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Friday, 23 August 2013

Not your usual bushranger

A note added later: this title ended up coming out as a print book, after all.  The principle remains, and some of these books may end up as e-books.  I have too much to say before I drop off my twig.  Hooray, though, for Five Mile Press who are less penguinish than most.

One of the things that I planned for the e-book version of Not Your Usual Bushrangers was  a handy set of hotlinks to the footnotes, so rather than waste it, these links are now online as a freebie. Please, now read on.

Tom Roberts' Bailed Up, one of the clichéd
items that is trotted out far too often.
I think I have already mentioned my dissatisfaction with print publishers at the moment.  They are slow and nervous, like penguins on the edge of an ice floe, waiting for some penguin to jump in first, to test the waters for sea leopards, lurking under the ice.  They stand there, they get cold feet, and they do nothing.

So I am jumping in on the e-book thing.

I have something like fifty print books to my name, published over 40 years, but I am getting on, and I want to say a few things before I get too old and boring.  So I have gathered up all my research notes, and come up with 27 titles that I may well write.  Probably 20 of them will get done, and if they sell as print books for $40 each, I will get $4, eventually.  I can sell them as e-books for much less. and still get the same return.

I plan to publish them all as e-books, as a series, with titles starting Not Your Usual...  First cab off the rank is to be Not Your Usual Bushrangers, and it is an attempt to get away from the usual five or six.  That one is definitely suited to the curriculum, though I am writing for adults rather than children: I am targeting the teachers and the parents. Some of the other books I have in mind will be less relevant to the curriculum, but they will all be packed with good yarns, and links to more information.

And I am publishing them myself, as e-books, through the Australian Society of Authors, which does the hosting and marketing for a 20% commission. They will be in mobi, epub and pdf formats, with no DRM,and the ASA is working on a way of selling site licences to school libraries.  I can sell for $5 and still get $4 each time, and much faster.  They will have ISBNs, and I will be open to print publishers picking up any of the titles. If they don't, I am hoping to put a dent in their sales, and make them match me in the e-book game.

If others follow suit, my initiative might just be a game-changer, but my plan relies heavily on the honesty of ordinary people. I will have more to say about this on a dedicated page on my writing site.

Moondyne Joe: after his
escape, he dressed himself
in marsupial skins
Now about those bushrangers: is it not more interesting to read of Moondyne Joe, who once escaped from gaol, dressed only in his flannel drawers, and who was later pardoned for his crimes by the governor because he was such a good escaper?  Or would you rather read of callous thugs?

The simple fact of the matter is that bushrangers were almost as common as bushflies and more of a nuisance, but most of the detail is buried.

I will have to deal with the career of the Kelly Gang briefly, but only to show how they were defeated by technology. Hall, Gilbert, Dunn, Morgan, Gardiner, Moonlite and Thunderbolt are all overdone, unlike Sam Poo, the Chinese bushranger, and Black Caesar, our first-ever bushranger (except the ones in January 1788, who are in there as well).

Anyhow, here's a sample, the tale of a rogue who never did anybody any harm (except, perhaps, himself and a naval lieutenant who probably deserved what he got).  I need to add here that in the book, this follows on from the tale of one William Page who was hanged for his crimes.

The whole idea is to inject some new life into an area of discourse which is sadly stultified.  If others pinch my ideas, I will have won.  That's what writing is about, really: changing and enlivening the content!

* * * * * * * * * * * * * * * * * * * *

The life and death of diver Fitzgerald

Almost as soon as there were newspapers in Sydney (or at least that have survived until today), people knew about John Fitzgerald who, along with John Taylor received corporal punishment (a flogging). Fitzgerald got his "stripes" for insolence to a Superintendent, while Taylor's whipping was for disobedience of orders. Back in 1803, nobody bothered to record in print how many lashes the two men took. Lashing was an everyday thing.

In January 1806, Fitzgerald fled from a gaol gang. The next day, Henry Kable's farm at Long Cove was robbed of clothes, food, a handsaw and a musket. A man who looked like Fitzgerald was seen nearby, and people drew their own conclusions.

On the following day, somebody robbed William Page's favourite target, John Harris, but Fitzgerald was soon captured. He promised to behave, was given a pardon for those offences—and immediately bolted once more. On January 25, he had been caught again. The magistrate ordered that he receive 300 lashes, and work in irons after that.

Although it wasn't mentioned in the report, Fitzgerald was sent to King's Town (which is now Newcastle). True to form, before long, he had escaped, together with one Bartholomew Foley. They made their way back to Sydney, where they were caught again in May. Their punishment: 300 lashes, and Fitzgerald was also ordered to work in the gaol gang, which meant he had fewer chances to escape.

In June 1808, he was on the loose again, as one of a gang of five "bolters", but as he was not one of the ring-leaders, Fitzgerald got off with a mere 200 lashes when he was caught. Was he downhearted? Far from it: in April 1809, he was posted again as an absentee.

He was taken again in August 1811, but in July 1812, he was back in the newspapers after he and Bartholomew Foley escaped from the brig Lady Nelson, while being carried to Port Dalrymple, near Launceston. In 1814, a reward of £10 was offered for his capture, and he was described in these terms "John Fitzgerald, a Prisoner of the Crown, and now a Runaway Bush-Ranger, [who] stands charged with divers Felonies and Misdemeanors..."

