What's up with that? Don't I mean 'Rithmetic?
Festschrift on the Anniversary of the University of Iowa, 25 February 1847.
Or, Back To School -- Oy!
When it's almost back-to-school time, along with all the sales in the stores, there's also all the usual stuff "for sale" too about the value of education. Trouble is, there's about as much of that stuff, as many ideas of what is an education, not to mention of what is its value, as there are kinds of pens, notebooks and clothes in the stores.
So let's start with the good old liberal arts education. We'll look at:
I. How and Where It Started
II. What the Seven Liberal Arts Actually Are
III. The Modern University
IV. How It Fell Apart
V. Where We Are Now
VI. Where We Could Be
and a little concluding note you might enjoy.
I. How and Where It Started.
These days, you may or may not hear that the ideas of liberal arts education, like those of democracy, originated in Greek antiquity. What you really don't hear these days is that those ideas were not at all what we mean by them now. In those societies, democracy didn't mean everyone participates, it meant that to participate in democracy, and to have an education adequate to do that, one must not be burdened by having to work; that was done by a slave class. Leisure, not work, is the basis of culture and society; "liberal" comes from the Latin for free, which translated the Greek for not what we think of now, but learning appropriate to the free and non-working class, not the slave class.
"Academy", "academic" and like words come from the school Plato founded in a sacred grove dedicated to Athena, Goddess of Wisdom, called the Akademia. Hekademia originally, actually. It lasted from about 387 BC to 83 BC. Its most famous graduate is a guy named Aristotle.
The Academy was refounded on Platonic philosophy in 410 AD and lasted until closed by the Roman Emperor Justinian I in 529. Well, Eastern Roman Emperor, but the Western Empire was gone, having collapsed in 476. Justinian was out to stamp out anything in the Empire but the state religion, the Catholic Church, defined and established by the Eastern Roman Emperor Theodosius and the Western Gratian and Valentinian II in the Edict of Thessalonica on 27 February 380. Which he pretty much did, the Second Council of Constantinople in 553 saying nothing happens in the church without the emperor. For which reason the 529 closing of the refounded Academy is often called the End of Antiquity.
The scholars of The Academy sought haven in the Persian Sassanid Empire, then when the Persian and Byzantine empires made peace in 532, some of the scholars removed to Harran in what is now southeast Turkey. After the Sassanids lost to the Arabs, by then Islamic, in 651, Harran became the first great centre of Islamic learning as the knowledge of classical antiquity was translated from Greek to Syriac to Arabic. Meanwhile Europe, where all this stuff came from, was a complete mess. So knowledge that began in Europe was forced out and wouldn't make its way back for a few hundred years. Helluva guy that Justinian, huh. The Eastern Orthodox think he's a saint, which I suppose makes sense for what's left of his old state church, but unfortunately so do some of us Lutherans.
So The Academy. Its best graduate Aristotle in turn founded the Lyceum in Athens in 335 BC, right beside the temple of Apollo of Light, Apollo Lykeios, hence the name. The Romans trashed it in 86 BC, and at an unknown point thereafter it ceased to be. Its location was rediscovered in 1996, just east of modern downtown Athens. The word Lyceum survives in modern European languages for roughly what we call high school in the US.
Here's how these ideas passed from the end of the ancient world with the fall of the Western Roman Empire to later times in the West. First was a guy named Martianus Capella, who sometime after Alaric, King of the Visigoths (Germanic types), trashed Rome in 410 wrote a book called De Nuptiis Philologiae et Mercurii et de septem Artibus liberalibus libri novem, which means "On the Wedding of Philology and Mercury, and the Seven Liberal Arts, in Nine Books". The first two books are an allegorical love story about how Mercury, the pursuit of learning, actually learns by way of Philology, communicated information, and the remaining seven are textbooks in each of the seven arts we will detail below. The books were largely based on existing ancient works, and the whole thing was pretty much an encyclopaedia of its time, but later, when the knowledge in that system began to show itself lacking, the whole thing started to appear lacking, and scholars now routinely diss him, when what is needed then as now is separating the system itself from its content at any given time.
Which is pretty much what the rest of this post is trying to establish.
