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Analytic vs synthetic knowledge
I think one of the great strengths of Inuit Knowledge (IQ) is its ability to synthesize and incorporate new knowledge with the old. It is for this reason, and because of my technical issues with variations of the Sapir-Whorf hypothesis, that I've always been reluctant to say "traditional Inuit Knowledge".
Sapir-Whorf hypothesis is basically:
the Sapir–Whorf hypothesis, or Whorfianism, the principle is often defined as having two versions: (i) the strong version that language determines thought and that linguistic categories limit and determine cognitive categories and (ii) the weak version that linguistic categories and usage influence thought and certain kinds of non-linguistic behaviour. (Wikipedia entry)
I tend to think that education is the single most influential determinant of one's worldview and behaviour because the notion of "culture" is also influenced by what we've been taught or have become aware of in the course of experiencing life (ie, "education" in its broadest sense including but not limited to school education). The human mind is a wondrous thing, and capable of learning so very much when and if applied the way it can comprehend the subject material. Granted, learning take perseverance and patience.
I take issue with statements that say, because of climate change, IQ is no longer applicable: it takes a while to adjust to new or novel factors but human intelligence always adjusts.
The strength of IQ is Inuti culture's willingness to learn and adapt new things and make it its own. New technology? -Inuit will figure it out and modify it for Inuit purposes. New materials? -Inuit will figure them out and make uses of them. But what I want to point out is:
the intellectual capacity of IQ is such that it will even adapt to new belief systems and incorporate what is new into the archetypal landscape. What I mean is that we, the Inuit, as children have all heard variations of Inuit legends incorporating new facts seamlessly because there is not one set canon (some of the dog-human children of Nuliajuq, for eg, who become the qallunaat and sent off in a boat made of a kamik sole, though I suspect before European contact the story might have been slightly different). The rise of Christianity and the fading away of shamanism is also "justified" by way of story-telling, the same way that unethical behaviour is discouraged by way of scary tales...
Having no set canon for Inuit legends also allow these legends to be used as mnemonic devices for remembering land marks: the Atanarjuat legend has variations in every Inuit community if it exists, the places and situations in the story themselves become incorporated into the local landscape: there is that such-and-such island where Atanarjuat fled... the island is different in every community.
The story is used to help Inuit children remember where that particular island is situated in their area because memory retention is easier/surer if facts are connected to a narrative/story. The story is also remembered by the parents/grandparents and passed on to the children whenever the island is passed by. The ancient Kiviuq legend is a perfect template for this type of remembering; the story itself never ends waiting for new things to be told. The "voice of authority" is not so much in people but in these evolving, adaptable legends.
Most people are unaware of this fact. The power of IQ to synthesize the old with the new is its greatest strength.
I like to think that I'm a spiritual man though I'm not much of a religious man. Dogma of any sort is antithetical to my nature because of my humanistic values and I've tried in my intellectual career to cultivate a critical, comprehending mind. I've tried to emulate the literary, scientific, political and spiritual masters, not to just ape their words, not to romaniticize their characters, but to try and use their principles to gain my own insights, to think my own thoughts.
I've been thinking about this for a while: it is said that there are seven deadly sins - wrath, greed, sloth, pride, lust, envy, and gluttony. But I think the image of the fallen humanity is not so much a divine judgement (if God is love He is aversed to such unimaginable cruelty) but a prophecy, a warning of our lot if we insist on indulging our hubris (both at the personal and civilization levels):
Hubris (/ˈhjuːbrɪs/), also hybris, from ancient Greek ὕβρις, means extreme pride or arrogance. Hubris often indicates a loss of contact with reality and an overestimation of one's own competence or capabilities, especially when the person exhibiting it is in a position of power. (Wikipedia entry)
As far as I can tell, every human society - not just the Judeo-Christian tradition - has a tradition of moral/ethical discourse; as sure as that every language has a grammar. The seven deadly sins are familiar to any mature person no matter what culture or language they come from.
Don't get me wrong. I don't think of such things in religious, moralistic and self-righteous terms. The scientific principle that "there is no free lunch" (ie, the conservation laws) is a sound, foundational principle extendable to other areas of a human life, including our moral/ethical sensibilities: everything that we do has consequences, some good, some bad.
As a connoisseur of well-constructed oratory, I take inspiration from the fruits of classical education, especially the best of American free-thinkers. But it is not just words that capture my imagination but the noble sentiments they embody (ie, the possibilities of human potential).
In his departing speech, Dwight D Eisenhower warned the world of the implications of an imbalanced worldview not informed by decency and reason:
Throughout America's adventure in free government, our basic purposes have been to keep the peace; to foster progress in human achievement, and to enhance liberty, dignity and integrity among people and among nations. To strive for less would be unworthy of a free and religious people. Any failure traceable to arrogance, or our lack of comprehension or readiness to sacrifice would inflict upon us grievous hurt both at home and abroad.
Progress toward these noble goals is persistently threatened by the conflict now engulfing the world. It commands our whole attention, absorbs our very beings. We face a hostile ideology -- global in scope, atheistic in character, ruthless in purpose, and insidious in method. Unhappily the danger it poses promises to be of indefinite duration. To meet it successfully, there is called for, not so much the emotional and transitory sacrifices of crisis, but rather those which enable us to carry forward steadily, surely, and without complaint the burdens of a prolonged and complex struggle -- with liberty the stake. Only thus shall we remain, despite every provocation, on our charted course toward permanent peace and human betterment.
Crises there will continue to be. In meeting them, whether foreign or domestic, great or small, there is a recurring temptation to feel that some spectacular and costly action could become the miraculous solution to all current difficulties. A huge increase in newer elements of our defense; development of unrealistic programs to cure every ill in agriculture; a dramatic expansion in basic and applied research -- these and many other possibilities, each possibly promising in itself, may be suggested as the only way to the road we wish to travel.
But each proposal must be weighed in the light of a broader consideration: the need to maintain balance in and among national programs -- balance between the private and the public economy, balance between cost and hoped for advantage -- balance between the clearly necessary and the comfortably desirable; balance between our essential requirements as a nation and the duties imposed by the nation upon the individual; balance between actions of the moment and the national welfare of the future. Good judgment seeks balance and progress; lack of it eventually finds imbalance and frustration. (The whole speech can be read here in this link: http://coursesa.matrix.msu.edu/~hst306/documents/indust.html)
The "hostile ideology" is as much within us as outside of us - as our (the world's) current state of affairs demonstrate so vividly. Liberty and living well and fully are not rights but hard-won rewards of a conscious life requiring vigilance and hard work. Einsenhower warns his compatriots in errily familiar terms:
Until the latest of our world conflicts, the United States had no armaments industry. American makers of plowshares could, with time and as required, make swords as well. But now we can no longer risk emergency improvisation of national defense; we have been compelled to create a permanent armaments industry of vast proportions. Added to this, three and a half million men and women are directly engaged in the defense establishment. We annually spend on military security more than the net income of all United States corporations.
This conjunction of an immense military establishment and a large arms industry is new in the American experience. The total influence -- economic, political, even spiritual -- is felt in every city, every State house, every office of the Federal government. We recognize the imperative need for this development. Yet we must not fail to comprehend its grave implications. Our toil, resources and livelihood are all involved; so is the very structure of our society.
In the councils of government, we must guard against the acquisition of unwarranted influence, whether sought or unsought, by the militaryindustrial complex. The potential for the disastrous rise of misplaced power exists and will persist.