The reward was still being offered in April, 1815, but he must have been caught soon after that, because the reward advertisements ceased. Still, whatever happened, he was loose again in January 1816. He was still posted as missing in June 1816, after which he disappeared from the public record until his death in 1817. At some point, he must have been arrested yet again.
On Wednesday last John Fitzgerald, a character well known in the colony for a number of years past, was accidentally drowned abreast the King's Wharf. The body has not yet been found. 
The Sydney Gazette and New South Wales Advertiser, Saturday 27 September 1817, 2,
A week later, there came a longer report in the Gazette which gave a different picture of Fitzgerald. He was, said, the paper, a simpleton of no real wickedness. He was a man who had taken his punishment without reacting very much, and his thefts were minor, more to do with surviving than anything else.

He just got restless, and took off, said the reporter. Proof was offered for the view that the man was simple: whenever he was captured, there was no need to interrogate him, because he would happily tell all the details of his crimes, they said.

They also say there are none so blind as those who will not see. Fitzgerald was an Irishman from County Cork, and the southern Irish knew how to pretend to be simple. They used to do it deliberately as a way of making fools of their English overlords who always fell for their acts. Indeed, this is why people tell "Irish jokes", even today.

Perhaps we should keep that in mind for the next few paragraphs, because if Fitzgerald was truly simple, how did he manage to escape so often? When I could see no evidence that his body was ever found after he was apparently drowned, I began to wonder if he had really died.

Fitzgerald was "the best diver in the Colony", so when the anchor of the brig Endeavour became snagged at her moorings, he was sent down to sort the problem out. He examined the situation and reported that the anchor was caught up with two others that had obviously been abandoned by earlier ships. By now, he said, he was determined to fix the problem, and dived down again with an extra rope so the Endeavour's anchor could be pulled free.

Fitzgerald had been known to stay down for three and a half minutes. After four minutes, he was seen on the surface some distance away from the boat, but he sank again, and never seen again. 
(The Sydney Gazette and New South Wales Advertiser, Saturday 4 October 1817, 3,
And that was the end of Fitzgerald—or was it?  Most of this sort of history is driven by the newspaper records, because those are easily searchable with a computer. That was how I found that in 1825, a John Fitzgerald and a Bartholomew Foley were each sentenced to receive 300 lashes each, and sent to the gaol gang.

It began to look to me as if Fitzgerald  might have surfaced from his dive, took a deep breath before diving again, to swim under a wharf and hide. It was quite possible that if he had pulled a trick, his later recapture might have just failed to make the papers, as other arrests had done.

The name John Fitzgerald was common enough in colonial Sydney: there were at least two others of that name in Sydney in the 1820s, so there might be some confusion there, but Bartholomew Foley must surely be a less common name?

Sadly, elaborate theories like that are most easily undone. There must have been at least two Bartholomew Foleys in the colonies, because one, almost certainly Fitzgerald's friend, was hanged for sheep stealing at Port Dalrymple in 1814. So John Fitzgerald probably did drown, after all.

If he did, it is probably because he used hyperventilation, taking a series of deep breaths to charge the blood with oxygen. Hyperventilation can work for a while, but sooner or later, it ends up killing the user, and that must have happened to him.

A curious story about Fitzgerald emerged in 1857. The Hobart Town Courier told a tale concerning Governor King and the ship's bell on board the Lady Nelson, which was then moored in Sydney Harbour. These events happened in 1803, and Governor King suspected that the watch on the vessel was not as alert as it might be. He decided to set a thief to catch some slackers. King was not only the colony's governor, he was the senior naval officer.

He sent for Fitzgerald, even then recognised as a good swimmer, who was brought to him in double irons, suggesting that he had recently been naughty. The governor ordered him to swim to the ship during the night. Once there, he was to go on board, remove the ship's bell and bring it to Government House.

In those days, each half hour in each watch on board ship was signalled by the sounding of the bell. Even if a thief got on board and made off with the bell just after the bell was rung, the theft should be discovered in no more than half an hour—if the ship's guards were alert.

The point King wished to make was that the crew of Lady Nelson, were expected to watch for signals that might come at any time of the night from the Governor, and pass them on to the other naval ships in the harbour, Supply, Reliance, Buffalo and Investigator. There could be no slackness on the ship, just in case there was an emergency.

Fitzgerald swam out to the ship safely, even in double irons, but he needed the help of a constable to make it back to shore again with the bell. He was rewarded with two gallons of rum and one set of irons was removed from his legs. When the lieutenant who commanded Lady Nelson handed in his report in the morning, stating that the bell had been rung every half hour, he was punished for submitting a false report.

Looking back on Fitzgerald's later 'career', it is all too likely that, having found favour with the slightly eccentric King, he may have been tempted to persist in his waywardness, which seems to have started around then.

* * * * * * * * * * * * * * * * * * *

Other contemplated and partly-planned titles, high on my list of 27:
Not Your Usual Medicine; mainly quack cures and theories, patent medicines. (Written, in revision.)

Not Your Usual Manufacturing; mainly about 19th century materials.

Not Your Usual Inventions; mainly eccentric inventions. (Written, in revision.)

Not Your Usual Rocks; rocks that float, bend, tilt, melt, polish up and more. (Being worked on in early 2016)

Not Your Usual Wee Beasties; the things in your garden, your house and on you.

Not Your Usual Power Sources; 19th century power supplies.

Not Your Usual Gold Seekers; the ordinary people who went looking for gold. (Due out in print in 2016.)

Not Your Usual Measures; the ins and outs of fast and slow.

Not Your Usual Place Names; Famous Beach, Useless Harbour and others odd places.

