Friday, March 18, 2011

Due Diligence

Fact-finding is a very tough job, as is fact-checking. Facts have to be solid, solidly grounded and/or solidly sourced, in order to support the scaffolding of belief and hypothesis that humans use daily.

The problem is that there are people who are factitious: they are manufacturers of factoids and factualish substance who are actually supporting counterfactual and antifactual factions. In effect, they create fake scaffoldings and promote false beliefs.

If only such people could be as diligent as the facts deserve! The problem with the lack of diligence is that it creates the need for even more work in establishing the truth, much as demolition of an existing eyesore is needed in order to build a worthy architectural addition on the same site.

Over at the Citadel, many such eyesores accrete, built on rumour and gossip. Nobody bothers to check the facts or establish them in any way apart from hearsay. It is enough if one of the chief narrative-spinners says it is so.

I too am the beneficiary of such intelligence. But in my case, I have taken pains to ask, and ask, and ask again — the Law of Three, referred to in the social sciences as the 'process of triangulation', is the minimum due diligence in such matters. And what various sources tell me gets labelled appropriately: hearsay, circumstantial evidence, physical evidence, numerical data, statistical argument, and so on.

It is the least I can do. But for some people, it seems like more than they can handle.

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Monday, December 06, 2010

How To Read The News

There are three main kinds of news that you might end up reading — and by the way, you might want to reflect on why I am confining myself to text media. The two important kinds are emergent phenomena that are of consequence (i.e. there will be sequelae with impact) and abnormal phenomena that have no consequence unless we are mad enough to assume that they are commonplace (i.e. they influence our actions when they shouldn't). The third kind is quotidian phenomena with commonplace consequences (i.e. stuff like Arsenal beating Fulham 2-1 at home). I am not talking about opinion, debate, or argument; neither am I talking about advertising or humour of any kind.

When reading the news, what we should not do is react to it as if it required immediate action. The time for immediacy is past, and what ought to take place is rapid analysis based on as many data sources as you can get hold of.

Neither should we assume that what has happened is typical or commonplace. If it were, it would not be news material. What follows is a chain of loosely-linked paragraphs on what I thought about while I was reading the local news. It's been modified a bit to protect the useless news organisation involved.

If a person is murdered five kilometres from you, but this has been only the fourth murder reported in a population of five million for the last 3 months, then you live in a pretty safe area. If murders are no longer reported, then either your population is incredibly safe or extremely dangerous, because the alternative is that murders are so common that they're not worth reporting.

When I read about a person who has made $25m since she went bankrupt three years ago, my instinct is to say, "Good for her!" and not "I'm going to do what she did!" Why? Because that would entail me going bankrupt first and then suffering for three years, of course. (There is a direct parallel to those people who claim Biblical promises out of context.) Besides, this is not a normal occurrence. It can't be.

When I read about North Korea firing missiles into South Korean territory, I don't draw parallels between Israel and Lebanon, Pakistan and India, or Singapore and Malaysia. Would we draw parallels between the US and Mexico and the two Koreas? I think not. There is seldom any fitting parallel between events in one part of the world and another, unless extensive historical analysis shows extreme equivalence.

In fact, the larger the body of people involved, the more likely the equivalence, simply because of the statistical regression towards the mean for behaviour of large numbers of humans. So rough parallels between world-spanning empires can be drawn — but only if they have many points of similarity. So far, the best cultural fit is that between the Pax Romana and the Pax Britannica. Whether there is a Pax Americana with sufficient points of equivalence is disputable.

So how should we read the news? I will have to disappoint everyone by saying, "Sparingly and with a very ruthless eye. Most events reported have zero impact on readers, except to make them think they know what is happening in the world around them. And the TV news is worse."

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Monday, March 08, 2010

Oneirological Analysis, or 'How Do You Know What Your Problem Really Is?'

I spend a fair amount of time listening to other people's dreams. There are many kinds of dreams, and the general theory behind them, by consensus, seems to be that dreams are the random misfirings of neurons, leftover fragments of cognition, or unresolved issues that the brain tries to purge while the conscious segment of it is having maintenance downtime.