The hijacking of our political systems by corporatism and the thinly veiled purchasing of our public policy processes is the exact "misplaced power" Einsenhower speaks of. In Canada, under Harper's tenure there has been an accelerated drive to complete this fascist agenda. In the interests of "public safety" and "patriotism" we are fed drivel and I am aghast by the uncritical response by Canadians. David Frum recently called this collective stupor "new-found and sustained nationalism"!
But just look at and into the gap between the promises of Harper and reality (whether the mistreatment of our veterans or arctic sovereignty as a window-dressing exercise) one sees clearly that our public weal is not in the CPC's radar. Corporatism is peopled by entitled spoiled brats (the very embodiment of greed and avarice) whose ineptitude is astounding because its bravado and bombast are untested and unproven.
The English language is increasingly made meaningless because sophistry is mistaken for intelligence, legalism for cleverness (though why we need cleverness in the public discourse is totally beyond any thoughtful person) - ie, bureaucratic euphemisms abound and are assumed by our politicians and other "leaders" as they fluff themselves up with partisan pride. The notions of accountibility and responsibility are murdered everyday as politicians and other "leaders" hide behind the very offices these noble ideals are intended to hold and embody.
The seven deadly sins are not just moralistic abstractions - as we've seen them only in light of subscribers to dogma and pretenders to moral virtues - and we ignore them as superstitions at our peril. Humanists and especially American free-thinkers have been warning us about the secular and personal effects of them since they stood up to tyranny and arbitrary power (which has shifted from the royal and ecclesiastical courts unto corporations and special interest lobbies). But the noble ideals they forwarded are not just givens but most be acquired and worked on everyday else they become dead words, the cruelest of jokes.
I am no mindless convert to sobriety and righteous life; I love sinning, drunken stupor and wanton destruction as much as the next guy, and am totally guilty of them vices. It is with deliberately cultivated humility and full knowledge of my short-comings and vulnerability to slipping back that I assume my endeavour to an austere and reasonable life, not because it's hard but because I cannot face the consequences of my mindless actions any longer. If I seem unduly harsh I hope it's not been frivolous but in the spirit of not suffering fools lightly.
A postscript on Barton's approach to teaching Mathematics
My readers already know that I suffer little of Barton's half-baked ideas on teaching maths. I don't know that guy from Adam, and I really am not attacking him personally. He just happens to be the one who wrote the book.
But my criticisms are more technical than personal. the fact that they have political implications make a critical analysis even more urgent. Not out of hatred but out of the need for honesty and to better serve the discourse.
To wit: when he brings up the notion of "commutativity" he doesn't do it in a natural way. He says that the arithmetic operations of adding and multiplication are "commutative" but he doesn't really show why the operations of division and subtraction are "non-commutative"; when he talks about the number zero he speaks only of the strange, non-intuitive numerical value of nothingness, and says nothing really of the place-value system of hindu-arabic numbers (101 does not equal 11 does not equal 1001, say); when he talks about the "set" he doesn't get into the historical motives for constructing such a theory (namely, Cantor developed his theorems of transfinite arithmetic to try and put the definition of "irrational numbers" and infinitesmals on a more rigorous analytic foundations). Instead, to Barton and so many others, these are just empty words and not living, breathing, dynamical concepts.
The motives and reasons for such mathematical ways of thinking (ie, commutativity; theory of sets; rational/irrational numbers; etc. etc.) only come about naturally as one comes up against the limitations of what came before. The narrative informs the student, and they are able to follow the lines of reasoning much easier.
Barton talks about transmission teaching and closedness of subject. His confused discourse is a perfect example of that approach.
Writing styles and literary genres
I've been reading this very interesting book on one of the luminaries of Canadian culture, a book by Georges Leroux called, Partita for Glenn Gould (translated by Donald Winkler, McGill-Queen's University Press, 2010).
In the book, Leroux talks about Gould's admiration for a Japanese writer named Natsume Soseki whom he quoted often in writing letters to his friends. Leroux writes that Soseki's style of writing was very cerebral and often based almost entirely on the characters' psychological reality rather than a narrative. I was blown away by this, and thought long and hard how Soseki managed to pull it off, then I realized that Gould also admired Kafka greatly, and Kafka's work is likewise often based on the characters' inner reality and sense/emotional impressions more than anything.
Not having had the opportunity to becoming a reader on Soseki and Kafka (though I've read a bit Kafka), I realized this morning that I'm an admirer of a writer of similar persuasion (though, admittedly he may be considered of a lower brow by the more fastidious readers), Arthur C Clarke. I love Clarke, and consider him a great writer (not just a sci-fi writer). His characters' inner realities make up a great deal of the pages he writes.
This writing style may be a bit slow for some tastes, but it provides an excellent space for self-reflection and self-examination and possibilities for identifying oneself with the characters. It also makes one appreciate the more technical aspects of writing and self-dialogue that is quite a technical and aesthetic feat to pull off if one pulls it off well.
Is there a word for "mathematics" in English? (part v)
This is the last entry on this subject because I'm at the end of the Barton book. I may have given the impression that I'm reacting as I read the book. But that's not the case. I've given myself some time to reflect upon what I'm reading before I write here because I love the subject of maths and its philosophical underpinnings (ie, where these ideas come from and how they developed over time) and have been reading up on these subjects for many years.
What I've been critical of is, first of all, the shoddy scholarship of Barton who is clearly a non-specialist nor a very interested one at that, and secondly, because I appreciate the highly political nature in which he talks about these issues (aboriginal-government relations, especially aboriginal education). I'm careful to distinguish between "people" and "governments", especially in a "colonialist" context, because people of influence and power are very often just pawns in a larger system who, in a bigger pond, would have been just small fish. There may be no disingenuous bone in his body. So, I'm criticizing more the fact the ersatz environment in which aboriginal child are expected to grow up in. The dangers of the "blind leading the blind" are very real in this type of context, not just the Maori experience.
Having said that, in the few examples Barton provides, the possibility of miscommunication in a cross-linguistic environment never seems to cross his mind; nor the possibility that "plain-language" explanations may not be the best basis for curriculum development; nor the undertraining/under-resourcing of aboriginal teachers or non-aboriginal specialist teachers teaching aboriginal children, for that matter. I mean, I totally appreciate all teachers in Nunavut and the work they do is noble in my estimation but these possibilities are all too real for Nunavut.
There is also the superficial treatment of profound ideas and insights (both linguistic and mathematical/philosophical). Says Barton in many spots: one language may be so "different" as to make different mathematical worlds possible; one language may be the best and most appropriate language for maths discourse. He smatters half-baked arguments around then in the end states in most definitive terms that his research supports his thesis. What that thesis is is never made clear so I'm wondering if this book was intended for a gullible, uncritical, indoctrinated audience rather than as an honest academic discourse. The whole project seems to be designed to discourage self-reflection, further investigation and political awakening of aboriginal education.
I know this last subject (ie, political awakening) is scary to a lot of people but that is to show mistrust and denial of the basic goodness, rationality and maturity in human nature in both aboriginal and non-aboriginal compatriots (ie, this bogeyman is a myth, as much a "fiction" as maths as the Middle Earth). We need each other, and nobody's going anywhere (ie, no one is getting deported) so let's try and make our institutions more humane and humanizing rather than perpetuate their alienating, dehumanizing aspects with "cultured" parochialisms.
From a John Dewey critical perspective statements like below would never be tolerated:
Children do not need to have 3 follow 2, they do not need to have the 'correct' number of objects to refer to. They can suspend their dependence on reality if that is part of the game. All young children can do mathematics in this very real sense. All older people can too.