Not Your Usual War Poems; The ones that don't get read on Anzac Day, but should.

Not Your Usual Consequences; Serendipity and Things That Went Wrong.

By December 2015, there were potentially 35 titles—and if you liked this unusual bushranger, I have just added another one.

Monday, 19 August 2013

Sitting beneath a banyan

Small banyan tree, Tanna, Vanuatu.
The name of James Cook, commonly known as 'Captain Cook', will forever be associated with the use of vitamin C foods against scurvy, in part because another James Cook published the notes on scurvy of John Hall, the physician son-in-law of William Shakespeare, in 1657.

I say in part, because the noted seafarer did also play a part in the story of the battle against scurvy, which he describes in his journal for April 13, 1769, just after he arrived at Tahiti:
At this time we had but a very few men upon the Sick list and thes[e] had but slite complaints, the Ships compney had in general been very healthy owing in a great measure to the Sour Krout, Portable Soup and Malt; the first two were serve'd to the People, the one on Beef Days and the other on Banyan Days, Wort was made of the Malt and at the discrition of the Surgeon given to every man that had the least symptoms of Scurvy upon him . . .
Two banyan fruits, sliced open to show that they are in fact from
a tree in the fig family. The scale is from my compass, and it is in
millimetres, so the shot is of material just over one inch across.
It is curious that such a large tree comes from one of those tiny
To people (as opposed to "the People", who are the ship's crew) unused to naval language, this may be a little puzzling, for a banyan is a tree of the fig genus, either Ficus religiosa, or Ficus indica.

Since the Banyan Days appear to be meat-free days, could it be that a Banyan diet is based on the leaves or fruit of these trees? I played with this for a bit, but then decided that I needed to learn more.

While my guess offers an attractive derivation, it would be a wrong one. The word 'banyan' (or 'banian' as some sources prefer) word is Portuguese, from the Arabic, from the Gujerati vaniyo, from the Sanskrit vanij, meaning "merchant" — among other things.

The banyan tree gets its name from a specimen near Gombroon on the Persian Gulf, beneath which Banian settlers had erected a pagoda, which became known as "the Banian tree".

The Banyan tree sends out branches which drop roots, which become trunks, which send out branches, and so it goes. Big banyans occupy five acres (2 hectares) or more, and you will sometimes encounter claims that the largest living thing in the world is a banyan tree, though some fungi are close to the same mark, and if you regard colonies of animals like corals and ant nests as organisms, the banyan tree may have some serious competition to face.

Some of the roots of a rather large banyan, Tanna, Vanuatu.
A Banyan, says the Oxford English Dictionary, which persists with the Banian spelling, is one of four things: a Hindu, a native broker in an Indian firm, a loose flannel shirt, jacket or gown, or lastly, a tree, but that is all — the OED has missed Cook's usage altogether.

Still, if anybody gives you figs in your Banyan diet, you needn't be too fussy — and considering the other Banyans that might appear there, the figs might even prove to be a welcome offering, though that was not how Cook's crew saw the Sour Krout he wanted to dose them with.

Luckily for their good health, the wily Whitby sailor was ready for them, as he explained in the same entry in his journal:
The Sour Krout the Men at first would not eate untill I put in practice a Method I never once knew to fail with seamen, and this was to have some of it dress'd every Day for the Cabbin Table, and permitted all of the Officers without exception to make use of it and left it to the option of the Men either to take as much as they pleased or none at all; but this practice was not continued above a week before I found it necessary to put every one on board to an Allowance, for such are the tempers and dispossissions of Seamen in general that . . . the Moment the see their Superiors set a Value upon it, it becomes the finest stuff in the World, and the inventer a damn'd honest fellow.
Here's a wide angle shot of that same banyan on Tanna:

* * * * * * *
This blog covers quite a few different things, so I tag each post. I also blog about history, and I am currently writing a series of books called Not your usual... and the first two have been accepted by Five Mile Press, The offcuts appear here with the tag Not Your Usual... . For a taste of Australian tall tales, try the tags Speewah or Crooked Mick.   For a miscellany of oddities, try the tag temporary obsessions. And language us covered under the tags Descants and Curiosities, while stuff about small life is under Wee beasties.

Friday, 16 August 2013

Bayesian testing

If you are starting here, I recommend that you go to the next entry down, or use this link: Bayesian statistics. That will give you some background.

Done that?  Fine, now back to the education examples that I started there.  In the mid-1970s, I was working on making mastery learning possible, by constructing mastery tests.  Now neither mastery learning nor mastery tests could be called new: acknowledging to the push for mastery learning, E. F. Lindquist had written of "mastery tests" in 1936, pointing out that they differed from achievement tests. (See E. F. Lindquist, 'The theory of test construction' in Hawkes, H. E., Lindquist, E. F. and Mann, C. R. (ed.) The Construction and Use of Achievement Examinations: a manual for secondary teachers. Cambridge, Mass.: The Riverside Press, Houghton Mifflin, 1936, page 36.)

One of the things I learned quite early in my working life was that many of my colleagues were careerists. These were people who would stop at nothing to enhance their careers. One future (now dead) Director-General of Education in New South Wales even went so far as to call in journalists to show them the work of a dying man, claiming it as his own.  That is how the great and powerful rise.

Others were more subtle, taking old ideas and giving them a new name, so they could say with a simulacrum of truth "I introduced autorical hermeneutics into the curriculum, you know."

