High Flat Skill Profile

An interesting piece of popular science with a spurious pedigree is the idea that brain function is determined by hemispheral activity. We say that the left hemisphere is for quantitative, precision thinking such as mathematics and spatial reasoning, whereas the right brain deals with holistic activity, recognising patterns and governing intuition. So we talk about somebody being either left- or right-brained, with right-brained people being creative, disorganized and impulsive while the left-brained are fastidious, numerate and boring. This belief isn’t just imposed on others, but governs self-belief as well.

It turns out that none of this holds much weight. Many of us go through our education emphasizing either the arts or sciences, with students who consider themselves more quantitative shying away from softer tasks like writing essays or analysing literature, and those who find painting a picture or writing poetry more interesting than solving equations tending to ignore the more rigorous subjects. There’s an idea that you’re good at either one or the other of these, and like many prominent ideas it’s gained a degree of accuracy simply by virtue of how seriously it’s been taken. Since we tend to believe these things and allow them to govern our life decisions, they can determine what we end up learning and being good at.

But it’s not true that you can only be good at one or the other. It turns out that, in terms of actual ability, whether innate or developed, those of us who are able to understand complex mathematical subjects also do well in tests of verbal intelligence, and vice versa. There’s a strong correlation between these abilities, but often, by the time we’ve completed our formal education, we’ve learned much more of one of these than the other. Testing students who’ve graduated or are attending university, you find that most of them favour one of these areas more than the other. Those of us who do okay at both have what’s called a “high flat” profile, scoring in the top deciles for both mathematical reasoning and understanding of language.

To me, this isn’t much of a surprise. So far as I’m concerned, both of these categories of tasks are variants of symbol manipulation. They each involve the construction and modification of meaning based on a set of underlying rules. The rules of natural language may seem inconsistent compared to the hard and fast rules of mathematics and formal logic, but the degree of fuzziness is something which can itself be precisely quantified. Linguistics as a science is one of the most rigorous disciplines you can study, and along with mathematics and information theory is one of the “formal sciences,” which collectively provide the framework with which the rest of our knowledge can be described.

So what does all this cold, hard analysis have to do with those of us who enjoy the musicality of poetry and prose, or the transformative imagery of our favourite fiction? To me there’s a richness available in both mathematics and language, a complexity and elegance which combine to create something beautiful. Although to many people mathematics seems dry and too much like hard work, much of what it reveals can be not only useful but surprisingly aesthetically pleasing.

So what educational impact does this have? I do think individual students demonstrate divergent interests and skills, and that some of them respond more readily to English or mathematics instruction. But this doesn’t mean they’re completely resistant to one or the other. For children with a proclivity for the order and neatness of mathematics I find I can appeal to them by focusing on the structural elements of grammar and the logical consistency of the underlying rules from which meaning is constructed. For students who are more interested in the arts or who have a phobia of numbers, mathematical instruction has to be flexible, and I keep in mind the multiple possible approaches to solving the same problem. Each student develops their own understanding of a mathematical topic, and the beauty of mathematics comes from its consistency, such that divergent approaches to the same question converge on a single set of correct answers. So long as a student can understand what they’re doing and how they find the solution to a problem, there is a surprising amount of room for innovation, unique approaches, and the integration of wider knowledge.

The Renaissance Man

People these days talk about how you need a trade, anything so long as it’s specialized. We live in an age of super-specialists, where people spend entire careers developing their skills. They do an apprenticeship, an undergraduate degree, a graduate course, on-the-job training. We have high level experts within sub-sub-disciplines, like somebody’s not just a physicist any more, not even just a nuclear or theoretical physicist, but a member of a team specializing in a particular application of string theoretic mathematics to some intractable problem. We all use products which are designed to make everyday life easier, like computers, but at the same time the operating systems and user interfaces of these products can be so complicated that tertiary institutions offer certification programs in their proper usage. Many of us drive a car, but gone are the days when most of us could fix them; this isn’t just because we’re too lazy to learn, but because when you look inside the engine you see what looks like a spaceship’s innards; all covered in shiny plastic and neatly encased, with that telltale label “no user serviceable parts.”

