own soldiers come to feel they should not be there (as I discuss here, regarding another decision to go to war).

Mainstream economists have a long way to go before they will have a theory of good decision-making.   In the meantime, it would behoove them to show some humility when criticizing the decision-making processes of human beings.**

Notes and Bibliography:

Oskar Lange [1945-46]:  The scope and method of economics.  The Review of Economic Studies, 13 (1): 19-32.

Dennis Lindley [1985]:  Making Decisions.  Second Edition. London, UK: John Wiley and Sons.

L James Savage [1950]: The Foundations of Statistics.  New York, NY, USA:  Wiley.

* I’m sure Robert McNamara, statistician and decision-theory whizz kid, never considered the reactions of self-immolating protesters when making decisions early in his career, but having seen one outside his office window late in his time as Secretary of Defense he seems to have done so subsequently.

** Three-toed sloth comments dialogically and amusingly on MEU theory here.




In defence of futures thinking

Published
by
peter
on 2010-08-18
in Argumentation, Computer Science, Decision theory, Forecasting, Marketing strategy, Planning, Prophecy, Religion and Uncertainty
. Closed

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

Published
by
peter
on 2010-08-09
in Argumentation, Decision theory, History, Joint-Action Society, Marketing strategy, Military strategy, Planning, Politics and Team working
. Closed

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 Harper’s 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 them.   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 Afghanistan.  The New Yorker, 2009-09-28, pp. 38-55.

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Symphonic Form

Published
by
peter
on 2010-08-03
in Argumentation, Mathematics and Music
. Closed
Composer and musicologist Kyle Gann has an interesting post citing David Fanning’s quotation of Russian musicologist Mark Aranovsky’s classification of the movements of the typical symphony, a classification which runs as follows:
  • Movement #1:  Homo agens: man acting, or in conflict (Allegro)
  • Movement #2: Homo sapiens: man thinking (Adagio)
  • Movement #3:  Homo ludens: man playing (Scherzo), and
  • Movement #4:  Homo communis: man in the community (Allegro)
This makes immense sense, and provides a neat explanation of the structure of symphonic form.  Many of my long-standing questions are answered with this classification.    Why normally 4 movements?  Why is the first one normally louder and faster and more serious than the next two?  And why does the first movement often seem more like an ending movement than a beginning one?   In other words, why is the climax to the first movement so often more impressive and more compelling than that for the other movements?  Why is there usually a middle movement that is noticeably less serious than the outer movements?  Why is the last movement often in rondo form?  Why do some composers (eg, Mozart, Mendelssohn) include a fugue in their last movements?  Why do some composers include a song to brotherly love  (Beethoven) or a hymn (Mendelssohn)  in their last movements?
Of great relevance here is that the German word for movement (of a musical work) is Satz, meaning “sentence”.  In the German art-musical tradition, a musical work first makes some claim or states some musical position, and then (in Sonata form) argues the case for that claim by exploring the musical consequences of the theme (or themes), or of its  component musical parts, before returning to a re-statement of the initial claim (theme) at the end of the movement.  In this tradition, the theme, being a claim which is developed, does not have to be very interesting or melodious in itself, since its purpose is not to please the ear but to announce a position.   Beethoven, for example, was notorious for not writing good melodies:  his most famous theme, that of the first movement of the 5th Symphony, has just 4 notes, of which 3 are identical and are repeated together.  But he was a superb developer, perhaps one of the best, of themes, even of such apparently insignificant ones as this one.
The distinction between writing good melodies and developing them well strikes me as very similar to that between problem-solving and theory-building mathematicians - both these cases essentially involve a difference between exploring and exploiting.



Five minutes of freedom

Published
by
peter
on 2010-08-01
in Argumentation, Heroes, History, Intelligence and Espionage, Literature, Mathematics, Matherati, Poetry and Politics
. Closed

Jane Gregory, speaking in 2004, on the necessary conditions for a public sphere:

To qualify as a public, a group of people needs four characteristics. First, it should be open to all and any: there are no entry qualifications. Secondly, the people must come together freely. But it is not enough to simply hang out – sheep do that. The third characteristic is common action. Sheep sometimes all point in the same direction and eat grass, but they still do not qualify as a public, because they lack the fourth characteristic, which is speech. To qualify as a public, a group must be made up of people who have come together freely, and their common action is determined through speech: that is, through discussion, the group determines a course of action which it then follows. When this happens, it creates a public sphere.

There is no public sphere in a totalitarian regime – for there, there is insufficient freedom of action; and difference is not tolerated. So there are strong links between the idea of a public sphere and democracy.”