As a rule, the reintroductions come around about every 40 years, and I estimate that this may be because two-score years sees all the old hands who had experienced the idea before, swept off into retirement.  For complex reasons, I avoided that.  I used the terms "mastery learning" and "mastery testing", but I concentrated on the mastery testing, because my skills lay there, and because I knew that the 1936 attempts to use mastery learning had fallen through because there were no mastery tests.

I worked as a classroom teacher in the bureaucracy, and I had little time for daffy theoreticians. A few years earlier, a Master's degree seminar was ear-bashed endlessly about an obscure Dutch philosopher and his ideas.  At the end of 110 minutes, the din ceased, and we sat stunned.  Then somebody (me, actually) asked of the presenter: "What exactly does your philosopher have to say to me about managing 2S7 (that was the lowest science class in a streamed Year 8) for a double period at the end of Friday afternoon?"

The plugger had no answer, because he had never, contrary to the by-laws for the Master of Education, taught in a school.  He was apparently deemed too bright to be put through that mill, but to practising teachers, he was, in the parlance of those days, among working teachers, as useful as a screen door on a submarine.

Bottom line: bright-eyed theorists don't impress me unless their ideas are firmly based in practice.  Keep that in mind in what follows.

As I came to the end of my master's studies, I needed to write something up, and started researching a "long essay" of 15,000 words on the mastery testing programs that were running around the world. The paradigm had taken root, if I may mix my metaphors, and mixing it with tailored testing, many higher degree students in the USA were messing around with Bayesian jiggery-pokery, but they all seemed to have it, if you will excuse the vernacular (and even if you don't) arse-up.

There fuzzy thinking resulted in sanguine acceptance of asking students 50 questions or more, just to make certain that mastery was attained.  This would provoke riots in the classroom and revolt in the staffrooms—and rightly so.  These people were clearly all post-grads with no experience with their equivalent of 2S7.

Yet there was the nub of an idea there, and based on the figures I had available from pre-testing about 60 mastery tests, I knew that very few students stayed in the middle.  They either got 19 or 20 items correct (most of the tests had 4 sets of five items), or they got about 5.  Making any kid answer 50 questions was just stupid.

Bayesian mastery testing

And so I came up with a model:

First: there would be about 15 questions in the test.
Second: most students would answer just a few of them.
Third: they would be re-assessed for mastery/non-mastery after each response.
Fourth: they would only be asked the minimum number of questions.
Fifth: the only way to do this was with what we then called a microcomputer.
Sixth: as each student was classified, item statistics would be updated.

There were several risks that needed to be eliminated. First up, there needed to be a base level of probabilities that would not be skewed by one or two students acting up, right at the start. That was fixed by seeding the response array with dummy data giving ten masters a probability of 0.8 of answering each question correctly, and ten non-masters a probability of 0.2 of getting each answer. These were arbitrary figures, and as each student was classified, his or her responses, either as a master or a non-master, would be added to the array, swamping the dummy data.

The occasional student who hovered in the middle, getting some right and some wrong would be asked to go and do some more study before trying again, and the student's responses would not be stored. To avoid any form of skewing, the test items were in a circular queue, so that if student A's last question was item 4, student B would begin on item 5, with the last item always being followed by item 1.

We got the whole thing programmed in BASIC (my thanks here to David Matheson, who was far better at that sort of thing than I and knew his way around the 64k Apple II), and I found some curious effects.  For example, items with negative discrimination, meaning poor students get them right and good students get them wrong, are usually avoided. In fact, it turned out that such items were just as useful in determining mastery or non-mastery!

What happened next

Not much. My "long essay" was in fact a thesis, and I packed it with lots of other curious findings (like the hidden fallacy underlying item analysis using the point-biserial correlation coefficient and dendrogram/cluster analysis of mastery test items), but the paradox of the negative discrimination items was nearly my undoing.

My examiner told a friend that when he read that, he knew it was wrong, and he was about to fail me, but then he did some figuring and studied the effect, which I had clearly labelled as counter-intuitive and paradoxical, so as to avoid numpties (like him) howling.  In the end, he realised I was right.  Lucky me.

I was asked to scrap most of the long essay and rewrite chapter 7 (the Bayesian bit) as I would be guaranteed an M. Ed. with merit, which would get me into a PhD program.  I had taken 7 years to get my first degree and 10 to get my second (in each case by cunningly misusing the by-laws which forbade such tortoise-like progress).  I thought "Thirteen years more? No thanks."  I went off and wrote books instead, because it's what I do best.

So I got my ordinary Master's, but the scheme was ahead of its time.  Nobody was prepared to tie up the only computer in the school as a testing machine, and I was moving on to other things. The only public record, the copy of what I justifiably call my thesis, was stolen from the Education library at the University of Sydney.

Well, the 40-year cycle is almost here, and I notice that Salman Khan of the Khan Academy is using a mastery approach very effectively, and now the technology is there, but the mastery measure he uses is too simplistic and oriented to low-cognitive-level arithmetic: 10 questions have to be answered correctly in a row.

So given that some scrote may be out there with my thesis and might be poised to launch my scheme in his or her name, I have decided to place this in the public domain.  I aitn't dead yet, but I enjoy cutting scrotes off.

If you like it, run with it: if you need more detail, I am ready and willing to share all the stuff that I have, but any half-way competent programmer, given what I have set out here, could easily implement a similar system using networked devices.

Bayesian statistics

This is an introduction, some parts of which are essential for most readers before they read the next post, Bayesian testing. That post, as is normal in blogs, appears above this one.