A relevant question to be asked is how this ability can be nurtured. How can I go about increasing my ability to think and act mathematically? A likely answer is to practice 'gossiping' with abstractions as often as possible, or, if I'm responsible for young children, to play such abstract games whenever the opportunity arises. (p. 147, The Language of Mathematics)
Even very young children sense when the supervisor/older person/teacher detects, even subconsciously, that something is not quite right in what they just said or offered as a response. This is how language is learned: through trial and error, and most importantly by feedback. This learning "technique" is embedded in the human consciousness. When they are not guided properly after realiizing themselves that they've made a mistake they quickly lose interest because they love playing within and with the rules of the game. When they do not get something out of it (ie, when no wrong or right can be measured or discerned) the reward system become meaningless.
In whatever language, in counting numbers 2 will always be followed by 3. Realiizing this is a great accomplishment for the child; their developing interpretation of the world is re-enforced, or if they got it wrong, they must be made to feel they have the creativity and wherewithal to figure things out (with proper guidance, mind). They love doing this: figuring things out. Anyone who has children know this, and no bureacratic reality nor academic theory will ever change it: their eyes light up, they become effervescent when they've done something right, or figured things "all by themselves". Denying young children the fact that 3 follows 2 in the counting system is to deny their innate intelligence.
Clearly, Mr Barton is a voice of authority in Maori education but like most self-appointed experts on alien cultures he has neglected to mitigate that pomposity and is now dancing like a fool for the world to see.
Is there a word for "mathematics" in English? (part iv)
When one's written extensively enough one sometimes realizes that towards the end of a piece that one has run out of gas - have exhausted one's resources and knowledge of the subject to such a degree that one is running on fumes. By the time Chapter 7 in Barton's The Language of Mathematics has come around he has definitely reached that point.
He claims, with little supporting evidence or arguments (whether historical or operational), that mathematics is like JRR Tolkien's Middle Earth - that profound and wonderful mathematical insights are nothing more than "fictions":
Mathematics is a created world, a world of the human imagination, and, like Middle Earth, we can write about it, film it, become part of it in our minds and emotions. Also like Middle Earth mathematics has been expanded upon by others apart from Tolkien (despite his family's best attempts to preserve copyright)...
...Once we have the number 1 and the number 2, then no mathematical Tolkien could have written anything other than 1 + 1 = 2. Once we construct a circle and its diameter, and then draw a triangle on the diameter to a point on the circumference, it is not just geometric poetic licence that says that the angle at the circumference will be a right angle. And it is not just a muse's whisper that requires that a right-angled triangle to have sides that obey Pythagorean relationship. These things must be so.
The mistake is to think that this situation does not exist for Middle Earth. If you are a hobbit of Middle Earth, and you get yourself into deep trouble with the Forces of Evil, then, in your moment of dire need, lo, the Elves will come to your aid. It cannot be otherwise. For if it were otherwise it would not be Middle Earth!!...
...In the same way, if 1 + 1 does not equal 2, then we are not talking about the world of mathematics, we are in some other world. The number objects 1 and 2 were [emphasis added by me] created into just the relationship embodied by 1 + 1 = 2. That is what mathematics is. Circles and triangles and angles were also [emphasis added by me] created into their relationships.
But when Tolkien wrote Lord of the Rings, he had all the relationships and consequences worked out in advance. As the mathematicians write mathematics, the consequencs of some of their supposed [emphasis added by me] imaginative constructions are still being discovered, many are suspected but not yet proven, and still more are not yet known - or so the hundreds of budding mathematicians hope. (pp. 121-122)
The sword Barton welds is too big for him. In his supposed anti-Eurocentric discourse on maths, he has squarely put back the Eurocentricism onto maths (rigour analysis vs geometric structures): ask any person unfamiliar with Tolkien's or Jackson's work what a hobbit is, and the more likely response would be a blank stare; ask anyone in the world who can count what 1 + 1 equals to, and the answer would be immediate.
Teach a child "pebble notation" and ask them to arrange and rearrange them into certain geometric shapes and they'd begin to realize that a given "set" cannot be arranged into just any, old shapes but just so. At a slightly more sophisticated level, they'd be able to demonstrate Pythagorean's theorem using only lengths of strings that by "squaring" the lengths of the two shorter sides will always equal the length of the longest one "squared" (or that a2 + b2 = c2 in analytic terms).
The increasing separation of European-style maths (analytic) from their origins (geometric) gives the impression that mathematics is just a word game (as per the abuse Barton wreaks upon the great Wittenstein) with all their wherefores and whatnots, but mathematical proofs are always based upon the foundations of what defines "number" or basic relational/structural aspects of geometric constructs of interest.
When Newton first wrote up his physics and his discourse on optics he hid much of the calculus (analytic) and chose to demonstrate his insights in geometric terms to the Royal Society; the geometric treatment of Einstein's theories of relativity are also simple enough for highschool students to understand and take something from them, though the differential and integral calculus of them are quite difficult.
Mathematics, if taught in a school at all, is never really taught in this way. Rote memorization of multiplication tables, log tables (if it reaches that far) are more the norm. But there is that old chestnut of the youth Gauss burning through the summing of numbers from one to a hundred.
Gauss realized immediately that he could add up the first and last numbers to 101, same thing with 2 and 99, and so on... if this story is based on reality he may have been too young to express this insight in a pat equation but his geometric (mathematical) intuition had never had the chance of being choked off by lesser mortals up to that point, so he visualized a triangular structure (called a partition) and came up with the answer in that brilliant flash of genius (the columns all add up to the same number if you reproduce the original triangle and match it up with the reproduction). That poetic image of the innocent being the vessel of the divine...
Barton is a fool. A dangerous fool, but a fool nonetheless.
The culture of overcompensation
I'm greatly bothered by the rise of Harper (not the person but the idea) and the entitled right-wing extremism that defines his brand of politics in Canada. This culture of overcompensation didn't just arise out of nothing nor is it an accident of history. The sense of entitlement and juvenile outlook is a result of the perversion of the so-called student-centered education experiment.
Ostensibly, if the child is given opportunities to gauge and direct their own learning, then learning should become an incentive. But the great advocate for this democratic approach, John Dewey, said that the teacher should not abdicate responsibility to guide and inform the student through a "meaningful experience". What this meaningful experience is exactly was very specific to Dewey: to promote civil society in a liberal democracy. In this respect he was much like my other hero, Northrop Frye.
A Wikipedia entry on John Dewey says:
Although Dewey is known best for his publications concerning education, he also wrote about many other topics, including experience, nature, art, logic, inquiry, democracy, and ethics.
In his advocacy of democracy, Dewey considered two fundamental elements—schools and civil society—as being major topics needing attention and reconstruction to encourage experimental intelligence and plurality. Dewey asserted that complete democracy was to be obtained not just by extending voting rights but also by ensuring that there exists a fully formed public opinion, accomplished by effective communication among citizens, experts, and politicians, with the latter being accountable for the policies they adopt.
In effect he expected a modernization of the classical education approach. Again, from Wikipedia:
...for Dewey, past doctrines always require reconstruction in order to remain useful for the present time.
I discovered Dewey and the American pragmatist movement when I was at Memorial studying linguistics by way of Rorty whose writings on text, meaning and language impressed me greatly(though Dewey impressed me more). I devoured whatever Dewey's writings I could get my hands on, and he was the single most influential thinker in my advocacy for aboriginal education in the years I spent as a policy analyst for Inuit org.s. Not many people knew what the hell I was talking about (crazy bastard), and I was too angry and impatient to try and explain. I should have kept going; I had such hopes for Nunavut then.
