Monthly Archives: December 2008

Experiments with paradox

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Pirates of PenzanceABC recently featured Dulwich Hill Public School’s admirable philosophy program.  Now, MJ (10) has been wandering around identifying paradoxes for the last week or so, probably inspired by W.S.Gilbert (represented by Toni Lamond and Jon English):

A paradox! A paradox! A most ingenious paradox!

So I delved into The Philosophy Gym and we tried on some of Stephen Law’s sample Seven Paradoxes. This book is written for adults but in fairly clear language, and uses dialogue and story to illustrate philosophic questions and reasoning processes. Law gives some general advice for solving paradoxes at the end of his book, but we found it more interesting to discuss why these stories seemed to be paradoxes, than to ‘solve’ them.

Seven Paradoxes

Mobius stripThe liar.“The first thing said to you by the first person you meet today will not be true.” Spun out into a story, this can be a little confusing, but it was quickly obvious that it was an example of: “This statement is not true.”  The statement itself, we discovered, is a subject in the statement. This is a circular argument on a Möbius strip!

The Sorites Paradox: How much can you take from a heap before it stops being a heap? MJ immediately spotted that this hinged on the definition of the word heap, and was a false dichotomy rather than a paradox.

Bob’s Balding Spot: There must come a point where, by losing just a single hair, I’ll turn from being not bald into being bald! Yes, this is the same logical form as the Sorites Paradox.

The Boastful Barber: I’m the only man who shaves all and only those men in Seville who don’t shave themselves. This quickly broke into two statements, one of which must be untrue:

(1) I do not shave any man who does shave himself, including myself; and
(2) I do shave every man who does not shave himself, including myself.

Venn diagramThis becomes clearer with a Venn diagram. I thought this would be a way to introduce the usage of “all and only”, but instead it made me question why I ever use the compound phrase instead of simpler, separate sentences.

Achilles and Tortoise: Zeno’s paradox. This puzzle is not suitable for fourth grade where infinity is still a new concept lacking plausibility.

The Ravens: Every coloured sight which is not a raven confirms that ravens are black. This one is loaded with special words and ideas. A generalisation can be disconfirmed by counter-example, or provisionally confirmed by many instances. The paradox arises from the claim that two statements are logically equivalent. When stated simply, it is obvious enough where the overlap is. This becomes clearer with a Venn diagram.

The Unexpected Examination: The teacher cannot give an Unexpected Examination, because if left to the last possible moment the examination would be expected on that date; a rule that also applies to every date before the that. Explaining the paradox is difficult. An HSC student pointed out that the reasoning is similar to that used in testing properties of infinite series. However, the cause of the paradox turns out to be quite obvious: a false dichotomy between expected and unexpected.

[Mythic Character] Doesn’t Exist: How can we say a concept does not exist, if it is clear enough to discuss? The example is not suitable for discussion in a group of varied beliefs, especially at this time of year.

Observations

Upper primary kids can learn language and ideas about thought, reasoning skills and social skills as they try to solve paradoxes. Some puzzles provide a good reason to develop graphical or experimental formulations of ideas. The absurdity of paradox can be very entertaining to upper primary children. Jon English is a kids’ entertainer.

References

    1. Law, S. 2008, Stephen Law, blog, http://stephenlaw.blogspot.com/
    2. Butler & Schaefer 1994, Pirates of Penzance, ABC
    3. Law, S. 2003, The Philosophy Gym: 25 short adventures in thinking. Review, London.
    4. Math Academy Online (undated), Zeno’s paradox of the tortoise and Achilles, Platonic Realms, http://www.mathacademy.com/pr/prime/articles/zeno_tort/index.asp
    5. Questacon 2008, Mobius Strip, Questacon on tour, http://mathssquad.questacon.edu.au/mobius_strip.html
    6. Holt, D., Chips, B., and Wallace, D., 1991, Cooperative Learning in The Secondary School: Maximizing Language Acquisition, Academic Achievement, and Social Development, NCBE Program Information Guide Series, Number 12, Summer 1991. http://www.ncela.gwu.edu/pubs/pigs/pig12.htm

      Outsourcing IT services

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      can make financial sense if:

      • the service is commoditised and low-priced;
      • the demand for the service is collapsing;
      • the skills are not sustainable in house;
      • the payroll size triggers problems that contract payments would not;
      • there is a cashflow crisis; or
      • liability can be transferred to the service provider.

      In Australia, a full-time employee on $70,000 pa works about 220 days of 7 hours per year. Employers’ on-costs (superannuation, insurance, payroll tax, administration) is typically 40-60%, so the effective hourly cost is about $68 per worked hour, and if outsourced will typically be billed at $140 per hour, so the agency profits if it exceeds 50% utilisation of its workforce. Very specific internal cost data is needed to justify outsourcing on a financial basis.