Consider the case of the teacher who asks a "checking" question to see whether some student has grasped a principle.  If the answer is satisfactory, the teacher may either think "Good, I thought X understood that", or "Funny, I didn't think X had caught onto that one: I'd better ask another question."

On the other hand, if the answer is unsatisfactory, the teacher may think "Yes, I thought X didn't know that", or "Funny, I could've sworn X understood that: I'd better ask again in another way".
In either case, the teacher has taken a prior probability into account, and used the new information to modify that probability to come up with a posterior probability.  The probability that we are dealing with is a continuous variable.

Yet if we were to rely on classical probability theory, the response to a single question can only yield one of two completely discontinuous values.  Either we are 100% certain that the student has understood the business under consideration, or we are equally 100% certain that the student has no clue at all.

The possibility that the student guessed the answer, or made a silly mistake while really understanding the principle, or heard the answer whispered by somebody, all of these are rejected in favour of a narrow, rigid black-and-white view of probability.

Well, you don't have to be a teacher to recognise that this is daft, but let me make it even easier for you.  Suppose we have just used a multiple choice question to assess where the student is at in terms of understanding the principle involved.

Now people who have little real understanding of probability reject these questions on the grounds that you might just get lucky and guess all the answers.  Let me assure you here and now that this isn't possible for any large number of well-written questions, but that isn't what I want to debate right now.

With a single question, offering four choices, however, there is a reasonable chance of guessing with no understanding at all, a 25% chance, in fact.  Anybody who thinks about it can recognise that: what is less obvious is that some students who do know and understand the principle involved will make a clumsy mistake, and get their answer wrong.

Anybody who knows about testing knows for a fact that this happens. In the pressure of a test or exam, students enter the results in the wrong place or do something else silly.  Sometimes, the fault lies in the question, which is badly worded.

So it's crazy to go around assuming that we can assert 100% probabilities about anything.  We teachers can, however, assert that we are pretty certain that somebody understands whatever the principle is, to the extent that we are willing to move on to something new, and teach that.

It's easy when we are talking about something simple like teaching sums, or dates of famous battles, any sort of rote learning: even Blind Freddy can see that we have to be flexible in how we calculate the probability of something.

Now let's turn to something far more important: the batting performance of our nation's cricketers.  Once again, I will start off with a simple and easy exercise: the average performance of Sir Donald Bradman in test matches.

If we look at The Don's last score, he was out for a duck.  Should that be his lasting record?  Of course not!  And if we look at a modern-day batter with a sequence of low scores in the past few months, should we write him or her off?  Tabloid journalists call for the executioner, sager minds look at the longer term.

Every measurement involves elements of chance, and even a consummate wielder of the willow (that's the bat, for heathens) will sometimes "blow it", sometimes several times in a row, and wise selectors usually look at prior performance, or as mathematicians say, prior probability.

The technical stuff

You don't need to read this: the maths-free description will do for most readers.  In what follows, if you do read it, the numbers in a1, a2 etc. ought to be subscripts, but this blog does not support that, so far as I can see.  This needs to be kept in mind when you see things like an and p(an).  Sorry!

Suppose we have a set of discrete alternatives a1, a2, a3, a4 . . . an, for a given set of trials, and that we can write the probability of a1 as p(a1). To make this easier, suppose we are looking at a set of test scores, and the probability that a student has mastered the skill being assessed in the test, which has twenty questions. The alternatives are the test scores, from 0 to 20, and what we need to assess is the probability that the student is a master of that skill, given a particular score.

Beginning with a prior estimate of probability p(a1|b), the probability of a particular score being obtained by a student who has mastered the skill, we can then use a simple formula to estimate the probability that a particular student has mastered the skill, given that student's score:

p(ai|b) = [p(b|ai) x p(ai)] / [p(b|a1) x p(a1) + p(b|a2) x p(a2) . . . . + p(b|an) x p(an)]

Or we may take this form of the equation, where there are two events, A and B:

p(A|B) = [p(B|A) x p(A)] / [p(B|A) x p(A) + p(B|~A) x p(~A)

Here we may define event A as 'mastery' and event B as a particular score, or we may look at them in terms of the likelihood of guilt in a particular situation, or almost anything else. If we only have a limited amount of information available, or a limited number of data points, this will tend to give us a better average estimate of the true situation.

To take a simple example, if four experimenters are trying to find out what the frequency of heads and tails should be when you toss two coins, there are four possibilities, which would give results of two heads, two tails, a head followed by a tail or a tail followed by a head.

Now suppose we take a Bayesian approach, beginning with the reasonable assumption that there should be a 'half and half' chance for heads and tails. Under the same conditions, the head-head and tails-tails observations will lead to a conclusion that the coin is biased to a particular result, rather than suggesting that the same result will always be achieved. The head-tail and tail-head cases will still lead to the conclusion that there is an equal probability of getting heads or tails, so the overall set of results is more accurate.

The examples here tend to relate to educational settings, simply because the writer devoted two years of his life to researching and developing such applications, but the same reasoning can just as easily be applied to estimating baseball batting averages, or almost any other measure which is mathematically equivalent to a probability.

Uses in the courts (still technical!)

You can skim this one as well, or leave it for now and come back to it, as it is a side-issue. The main thing to note is that Bayesian statistics have many uses.

Bayesian probability has now become important in the law courts of the world, where it provides the most appropriate way of dealing with DNA evidence or blood grouping. This need arises because of a peculiar situation that arises when a lawyer says something like "there is a one in a hundred thousand chance of somebody else having this DNA profile".