The Wikipedia entry continues:
In addition to his ideas regarding what education is and what effect it should have on society, Dewey also had specific notions regarding how education should take place within the classroom. In The Child and the Curriculum (1902), Dewey discusses two major conflicting schools of thought regarding educational pedagogy. The first is centered on the curriculum and focuses almost solely on the subject matter to be taught. Dewey argues that the major flaw in this methodology is the inactivity of the student; within this particular framework, "the child is simply the immature being who is to be matured; he is the superficial being who is to be deepened" (1902, p. 13). He argues that in order for education to be most effective, content must be presented in a way that allows the student to relate the information to prior experiences, thus deepening the connection with this new knowledge.
At the same time, Dewey was alarmed by many of the "child-centered" excesses of educational-school pedagogues who claimed to be his followers, and he argued that too much reliance on the child could be equally detrimental to the learning process. In this second school of thought, "we must take our stand with the child and our departure from him. It is he and not the subject-matter which determines both quality and quantity of learning" (Dewey, 1902, p. 13-14). According to Dewey, the potential flaw in this line of thinking is that it minimizes the importance of the content as well as the role of the teacher.
In order to rectify this dilemma, Dewey advocated for an educational structure that strikes a balance between delivering knowledge while also taking into account the interests and experiences of the student. He notes that "the child and the curriculum are simply two limits which define a single process. Just as two points define a straight line, so the present standpoint of the child and the facts and truths of studies define instruction" (Dewey, 1902, p. 16). It is through this reasoning that Dewey became one of the most famous proponents of hands-on learning or experiential education, which is related to, but not synonymous with experiential learning. He argued that "if knowledge comes from the impressions made upon us by natural objects, it is impossible to procure knowledge without the use of objects which impress the mind" (Dewey, 1916/2009, p. 217-218).
I mean, wow. Who wouldn't want that for their own children?
The book that I've been criticizing in my last few blog entries, The Language of Mathematics, tells me everything that is wrong with the various forms of student-centered teacher education programs. Bill Barton speaks with such definitiveness and certainty, and is actually convincing in some parts. But he has superficial knowledge and little appreciation of mathematics as a historical process and quite selective in his speech. He constructs arguments then "proves" his propositions without telling the whole story. His is not historical development-based pedagogy, but sophistry and thinly veiled intellectual laziness aimed at the uninitiated (the aboriginal student teachers of New Zealand).
This type of teaching style is also evident in Harper and the disingenuous "dogs of war" that make up his core people. They gloss over subjects rather selectively that serve their short-term goals and interests, and show complete disregard for accepted and hard-won "rules of the game". When anything goes, society loses confidence and trust in their own governments and institutions.
Barton says something about the "problem" of Eurocentric maths saying that eastern and non-European traditions are ignored and dismissed as not mathematics. But that is not true. This is an attempt at creating artificial barriers and subconscious resentment. The European tradition of maths, and scholarship in general, always cite extant works including eastern mathematicians and non-european traditions and pay tribute as well-informed scholars demands of them. But the discourse has high standards and is qualitatively different as a human endeavour than what came before: strive for these standards of excellence, I say, rather than resent the "exclusive" club if you want to be part of the discourse. It sometimes seems to be the only democratic institution left: this academic discourse.
But Harper and his ilk clearly do not subscribe to the notion of these standards of excellence. We are watching the destruction of a fragile thing. I'd say that Dewey's alarm and dismay was far-sighted and proving to be well-founded by our culture of overcompensation.
I know many excellent teachers and have had the privilege of working with some of them. I'm not criticizing any of the Nunavut teachers but the lax and haphazard way policy is developed by mandarins in their splendid isolation (ie, those with no experience nor regard for teachers needs). The curriculum will work if given a fighting chance. But it requires training and resources so precious and hard to come by.
Is there a word for "mathematics" in English? (part iii)
One of the reasons why I said earlier that English may not be the best language to do maths in has to do with confusing technical concepts for commonly used words. These are words like "set"; "proof"; "rational vs irrational". At a deeper level, sometimes we think that since we are able to read certain words that we immediately comprehend what those words mean.
Take for example human activities (non-human structures, even) that can be described in mathematical terms - (from Barton's book, The Language of Mathematics) like "Pacific navigation" or the kolam patterns drawn by women and girls in many eastern countries (or the hexagonal patterns of honeycombs, spider webs, the fibonacci patterns in nature for that matter) - and actual mathematical discourse. Pacific navigation and kolam drawings are no less beautiful and elegant simply because the practitioners of these "arts" do not describe them in strict mathematical terms - it is their insights and methods that are mathematical and can be described so. In pedagogical terms, especially in construction of maths in an indigenous language, these activities would be a rich source of insights and neologisms.
In fact, I contend that numbers were not the first elements that caught the mathematical imagination of human societies all over the world, geometric shapes are the more primitive in our notions of maths par excellence. The ancient Greeks, Pacific navigators, kolam drawers, etc.
In Inuktitut, the demonstrative morphemes (pointing and locating words called "prepositions" in English) are rather complex and elegant at the same time. In the Inuit languages we can say not only "here/there" but have specific words that denote elevation, proximity, in relation to the speaker, in relation to the spoken to, inside/outside.
Now, going back to that statement that English may not necessarily be the best way to talk maths:
...the Greeks discovered that if you draw a square, say with sides of length unit one, and then you draw the diagonal of that square, then there was no small length that would divide exactly into both the diagonal and the side (Lasserre, 1964)...This was the first irrational number, that is, a number cannot be represented by a fraction. All numbers had previously been thought to be expressible as ratios [emphasis added by me] of two numbers (that is, fractions). They were rational. Now here was a number that could not be written as a ratio [emphasis added by me]. The Greeks thought they were going mad - and there is the origin of the everyday meaning of irrational: the human condition of being without sense or reason. (Barton, The Language of Mathematics, p. 85)
That may be, but there is a sound technical and conceptual difference in meaning of rational and irrational numbers than from the everyday English sense of being rational or irrational. In the mathematical sense the words irrational/rational comes from "ratio" (ie, expressible as a proper fraction); whereas the everyday sense of being irrational/rational comes from "reason" (or lack thereof).
Another word in English maths and everyday English that is the cause of no end to headache is the word "dimension". Many a great thinker struggles with this concept, let alone the laity. Many math-physicists have said without irony that they cannot visualize "four dimensional spacetime" - inadvertantly adding to the mystic of English maths. But what they fail to realize is that the word "dimension" (in maths sense) has two distinct meanings: geometric and arithmetic. The four dimensional spacetime incorporates both senses: the 3-fold space (geometrical) along with the tracking function (arithmetical) that tracks movement/velocity (ie, time as a length). The word "dimension" in the notion of Einstein/Minkowski's four dimensional spacetime is an orthogonal system that has the capacity to track a pointlike particle within that generalized space.
I'm a believer in the "standard model" of "classical" particle physics because I've never seen nor heard a convincing argument for the so-called super-string theory - when someone constructs a convincing argument that one can definitely divide by zero or define a workable boundary of a black hole then I'll believe the string theories.