I would add that most totalitarian states often force their citizens to participate in public events, thus violating two basic human rights:  the right not to associate and the right not to listen.

I am reminded of a moment of courage on 25 August 1968, when seven Soviet citizens, shestidesiatniki (people of the 60s), staged a brave public protest at Lobnoye Mesto in Red Square, Moscow, at the military invasion of Czechoslovakia by forces of the Warsaw Pact.   The seven (and one baby) were:  Konstantin Babitsky (mathematician and linguist), Larisa Bogoraz (linguist, then married to Yuli Daniel), Vadim Delone (also written “Delaunay”, language student and poet), Vladimir Dremlyuga (construction worker), Victor Fainberg (mathematician), Natalia Gorbanevskaya (poet, with baby), and Pavel Litvinov (mathematics teacher, and grandson of Stalin’s foreign minister, Maxim Litvinov).  The protest lasted only long enough for the 7 adults to unwrap banners and to surprise onlookers.  The protesters were soon set-upon and beaten by “bystanders” – plain clothes police, male and female – who  then bundled them into vehicles of the state security organs.  Ms Gorbanevskaya and baby were later released, and Fainberg declared insane and sent to an asylum.

The other five faced trial later in 1968, and were each found guilty.   They were sent either to internal exile or to prison (Delone and Dremlyuga) for 1-3 years; Dremlyuga was given additional time while in prison, and ended up serving 6 years.  At his trial, Delone said that the prison sentence of almost three years was worth the “five minutes of freedom” he had experienced during the protest.  

Delone (born 1947) was a member of a prominent intellectual family, great-great-great-grandson of a French doctor, Pierre Delaunay, who had resettled in Russia after Napoleon’s defeat.   Delone was the great-grandson of a professor of physics, Nikolai Borisovich Delone (grandson of Pierre Delaunay), and grandson of a more prominent mathematician, Boris Nikolaevich Delaunay (1890-1980), and son of physicist Nikolai Delone (1926-2008).  In 1907, at the age of 17, Boris N. Delaunay organized the first gliding circle in Kiev, with his friend Igor Sikorski, who was later famous for his helicopters.   B. N. Delaunay was also a composer and artist as a young man, of sufficient talent that he could easily have pursued these careers.   In addition, he was one of the outstanding mountaineers of the USSR, and a mountain and other features near Mount Belukha in the Altai range are named for him.

Boris N. Delaunay was primarily a geometer – although he also contributed to number theory and to algebra – and invented Delaunay triangulation.  He was a co-organizer of the first Soviet Mathematics Olympiad, a mathematics competition for high-school students, in 1934.   One of his students was Aleksandr D. Alexandrov (1912-1999), founder of the Leningrad School of Geometry (which studies the differential geometry of curvature in manifolds, and the geometry of space-time).   Vadim Delone also showed mathematical promise and was selected to attend Moskovskaya Srednyaya Fiz Mat Shkola #2, Moscow Central Special High School No. 2 for Physics and Mathematics (now the Lyceum “Second School”).   This school, established in 1958 for mathematically-gifted teenagers, was famously liberal and tolerant of dissent. (Indeed, so much so that in 1971-72, well after Delone had left, the school was purged by the CPSU.  See Hedrick Smith’s 1975 account here.)  Vadim Delone lived with Alexandrov when, serving out a one-year suspended sentence which required him to leave Moscow, he studied at university in Novosibirsk, Siberia.   At some risk to his own academic career, Alexandrov twice bravely visited Vadim Delone while he was in prison.

Delone’s wife, Irina Belgorodkaya, was also active in dissident circles, being arrested both in 1969 and again in 1973, and was sentenced to prison terms each time.  She was the daughter of a senior KGB official.  After his release in 1971 and hers in 1975, Delone and his wife emigrated to France in 1975, and he continued to write poetry.   In 1983, at the age of just 35, he died of cardiac arrest.   Given his youth, and the long lives of his father and grandfather, one has to wonder if this event was the dark work of an organ of Soviet state security.  According to then-KGB Chairman Yuri Andropov’s report to the Central Committee of the CPSU on the Moscow Seven’s protest in September 1968, Delone was the key link between the community of dissident poets and writers on the one hand, and that of mathematicians and physicists on the other.    Andropov even alleges that physicist Andrei Sakharov’s support for dissident activities was due to Delone’s personal persuasion, and that Delone lived from a so-called private fund, money from voluntary tithes paid by writers and scientists to support dissidents.   (Sharing of incomes in this way sounds suspiciously like socialism, which the state in the USSR always determined to maintain a monopoly of.)  That Andropov reported on this protest to the Central Committee, and less than a month after the event, indicates the seriousness with which this particular group of dissidents was viewed by the authorities.  That the childen of the nomenklatura, the intelligentsia, and even the KGB should be involved in these activities no doubt added to the concern.  If the KGB actually believed the statements Andropov made about Delone to the Central Committee, they would certainly have strong motivation to arrange his early death.