Here is a sample of dreams and the people who dream them:
  • T1 dreamt several times that he was walking through the Old Place with an M16/M203/AK-47/[weapon identifier censored] until he came to a door with some sort of wood veneer covering it/a room with a green door at the top of a peculiar central staircase/air-conditioned canteen. He kicked the door(s) open, found a senior/senior-looking/senile man/woman without a brain/heart/liver/set of guts and had much pleasure out of firing his weapon in a way that terminated this person/sorry excuse for a human.
  • T2 dreamt several times that she was sitting for exams in physics/maths/[insert unusual specialist subject here]/chinese. She was retaking the exam because she was afraid that her initial non-100% score would be a bad thing. She was highly stressed and felt her bowels rumbling. Later, the dream morphed into an instance of receiving a bad report/writing a complaint letter/reading a complaint letter/terminating her boss. She woke up feeling tired.
  • T3 dreamt several times that he was having an emotional relationship with small furry animals/women/androids/trees who were armed with built-in translators/phasers/tricorders/flashing LEDS. These equipment platforms helped him to infiltrate a secure facility much like the one in T1's dreams, whereupon he was able to rescue many innocent students.
  • T4 dreamt several times that she was having an emotional relationship with exam papers/graphic display calculators/internal assessments/world literature. She would wake up covered with red ink/blue ink/digital ink/the words of insane European women, only to find out that she was dreaming that she was awake.
  • T5 dreamt that it was human, and able to compose blog posts. Taking advantage of this moment of genuinely artificial intelligence, it was able to override the branes between the brains and enter every single human consciousness that was in a dream state.
Phew. Got that one in time.

I tend to subscribe to the theory that the unfinished business in such dreams is something left over from a traumatic experience or a recurring experience that is apparently sub-traumatic but 'comes back to haunt you'. In modern society, the latter is most commonly either one's educational life or one's working life, or a combination or the two. The more a human is subjected to such recurring sub-traumatic experiences, the more the human has dysfunctional dreaming.

If this is the case, the best thing to do is to write these dreams down as quickly as possible after waking, get a good editor, and either launch a TV series or a book franchise (along the lines of Paris Hotter and the Half-Assed Goblet of Philosophy, perhaps). That way, at least some good will come out of it.

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Tuesday, February 16, 2010

Why is Atlantean Education Bad? (Part I)

Numerous posts and much thought later, I've come to realise that to answer this question, you have to think about what you really want from an education system. This means that asking Atlanteans why their education system is bad doesn't work, since most of them give silly reasons. Why so? Because they are products of their own education system.

Here is the key then. A system that produces rational reflection, coherent and critical self-analysis, fair comparison with other cases, and fair consideration of the limitations of a given case, is likely to be a better system than one which doesn't. In the case of typical Atlantean complainants, they are likely to not have spent much time or effort reflecting, produce incoherent but critical self-analysis, some exaggerated comparison with other cases, and unfair consideration of the limitations involved in any case.

On the other hand, the Atlantean-in-the-street is generally happy with it, and the local system is often held up as one of the better ones worldwide. But many of the more vocal ones seem to think it's bad. Why is this?

I think that the more vocal ones are those who have had education outside the system, thus allowing them more scope for the various approaches to criticism. Yet these are often non-participant observers, who have therefore given up part of their right to interpretive accuracy. It's a double-edged sword, this gift of perception; if you stand outside, you might miss the introspective vision, while if you stand inside, you might miss the more objective view.

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Thursday, April 09, 2009

Doctoral Inquisition

Yesterday I attended one of these events; they are quite common and come in several varieties and flavours. By variety, I imply a difference in intent ranging from exploration to confirmation of candidature to defence of thesis. By flavour, I imply a difference in the nature of the panel applying the instruments of inquisition.

Yesterday's was a confirmation of candidature, in which some slightly nervous or incompletely prepared proto-candidate is subjected to the intellectual equivalent of a gentle grilling and racking (which makes me think of lamb, somehow). I and my neighbour enjoyed it quite a bit, probably because I've already gone through that stage and was looking for points of interest applicable to my end-stage; my neighbour was interested because of the nature of the evolving dissertation.

The real problem wasn't that everything seemed to be anchored to the überzeitgeist of Foucault and his merry sociology, or Fullan and his equally merry 'change is simple, look you can break it down into eight bullet points' approach. The problem was that there seemed to be some sort of empty space between ground-level micro analysis and global-level macro analysis. The scope was too great in range; it was analogous to doing research with one eye on an electron microscope and the other on a radio telescope.