In The Language of Mathematics, Barton also talks about what he calls "mindlocks" and "metaphors", especially the "Container metaphor" vs "Path metaphor", that sort of implies (perhaps inadvertantly) the futility of trying to use indigenous languages for maths discourse; that English is the best we can do. He sort of skirts around deep and wonderful (in my estimation) philosophical insights that are the purview of European maths/philosophy but to which other traditions may add. But this, like so much of his thesis (whatever that is is still unclear to me), is confusing superficial accepted terms (ie, static word locks) from the conceptual framework (dynamical, evolving discourse) that is mathematics.
My above comments and insights (ie, "dimension" and "rational/irrational" especially), I hope, show that possibilities for cross-pollination between languages are infinitely rich (if somewhat daunting). This is the great strength of conceptual-/meaning-based translation method that has always served me so well. The psychological/spiritual/intellectual worlds of humanity are not language-specific but rather depend on our willingness to learn and discover these great insights that various traditions have to offer freely if we can/would accept them.
Is there a word for "mathematics" in English? (part ii)
The more I read Bill Barton's book, The Language of Mathematics: telling mathematical tales, the more I become dismayed. I mean, I think there are excellent points in the book, but he treats everything so cursory that the points he make are never really carried to their logical conclusions. He says that he has no linguistic expertise but he's not really a maths expert either (confuses maths for arithmetic in many spots).
But what really concerns me is that what he calls "evidence" is not really discussed in dialectic terms but are rather more selective than that (many times he says that "evidence" supports his thesis, though what that is he never really makes explicit). I'm pretty sure that Barton is an excellent teacher, a decent human being, and utterly well-meaning. But his goal seems to be a foregone conclusion: English good; aboriginal languages not so good:
...if mathematics arises from language, then we must consider mathematics in the same way we consider language. Different concepts are expressed in different languages, and some concepts are extremely difficult, some say impossible, to translate between languages. The implication is that different quantitative, relational, and spatial concepts may also not be easily transformed into each other. The language investigations reported in Part I confirm this. [emphasis added by me] (p. 69)
I would suggest that English itself is relatively "inferior" as a vehicle for mathematics discourse as compared to French (a descendent of Latin) and German (which has the capacity to agglutinate grammatical/lexical elements together to construct new concepts all in German), demonstrably contrary to Barton's statement that English is "naturally" adaptable to mathematical speak (based solely upon notion that English can change the grammatical function of number from adjective to noun - so can every other language, the polysynthetic Inuktitut being an epitome of that wonderful adaptability: a verb can be changed into a noun, and vice-versa):
Sometimes numbers are used in their adjectival sense and in their nominal sense in the same sentence. "Three fives are fifteen." The three is adjectival, the five and fifteen are nominal - the five is even made into a plural (there are three of them, just like you can have three hugs or three kisses). The important point is that all of this feels [emphasis added by me] quite natural in English, we are not even aware of the different grammatical uses of number words, and we move between them quite easily depending on what we are trying to say.
This is not the case with all languages. (p. 42)
Barton mentions Wittenstein (one of the thinkers I myself consider great) but fails to mention that Wittenstein treated language and mathematics in Formalist terms in his Philosophische Untersuchungen (Philosophical Investigations, 1953). Barton doesn't take anything from Wittenstein, really: the grammatical rules of language and maths are, at their cores, just formal rules (Wittenstein says) but it is the social uses of them that imbue "meaning" upon the human act of "communication". Take care not to forget this (says Wittenstein in not so many words) lest language is used against you.
I think Barton suffers from covert (or subconscious, or unexamined) Anglophilism. Like many others living in a colonialist countries, he seems to suffer from unvoiced historical "guilt" of subsuming a whole group of people so he's making half-hearted attempts at justifying the whys and wherefores English is the language of modernity rather than focussing on what each language has to offer to the discourse.
I say: get over it. You have so much to offer; there is also no shame in learning from other languages. Re-read your Wittenstein, your John Dewey, your Vygotsky... English is no more privileged than any other language. You owe the Maori your whole being as a teacher: nothing less is social justice.
Epistemological cross-pollination is what makes human intelligence/knowledge/potential so rich and diverse (but there's always room for improvement). This should be an axiom in cross-cultural relations. The other axiom should be that human knowledge and intelligence is not language-specific, and is, at its core, completely democratic. It takes talent to bring that out; talent can be cultivated.
Tuktugiaqarunniiqtut
I'm listening to CBC radio right now, and I just heard someone say: tuktugiaqarunniiqtut "they no longer need to hunt caribou". Since he's talking about declining stock of George River Caribou, I think what he's trying to say is: tuktuttailititauliqtut "they are now prohibited from hunting caribou (from that stock)".
I mean, I understand that speaking on the radio can make one nervous and prone to make mistakes. But these are two Inuit speaking Inuktitut.
Tukisimainnaqattarattigut (also from the interview). In Inuktitut, there is an ergative case:
[-jara]; [-javut], etc. that makes the actor "own" the action: tuktu takujara "I see the caribou", but there is also a "case agreement" morpheme [-si-] that may occur on it's own but still imply ergativity: tukisijuq "she understands". For the notion of "comprehension"/"to understand (something)" the ergative agreement [-si-] is obligatory but it is missing in tuki[-si-]simainnaqattarattigut.
I'm not criticising frivolously but trying to demonstrate that grammar-, narrative-based Inuktitut instruction is required if we want to perserve and promote the use of Inuktitut in society, media and personal communication.
Is there a word for "mathematics" in English?
I'm reading a very interesting book by a Bill Barton right now called, The Language of Mathematics; telling mathematical tales (ISBN 978-0-387-92937-8). He's describing attempts at creating a maths curriculum for Maori schools.
The book got me thinking about whether there is an English word for "mathematics". The word is of Greek origin: μάθημα máthēma, "knowledge, study, learning" but there seems to be no word in the English language for "mathematics". The etymology of "arithmetic" is even more convoluted covering, it seems, the whole Indo-European language family except English. There is tælcræft, lit. "tell-craft" that seems to have been rejected early on.
In the synopsis of the book it says "Simple English language statements are expressed quite differently in some other languages, not simply represented with different vocabularies or an underlying base of the number system". What he means here is that some languages may treat numbers as if they were verbs: the bottles are three-ing on the table; my fingers five (p. 5) - all very well in linguistics analysis though it may sound a bit strange in everyday English. But these are grammatical functions (ie, not -emically different than treating numbers as adjectives as English does: five, little ducks, for eg) not to be confused with statements like when he claims that 1 + 1 = 2 may not necessarily be "true" in other languages.
I'm just in the beginning of the book, but he says that he'll "challenge the idea that mathematics is the same for everyone, that it is an expression of universal human thought - and explain the questions about the bridge and 1 + 1 posed incredulously above" (p. 8). Tælcræft, I look forward to it.
Understandably, he tells of a Maori woman demanding a change in some constructed word that was being "misused" by children that she overheard (upwards talk) for the word "praise". But I think this is confusing the "grammaticalization" problem with the "lexicalization" problem. Let me try and explain:
I was talking to a very excellent friend of mine a few years ago when he described to me that some Inuit children were starting to simplify the words for "deep" and "shallow" (in Inuktitut, one says itijuq for "it is deep" and ikkattuq for "it is shallow") using the word for "deep" as the base and inserting the negation [-nngit-] and dimunitive [-kuluk-] to denote "shallow" = *itinngittukuluk.
This is a lexical error but not a grammatical error, strictly speaking. It is like over-extending the prefix [de-] (as in demoralizing) to other words that may not readily accept the prefix: *decontinued rather than discontinued.
The problem with constructing neologisms, especially specialist terms, is that it is often forgetten or neglected to define the newly minted term in logically productive terms, let alone provide an explanation that the new term is different from common usage of the root, that it means something highly specific in highly specific context (providing examples where the new term is acceptable and where it is not acceptable, say).