Second was a guy named Anicius Manlius Severinus Boethius, who lived shortly thereafter. His best known work is On the Consolation of Philosophy (De consolatione philosophiae), written while awaiting execution by the Arian Western Roman Emperor Theodoric for supposed treason with the Catholic Eastern Roman Emperor Justin. Boethius translated a bunch of ancient Greek works into Latin. In his rather free translation of Nicomachus' book on arithmetic he also set out the liberal arts, giving them the trivium and quadrivium names. In his On Music set out the three-fold division of music we shall detail below. His books remained standard authorities in universities for hundreds of years, and the Consolation is one of the most influential books ever written. While not part of the church's general calendar, in some places he is commemorated as a saint, St Severinus, with feast day 23 October.
You might hear that the liberal arts were originally seven, the first three being grammar, rhetoric and logic, also known as dialectic, a three-part way known in Latin and consequently to the West as the Trivium (from which our word trivial comes, trivial matters originally being not minor details but what you learn in order to get on to the heavy lifting of reality itself), and the last four being arithmetic, music, geometry and astronomy, the four-part way called the Quadrivium.
Nice to know, but doesn't tell you a damn thing about what this was all about, though it looks like it does, which is most of the problem understanding this stuff.
II. What the Seven Liberal Arts Actually Are.
Here is the structure of the Seven Liberal Arts.
The Three Part Way, the Trivium.
3. Logic (dialectic).
The Four Part Way, the Quadrivium.
4. Arithmetic. (Absolute Multitude)
5. Music. (Related Multitude)
6. Geometry. (Stationary Magnitude)
7. Astronomy. (Mobile Magnitude)
Again nice to know, but again doesn't tell you a damn thing about what this was all about, though again it looks like it does.The Trivium was not grammar, rhetoric and logic exactly as we mean them now, nor even something learned for its own sake. Rather, it was learning the tools by which one learns anything at all, just as a tradesman learns the tools of his trade before learning how to use them in the trade itself. Basically, Grammar was the study of how thought is written down in symbols (language), Rhetoric was the study of how thought is communicated from one person to another, and Logic was the study of how to think to reach supportable conclusions. Thus a person will be able to write down or speak his own thoughts rather than just let them rattle around in his head (Grammar), evaluate whether the written or spoken thoughts of others are well written down or written to hide or disguise things (Rhetoric), and evaluate his and others thoughts as to whether the content is supportable or based on unsupportable assertions and/or hidden assumptions which are deceptive (Logic).
Here's what the names of the liberal arts in the Quadrivium mean. Once you learned how to study anything at all, the stuff to be studied was divided into two big categories, things that are what they are as combinations of units, and things that are what they are as units that divide into further units. The former were called Multitudes, and further divided into those that are not applied to anything but abstract, which was called Arithmetic, and those that are applied to something, and that is called Music. The latter were called Magnitudes, and further divided into those that do not move, called Geometry, and those that do, called Astronomy.
Arithmetic then simply meant the study of number in the abstract, not applied to anything, just how numbers can be combined and used -- what is generally called math to-day. Music was using numbers to understand a phenomenon, and was further grouped into three areas: musica mundana, using number to quantify and understand the world outside ourselves, thus including what we generally call to-day physics, chemistry, and the like; musica humana, using number to quantify and understand the world inside ourselves, thus including what we generally call to-day biochenistry, psychology and the like; and finally and at the lowest level, musica instrumentalis, using number to understand the tones and combinations of tones produced by the instruments that produce them, including the human voice, which is what we generally now only mean by music -- except, it includes only the understanding part, the actual making of this kind of music being simply a skill and not included for its own sake but left to the uneducated. Ironic: from a skill left to the uneducated, these days, being able to strum a few chords on a guitar and belt out a few words seems to immediately confer that status of prophet, revelator, visionary, and authority on whatever one belts out about.
Education had nothing whatever to do with earning a living. When the idea began, work did not ennoble, it debased. Work was done by a class that, precisely because it had to work, could not possibly have time to learn what one needed to know to participate in democracy or high positions. Later, trades, something that is learned for the purpose of making a living, were learned in guilds, not universities, with the interesting twist that the guilds formed first, and universities began by borowing their ideas of how to organise from them! So show a little respect to the repairman that shows up next time you need one.
So, it's a system, first for learning how to learn, then for classifying what is to be learned, in order to be educated to fulfill the responsibilites of democracy and high office.