Suppose a random citizen (we will call him Fred) has been accused on the basis of a blood spot left behind at a murder, which matches Fred's profile to a level that the prosecution are calling "one in a hundred thousand". Further, they say, somebody of Fred's racial group was seen leaving the area. That makes the odds even better, because his race are just 10% of the population. "That makes it one in a million", says the prosecutor.

In fact, it brings the probability down, not up, says the defence lawyer, who has read up on this topic. The defence may well be correct, if they can show that most of the people of that DNA profile type are in AB's racial group, so what we need to do is use a Bayesian probability, but this example gets a bit confusing.

So let us look at a case where paternity has been alleged, and DNA evidence seems to support the claim. Once again, the frequency of that DNA type in a small community can be quite different to what you get in the whole nation, so we do a calculation of the probability of the accused being the father of the child at the centre of the case.

We have, from all of the tests, a Combined Paternity Index, (CPI). This is calculated as the product of the paternity indices for each individual system tested. The CPI tells us how likely it is that the alleged father (or a man genetically identical to the alleged father) contributed the paternal genes to the child, divided by the likelihood of another unrelated man of the same race contributing the paternal genes.

As well, we have a Prior Probability (Pr). This is a numerical value in the range 0-1 (that is, ranging from impossibility to total certainty) which indicates the likelihood of a certain event occurring. This value is estimated, before genetic testing, on the basis of known, non-genetic circumstances surrounding the event.

That means taking into account non-statistical evidence, such as casual acquaintance versus an intimate relationship. Since the laboratory does not know of the existence or the substance of these circumstances, a prior probability of 0.5 is customarily assigned for the purpose of neutrality, but this can be varied.

Now we can calculate the probability of paternity:

P = (CPI) (Pr) / (CPI) (Pr) + (1-Pr), where P = Posterior Probability of Paternity, CPI = Combined Paternity Index and Pr = Prior Probability.

Uses against spam

The common methods of filtering spam, back in 2003, such as rejecting mail from known spammers (black lists), and only accepting mail from friends and colleagues (white lists), were not enough. Merely filtering known spam messages was always one step behind clever spammers. More aggressive filtering posed an unacceptable risk of killing legitimate messages.

Take a simple trap that rejected e-mails mentioning the word 'Viagra' in the subject line: the word 'V1AGRA' will pass straight through, but in nine out of ten cases, it will still be read by a human as 'VIAGRA'. New filtering methods were brought in to analyze e-mail messages in their entirety, instead of just looking at a handful of key words.

These filters (and we still use them) make sophisticated models, based on probability and statistics theory going back to the ideas of the 18th-century mathematician and cleric, Thomas Bayes, that determine whether new messages are spam or not.

Such a system allows a message about sextants which mentions that the pen is mightier than the sword will be examined and passed, rather than being examined and hurled into the outer darkness.
Rhe basic notion of Bayesian statistics is that it begins with a certain assumed probability that a message should be rejected, and then uses a variety of observations to adjust that probability, only acting if the probability rises above (or falls below) a certain level.

Some findings may increase the probability, others may reduce the probability, and in more sophisticated forms, testing may be exited fast by the use of white lists and black lists, while indeterminate messages can be given a more thorough scrutiny, even to looking for any of a few thousand terms and phrases, all of the usual weasel claims about mail not being sent unless people have opted in.

By the same token, the name of a known sender might be used to validate e-mail, so that a message about e-mail from the New England Journal of Medicine or Nature, for example, would be allowed to pass, even if it mentioned a number of otherwise 'black mark' terms. It would also get around the problem encountered by some Thai people, whose names end in '-porn', leading to all sorts of problems, and in the past, words like Middlesex and Essex have been known to trigger poorly designed guardian software.

Which is why we now rarely see this once-popular tagline on e-mails:
When they come for the anarchists, I shall speak up even though I am not a anarchist. When they come for the Jews, I shall speak up even though I am not a Jew. When they come for the Muslims, I shall speak up even though I am not a Muslim. When they come for the Christians, I shall speak up even though I am not a Christian. When they come for the spammers, I'll say "You missed one over there!"

Sunday, 11 August 2013

On the trail of the assassin

Tradition has it that assassins were originally drug-crazed murderous types who took hashish to prepare themselves for murder. And not just any murder, either — these were fanatics sent forth by their Sheikh to murder the good Christian leaders of the crusades.

Well, if we are dabbling in myths where the crusaders were good Christians, then perhaps their Sheikh, sometimes called the Old Man of the Mountains is believable.

In Arabic, the name for the eaters of hashish, who fed on cannabis resin, was hashshashin. This is one of those rare Arabic words that has come through into English in the Arabic plural, like Bedouin, or the fellaheen, who were, and are, peasants — or muhajideen, but we get 'assassin', not directly from Arabic, but by way of Italian, where an assassin was an assassino.

Marijuana, in one form or another, was certainly an old tradition in the Middle East, though not necessarily to inspire one to kill. Almost two and a half millennia ago, Herodotus wrote about the Scythians in his Histories:
On a framework of three sticks, meeting at the top, they stretch pieces of woollen cloth, taking care to get the joins as perfect as they can, and inside this little tent they put a dish with red-hot stones in it. Then they take some hemp seed, creep into the tent, and throw the seed onto the hot stones. At once it begins to smoke, giving off a vapour unsurpassed by any vapour-bath one could find in Greece. The Scythians enjoy it so much that they howl with pleasure. This is their substitute for an ordinary bath in water, which they never use.
Cannabis, or hemp, has a number of non-drug uses, as any hangman knows, or any sailor, because hangmen and sailors once used hempen rope and sails made of canvas, which got its name from a corruption of cannabis, although canvas was made also from flax.