This is a huge problem in Inuktitut terminology exercises where explanatory phrases tend to be used rather than lexicalized root nouns or verbs that are grammatically/logically productive. An over-used example: the now-accepted term for "uranium" nungusuittuq which loosely translates as "that which never depletes, or never-ending (source of energy)", which makes sense in some way but is not entirely true or accurate enough for productive discourse. In an ideal situation, one could have looked into the notion of "radioactivity"/"beta-decay" and constructed and defined a better, more useful term: say, tangiingajuq or some other invented term (doesn't really matter as long as we can define it specifically; in fact, the more removed from common usage the constructed term the better to minimize confusion), and describe what the new term means or denotes and how it fits in the larger scheme or framework of quantum chemistry.
Now, back to the question: Is there a word for "mathematics" in English? -the answer is yes and no. The original Greek term does not make any outward reference to the notions of "number", "numeral manipulation" or "quantology" for that matter, but the English usage is common enough to be understood by laity (though specialists would argue that their field of study should rightly be called "set theory" "algebra" "geometry", etc, etc.)- like nungusuittuq I guess.
The other day I was having a meal with my best friend when I went outside for a smoke. While I was smoking a compatriot of mine came over and asked me if I had gone completely "qallunaaq" (non-Inuit). I must admit that the question hurt me a bit. But I understood where she was coming from: my aippakuluk is an uiviiq (Quebecoise); my best friend is a qallunaaq.
These facts are incidental to me. The people I love and am close to are not deliberately chosen; they being qallunaat or Inuit is never (has never been) an issue to me. I have many friends and family that are Inuit. The colour of their skin has nothing to do with my love for them. I, myself, am truly proud of my being Inuk.
I know there is a fascination on part of some Inuit with the qallunaat; that being with, having some qallunaaq blood, or acting and appearing qallunaaq is very important to them. This, to me, is wrong-headed thinking. Stupid.
I'm "westernized" but I have no intention of being a "qallunaaq" - totally happy and proud of being an Inuk. I don't romanticize being an Inuk; I don't romanticize qallunaat either. I have some idea about genetics and feel that the variety of its possibilities as a richness of nature, not as a badge of superiority/inferiority. I view things at the -emic level - superficial appearances mean little to me. It is the substantive material of people I either admire or am aversed by - ie, their personality.
The notions of integrity and honour are very important notions for me. I may slip and fall or be found wanting but the ideals I hold dear to my heart are not determined by societal norms nor influenced by mass media. To me, the question of "to be or not to be" is an indication of ambivalence and second-guessing of one's self and one's values. How we act and treat each other are the true measures of our humanity.
What is the difference between romanticism and antiromanticism?
(by xXdramaq...) i would guess that romanticism is when somebody is romantic and anti romanticism is either somebody that isn't romantic or somebody that is against being romantic. so romanticism is the opposite of anti-romanticism. I kinda confused myself typing that so sorry if it doesnt make sense... i hope it helps. :) (http://answers.yahoo.com/question/index?qid=20090322185848AAt9jP5 )
When I was in treatment there was a guy who was genuinely shocked that he was not just a free-base coke addict but actually a crackhead. I blame our sorry state of affairs upon the hippy movement and uncritical romanticism, which, contrary to the circular argument above, actually means something like this:
Romanticism can be viewed as an artistic movement or state of mind or both. It favors imagination over reason, intuition over facts. Talks of the "natural" man and the loss of innocence are common. Also common is the idea of nature verses civilization. Romanticism has an intense interest in and reverence for nature. It has an accent of mystery on strange and fantastic aspects of human experience.
Anti-Romanticism consisted of two main writers - Nathaniel Hawthorne and Herman Melville. Anti-Romanticism focused on limitations and potential destructiveness of human spirit rather than on its possibilities. Many of these writers used allegory in their writings. Allegory is a work of literature in which events, characters, and details of settings have symbolic meaning. Allegory is used to teach or explain moral principals and universal truths. (Last Action Gyro) (also taken from: http://answers.yahoo.com/question/index?qid=20090322185848AAt9jP5)
I fight hard not to get cynical and believe in humanism almost like a religion. I mean, I believe in God and believe Him to be an archetypal antiromantic - how else can He be? Jesus spoke in parables; all the major and minor prophets speak in symbolisms and eldritch terms, which I've always taken to mean that since we humans are thinking, reasoning animals we should always try and arrive at our own conclusions, to always examine our value systems and act according to our (informed) conscience.
I think had I been born Jewish I would have been a Talmud prodigy. I blame my iconoclastic tendencies on not being born Jewish - lack of structure does that. I just have a higher demand to base my belief system on than the banal romanticism of the protestant church, and not much into the S&M of the catholic church. So, I'm stuck without a country. Like a transgendered person, I'm Jewish without actually having been born Jewish.
The other day I saw an excellent film with my aippakuluk called, Detachment, starring Adrian Brody. His character spoke of "ubiquitous assimilation" to his wayward class in lecturing on Orwell's 1984:
Mr Barthes: What does that mean, "assimilation"?
Student girl: To take something in.
Mr Barthes: Okay, excellent. To absorb. -Anyone, "ubiquitous"?
Student girl: Everywhere, all the time.
Mr Barthes: So what is "ubiquitous assimilation"?
Student boy: Always absorbing everything everywhere all the time.
Mr Barthes: Well done, George. -How are you to imagine anything if the images are always provided for you?
Then, he went on to speak about how the youth subculture off-handedly speaks and acts in highly misogynistic terms where the whole world and everything in it is treated and abused as the women hated, how most are completely oblivious to their own hatred and anger, that their subculture is an unconscious reaction to perceived and real injustices, etc. etc.
This, to me, is unmitigated romanticism (or, at least a visceral reaction to the drivel that is passed for "education" - Max Weber's "iron cage" (you'll see what I mean when you check out the movie)). The movie, Detachment, is one-sided and somewhat shallow at times. But it's still an excellent movie.
There is a scene in there as well when Brody's character talks about Poe's The House of Usher. I don't want to spoil anything, but I'd say Poe is up there with Hawthorne, Melville, Conrad - well, with the best of American classics right up to Kurt Vonnegut, Tom Robbins, and Hunter S Thompson (clearly not nihilistic but antiromantic, I'd say). I'd also claim that Timothy Findley is the only Canadian antiromanticist of note. Richler is just baaad... (in Stewie Griffins' ironical voice) - sort of like a cultured, polite Thompson (if such a thing were possible).
What is happening to Canada?
Below is taken from the Globe and Mail website. It is the readers' comment section on a story about Kenney's latest attempt to single out the Roma as "bogus refugee claimants". This fact in itself (singling out an identifiable group) reeks of bigotry and arbitrary (ab)use of power (this from a democratically-elected federal official) but it is some of the comments (granted, typical in most other stories) that kind of took me aback after reading recently that Canada is not immune or is likely to suffer Breivik-type attacks from extreme right-wing nuts. Notice how few reasonable voices are (again, typical of G&M comments sections):
Federal government considers detaining Roma refugee claimants, report suggests
MSM is making me barf
http://www.coe.int/t/commissioner/source/prems/prems79611_GBR_CouvHumanRightsOfRoma_WEB.pdf
Please read this report before all of the ugliness on this board starts. The last article in the Globe concerning the Roma spawned some very ugly racist comments. (connect the ht and the tp for the link!)