This is all echoing through into our educational paradigm, where from an increasingly early stage we start pushing people to develop the skills they need for a specific career path. Louis C.K., the famous comedian, talked about the American concept of the technical high-school, describing it as the place where dreams go to die. A technical high-school is an institution for teenagers where they learn skills related to a series of trades, as opposed to focusing on more general academic skills. C.k. talks about how we tell kids they can do anything, that any one of them could grow up to be the president of the united states, so long as they were born there, but by the time they go to a technical high school that’s been narrowed down to a much shorter list, like, you can be these eight things. Pick one of these and that’s what you’re going to do for the rest of your life.

So we live in a world where many of us define ourselves by what we do for a living, like saying, instead of “I teach,” “I am a teacher”. We also live in a world built by specialists, where their hyper-specialized skills go into producing ubiquitous products that most of us have only the most limited understanding of or ability to modify, improve or repair, let alone conceive and create.

This hasn’t always been true. While there have always been trades, of a sort, and division of labour, the educational system which our own is based on, the old English style, was one based on what were called the classics. The idea was that at one of these schools, everybody was given what some these days call the burden of a classical education. A classical scholar could read, understand and speak some form of Latin, possibly classical Greek as well, and was conversant in a body of canonical literature that included, I suppose, such lights of the western tradition as the King James Bible, probably the works of shakespeare, and then some of the ancients, like Plato, maybe, or virgil, Homer. Boring as anything, really, but everybody learned the same thing, and an educated man had a definable set of  skills and body of knowledge which identified him and informed the way he spoke, the references he made and the company he kept.

This whole idea of a classical education is defined by the historical context within which it emerged. The need for an educated public became apparent when the development of the printing press meant kings and rulers could disseminate mass propaganda to the entire population, communicating directly to individual, private citizens en masse for the first time. This ability was relatively ineffective, however, if the masses couldn’t read, and at the same time it was necessary to educate a class of writers who would produce the material for the kings. This process of educating the populace meant, eventually, that the autocratic style of rule became much more difficult as the people were no longer kept weak and disorganized through their own ignorance, but like any transformational technology the press had to be embraced, for fear that if one ruler failed to do so, somebody else would be doing it instead and thereby gaining an intolerable advantage.

But this whole process, the press, mass education, and mass industrialization and standardization in general, were all products of the changing times. The middle ages had ended with the renaissance, which means rebirth. This period was named as the rebirth of knowledge, of scholarship, as the civilization of Western Europe looked back to the time of the Roman Empire and the other so-called classical civilizations, when the continent had been ruled by one government, the infrastructure was organized and there was a stable economy and an educated class of scholars and clerks. This had all been supposedly lost, although really it just shifted elsewhere*, and the resurgence of new ideas in the 14th to 17th centuries was an attempt to regain the heights achieved by the ancients and, eventually, to surpass them. The press itself originated in China, but its impact was perhaps most fully felt in the Europe of the early industrial era.

The renaissance, with its emphasis on education and striving after ancient ideals, is responsible for the term renaissance man. Its closest synonym is perhaps polymath, and it means somebody who excels in multiple fields. The ideal of a renaissance man was somebody who could fight a duel, speak multiple languages, recite poetry, play musical instruments and win a debate. He should be a student of multiple disciplines and current in as many fields as possible. This was perhaps easier to do, back then, when many noblemen led lives of leisure, without the pressure to earn a living, and when the total body of knowledge available was probably a fraction of what currently is produced in a single day. But this ideal influenced the development of the education system, especially in England, where we and much of the world get our current system from.

This system developed in a time of mass production and industrialization, when these ideas were new and shiny and appealing. The King needed an educated populace and a standardized, one-size-fits-all style of rote learning and harsh discipline was instituted. This ethic, as well as having a generalist focus, was also reminiscent of an assembly line, with the pupils being stamped into a mold established by generations of their fellows going through before them. While this has succeeded in reliably producing large numbers of young men who can recite classical Latin, it has proven less than entirely adequate for the modern world of specialization and diversity, and enjoys significantly less favour now than it once did.