III. The Modern University.
In the original universities, a person who had completed a course of studies in the Seven Liberal Arts, and passed final examinations by his masters (teachers), was awarded the degree Bachelor of Arts.
What does this mean? Not what you would think based on the ordinary current meanings of these words -- the same problem again. "Arts" does not mean painting or sculpture or whatever, but the Seven Liberal Arts. "Bachelor" does not mean an unmarried male, but comes from the Latin baccalaureus, and originally referred to the lowest class of knight, a squire, or apprentice, to a knight, or a knight in the service of another knight. The word itself seems to have come from baccalaris, a man employed on a dairy farm. Bacca was a variant of late Latin vacca, which still survives in Spanish as vaca -- cow. The progress is similar to that of learning a trade in a guild.
A Bachelor could then go on to further study, and then participating in and moderating disputations (disputationes). These were highly formalised debates on the truth of specific propositions, usually based on arguments from appropriate authorities, called argumentum ad verecundiam. These are inappropiate to syllogistic logic, in which the syllogism is true or false based on its on its correct process and not who does it. But they are common in informal logic, where, since no-one can be an expert on everything one relies on those who supposedly are experts on this or that thing. This is the origin of the ad hominum (against the man), which is not name-calling, but refuting a statement on the basis that the authority cited is no authority at all. On such further study and activity, a person would be awarded the degree Master of Arts, the Arts being the Seven Liberal Arts, and "master" deriving from the Latin magister, which looks like master but actually means teacher; one may now teach the Arts.
Luther's so-called "95 Theses" were an invitation to exactly such a Disputation.
A degree was simply a step, in Latin gradus, to becoming a teacher or master, hence the term "graduate", a progression again similar to the trade guilds and still seen in the apprentice, journeyman and master structure of qualification in the trades. Since the masters were teachers, they were also called doctors, from the Latin for "to teach". Over time, since the three higher fields of study were Law, Medicine and Philosophy, masters who went into these fields earned a final doctor degree in them, and the doctoral degree in these higher faculties came to be regarded higher than the master teachers/doctors, eventually becoming the present Bachelor, Master, Doctor hierarchy, with later fields coming under the division of philosophy along with philosophy itself.
The story of the modern universities begins with the schools attached to monasteries, generally Benedictine, real monking monks, not just monked over, preserving some light against the darkness of the times, which times are known as the Dark Ages. Karl der Grosse, known to some as Charlemagne, who forged the first more or less unified state in Europe since the Roman Empire, was crowned Imperator Augustus by Pope Leo III on Christmas Day 800 at St Peter's Basilica (the old one; the current one is on the same site) to re-establish a Western entity against the still standing Eastern Roman Empire, and thus is considered the Father of Europe. Among his many accomplishments, he encouraged education. With the reforms of Pope St Gregory (died 12 March 604) for learning to include more than liturgy but also theology and canon law, bishops began to establish schools in their cathedral parishes to teach things beyond the monastery schools. Then, with demand far in excess of supply, plus the original town and gown tensions between students and townspeople, which were not pretty with rape and murder not uncommon and often protected by clerical immunity, schools gravitated to big cities.
The word university comes from the Latin phrase "universitas magistrorum et scholarium" which described and denoted these institutions, associations of students and teachers chartered by civil and/or ecclesiastical powers that be in their cities, with degrees granted by the institution itself, at bachelor, master and doctor levels. rather than licences or certificates from individual teachers as before, which adapted from the trade guilds the advancement stages of apprentice, journeyman and master onto a model drawn from the madrasahs of the Islamic world. (Notice how all this stuff, from Plato's Academy to the modern university, begins with schools attached to houses of worship? Hmm.)
The first of the modern degree-granting universities, growing out of existing centres of higher education, was established in Bologna (1088), followed by Paris (1160), Oxford (1167) and Cambridge (1209). The final step was recognition by papal bull of a university's autonomy from the city, the church, and each other, meaning non-interference from the state and/or the church (this is what "academic freedom" means) and also that a graduate from one could teach anywhere jus ubique docendi, with no further examination.
In Bologna, the students ran things, hiring the teachers; in Paris, the church hired and paid the teachers who ran things, and in Oxford, the crown did. These differences had major consequences. All four are still around, but in different ways. Bologna was not a comfortable place for teachers and fell into decline; Paris became the leading university and really the great granddaddy of the modern university but was abolished as such in the French Revolution centuries later though parts survive with historical ties; government sponsorship of Oxford and the later Cambridge (1209) allowed them to survive the replacement of the church with the state Church of England.