Coreolanus
Detention in humane and secure conditions removed from an urban environment would make sense, especially if an accelerated refugee determination process followed by expeditious return of those found ineligible so that the sojourn in a holding facility would not be long makes perfect sense.
Not all Roma are itinerant thieves, just a very large proportion. Which is, in large part, why they face poor treatment everywhere else.
HarpO Faslst Threat T0 Canada
another warning sign of harplers march towards a fasist state
J.E.R.
I am really not sure what evidence is needed. The EU has very robust anti-discrimination laws and is probably the most liberal part of the planet. The Roma have lots of protection under EU laws to which they can resort, whether in Hungary, the Czech Republic or elsewhere. If they want to come to Canada they should go through the immigration process and prove that they can add value to Canada. Of course, if they could add value to Canada they could probably do so in Europe and would then face fewer problems in Europe.
C0Nservat1ves L0ve T0 lIe
South Africa police open fire at striking mine workers
Coming soon to harperland
dexx8
Kenney should consider lifting harper's Visa. Harper's CPC is committing treason by selling off Canada's resources to communist China, while China is building it's war machine to take on the U.S. Harper is suspected of being a foreign agent working to undermine the North American democracy. I'm hoping that the U.S. CIA has some immediate plans for Mr. Harper.
Federal government considers detaining Roma refugee claimants, report suggests........"and will have significant legal implications,"
"Significant legal implications" is an understatement of the year.
Under what 'stature" or legislation can the government target a certain group of "refugees" for interment, while the only criteria being ethnicity. It will take a lawyer 6 months out of university to punch "holes" in the governments argument without working up a sweat.
Should the government be serious (and have supporting evidence) that the Hungarian Roma are indeed arriving in Canada under false pretenses, slap a visa restriction on Hungary. The Hungarians will scream bloody murder, but the said visa restriction is fair to the Roma as well as to Canada.
HRoss
This story, and many of the comments on it are deeply disturbing. There has been a great deal in the news lately about the growing neo-nazi movement in Hungary. The government there is doing little or nothing to stop them. They are targeting Jews, Romas and anyone else that they see as inferior. No, the Roma do not get all of the protection that they need from the EU or any other governmental body. These are human beings and people are speaking of them like they're animals.
I fear that we have truly learned nothing from history and are on the precipice of repeating it.
We can see already that the racists are finding their way to this story, it's like they have some automatic alert going for the word 'Roma'.
Let me ask the Globe monitors this, would you tolerate Recti's comment if it was pointed at some other group? Jews perhaps? The answer of course is no, but for the other major group of holocaust victims it's open season isn't it? The injustice shows itself at all levels.
I think in the end the Roma need to find sanctuary in another country. Canada is an inherently racist state. Always has been, always will be, just with different targets.
Invictus99
MSN...
You might want to go to Budapest, Praque, etc to see what the Roma are doing there.
Yes, they are a bunch of thieves, and nothing that some bleeding hearts want to do will change that.
That's the problem with someone like you: You have no practical experience, and you only re-hash the politically correct garbage that is rained upon us daily.
Wolfe1Montcalm0
We have enough problems here. We don't need the Romany aggravation.
Keeping them out will be a victory for common sense over political correctness.
Molson Light
Watching Roma families documentary show on CBC in Italy & Spain makes me sick. They like their Asia cousins, are thieves, child abuse and leeches. It also makes me sicker when I realize our lawyers using our legal aids funded by our hard earned money aka taxes to defend their claims and abuse of our generous systems designed to protect genuine refugees.
It 's time to boost Roma and those phony refugees out and cut off Legal Aids for those cases.
Anthony S
"Federal government considers detaining Roma refugee claimants, report suggests "
How can anyone be a "refugee" from the European Union, for Pete's sake?
Forget detaining them, forget investigating their admissibility; anyone from Europe claiming asylum should on the next plane back to Europe.
I'm wondering if the family I saw in an Ottawa department store earlier this year were Roma. They looked a little South Asian to me, but not quite.
They let their young son run his fingers, which never seemed to stop moving, over the displays and didn't interfere as he was making a small pile on the floor out of gift cards. He then joined his mother at an expensive perfume display and immediately reached up to touch the boxes. When he removed a box from the shelf, his mother said nothing but immediately turned around and scanned the room behind her. As her eyes met mine and I continued to stare right at her, she turned to her son, murmured something, and the perfume box went back up.
The Immigration service is correct to give more detailed attention to the Roma applicants. This is a wandering nation of people who have over centuries been thieves and robbers and have in recent history continued to maintain this lifestyle.
To tar them all with the same brush is unfortunate, but they have constantly failed to demonstrate any change in lifestyle whilst in any of the countries which have allowed them entry.
SS Ontario
Hey, Globe and Mail "moderators"--how about censoring this comment thread full of right-wing neo-nazi haters? Or is this racism "good racism"?
H. Incandenza
Anyone who has seen the condition of the Roma, particularly Eastern and Southern Europe, has to say they are legitimate refugee claimants
Little, green ideas
I'm no mathematician but am utterly fascinated by certain aspects of maths, such as the axiomatic set theory, Gödelian logic, etc. - or, the foundational structures of maths and not so much the computational tricks that seem to define maths for so many people (I could hardly mentally calculate two integers if my life depended on it).
In Feynman's book, Surely You're Joking, Mr Feynman - in classic Feynman understatedness - he peppers throughout the book profound mathematical and physics ideas in a rather casual way (many of which he himself initated or had intimate knowledge of). A couple of these are the Tarski sphere (which results in an incredible statement that one may cut a single sphere into infinite, infinitely tiny pieces and reconstitute it back into two spheres of the same size as the original! - that is, if the continuum condition applies), and the other is the Riemann Hypothesis.
The Riemann Hypothesis is a pivotal result in analytic number theory that Riemann used to refine Gauss' analysis of the logarithmic distribution of the prime numbers. The Hypothesis, if ever proven, will not only have profound impact on our confidence in mathematical physics, probability theory and statistics among other very important results that depend upon the Hypothesis being true. The Riemann zeta function extends Euler's landscape (generated by summing the infinite series whose denominators are prime numbers) into the complex plane.
The devastating effects of Gödel's incompleteness and consistency theorems have been felt in the analysis of the Riemann Hypothesis too. Many luminaries of maths believe that the Hypothesis cannot be proved using the current axioms of maths alone.
I think part of the problem lies in the fact that the Riemann zeta function has largely only been regarded as a distributive analytic function rather than looking at it as a question of whether it will always converge to (1/2 + bi). Riemann was a genius of the first order but he was also a geometer of the first order - ie, he did not regard the function in merely analytical terms but also in geometric terms (ie, as a graphing tool).
In analytical linguistics there is a fascinating problem of grammar that in its present state allows the construction of such sentences as 'little, green ideas dream furiously'. I think this happens because we've yet to define the noun function in refined, sophisticated enough terms to preclude such absurdities as 'little, green ideas' constructs - ie, the legalism of analytical linguistics is similar to the analytic distributive treatment of the Riemann zeta function.
The logical implication that Socrates is mortal in a syllogistic premise as "all men are mortal"..."therefore Socrates is a mortal" illustrates the lack of resolution because it treats the noun function without bothering to define its possible abstract and concrete terms - ie, the pattern is too flexible that it allows any premise at all: all ideas are green; Socrates is an idea; therefore Socrates is green.