Despite all this, the idea of a generalist education, a fundamental set of skills with which to face the modern world, is still interesting and may be of some merit. While Latin may no longer be the highest priority of modern educators, the hyper-specialization of academic and technical disciplines may in some ways be counter-productive. Inter-disciplinary research and collaboration has yielded fruitful results on numerous occasions, with surprising insights from outsider knowledge workers being able to shake up disciplines which previously had been experiencing stagnation. The specialized jargon of each area of research is supposedly intended to allow the convenient communication of equally specialized concepts, but may in fact do little more than indicate the learned status of the speaker within their own branch of the academic hierarchy. This kind of jargon is especially rampant in the humanities, and can serve as a barrier to collaboration.

This disjoint set of jargons and technicalities can leave many effectively disenfranchised from our highly technical world, and this means a generalist understanding of science would be highly useful. It would be advisable, however, to avoid creating a class of jacks of all trades, masters of none, and finding a way instead to give the students an advanced understanding and high level of fluency in the most general set of skills practical, rather than merely giving them a low-level introduction to a broad yet disconnected array of possible skills. To do this it behooves us to examine the academic sphere for the most general and abstract set of topics and find the best way of communicating these to the student.

A friend of mine teaches guitar, and says that the solo from Michael Jackson’s beat it, played by Eddy Van Halen, features so many techniques executed with such elegance to produce such a catchy and appealing sound in its brief, minute or so execution, that it provides an exemplary learning tool. I always thought it’d be cool to do something like that but in a more general sense. He figured that once a kid learned the Beat It solo, they could use that as a practice exercise, improving one technique or another until they could play the whole thing and make it sound like the CD. Once they had that down, they would have learned a whole set of skills which they could extend to almost any other song. My friend was trying to develop a better solo, something even more feature-rich than Beat It but which would still sound cool and be fun to listen to rather than just flashy. This makes me wonder how you could teach something like that in the academic world.

The solution I came up with was to focus on two main things, English and mathematics. English, if understood and developed correctly, allows you to communicate and understand almost any idea. Mathematics allows you to express more concepts than English can, with greater precision but with less ease. Mathematics is an enormously broad topic, and research indicates that unlike many other disciplines, developing one skill in mathematics won’t necessarily improve any others. Many concepts within mathematics are logically related and they form a giant tree of dependencies, but there are still many distinct branches which need to be individually practiced.

English, on the other hand, is much less systematic, and different elements of the study of the English language mutually reinforce each other. I have, however, a great affection for the form of the essay, and evidence shows that writing free-form essays presenting the individual’s understanding of a scientific topic has an unparalleled effectiveness in the memorization of the material covered. The essay is also a difficult thing to get right, requiring both style and diligence, and brings together multiple skills. The essayist needs to be able to present an argument, be conversant with spelling and grammar, appeal to the audience and maintain readability and interest.

A combination of mathematical practice and free-form essay writing strikes me as a good basis for any child’s education, and can be combined with less rigorous influences such as student-directed learning to create an overall package. The idea behind student-directed learning is that children learn best when pursuing knowledge which interest them directly. To this end I’d propose allowing students to study pretty much whatever they want, so long as they can write an essay about the topic and are willing to submit their written work for assessment in terms of their compositional skill as well as their knowledge of their chosen subject. This way, they can develop not only their understanding of their chosen subjects, but also their skill as a writer and and their general academic ability.

This idea of combining language and mathematics into a complementary whole makes me wonder about what area covers both of these. To get this kind of coverage you need to look at things from the most general and abstract level possible, which is the level of the so-called formal sciences. These include linguistics, computer science, cognitive neuroscience, analytic philosophy and abstract mathematics. They’re all descriptions of informational structures, and the same basic essence defines all of them, whether the information is being processed or communicated by a machine or a human brain, or whether it exists in the abstract world of mathematical objects, as lines of code in a computer program or in the symbolic features of a natural human language. These are all pretty much symbol manipulation regimes, and it strikes me that this maximally abstract level of study provides an opportunity to be both entirely general and highly specialized, simultaneously cutting edge and open to anything. It’s in this area where I can see the possibility for some kind of grand unified theory of knowledge or whatever, some way to describe everything in one common language instead of this almost Biblical babel of competing theoretical and conceptual lenses through which to interpret reality.