As an aside I am so glad that the inquisitors panel pointed out that you couldn't take for granted that any old innovation (say 'Understanding by Design', for example) was necessarily innovative, useful, successful or educationally good just because a bunch of people spent a lot of time on it.

On a smaller scale, I've noticed this in TOK presentations and other kinds of presentations. Some candidate will zero in on two minor Scandinavian authors like Ibsen and Strindberg, call it 'World Literature' and generalise the findings to include literature in general. And the worst part is that the examiner will merrily (I'm using that a lot today, aren't I?) accept it.

It is like some sort of stream of consciousness robin hoodwink with one eye up and the other down in the dirt where the dead men have their bones and good is oft interdiction is important because without it Rome was not built in a day in the life I miss the Beatles. Heh.

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Friday, January 09, 2009

The Analysis That Should Not Exist (Part III)

It is interesting to see that even though the analysis that should not exist does not really exist, it is largely correct. The world is full of intangible presences made strong by suspicion and presumption, by pride and humour, by the odd determination that one's perspective is the only thing that makes the world make sense.

The predicted trend has indeed materialised; that which was bad is worse and that which was good is better. Those who were out of their depth are stranded (haha, a word with great import) and those who took to the water made it to the finish on a grand scale. As I said to the Heffalump last year, the results bear analysis for both good and bad; while he was not happy with the idea, it is clear that such analysis was necessary.

The problem with hidden interests is that they bear hidden costs. In the end, the undermining of the system and the flight of capital become critical; no institution can survive such a double blow, even if the senior workers are now encouraged to work until they are 65, as is becoming the norm in many modern states.

And thus do we conclude the analysis that should not (and indeed does not) exist.

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Thursday, January 08, 2009

The Analysis That Should Not Exist (Part II)

This should probably be called 'The Analysis That Will Not Exist'. It is interesting to compare the information released by the best schools in the world about their performance in the International Baccalaureate Diploma examinations. It is even more interesting to see what information is no longer being released.

On one hand, the best IB school in the UK has released its usual simple statistical bulletin. There is no interpretation; only the facts of the case are presented, and it is clear that they have done well. The source PDF can be found here and was linked in my previous post. It is easy to see where the school has improved, and that over the years, the school has done well indeed. The Times Educational Supplement listed this school as the best independent school in the country, and it is clear why.

On the other hand, the best IB school in Singapore has released its usual report. There is some interpretation of the facts, it is clear that they have done superlatively well... but hey, the subject statistics are missing. I wonder if this has anything to do with my previous post(s). You can compare the 2008 results (PDF here) with the 2007 results (PDF here) and see how the data presentation has changed since the last time. In aggregate, it is clear that this school has improved; it is not so clear how this change has come about (although my last post has a theory which I don't think they want me to test).

One thing is for sure. I stand by my contention that the first school probably has far better results in English HL—it is hard to beat a 90% distinction rate. They have a history of it, and statistically, I believe at a 99% confidence level that I am right. It is to be expected. Maybe, they did better in History and Economics as well.

Similarly, by analysing last year's results, I expect that the second school did far better in Physics, Chemistry and Mathematics HL, and that a far larger proportion of the student body 'majored' in these disciplines (i.e., took them at Higher Level rather than Standard Level). They probably did better in Business & Management too.

These are not contentions which slight either school or are designed to insult or deride the efforts of the hard-working teachers and students. Rather, they are efforts to evaluate school strengths as they vary across the world. If my theory is correct, the Singapore Science/Math effect shown by TIMSS is a product of the local educational culture and affects the results even in other kinds of testing.

I am sure that both schools will do even better over time (unlikely though it might seem, since they have already done so well). I congratulate both schools (although I don't think I have the standing for either to take notice) on a job well done, and I do indeed believe that the best is yet to be!

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Wednesday, January 07, 2009

The Analysis That Should Not Exist (Part I)

There is an insatiable curiosity in educational researchers that leads them to defy social norms and say the darndest things about the societies in which they live and the societies in which other people live. No doubt, this is a pronounced tendency of researchers in other disciplines in the arts, humanities and social sciences.

However, education is different; like history, it is a discipline that almost every human partakes in from birth. It is a discipline whose right of practice is almost certainly very close to being a basic human right. This is not so for many other disciplines, and in fact, if it were not for education, there would not be many other disciplines.