Sailors wore clothes made of canvas, or else tarpaulin, which was canvas covered with tar. Originally, this tar was probably tree resin, though not cannabis resin, and the name probably derives from an Old Teutonic root for 'tree'. Later, 'tar' meant stuff made by the destructive distillation of wood.

Mixed with water to make tar water, the wood tar was a sovereign remedy, according to Bishop Berkeley (he was the one who had a bit of a thing about trees falling in forests and nobody hearing them). He seems to have adopted the idea while in Rhode Island, supposedly planning a college in the Bermudas, and where he had time to state an early version of "go west, young man", which is why Berkeley California carries his name. He said of the tar water:
It is good not only in the fevers, diseases of the lung, cancers, scrofula, throat diseases, apoplexies, chronic disorders of all kinds but also as a general drink for infants.
Back to the tarpaulin, though, this word was a contraction of tar-palling, with the second part coming to us from the Old English pæll, or maybe even the Latin pallium, which was a cloak or cloth, and which also gives us the type of care we call 'palliative', care for the dying where the illness is cloaked by the care. In Australia, incidentally, the sick or others in need of charity may be the subject of a tarpaulin muster, where coins are collected in a canvas sheet or 'tarp'.

The smoke in the small Scythian tents might also be seen as a pall, but it probably would not be good for your health, any more than being canvased or canvassed, which was rather like being tossed in a blanket, or knocked about and beaten. In Henry IV, Part 2, we read
FALSTAFF.  A rascally slave! I will toss the rogue in a blanket.
DOLL TEARSHEET.  Do, an thou dar'st for thy heart. An thou dost, I'll canvass thee between a pair of sheets.
None of which sounds very palliative at all — any more than being canvassed for a vote, which may come from an old hawking usage, where a bird caught in a net was said to be canvassed. Oddly enough, people are now proposing that cannabis be used in palliative care, which probably puts a new meaning on 'stoning to death', also a tradition in the Middle East.

Canvassers of a political kind, take note in this election time in Australia.  I have rocks a-plenty, after my recent travels.

Friday, 9 August 2013

Cracking the whip

Having been whipping around the world for eight weeks and a bit, it struck me on the way in to think a bit more about the various meanings of "whip".

When Charles Dickens wanted to paint a picture of the route to be followed to reach the degraded Jacob's Island haunt where Bill Sikes took refuge at the end of Oliver Twist, he wrote of: 
Jostling with unemployed labourers of the lowest class, ballast-heavers, coal-whippers, brazen women, ragged children, and the raff and refuse of the river . . .
(Let me note here that when we were in Rome, three weeks ago, we were caught by a thunderstorm, a few blocks from the Spanish Steps, and took refuge under an awning of the Hotel Royal Splendide in the Via di Porta Pinciana. We walk everywhere, and had neglected to carry waterproofing.  Immediately, a flunky with a top hat opened a window behind us and offered us an umbrella. We thanked him and declined, but he insisted. We weren't guests, we said, but still he proffered the umbrella.  It was easier to accept and we sauntered off, please with our good luck. He retreated, no doubt pleased at ridding his five-star hotel of such riff-raff, or as Dickens had it, such raff and refuse. Now back to the story...)

Whipping coal, which seems like a particularly useless occupation, was of considerable interest to Dickens: in Dombey and Son, we learn of a ballad which set forth: 
 . . . the courtship and nuptials of a promising young coal-whipper with a certain 'lovely Peg,' the accomplished daughter of the master and part-owner of a Newcastle collier . . .
 That, however, leaves us little further ahead, save that now we have a hint that this is something to do with shipping coal from one place to another. Also in Dombey and Son, Captain Cuttle walks at peace:
  . . . down among the mast, oar, and block makers, ship-biscuit bakers, coal-whippers, pitch-kettles, sailors, canals, docks, swing-bridges, and other soothing objects.
 Finally, in Great Expectations, we find the answer: 
 . . . here, were colliers by the score and score, with the coal-whippers plunging off stages on deck, as counterweights to measures of coal swinging up, which were then rattled over the side into barges . . .
The coal-whipper, we are assured by many learned authorities, was a man who operated a whip, a long pole, suspended in the middle. This could be used to lever up baskets of coal, provided a suitable weight, in the form of a person, was applied to the other end.

When we think of whipping and ships, most of us would think first of floggings meted out by cruel Captain Blighs  and the like (no, Bligh was by no means cruel: that was a foul calumny put about by political opponents and the supporters of the syphilitic son of a Portsmouth tailor who wanted to be accounted a gentleman), but in fact most of the whipping seen by sailors at sea was when a line was whipped, rather than being spliced at the end.

Splicing made a line thicker, and so harder to reeve, or pass, through a block, which is a pulley when it leaves the land, so a back-splice on a line's end could be a problem. A nautical whip can also be a line which needs to be rove through a block, to allow simple lifts — again using human counter-weights, and making the long-pole explanation of the coal-whip a bit dubious.

The Bible hardly mentions whips, save for a passage in 1 Kings 12:11 " . . . my father hath chastised you with whips, but I will chastise you with scorpions." All the same, English churches had dog-whippers — one was appointed as late as 1856, according to Cobham Brewer, who cared about such things: this official was responsible for controlling working dogs who accompanied their owners to worship.