So that’s pretty much the stuff that I find the most interesting. It sounds dry and highly abstruse but it covers the most fascinating topics, from the study of the brain’s function and the results which are finally freeing psychology from its Freudian roots and turning it into something resembling an actual science, to the mathematical physics that describes the universe at the largest scale and points to exciting new possibilities for exactly how the world works. Some kind of unified theory of symbol manipulation and information system would allow students to better  understand people, concepts, technology and science. If it’s possible to take these abstract disciplines and break them down into step-by-step progressions and simplified, bite-size chunks, to make them accessible while maintaining an awareness of the advanced, cutting-edge applications which make them exciting, then this could be a great educational tool.

 *We talk about the fall of Rome as if the entire civilization collapsed in the first half of the first millenium AD, but really there was an entire Eastern half that continued for hundreds of years. We refer to these people as the Byzantines, after Byzantium, their capital city, but at the time the Byzantine Empire self-identified as Roman and Byzantium, or Constantinople (modern day Istanbul) was just another Rome. The Empire had been split in two and divided between two emperors when it grew too large and unwieldy to maintain under one banner, and the continuation of the Eastern Empire isn’t some trivial remnant. The classical age flourished and the knowledge and technological development from the times of the ancients continued in the hands of the Eastern Empire, to begin with, and later the Arabs. The strong tradition of scholarship within Islam is clearly evident to any student of history and religion, and the Muslim imperative to study God’s world and the laws of nature so as to better understand God’s creation compelled them to faithfully preserve and diligently extend many of the ancient Greek scientific texts. This process of development generated many innovations in fields as diverse as engineering, astronomy and mathematics. In fact, though the name “Arabic numerals” is a misnomer, it is the Arabs who taught the European civilization its current base-10 number system, which they had in turn originally learned from the Indians. Not only this, but many modern mathematical concepts have arabic names, which many people may not recognise. Terms such as Algebra or algorithm come respectively from the Arabic Al-Jabr and the Latin Algoritmi, a transliteration of the name al-Khwārizmī. The universities of the Islamic world have long been centres of great scholarship, and the oldest continuously operating tertiary institution is the University of Ez-Zitouna in Tunis, which was founded as the Ez-Zitouna madrassa in 737 C.E.

The Vagaries of the English Language

The English language, like the English nation, has come into contact with an extraordinary range of other cultures and languages. The Telegraph recently reported that Britain has invaded or fought with nine out of ten countries in the world, leaving only twenty two nations historically unmolested. Similarly, England itself has experienced waves of immigration, invasion, settlement and occupation. All of this is reflected in the diversity and complexity of the English language, little pieces of history echoing through the ages to leave their mark in the form of various linguistic peculiarities.

Despite all this, some of the grandest claims as to English’s sheer size and complexity are in fact plausible sounding misconceptions. Steven Fry, the popular actor and public speaker, has been quoted in support of the oft-repeated but erroneous claim that the English language has the largest vocabulary of all languages, ever, throughout history. It’s presumed by the people who adhere to this belief that because of its sheer complexity and the history of extra—linguistic contact the English language has gone through that it has taken on the characteristics of, and many of the words from, these various other languages. Not only is this supposed to have left English with a “larger vocabulary” than any other language but it is sometimes claimed this sheer volume of words is larger than all the other languages combined, or some similar piece of hyperbole.

A relatively simple thought experiment can discount the possibility of such suppositions. Different languages can be classified according not only to their linguistic family in terms of relatedness to other tongues but also to their functional nature. English is what we call an analytical language, as opposed to languages like German which we call synthetic. This means that in English we modify meaning by changing word order and appending adjectives, adverbs and conditional clauses to the statements we make, whereas in synthetic languages a lot of this work can be done by combining words into new neologistic constructions. We’re all familiar with German’s comically over-complex words formed from the Frankesteinian combination of what might account for an entire sentence in English. These new words aren’t necessarily new in the sense that they need to be added to the lexicon, because German speakers have a clear and established set of rules for how these compound neologisms are formed, such that the meaning of each is often apparent so long as the speaker is familiar with its component words.