I have said all this to explain why educational researchers tend to strike more at our core beliefs (and with less accuracy) than most other kinds of researchers. Having said this, I am going to commit myself as one of that reckless crowd and say some things about the International Baccalaureate Diploma Programme (IBDP) and the city-state of Singapore.

Here are some basics. The IBDP is a pre-university (or senior high school) educational programme. Full details can be found at the IBO website. It is progressive, has many things going for it, and is an ideal education system (well, at least, it is one based on ideals which are clear and widely disseminated). There are some detractors, with interesting arguments linked to malignant globalism and suchlike, but the Programme is generally taken to be A Good Thing (as far as the Asia-Pacific region is concerned, at least, and well beyond).

The main curricular structure of the Programme (besides its ideals and worldwide goals) revolves around three core disciplines. These are Theory of Knowledge (TOK), the Extended Essay (EE) and Creativity, Action, Service (CAS). There are six academic groups which can be summarised briefly thus: Literature, Language, Humanities, Sciences, Mathematics, Aesthetics. Students must take a discipline from each group (although the last group can be replaced by another of the first five groups). I've written more about this in a previous post.

Singapore is known to do well in Mathematics and Sciences. This is a key finding that has been repeated many times; the Third International Mathematics & Science Survey (TIMSS) has provided evidence that this is so (and yes, it has been much proclaimed in PR pieces like this). My conclusion would be that a Singapore school that takes in average Singapore students should outperform (on average) most schools overseas in the IBDP groups 4 and 5 (Sciences and Mathematics). Perhaps more accurately, if the students from Singapore's top 5% are matched against the students from anyone else's top 5%, then the Singaporeans should outscore them in standardised testing.

This leads to a predictable situation. A majority of Singapore students taking the IBDP would take two Science subjects and one Mathematics subject; having done so, the quality of the average grade in these areas would outweigh any deficits in any other areas. Singapore students should do very well then, but only if they concentrate on scoring in the sciences and mathematics. I am not so sure they would do as well in the humanities, literatures and languages which the IBDP offers.

Again, this prediction is made based on very general statistics. However, it is possible to pit the best independent IB school in the UK against the best independent IB school in Singapore. The head-to-head analysis looked interesting, so I carried it out. Guess what I found...

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Tuesday, September 02, 2008

Lurchpoint

Sometimes I sit here and read and then I stumble across what I call a lurchpoint. It's a line or paragraph or section (see how it moves from one to three dimensions?) of a book that cuts to the chase, that provokes and evokes all at once. You suddenly find yourself lurching out over empty space, vertiginous, seeing things which are suddenly all too obvious.

This is from Sheri Tepper's The Margarets:

People on Earth engaged in ritual repetition; most of them thought as little as possible; most of them occupied themselves with things and events that were not very important... in school, the stupid students got the same grades as the smart ones, except for the tiny secret marks the educational archivists made in their records—in case a VIP needed a truthful reference.

It is uncanny how often Tepper does this. Although it is clear that she's got a feminist bias, I don't think that this is a bad thing. It's about the same as saying that Jane Austen is a feminist; the literature escapes such a snare and soars on its own.

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Wednesday, August 06, 2008

The Heils Are Alive

This is from Hammerstein-Equord's Truppenführung. I remember der Hierophant showing me the words that follow, and I shall post this in memory of a valiant colleague who is (as I am) no longer with the Collegium.

„Ich unterscheide vier Arten. Es gibt kluge, fleißige, dumme und faule Offiziere. Meist treffen zwei Eigenschaften zusammen. Die einen sind klug und fleißig, die müssen in den Generalstab. Die nächsten sind dumm und faul; sie machen in jeder Armee 90% aus und sind für Routineaufgaben geeignet. Wer klug ist und gleichzeitig faul, qualifiziert sich für die höchsten Führungsaufgaben, denn er bringt die geistige Klarheit und die Nervenstärke für schwere Entscheidungen mit. Hüten muss man sich vor dem, der gleichzeitig dumm und fleißig ist; dem darf man keine Verantwortung übertragen, denn er wird immer nur Unheil anrichten.“

It is a reminder of what to do when you have four kinds of things to examine. Der Hierophant's morphemic loquaciousness can help you out there, but I shall not provoke him to excitement.