The dog-whipper did this using whips and dog-tongs. In the Anglican church, St Luke's Day, October 18, is dog-whipping day, supposedly because a dog once ate a consecrated wafer on this day.

Lola Montez was a dab
hand with the horse whip.
She is shown here, wielding
it left-handed.
There seems to have been a convention
that damsels planning to ply the horse
whip ought, first, to adopt a state close
to déshabillé.
The English seem to have far too much interest in dog-whipping. The French, on the other hand, do not seem to whip dogs at all, but where we would speak of having other fish to fry, a Francophone will have another cat to whip — but to sailors, the whip is a cat, one with nine tails.

At last we have got to the beating whip, as in horse-whipping an editor as Lola Montez famously did on one occasion, and the same origin gives us the party whip in English-style Parliaments.

This is somebody who plays the role of a whipper-in. In the art of fox-hunting, a whipper-in, keeps the hounds on the straight and narrow. The party whip keeps the other members in line, and can even issue a three-line whip.

The word relates to a German word wippe, meaning a quick movement or a leap — which takes us straight to the coal-whip, or to the Dutch wippen, which means swing or leap: the Dutch wagtail, for example, is a wipstaart. Here, staart is the tail, but we see the word in English in stark naked, which is a politer way of saying with a bare bum.

Most uses of whip seem to be more to do with fast movement, as in the fast movement of a whip's tip as it cracks, which is very fast indeed. In fact, if the physicists are to be believed, the tip actually exceeds the speed of sound, and causes a small sonic boom. Luckily coal whips did not travel that fast, or the coal would be launched skyward, and take about 66 seconds to come back down again.

Sunday, 4 August 2013

The curious coach

Where would American fiction of a certain kind be, without stage coaches to be robbed?  And where would that genre's blood brother in Australia be, with the mail (coach) to be bailed up?

The next cab off my writing rank when I get home, later this week, will be bushrangers, though not the usual ones, though even they used to bail up coaches, to rob passengers and/or to pillage the mail and/or to win gold the easy way.  So coaches have been on my mind as I blatted around Croatia, Slovenia, Montenegro, Switzerland and Italy. The one above, oddly enough, was in Kowloon, Hong Kong, and it was added later.

S. T. Gill, The Arrival of the Geelong Mail in Ballarat.
The word 'coach', in one form or another, is common in many European languages as the name for a four-wheeled horse-drawn vehicle with seats inside and out.

In French, Spanish and Portuguese, the word is coche, while it is cocchio in Italian, and kutsche in German.

This sort of pattern of consistency usually indicates a recent origin, and indeed this is the case with coach, which was first used in English, according to the OED, in 1556. All of the words come from the Magyar (Hungarian) word kocsi, meaning 'of Kocs', this being pronounced 'kohtch', near enough.

This Kocs was a town, between Buda and Raab, where these vehicles were made. The Shorter OED quotes without attribution the Latin tag "ungaricum currum [quem] kotczi vulgo vocant" — the Hungarian carriage [which] the common people call kotczi.

The word was quickly pressed into service, and when Ophelia is going mad after Hamlet kills Polonius, she says "Come, my coach! Good night, ladies. Good night, sweet ladies. Good night, good night." before wandering out, leaving those behind to conclude that she really is going bananas (or possibly that Shakespeare felt the scene needed padding?). All the same, the limitations of a coach are readily apparent to us today, when we read Portia's words in:
But come, I'll tell thee all my whole device
When I am in my coach, which stays for us
At the park gate; and therefore haste away,
For we must measure twenty miles to-day.
But if the vehicle itself has held that name for that length of time, there are more meanings that have tagged onto the word since it was first used. A coach can be a cabin on a ship, usually somewhere near the stern, for the use of the captain.

This coach was also called a 'couch', which gives us a hint of its origins, since the captain often needed to be awakened regularly in bad weather, and could snatch some sleep in his wet-weather gear. This became grander as ships grew larger, and at one stage, 'to dine in the coach' was like eating at the captain's table.

By 1866, the word was being used for a sleeping carriage on a railway train, though the logical French insist on calling it a wagon lit, a 'bed wagon'. In more modern times, the fancier long-distance passenger vehicles otherwise called a bus or an omnibus may also be referred to as a coach.

The coach gave its name to the coach box, the seat where the driver sat, to the coach horn, blown to signal the next staging point as the coach approached, the coach whip which needed to be long and thin to reach the lead horses, and so came by transfer to mean other long thin items such as the pendant flown at a ship's masthead under certain circumstances.

A fearful kind of coach.
For the past century and a half, a coach has also been a person who acts as a private tutor for students. And since 1885, it has also been a person who trained athletes of one sort or another.

I started thinking about this overlap, knowing the Magyar origins of the word, as I watched a Hungarian coach with his charge in a gymnastic event on the television, and I wondered what he would make of it, if he knew the origins of the term, but then I decided there was probably no relationship at all. I set it aside until I saw a royal  coach in Palermo the other day.

A bit of checking suggests that I was right the first time. The verb 'to coach' meant originally to travel in a coach, and it seems that when tutors had just a few students, they worked together, with the tutor carrying them to the passing point, as it were, acting as a form of transport. Perhaps there was an element of punning here, since the word 'curriculum' comes from Latin, and means 'a small currum' in that language, though not necessarily an ungaricum currum.

Then again, perhaps the point in your career where you need coaching is just a stage you pass through.