A student entered the university at about age 15, and after a six year curriculum in the Liberal Arts, usually with an emphasis on logic, if they passed they graduated a Bachelor of Arts. Courses were not by subject so much as by the authoritative book studied, often from Aristotle, the Bible, or the Thoughts (often called the Sentences, from the Latin title Quattuor libri sententiarum, or Four Books of Thoughts, still reflected in the idea that a "sentence" should express a complete thought) of Peter the Lombard, who taught in the cathedral school at Paris. Having graduated from the Faculty of the (Seven Liberal) Arts one could go into the world, or continue in one of the three other, further, fields of Law, Medicine or Theology, which would take another 12 years or so.
IV. How It Fell Apart.
So what's the point of all this -- I'm into old stuff that isn't the way it is any more and think you should be too? No, and hell no. For as much "old stuff" as I post on this blog, I wouldn't consider any of it worth a ginger snap if it didn't do two things for us now: make where we are a little clearer and more understandable by seeing how we got here, and make where we are a little clearer and more understandable by seeing what was the idea of where we were supposed to be going in the first place.
Here's what happened. New knowledge did not replace invalidated knowledge in the system as it should have, but was confused with the system itself and brought the system down, and thus we have the start of our fragmented knowledge and view of learning to-day. This began when difficulties in reconciling Aristotle with Christian doctrine became more and more apparent, and the bishops of Paris issued a series of formal Condemnations, most notably those of 1277 by bishop Etienne Tempier, which had the effect of allowing scientific investigation to proceed without reference to Aristotle the great authority.
Beautifully ironic, especially in view of the nonsense peddled in so many contemporary universities, that scientific freedom from existing authorities in investigation resulted not in spite of the church and its doctrine but from bishops responding to the inherent problems in expressing doctrine in terms of the prevailing science of the time.
Which was great for science, also great for Aristotle since he never thought he wrote the last word on everything, but, it also had the effect of making everything previously held now seem possibly wrong or soon to be found out to be wrong.
A new direction in thought arose, best summed up in the maxim of the English Franciscan William of Occam, entia non sunt multiplicanda praeter necessitatem, or no more things should be thought to exist than necessary. This was a lex parsimoniae or law of parsimony that brought about a new way of thinking that was skeptical to agnostic. This new way consciously saw itself as a new way and called itself such, the via moderna or modern way, as opposed to the trivium and quadrivium which became by default the via antinqua or old way. This turned up in every field, in music (as we use the term now) it was called the Ars nova, a term first used by the theorist Phillippe de Vitry in a book by the same name of in 1322.
Music that was not monophonic chant but polyphonic, with secular themes being placed over a base of a piece of chant, music in duple time rather than triple reflecting the perfection of the Trinity, music written this way for religious purposes -- such things were utterly revolutionary, and part of the shift in the times that was happening from the arts to theology itself. What a modern irony that some to-day will perform the motets of Machaut, the greatest of ars nova composers, and be thought to be real fuddy duddys, but Machaut himself in his day was thought of as an affront to everything right and proper for worship!
It was into this world turned upside down and inside out that Martin Luther, having graduated from schools that focussed on the trivium, enrolled at 17 in University of Erfurt in the first year of the 16th century, 1501, graduated with a Master degree in 1505, and went on to the Law school following his father's wishes and the usual pattern. He soon dropped out. Questioning everything, positing as little as possible, and so on was all fine, but at what point did it yield reliable results, also known as answers, which is particularly upsetting regarding the claims of Christian doctrine which have some pretty extreme claims of salvation and damnation.
There being no answers, he sought one in what was available, the rigours of the actions of monastic life, to the extent that his superior, Johann von Staupitz, Vicar General of the Augustinian Order in Germany, had him continue an academic career in theology to take his mind off his own salvation, and also spoke to him about the Means of Grace and salvation through the death and resurrection of Christ, which, though Staupitz was no Lutheran and lamented the breaking of visible church unity, got him put on Rome's Index of Forbidden Books!