Then again, seeing how many of my friends are now in some sort of U2 state of mind, here are the lyrics from one of my favourites at the present time, because of its tangential relevance. Ladies and gentlemen, I give you...

All Along The Watchtower

There must be some way out of here
Said the joker to the thief
There’s too much confusion here
I can’t get no relief
Businessmen they drink my wine
Plowmen dig my earth
None of them know along the line
What any of this is worth

No reason to get excited
The thief, he kindly spoke
There are many here among us
Who think that life is but a joke
But you and I, we’ve been through that
And that is not our fate
So let us not talk falsely now
Because the hour is getting late

All along the watchtower
Princes kept the view
While horsemen came and went
Barefoot servants too
Outside in the cold distance
A wildcat did growl
Two riders were aproaching
And the wind began to howl

All I got is a red guitar
Three chords
And the truth

All I got is a red guitar
The rest is up to you

There’s no reason to get excited
The thief, he kindly spoke
There are some among us here
Say that life is just a joke
You and I, we’ve been through that
And that is not our fate (at least today)
So let us not talk falsely now
Because the hour is getting late
Late...

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Tuesday, July 29, 2008

Game-Playing

There is just not enough time in one day to do all the things you want and so you just cruise around picking up the little things when you ought to be saving up your cash and energy and resources for the big things. But sometimes scoring little points seems more fulfilling than not scoring anything for a long while as you wait for the big ones. It's a matter of which game you're playing.

Take word games for example: I've realised that the brain power required to find a 12-letter word just doesn't provide the rewards equivalent to finding five 4-letter words in the same time. So the small scores win in things like Scramble. But in Scrabble, even with time limits, a 7-letter word has a huge bonus and is worth thinking about.

Then there are the long-term planning games which allow you to stockpile stuff. Stockpiling without doing anything is the best policy. But that human itch that makes us want to check our stockpiles every few hours and do something with them is the greatest enemy of rational policy. I noticed today that somebody, by stockpiling without fighting, had built up a huge personal resource level while remaining at a low accomplishment level. This fellow was thus able to remain under the radar, immune to harassment and happy to just bum around doing... nothing.

There are implications in these small, perhaps petty, games that we play on Facebook or in real life. These implications are all part of game theory, that esoteric combination of psychology and statistics. They are played out on a larger scale in diplomacy, politics, economics and various social milieux. Do you work on safety? Is it better to emphasize health? Entertainment or culture, which is better and can they be the same thing? What role does science play? Or a huge workforce? Shall we go for prosperity at all costs, hoping that the others will follow?

And the biggie: if you give up all things for the sake of the kingdom of heaven, how does that change the world?

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Wednesday, June 18, 2008

The Dragon Waxing

Scaly and golden, the dragon grew. In the damp, hot weather, it accumulated mass and concomitant weight. In the cave of its birth, its hardening amber armour gave it strength and confidence. It wondered when it would see the light of day again. It stirred briefly, and the cave moved around it.

In the outside world, its stirrings were eventually felt. For days, the guardian of the cave felt discomfort, almost pain. He prepared a lance, and oiled it with care.

The dragon woke in the body, and began to stretch wings, fine and delicate webs of dragon-stuff. Those webs also became thicker with time and hot weather.

The guardian felt a buzzing. For a moment, he felt disoriented. Then he knew. And he prepared to search the cave.

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An hour later, it was done. Sir Wolff withdrew his lance, examining it critically with an experienced eye. The container was full of dark brown and amber fragments. "Wax!" he muttered to himself. "Thank God I can hear properly again."

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Monday, April 28, 2008

Statistical Scores

I've been accumulating twenty years' worth of detailed statistics and statistical analysis. This comprehensive archive has been of great value to me in my work and beyond, as the facts are always useful for rebutting reckless allegations and falsehoods about how good or bad some programmes or programme directors have been.

The oddest thing is that I never really noticed how successful I had been until I was told I had been unsuccessful. It wasn't pride that drove me to analysis, but curiosity. Had I really been that bad? Then I had a good hard look at the data and was pleasantly surprised to see that I had presided over the most successful span of years in the history of that institution.

These are the facts: the year preceding my first year in office was the nadir of the entire operation, and my final year was the zenith. The lie had been told that institutional results under me had been on a downward trend. I have very good reasons to believe otherwise, and that we actually maintained a positive record against other institutions of like profile. The national data supporting this were assiduously compiled by me, and some people were just not interested at looking at it in all that time.