      Wheeler notes some other considerations and counter-examples, and lists a few Australian external service providers.

      References

      1. Wheeler, M. 2005, When to outsource helpdesks, ZDNet Australia, http://www.zdnet.com.au/insight/business/soa/When-to-outsource-helpdesks/0,139023749,139199827,00.htm

      Felt is a non-stretch fabric

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      Peter Pan costumeand other discoveries in the Costume department of Peter Pan on Ice.

      1. Felt is not suitable for tight skating costumes. (Um.)
      2. Tight-leg pants and ice-skates don’t go with quick changes.
      3. Any unmeasured skater might not fit in the nearest-sized available off-the-rack costume.
      4. The glass-fronted balcony is not a suitable fitting room.
      5. Some kids come with a male parent to chaperone.
      6. An all-new uniform can be very hurtful … to a team member who wasn’t told.
      7. Changing advertised fitting and rehearsal times can ruin a kid’s ability to fulfil her commitments.
      8. The costumier affects every performer’s mood.
      9. There is never too much chocolate in the world.

      Acknowledgement

      1. Image: radialmonster 2007, 20071103_536, from http://www.flickr.com/photos/13122632@N00/1879521884/ (Creative Commons ANSA 2.0)

      Reading: Three Years

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      Chekov, A. 1895, Three Years. (Alpin, H. (tr), 2004, Hesperus, London).

      Chekov reputedly had an enormous influence on Russian literature, twentieth century playwrights and short story form. This work is almost novel length, but with a small enough cast of characters for me to follow!

      Setting:
      Provincial Russian town and Moscow, 1890s.

      Main characters:
      Alexei Laptev – painfully loves Yulia, hates his brutal father and ruins everything
      Yulia Sergeyevna – marries Alexei without love
      Nina (Alexei’s sister) – dies
      Fyodor (Alexei’s industrialist brother) – contrasts with Alexei
      Polina (Alexei’s former lover) – stops passionately loving Alexei

      Impressions:
      Mood is all important, and various flavours of despair waft through this short novel. There is a story full of dramatic events, but they are delivered so concisely that they seem almost unimportant. The text is dominated by thought, leading to, during, reflecting on or triggered by the characters’ actions. A host of ‘messages’ could be read into this book, depending on the context against which it is read. This is exactly the core problem faced by the central character, Laptev: how to interpret the most subtle and possibly accidental of indications,

      There is a particular style about this, that takes a while to love. And that too is paralleled in the book, as the characters gradually change in the most likely ways, but with no sense of inevitability.

      At the start of the book, we gradually discover that Laptev is not dashing, heroic, creative or otherwise especially worthy of attention. In passing we note that he is rich, but it seems unimportant: except that the entire plot comes to hang on that point.

      Constrained by propriety, principles or aesthetics, characters over-analyse the vaguest, most inconsequential observations, and wallow in uncertainty or indecision. Under intense self-examination, feelings prove ephemeral, unstable, even when devastatingly powerful. Yet characters struggle to be true to their feelings.

      The characters have passion, but its flux is often unexpected and yet inevitable. Laptev explodes in anger at his brothers’ family pride, after giving us over a year of wistful or wishful thinking rather than decision over his desparate infatuation with Yulia. Polina suddenly settles for banal security after an endlessly drawn out passionate love/hatred of Alexei.

      Aftertaste:
      Strangely, I like this book better, three days after finishing it. Perhaps the ennui, despair or frustration of the characters was too intense for my reading pleasure. I am sure I’ll reread it in a year or two and see much more in it.

      References:
      Text: http://www.online-literature.com/anton_chekhov/1277/
      Synopsis: http://litmed.med.nyu.edu/Annotation?action=view&annid=12114
      Image: http://people.brandeis.edu/~teuber/chekhovbio.html

      Laptop trolleys: Metal or wood?

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      What should that mobile lab of laptop computers be made from?

      Modern Office Interiors - 3 inch grommetElectrical risk

      A few years ago I was shown a 240v cable with outer layer of insulation rubbed through where it passed through a metal laptop trolley. Apertures for electrical cables need rounded and non-conductive cable grommets. This is also true of wood furniture; wood is much harder than the PVC insulation on electrical cords.

      People walking on carpet build up a static charge. Some feel it discharge when they touch a metal trolley, and leap to the conclusion that they have been electrocuted by the trolley – an inaccurate but distressing perception of a risk to life. In fact, touching the trolley allows static potential to equalise with the trolley and perhaps the notebooks – a desirable reduction in risk to electronically sensitive equipment.

      Pyrolysis of woodIgnition

      Suggested origins of fire include flammables resting against overheating batteries or transformers, battery failure, or damage on the powerpoint side of transformers. Wood probably provides no better protection against electrical fire than metal, and (assuming appropriate circuitbreakers), electrically conductive construction might slightly reduce the chances for fire by dissipating accumulated charge.