The comparison of English to German may seem extreme, with the monstrosities of German linguistic synthesis such as Donaudampfschifffahrtsgesellschaftskapitänsmütze seeming almost absurd*. But there are all kinds of similarly confounding complexities to the question of exactly what counts as a word. Think of the relatively simple case of different verb forms in English; to run, running, ran, did run etc. Or think instead of the differing degrees of modifiable adjectives, such as big, bigger, the biggest. Are these multiple forms of the same word, or is each a word in its own right? What about compound words? I used German because it’s probably familiar to most people, but there are also less obvious but more instructive examples of synthetic languages, such as Czech.

In Czech, for one root you get something like twelve words for free. If I’m addressing you in the second person, I add the suffix “-íš,” pronounced “-eesh,” whereas if I’m speaking in the first person I use “-im.” There are different forms of the word if I’m using it in the general sense, different tenses, and depending also on conjugation. The language also sometimes dispenses with vowels, resulting in apparently unwieldy clusters of consonants like the children’s tongue twister “strč prst skrz krk.” As difficult as that kind of thing is for English speakers to get their tongues around, however, the apparently complex rules of the Czech language are in fact almost entirely consistent, and compared to English the spelling is almost entirely logical and phonetic, albeit in a weird, uncannily altered version of the Latin alphabet. It’s rated one of the hardest languages for other people to learn to speak, but English is right up there with it.

One factor often making it difficult for learners of English as a foreign language is that of its countless inconsistencies and irregularities. One historical peculiarity is that in the past, many of these rules didn’t exist at all. It was only with the implementation of the printing press that familiar standardized spellings began to emerge. Printers used mounted blocks to transfer letters and words to the page, and it was more efficient to have a block for an entire word than to arrange it every time with individual letter blocks. This combined with the existence of multiple rival publishing houses to generate a profusion of standardized and yet differing sets of spellings for commonly used words. The need to create these blocks also led to certain rules for the creation of sensible spellings, so that one house would create word blocks according to one principle and another to a quite different rule. It is from this chaotic evolution that we get the written word of today, with the added confounding factor of differing dialects and their canonical texts, such as American English and Webster’s dictionary.

Webster is the reason many American spellings differ from their British counterparts, in that Webster decided it would make more sense to start spelling in phonetics, according to some kind of logical plan. But this didn’t always stick, and a lot of his simplifying influence has been lost or rejected as people have clung to the old ways. He still managed to push a few of his innovations through though, such as the change from “colour” to “color”, “favour” to “favor” or “realise” to “realize.”

Beyond rivalry between printing houses and dictionary publishers for the right to wrest control of the English language once and for all from the chaotic inconsistencies that had determined its evolution to that point, there is one fundamental schism at the heart of English’s history which leaves it and many other European languages greatly affected. This is the fact that English is a Germanic language, but from the time of the Roman occupation a thousand or so years ago it has been written in a Latin script. There are some linguists today who argue that English has effectively become a Latin language, shifting from one historical branch of the Indo-European language family to another by virtue of accretion. The sheer weight of Latinate terminology which has injected itself into English, as well as the fact that its script is based on the Latin alphabet, means that English as we know it today has both historical and incidental connections to Latin. It could be argued that in some sense English is more “purely” Germanic, that its origins come from the Celtic tongues spoken in the British isles before the Roman occupation, but questions of what came first are difficult to settle given that English’s evolution into its present form has involved from multiple branches of linguistic development merging over time. How can we determine that one is the original branch, simply by virtue of its continuous occupation of the same physical location, when the language itself has expanded out to become what is effectively the universal auxiliary language for almost all international affairs? Is the most defining aspect of English its history in the land of England, or its history as a promiscuously mongrelized meta-tongue?


*This example is actually a joke, but in some scientific disciplines such as chemistry, where names are required for enormously complex chemical compounds, the length of these constructions can be virtually unlimited.

Secondary English Tuition

Hi, my name’s Tobias and I’m the new English tutor here at Emerson Willard. My job is mostly to extend students’ writing ability and go beyond what they learned in the primary course. By now they hopefully have a functional level of spelling and grammar and so I focus on a combination of revising these basics to find problem areas, and trying to get the students to write. That second part is actually most of the program.