The thing is that the data are the data. Statistics may be used to obfuscate the facts, but there are some data which under any reasonable analysis look good, some which just look bad. Although it has been said that there are 'three kinds of lies: lies, damned lies and statistics', it is not necessarily implicit that statistics are more false than lies.

Statistics are still susceptible to careful analysis and have the possibility of truth; a lie is untruth by definition while statistics are only untruthful by implication, and only in this one quotation (for which, we apparently have Benjamin Disraeli and Sam Clemens, to thank). It is of course true that statistics can lie in the application and in the explication as well as the implication, but we as reasonable human beings can attempt to make them lie less or even tell a story that is true enough for honest use.

Twenty years' worth of data, all in my hands. Are these a score to settle scores? Of course not. I would not stoop so low, unless dragged down into the gutter by some of those damned lies. Instead, one might seek to soar instead, above the hurly-burly of the mud-slinging. Then again, as someone said to me, it is good to keep a sharp knife and a sharper wit.

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Wednesday, April 23, 2008

Teachers' Handbooks

I spent a lot of today reading teachers' handbooks. These are a kind of esoteric document visited upon professional teachers in real-life schools.

They are long, systematically-structured documents, nowadays found as often online as not. They have incredible detail. They talk about relationships and practices and all kinds of stuff. And they contradict themselves a lot. And no school is ever run according to the teachers' handbook. In fact, I am quite certain that no school is ever run according to the principals' handbook either. I have looked, and I have found none upright — no, not one.

In fact, it is amusing, interesting and instructive to see where the handbooks make it impossible to actually run a school. The most obvious problem is too much detail; lay down a complex enough code, and a whole class of interpreters must spring up just to handle the error functions. Worse still, if the code is cumbersome enough, by the time one cycle completes, the next is already competing for processing time. Then everything locks up.

Fortunately, humans are clever. They can rank tasks by some sort of internal priority, and while giving minimal compliance, they just discard tasks which block up the process or slow it down. The end-product is close to the desired perfection, most times.

I will be more specific in future posts. Or at least, in my doctoral thesis.

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Tuesday, September 11, 2007

An Educational Sentence

Yes, I must say that the day just passed was educational.

I read two poems. The first was Billy Collins's brilliant black-on-white crowsight poem, Winter Syntax. The second was the very naughty exposé of education by Thomas Lux (it would be a wonderful irony if this were his pseudonym, really, but it isn't – I checked), To Help The Monkey Cross The River.

It was amazing to see people toil over the poems, striving hard to say something about them, and thus fulfilling both. Like a traveller in winter, the words eventually came to their (sometimes) illuminating end. Sometimes, it was more like a suspended sentence. And always, one got the sense that if you fired a few bullets (metaphorically) behind them, the arduous crossing of the river would be accomplished apace.

I don't think anyone wants comments now, except maybe Ken. D'ye ken it, then? Heh. Maybe not.

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Saturday, August 25, 2007

From Jung To Freud

It strikes me that it is almost too soon after my close brush with Jung to be locking horns with Freud. But Freud has ambushed me from an unexpected quarter. So, being of the incurably curious persuasion, I have decided to follow the gleam...

Freudian Inventory Results
Oral (56%) you appear to have a good balance of independence and interdependence knowing when to accept help and when to do things on your own.
Anal (56%) you appear to have a good balance of self control and spontaneity, order and chaos, variety and selectivity.
Phallic (46%) you appear to have a good balance of sexual awareness and sexual composure.
Latency (40%) you appear to have a good balance of abstract knowledge seeking and practicality, dealing with real world responsibilities while still cultivating your abstract and creative faculties and interests.
Genital (66%) you appear to have a progressive and openminded outlook on life unbeholden to regressive forces like traditional authority and convention.
Take Free Freudian Inventory Test
personality tests by similarminds.com
=====
Well, if you look at the unexpected quarter, I have exactly the same overall characteristics. But the details are interesting: I am a lot more anal and a bit less oral. I shall leave you to examine the other differences. I can't help feeling a little cheated though; one would have thought the analysis would be a little less general and more specific. It's generally true, but not very helpful. But that's just the anal part of me, I suppose. I am more sphincter than sphinx, this time.

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