V. Where We Are Now.
Seems long ago and far away, but it is into exactly this same world turned upside down and inside out than we are born now, just with better means of communication. Each age along the way seems to think it has started a new age, a new way, a modern way, an Age of Aquarius, an Enlightenment, or whatever, all just simply repeating the confusion of the via moderna with better technology. Likewise our supposedly enlightened modern world, where graduates can't count back change in their minimum wage jobs, or reliably point on the map to where the people came from toward which they have been taught warm inclusive fuzzies, or hear a news report with an ear to whether or not it contains unexamined assumptions from which supposed conclusions are drawn.
Of the four original universities, three are still around right now, namely Cambridge, Oxford and Bologna. The fourth, Paris, was abolished by the French Revolution, but a number of institutions with historical links to it survive. More remarkably than that, all of these are routinely ranked as among the very best universities in the world. Cambridge and Oxford always rank in a superclass by anybody's rankings, always in anybody's top ten. The other superclass members btw are Harvard, MIT, Stanford and U California-Berkeley. Harvard has roots in Cambridge and is named for its original benefactor, John Harvard, a Cambridge alumnus. Bologna regularly places in the #150-300 range.
In fact, there are even older continuously existing institutions which exist now as modern universities but were not founded that way. Al-Azhar University, in Cairo, much in the news in recent years, was founded as a Shia madrasah by the Fatimid dynasty in 975, became Sunni under the Ayyubid daynasty (the great Jewish philosopher Maimonides taught there in the 12th century) and became a university in 1961 under President Nasser of Egypt. Arguably the oldest degree-granting institution in the world is the University of al-Qarawiyyin (sometimes given as al-Karaouine) in Morocco, founded as a Sunni madrasah by Fatima (yes, a woman) al-Fihri in 859, when Europe was largely a bloody mess barely held to-gether educationally by the grand and glorious hard-working and uproarious Benedictines, but became a university in 1963 following the independence of the Kingdom of Morocco in 1956 (from France, but hey the Romans ruled it for about 400 years, under the name Mauretania, not the same as the modern Mauritania).
And, topping it all off, Nanjing University was founded in China in 258 by the emperor Sun Xiu (Jing of Wu) as a school for the Confucian Six Arts (man am I tempted to go on about those in comparison/contrast to the Seven Liberal Arts!), and after a TON of bumps along the way became a university in the 20th century, and you know what, STILL hangs in there ranked among the top universities in the world by all major rankings!
"All major rankings" means the QS World University Rankings (QS), the Times Higher Education World University Rankings (THE), both British, and the Academic Ranking of World Universities (ARWU) from Shanghai, with US News & World Report lately jumping in with a revised QS ranking.
Recent decades have seen an astounding increase in the ability of thoughts and information to be communicated, starting with mass printing some time ago but exploding first with the coming of radio, then TV, and now the Internet and other forms of digital media; and at the same time have seen an alarming decrease in the apparent ability of people to form, communicate and evaluate thoughts and information. Where the ability to smarten up exists to an unprecedented extent, the fact of dumbing down is seen everywhere.
Amid an unprecedented ability to communicate information, people seem to have less information and less ability to critically evaluate information than ever. And this largely not because people are any more smart or stupid than before, but because educators themselves have nearly totally lost sight of this, that the magnificent increase in the media of communication does not invalidate but in fact makes more needed than ever the basic tools for forming, setting forth, and understanding what is communicated.
This general dumbing down of society is not new, it was noticed decades ago, but it has assumed warp speed as the very means of communication develop at warp speed too. One of the earliest, and still best, more applicable to-day to the means that did not exist when it was written than ever, is an essay called "The Lost Tools of Learning" by Dorothy L Sayers in 1947. She was best known for her detective novels, a genre generally considered "low brow", and that such a magnificent and magnificently educated mind as hers should equally well write best selling detective novels exemplfies what this is all about.
Her essay is online now. You can read it here.
Another, and more recent, modern exposition of these tools of learning is by Sister Miriam Joseph of the Sisters of the Holy Cross at St Mary's College in Notre Dame, Indiana, called, guess what, "The Trivium". Philadelphia: Paul Dry Books, 2002. Available through Amazon easily.