Several of the Moscow Seven were honoured in August 2008 by the Government of the Czech Republic, but as far as I am aware, no honour or recognition has yet been given them by the Soviet or Russian Governments.   Although my gesture will likely have little impact on the world, I salute their courage here.

I have translated a poem of Delone’s here.   An index to posts on The Matherati is here.

References:

M. V. Ammosov [2009]:  Nikolai Borisovich Delone in my Life.  Laser Physics, 19 (8): 1488-1490.

Yuri Andropov [1968]: The Demonstration in Red Square Against the Warsaw Pact Invasion of Czechoslovakia. Report to the Central Committee of the CPSU, 1968-09-20.

N. P. Dolbilin [2011]: Boris Nikolaevich Delone (Delaunay): Life and Work. Proceedings of the Steklov Institute of Mathematics, 275: 1-14.  Published in Russian in Trudy Matematicheskogo Instituta imeni V. A. Steklov, 2011, 275:  7-21.  Pre-print here.

Jane Gregory [2004]:  Subtle signs that divide the public from the private.  The Independent, 2004-05-20.

Hedrick Smith [1975]:  The Russians.  Crown.  pp. 211-213.




Argument mediation signals

Published
by
peter
on 2010-04-07
in Argumentation
. Closed

Here are signals for argument mediators, for your next blog argument. (From here.  HT: SP) 

APA Argument Signals




Maps and territories and knowledge

Published
by
peter
on 2010-01-06
in AI, Anthropology, Argumentation and Art
. Closed

Seymour Papert, one of the pioneers of Artificial Intelligence, once wrote (1988, p. 3), “Artificial Intelligence should become the methodology for thinking about ways of knowing.”   I would add “and ways of acting”. 

Some time back, I wrote about the painting of spirit-dreamtime maps by Australian aboriginal communities as proof of their relationship to specific places:  Only people with traditional rights to the specific place would have the necessary dreamtime knowledge needed to make the painting, an argument whose compelling force has been recognized by Australian courts.  These paintings are a form of map, showing (some of) the spirit relationships of the specific place.  The argument they make is a very interesting one, along the lines of: 

What I am saying is true, by virtue of the mere fact that I am saying it, since only someone having the truth would be able to make such an utterance (ie, the painting).

Another example of this type of argument is given by Rory Stewart, in his account of his walk across Afghanistan.   Stewart does not carry a paper map of the country he is walking through, lest he be thought a foreign spy (p. 211).   Instead, he learns and memorizes a list of the villages and their headmen, in the order he plans to walk through them.  Like the aboriginal dreamtime paintings, mere knowledge of this list provides proof of his right to be in the area.  Like the paintings, the list is a type of map of the territory, a different way of knowing.  And also like the paintings, possession of this knowledge leads others, when they learn of the possession, to act differently towards the possessor.  Here’s Stewart on his map (p. 213):

It was less accurate the further you were from the speaker’s home . . .  But I was able to add details from villages along the way, till I could chant the stages from memory.

Day one:  Commandant Maududi in Badgah.  Day two:  Abdul Rauf Ghafuri in Daulatyar.  Day three:  Bushire Khan in Sang-izard.  Day four:  Mir Ali Hussein Beg of Katlish.  Day five: Haji Nasir-i-Yazdani Beg of Qala-eNau.  Day six:  Seyyed Kerbalahi of Siar Chisme . . .

I recited and followed this song-of-the-places-in-between as a map.  I chanted it even after I had left the villages, using the list as credentials.  Almost everyone recognized the names, even from a hundred kilometres away.  Being able to chant it made me half belong:  it reassured hosts who were not sure whether to take me in and it suggested to anyone who thought of attacking me that I was linked to powerful names. (page 213) 

Because AI is (or should be) about ways of knowing and doing in the world, it therefore has close links to the social sciences, particularly anthropology, and to the humanities.

References:

Seymour Papert [1988]: One AI or Many? Daedalus, 117 (1) (Winter 1988):  1-14.

Rory Stewart [2004]: The Places in Between. London, UK:  Picador, pp. 211-214.