      However, metal conducts heat much better than wood, quickly reducing hotspots. (Compare lighting candle wax dripped on wood and candle wax on a metal tray.) A metal trolley is likely to need more heat before its flammable contents will sustain a fire.

      PC LOCS Super Calf 12 trolley

      Spread

      Fire-retardant treated wood is unlikely to sustain a fire until the local temperature exceeds 400ºC for several minutes (VTT undated). A trolley that ensures adequate convective ventilation of the equipment is unlikely to reach that temperature in any part until a fire is well established. (I once tried running a notebook wrapped in a blanket: it shut down before the hottest point on the blanket reached 100ºC. I suppose the experiment bears repeating.)

      However,  computers should be stored on edge, to allow natural convection to prevent overheating. This means, once a fire does start, as hot air rises it will establish a strong updraught drawing fresh air to the fire. The temperature at the top of the trolley is likely to be high.

      The most important step

      Ensure that no flammable materials accumulate in the trolley. It is probably a good thing to rest computers on rollers or a very open grid rather than solid surfaces, in order to expose rubbish to view and to allow it to drop through.

      References

      1. VTT undated, Burning of Wood, http://virtual.vtt.fi/virtual/innofirewood/stateoftheart/database/burning/burning.html
      2. PC Locs 2007, The Super Calf 12-bay Notebook Computer Cart, http://www.pclocs.com.au/laptoptrolleys-supercalf-12-bay.htm
      3. Wilson, T. 2006, What causes laptop batteries to overheat? How Stuff Works. http://computer.howstuffworks.com/dell-battery-fire.htm
      4. Image: http://www.modernofficeinteriors.com/3grm10.html

      Reading The Action Research Planner

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      Action Research is a methodology widely used in school improvement. It is easy to justify to school administrators because it works with regular teachers in existing courses with real students, to deliver improvement that teachers and students recognise. It is credible to teachers because it addresses the phenomenon they can see. It is credible to students because it values their voice, and does not necessarily rely on obscure abstract concepts or expert statistical tricks.

      The following guidance is quoted and adapted from Kemmis and McTaggert 1988.

      Action Research SpiralAction Research Spiral

      1. Select a thematic concern
      2. Plan for improvement of current practice.
        1. Prospective, flexible, considering risks and constraints.
        2. Empowering practitioners
      3. Action to implement plan.
        1. Dynamic, responding instantly to cricumstances and effects
        2. Observed
      4. Observation of effects of action.
        1. planned, “responsible, open-eyed and open-minded”.
        2. observe the action process, effects of action, circumstances and constraints
        3. intended to inform reflection
      5. Reflection on effects
      6. Iterate PAOR

      Not

      1. “the usual thing teachers do.” (Should include “rigorous group reflection“.)
      2. Problem solving. (Should include problem posing.)
      3. Research done on other people. (Should be participants.)
      4. Scientific method. (Should be broader than objectivism.)

      Key elements

      1. improving education by change
      2. participatory
      3. self-reflective spiral (above)
      4. collaborative
      5. self-critical communities
      6. systematic learning process
      7. theorising: inquisitiveness, understanding, rationales
      8. testing ideas
      9. data: include records, judgements, reactions, impressions
      10. personal journals of learning about (1) teaching practice; (2) research method
      11. a political process
      12. critical analyses including organisational and conceptual structures
      13. starts small
      14. small cycles that grow as questions do
      15. small groups of collaborators and widens
      16. records of change in (1) practice, (2) language and discourse, (3) relationships and organisation, (4) action research.
      17. produces reasoned justification

      Reference

      1. Kemmis, S., McTaggert, R., (eds) 1988, The Action Research Planner, 3rd edition. Deakin University, Geelong.
      2. Image: Dick, B.  (2002) Action research: action and research  [On line].  Available at
        http://www.scu.edu.au/schools/gcm/ar/arp/aandr.html

      Gallipoli pride

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      PoppiesRANT

      “The pride of our nation was forged at Gallipoli.”
      (Speaker at school Anzac Day ceremony, 2008)

      Say what? I hope we have better reasons for pride than that!

      Honour. We do right to honour our servicemen and women and remember that death and suffering are real, personal experiences. We observers have no right to attribute any other meaning to them. We have no right to take credit for their choices.

      We should also honour the campaigners against conscription, the objectors, pacifists, deserters, communists and relatives who – for good reason or bad – opposed the obscene wastage of men, despite uncertainty, opprobrium and risk.

      Shame. We should remember that war sets even the best men to do foul deeds. The pointless deaths (including 86,000 inflicted by our army in Turkey) were the product of personal qualities (courage, initiative, tenacity, loyalty) alloyed with colonial values that we surely can now see as perilous (tribalism, elitism, militarism, racism, obedience).