VI. Conclusion. Where We Could Be.
So, again, the Liberal Arts are a system for first learning how to learn, the Trivium, then for classifying what is to be learned in order to be educated to fulfill the responsibilities of democracy and high office, the Quadrivium. This is not at all about going back to the "Music of the spheres", in which the mathematical ratios in tones and in the orbits of the sun and planets around the earth were though to be the same, or about reading Aristotle, learning Latin, and things like that -- though there's good reason to read Aristotle and learn Latin -- or about going back to earlier social structures. What happened was, as some of the knowledge taught within the system was later found to be either incomplete or just false, like what orbits around what, the system itself, and more importantly the overall unity of things which it expressed, also came into question.
In religion, the point of the Lutheran Reformation was not to create a new church or even split the one there was, but to bring back to front and centre the Means of Grace through which salvation is communicated and the message of salvation through the blood of Christ itself -- to paraphrase Luther, making the most clear things about the church what had become the most obscure amid the Roman confusion. The direction in which the later more general Reformation went, which began even in Luther's lifetime, was as opposed by Luther and Lutherans as the errors of Rome.
In education, perhaps another reformation is needed, not a religious but an educational one. One where besides what one learns to earn whatever living one earns and has whatever career one has, that in order for society to function, ESPECIALLY in one where all and not just some classes participate, there is a skillset and a basic body of knowledge needed by all, where the tools of learning are actually taught (there's the trivium), where a person is then taught how to handle abstact operations, operations applied to things as they add up, how complicated things break down and how that is applied to things (there's the quadrivium). That would be education, the basics for participating in our society, open to all now, rather than the latest theories of what is "enlightened" this week, which are handed down as so modern, but amount to no more than secular articles of faith handed down "ex cathedra" from an authority which, when it takes itself to be such, violates the very parsimony and science it thinks it passes on, as it neither guarantess a correct conclusion nor prevents a false one and may not even be applicable to a particular field, and, if applied to all fields as a universal principle, violates its very definition!
Oh Yeah, an Addendum.
There was this second cousin of Martianus Capella, with a variant spelling of the last name, Antonius Cappella, who wrote thousands of pieces of music, in a wide array of styles but all vocal, that are still performed to this day. You can spot them easily. They are all identified by the way he signed his name, A Cappella.
OK, I'm just jacking around now. A cappella actually means "from the chapel" and was used to designate purely vocal Renaissance polyphony generally for the church from the later Baroque concertato style which featured alternating vocal and instrumental parts in a piece of music. Oddly enough, we now know those "vocal" motets were often doubled on instruments, but the first modern "musicologists" didn't know that, so singing "a cappella" has come to mean pretty much any music that is singing only, no instruments.
Except for a small school of hard cores, in a city named for its big reeds, Acapulco de Juarez in Mexico, who wouldn't use the reeds for instruments, so the style is also called singing Acapulco. OK I'm jacking around there too.
But for real, I'm happy to say my alma mater, the University of Iowa, from which I got my MA and PhD degrees, ranks #121 in the USNWR rankings, 175 in THE, 269 in QS, and in the 151-200 band in ARWU. Not too shabby for a relative newcomer only organised 25 February 1847 in what had just become a state only 59 days before! It is also listed among the "Public Ivies", a list of 30 public US institutions considered to offer an educational level comparable to the "Ivy League" schools. And I'm also happy to say that Luther thought the plays of Terence, after whom I was named IRL, were excellent for children's learning.
And what's an "alma mater"? Hoo boy. It's Latin for "nourishing mother". In the Roman Empire it meant the Mother Goddess, Venus, the Roman version of Aphrodite, who was called Venus genetrix, Mother Venus. In the Roman Church this became adapted to Mary, Jesus' mother, as Mater dei genitrix. As an academic reference it has been used since the 1600s and comes from the phrase "alma mater studiorum", which means nourishing mother of studies. It's from this that we get the Latin term "alumnus" (male) or "alumna" (female), plural "alumni", meaning "one(s) who is/are nourished", as in educated.
In 2000 it was adopted as the motto of, guess who, the oldest modern university, the University of Bologna, right on the heels of the 1999 signing of the Bologna Declaration signed there by the ministers of education of 29 European countries, which while aiming at a greater standardisation of European higher education, seems to do so from the standpoint of corporations and the World Trade Organisation (WTO)-- cutting costs, getting a job. getting competitive -- read, winning against or at least getting your slice of the pie with other players -- etc.
Textual Note: This post is a complete revision of my original similarly titled one, incorporating additional material from 2009 and new material in 2010, then revised here and there in 2011 and 2013 - 2016.
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