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Mathematics and proof

Published
by
peter
on 2009-12-30
in Argumentation and Mathematics
. Closed

One of the great myths of mathematicians is that mathematical knowledge, once proven, is solid, and not subject to later contestation.   Thus, Oxford mathematician Marcus du Sautoy, writing in the New Scientist (2006-08-26), says:

Proof is supposed to be what sets mathematics apart from the other sciences. Traditionally, the subject has not been an evolutionary one in which the fittest theory survives. New insights don’t suddenly overturn the theorems of the previous generation. The subject is like a huge pyramid, with each generation building on the secure foundations of the past. The nature of proof means that mathematicians, to use Newton’s words, really do stand on the shoulders of giants.

In the past, those shoulders have been extremely steady. After all, in no other science are the discoveries of the Ancient Greeks still as valid today as they were at the time. Euclid’s 2300-year-old proof that there are infinitely many primes is perhaps the first great example of a watertight proof.

The reason for this widespread view is that mathematics uses deduction to reach its conclusions.  At least, that is true of pure mathematics, or was so until computers began to be used in proofs (a topic which du Sautoy discusses in that article).  But all deduction does is to show that, given some assumptions and given some rules of inference, a certain conclusion follows from those assumptions by applying those rules of inference.  If either the assumptions are false or the rules of inference not acceptable, then the stated conclusions will not, in fact, follow.

Du Sautoy is quite wrong to claim that new insights do not overturn the theorems of the previous generation.  The history of pure mathematics is replete with examples where proven conclusions were later revealed to depend on assumptions not made explicit, or on assumptions previously thought to be obvious but which were later shown to be false, or on rules of inference later considered invalid.   For over a century, mathematicians thought that everywhere-continuous functions were also everywhere-differentiable, until shown a counter-example.  For a similar period, they thought that the convergent limit of an infinite sequence of continuous functions was itself also continuous, until shown a counter-example.  They thought that there could not exist a one-to-one and onto mapping between the real unit interval and the real unit square, until shown such a mapping (a so-called space-filling curve).  In fact, there are infinitely-many such mappings; indeed, an uncountable infinity of them.  In all these case, “proofs” of the erroneous conclusions existed, which is why the earlier mathematicians believed those conclusions.  The proofs were later shown to be flawed, because they depended on (usually-implicit) assumptions which were false.   For the differential calculus, the fixing effort was begun by Cauchy and Weierstrauss, using epsilon-delta arguments which were more rigorous than the proofs of the earlier generation of analysts.

Not only does Du Sautoy have his history wrong, but there is shurely shome mishtake in his mentioning Euclid here.  The 19th century was consumed by a controversy over the truth-status of Euclidean geometry, and the discovery of apparently-logical alternatives to it.   As clever a man as the logician and philosopher Gottlob Frege (an intellectual hero of Wittgenstein) could not get his head around the idea that these different versions of geometry could all simultaneously be true.   Yet that is the conclusion mathematicians came to: that, depending on the assumptions you made about the surface on which you doing geometry, there were in fact valid alternatives to the discoveries of the Greeks:  draw your triangles on the surface of a sphere, instead of on a flat plane, for example, and you could readily draw triangles whose three angles did not sum to 180 degrees.  You choose your assumptions, you gets your geometry!  This is not a secure pyramid of knowledge, but many pyramids, post-modernist style.

And in the first part of the 20th century, pure mathematics was consumed with a bitter argument over whether a particular rule of inference – reductio ad absurdem (RAA), or reasoning from an assumption thought to be false – was valid in deductive proofs of the existence of mathematical objects.   The dissidents created their own school of pure mathematics, constructivism, which is still being studied.  Indeed, it turns out that a closely-related logic, intuitionistic logic, appears naturally elsewhere in mathematics (as part of the internal structure of a topos). Once again, you choose your rules of inference, you gets your mathematical theorems.

There is no single, massive pyramid of knowledge here, as du Sautoy claims, but lots of smaller pyramids.  Every so often, a great mathematician is able to devise a new conceptual framework which allows some or all of these baby pyramids to appear to be part of some larger pyramid, as Pieri and Hilbert did with geometry in the 1890s, or as Lawvere and others did with category theory as a foundation for mathematics in the 1960s.   But, based on past experience, new baby pyramids will continue to be created by mathematicians arguing about the assumptions or rules of inference used in earlier proofs.    To consider this process of contestation, splitting, and attempted re-unification to be somehow different to what happens in other domains of human knowledge may be comforting to mathematicians, but is myth nonetheless.

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