      We should remember the findings of the 1917 commission of inquiry, and repent of trusting military leaders or attacking foreign ground.

      Consequences. We should remember that dangerous demagogues exploited the resentment of the vanquished; we should not offend the dignity of another nation even in war. We should remember that industrialists profited enormously in World War I while the deaths, injuries, illness and economic distortion laid the ground for the great depression; WW1 Anti-conscription posterwe should never expect war and its sequelae to be affordable.

      A fruitless, bloody WWI campaign at Gallipoli is now studied every year, Year 4 to Year 9, in NSW schools. Even so, in 2001 our then Prime Minister offered our troops to an ally before they were even requested, for an invasion that is now known to be illegal, ill-informed, ill-conceived and internationally abhorred.

      I am not proud.

      References

      RSI for teachers

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      What happened to the epidemic? Was it just panic? That depends on whether you were referred to a rheumatologist, occupational therapist, musculoskeletal surgeon or psychiatrist!

      “The Australian RSI epidemic burnt out not because any one notional cause or series of causes was identified and successfully addressed. It burnt out because in the end doctors stopped certifying as physically injured largenumbers of uninjured workers.” (Awerbuch 2004)

      Some injuries described as Repetitive Strain Injury (RSI) encompass real, long-term physical injuries wrapped in psychosocial issues. Unfortunately, the industrial climate in the 1980s and personal circumstances fueled anxiety and resistance to ameliorative measures, by both employers and employees (Reid and Reynolds 1990). Reports of RSI dropped drastically when compensation rules became less supportive (Tyrer 1998). Clinicians have to discriminate between physical symptomatology and psychiatric phenomena (Bell 2000).

      Alleged risk factors include genetic factors, mental disposition, specific movement patterns, obesity, smoking and inactivity (Quilter 2003). The genetic aspect is out of our control. People have difficulty managing stress, especially when their symptomology is not respected. The easiest thing to do is to alter behaviours.

      • We break up highly repetitious movement and confined exertion patterns by varying people’s tasks in the course of the day.
      • We design equipment, furniture and tasks to avoid static loads (habitual hunching, twisting and tension, etc) and reduce inflammatory triggers (ulnar deviation, etc).
      • We remind users to avoid pain. (Duh!)

      Fortunately, teachers and students have a great deal of autonomy (mental disposition) and variation (physical behaviours) in their physical work, which should reduce their risk compared to, say, data-key operators.

      Remarkably, Canadian metanalysis of RSI treatment studies found:

      • “Moderate evidence … that workplace adjustments as implemented in the studies reviewed have NO effect on musculoskeletal or visual outcomes.”
      • “Moderate evidence … that rest breaks together with exercise during the breaks have NO effect on musculoskeletal outcomes.”
      • “Evidence was insufficient to conclude that exercise training, stress management training together with workplace adjustment, new chairs, lighting plus VDT glasses, new office lens type or VDT glasses had effects on musculoskeletal outcomes.” (Strauss 2007)

      Take away messages for teachers

      • Avoid obviously unsafe work practices, perhaps using use guidelines for teachers from RSI/OOS ACT.
      • Teach about lifestyle risk factors (smoking, exercise, stress, etc).
      • Feeling bad increases your risk of injury, and makes symptoms seem worse. Address psychosocial issues.
      • On symptoms, see a doctor. Diagnosis requires medical expertise.
      • There is no universal or guaranteed treatment.
      • Respond to the present circumstances of each individual, continuously.

      I thank Martin for pointing out these guidelines for kids:

      References:

      1. Awerbuch, M. 2004, Repetitive strain injuries: has the Australian epidemic burnt out? Internal Medicine Journal 2004; 34: 416–419
      2. Bell, DS, 2000, Epidemic Occupational Pseudo-Illness: The Plague of Acronyms, Current Review of Pain 2000, 4:324–330
      3. Quilter, D. 2003, Risk factors for repetitive strain injury, RSIHelp.com, http://www.rsihelp.com/risk_factors.shtml
      4. Reid, J. and  Reynolds, L. 1990, Requiem for RSI: The Explanation and Control of an Occupational Epidemic, Medical Anthropology Quarterly, New Series, Vol. 4, No. 2, Medical Anthropology and the Construction of the Medical Conditions (Jun., 1990), pp. 162-190
      5. RSI and Overuse Injury Association of the ACT 2006, Frequently asked questions about RSI/OOS, RSI/OOS, http://www.rsi.org.au/faqs.htm
      6. Strauss, VP 2007, Whatever happened to the crippling RSI epidemic? CBC News, February 23, http://www.cbc.ca/news/viewpoint/vp_strauss/20070223.html
      7. Tyrer, SP, Repetitive Strain Injury, in Manu, P. 1998 Functional Somatic Syndromes: Etiology, Diagnosis and Treatment, Cambridge University Press.