I learned to be an English teacher in Prague, at the Edua Languages TEFL course. My trainer there, an American, was talking about the basic approach required to help people learn English. Most of his student teachers were already university graduates, and some of them even had master’s degrees in certain disciplines, and so most of us thought of ourselves as able speakers and writers of academic English already. But John asked us, “If you were a baseball coach, would you get up in front of your team and say ‘Look how many home-runs I can hit?’ Or would you try and get the players swinging the bat for themselves?”

Most of the task of being an English teacher was eliciting content from the students, while maintaining an actual language goal in mind for them to develop. Maybe that day you wanted to work with them on the difference between “had had” and “had,” or difficult verb tenses like “will have been.” Whatever it was, the important thing was being able to engage the students and get them thinking about the language goals you had for them.

After gaining my qualification as an English teacher I promptly went on to never work as a TEFL teacher, ever again. I’d given several practice lessons throughout the course of the four week program in order to gain my qualification, but after that I eventually left the country and came back to New Zealand. Apart from that brief stint in the TEFL world, I’ve also worked as a physics demonstrator and a private tutor for university students. As a physics demonstrator, my job was to show university physics students how to perform experiments and then to help them when they had trouble and mark their work when it was done. As a private tutor I spent most of my time with students from Saudi Arabia, going over their written essays and finding the obvious mistakes and opportunities for stylistic improvements, while at the same time helping them with whatever course material they were struggling with. This often involved taking the subject matter from their prescribed texts and processing it into bite sized chunks to help their comprehension during test preparation.

In all of this and the course of my own academic studies, I’ve found that the most powerful revision and memorization tool is the essay. The process of writing an essay requires not only the recall but the organization of a disparate array of facts and concepts to form a coherent and easily readable argument. The essayist must take items scattered throughout their conceptual space and render them into a one dimensional string, putting one word and one paragraph after another. At the same time they have to exercise theory of mind, and understand how the reader will approach the text they’re creating, how to make it engaging and comprehensible. They need not only to present the facts but get a point across, and there are few other techniques which bear these complementary features.

This isn’t just my hunch, either. A 2011 study, published in the journal Science showed that using essays as a form of retrieval practice was one of the strongest techniques for encouraging the memorization of information, out-performing rote memorization or more modern techniques such as mind-maps. This process required that students write an essay based on material they had learned and that in the act of writing they attempted to recall what they had studied, rather than looking it up again. This meant the essay writing acted as a form of retrieval practice, and the process of manipulating the information as well as actively recalling it helped to cement the information in the learners’ brains while also establishing rich connections to multiple areas due to the necessity of fitting the information into a logically structured text. This wasn’t limited to the arts, either, as the original study was carried out with students a week after reading brief passages about scientific concepts.

The surprising applicability of tools from the English department in studying scientific topics is of particular interest to me. My academic history covers a wide range of topics but right now I’m working on a degree in English and mathematics. The double major isn’t just because I’m a glutton for punishment but because the interdisciplinary approach has always been attractive to me. The areas that interest me the most are the so-called formal sciences, the overlapping set of disciplines including linguistics, mathematics and philosophy from which more specialized areas are developed. At the core of all this are the questions of how information works, how it can be communicated and how it is understood, from which such disparate areas of study as psychology, computer science, physics, and language all draw much of their theoretical underpinnings. Some of the deepest and most intractable unexplained problems in science today are the questions of consciousness, cosmology and comprehensibility. In short, what is the mind, why is there anything and why does any of it seem to make sense? These questions, esoteric as they may seem, are all related by concepts drawn from areas such as information theory and abstract mathematics, and the most recent and promising answers to many of them come at times from unexpected quarters. The current consensus in physics, for instance, is moving towards the ideas of the “mathematical universe,” the universe as an abstract mathematical object, and the holographic principle, the idea that our apparently three dimensional world is really the projection of a two dimensional space.

These developments are as exciting as they are intriguing, and I hope to be able to convey something of my passion for knowledge to my students. Another interesting development is that student-directed learning is one of the most powerful educational paradigms, in that when allowed to direct their own course of study students tend to learn more than when a course is imposed upon them from above. While my approach involves a fair amount of simply pushing the student to achieve a greater level of understanding and fluency in their writing, I also hope to be able to engage students’ interests from a wide range of subject areas and find topics which appeal to them, using the process of learning to write as an opportunity to learn about other concepts as well.