I suspect this is similar to the problem of the zeta function where Hardy proved that an infinity of Riemann zeros fall into the real part 1/2 but he didn't specify which cardinality the set of these zeros belong. These are not just zeros (ie, not just analytic) but geometric points where the negative values turn to positive values (or vice versa) as plotted in a graph of the Euler function as extended below 1 in the complex plane.
I appreciate that things aren't ever that simple, especially when we view transfinite arithmetic and the axiom of choice, but we are assuming that the "set of all sets" allows sets to be elements in a set. Defining a set as a class doesn't carry us any further. S(x) is not an element, not a set, not a class, not a number but properly a function that "chooses" which elements are allowed/not allowed in a set: the Riemann zeta function converges, but where and how the condition applies rather than where the zeros are distributed might be the more proper formulation as Riemann originally posed the Hypothesis.
I mean, I've read in many authoritative and informative books that Riemann's geometrical intuition is what gave him confidence that his function would always converge to the leyline whose real part is 1/2 though he at the moment of writing his seminal paper didn't pursue it rigorously.
The League of Super Evil
There is an animated show on YTV called, the League of Super Evil, which has characters that seem tailor-made for CPC's Toews (Voltar), Harper (Reginald 'Red' Menace), Poilievre (Doktor Frogg), and (if you squint your eyes) Baird (Doomageddon):
I was flipping through the channels one day when I saw an episode and thought: No way! This is too good to pass.
Yesterday I was watching with my aippakuluk a movie about the Gore-Bush fight for Florida called, Recount. There are a couple of scenes in the movie where the Republicans' war room is shown where Baker and his minions plot and conspire to disenfranchise the voters of Florida. These people are serious zealots of Conservativism/sophistry the way CPC can only dream of achieving (much like the League when it locks horns with more "important" super villians in the show but are invariably bettered because they're just silly). Republican wanna-be's.
The "cyclical" aspect of the human mind
There seems to be two general types of the treatment of time: linear and cyclical. Inuit Qaujimaningat (Inuit Knowledge) seems to be able to see time as both linear and cyclical. Social grace and forgiveness, and personal growth, demand that we view time as a linear phenomenon, that all things pass. Some are fleeting but recurrent, like emotions.
In fact, in IQ the root word for "consciousness" and the "universe/nature" have the same form: sila. I've always taken this to be evidence that IQ spiritualism was some form of ancient Taoism because silatujuq 'wisdom' and its opposite silaittuq 'foolish' suggest that wisdom/intelligence or lack of it is the ability/inability to reflect the way of nature in the mind. Emotions are regard as weather; demeanor, memories, one's name, these things take more permanent hold in our psyche.
In Jewish and other mystical traditions, people talk of rapture and abandonment: that our sensitivities to God wax and wane. I, and have always, felt this too. In my more "religious" days, especially, I felt the approach and withdrawal of God, the Holy Spirit and Jesus, and would always look forward to the day when I felt the closeness of divine grace which I appreciated more because I also felt the darkness of its withdrawal (the dark, cold dankness the Jewish mystics call it perhaps in reference to being able to read the script (the waters) but not feel the Spirit (fire)).
I think intellectual knowledge is like that too. I have many books and many of them are scientific and mathematical. There are days (or periods) when I can peruse with ease and comprehension and insight come almost unbidden; then, there are days (or periods) where I'm uncertain of my ability to understand - these, often the same text.
When I was child just learning I used to be able to say to myself: remember, recall into your atavistic memory and you will understand what's before you. -I used to take the notions of reincarnation literally and felt that I already knew and if I tried hard enough I'd remember. Insight is like that: it comes in leaps and bounds, oftentimes comprehension comes in whole, complete chunks. Epiphanies are wondrous things. Mystical.
Sometimes my aippakuluk asks me a scientific or mathematical/physics question, and my insights come tumbling in. I don't pretend to comprehend the often-complex commentaries and provisos of such technical knowledge but often I can "see" the first principles clearly - clearly enough to know that my insight was anticipatory and on the right logical track when I check/recheck whether I was right or wrong.
The human mind is a magical thing. It can be trained and cultivated to perceive what it could not see before learning to place: when comprehension takes hold, whole vistas are opened out, original insight becomes possible. I love drinking to get drunk, smoking up to get high, but I love my brain more so I've stopped drinking (but still unwilling to admit with confidence that I've quit for good - knowing how fragile and vulnerable we really are).
This realization makes me appreciate my aippakuluk and my loved ones even more. I need her, I need the people I love, to carry me beyond my addictive/self-destructive patterns of behaviour: without love, I am nothing. I highly suspect that I'm neuro-atypical - my pedantry, my fascination with abstract patterns, my set ways, my inability to acquire social graces and express emotion but the strong ones, etc. - but that doesn't mean I don't get it. That's the thing: I can understand emotional content, it's just that I have a tendency to not appreciate its relevancy very well. I love art, literature and music: these show I'm human. It's just that after a mystical experience it is often difficult to get back on the ground sometimes.
"Brother John" as a question of climate change
Last night I watched with my aippakuluk a very interesting movie starring the incomparable Sidney Poitier called, Brother John. The movie, I think, was based on a short story and was rather cursory in the treatment of very interesting question of "personal responsibility" vs "(judgement on) humanity as a collective" and it got me thinking about the climate change discourse.
Now, we've all heard of that old chestnut about "acting locally" that we do not hear of anymore. I think the rise of intransigent partisanship and corporatism has a huge part to do with this sad comment on humanity's recently acquired collective ADHD. After Al Gore's Inconvenient Truth, people like David Suzuki (and other public figures and luminaries especially in the 1960s and -70s) have slowly been silenced by relentless attacks on their credibility by corporate propaganda and sophistry (through commercials on nothing in particular that praise the virtues of... what?). Our uncritical shift in focus has come about as if we were dreaming.
Brother John is asked by his love interest in the movie whether we have a chance of personal redemption but his response is that humanity might be judged collectively as a species.
I like to think that deliberate personal acts and global consequences are still intimately linked. I read just this morning in the Canadian edition of the Huffington Post website about the alliance of Christian Churches' open letter to Harper about their opposition to the Enbridge proposal for the Northern Gateway pipeline because of the recent gutting of federal environmental and social impacts review processes, and the Anglican clergy's stated decision to exclude Enbridge stock from its investment portfolio to demonstrate in practical terms their opposition to the unmitigated assault on the planet and indigenous peoples. (the question begs how and why the new-found conscience of the church, but we take improvements where we find them).
The ability to exercise collective power in this way is heartening to me: big things have small beginnings. I mean, remember "Silent Spring" by Rachel Carson? After the book came out certain toxins and pollutants were banned globally and many species of birds and animals were given reprieve. Then, as now, the book created oppositions along the lines of the corporate world vs public interests, as shown in the Wikipedia entry:
In 1999, celebrated writer, naturalist, and environmental activist Peter Matthiessen wrote in Time Magazine that before Silent Spring was published by Houghton Mifflin in 1962 there was vicious opposition to it:
Carson was violently assailed by threats of lawsuits and derision, including suggestions that this meticulous scientist was a "hysterical woman" unqualified to write such a book. A huge counterattack was organized and led by Monsanto Company, Velsicol, American Cyanamid – indeed, the whole chemical industry – duly supported by the Agriculture Department as well as the more cautious in the media.
In the 1960s, biochemist and former chemical industry spokesman Robert White-Stevens stated, "If man were to follow the teachings of Miss Carson, we would return to the Dark Ages, and the insects and diseases and vermin would once again inherit the earth."
Silent Spring, continues to be criticized by a number of different sources and in recent years Carson and her book have come under increasing attack from authors, particularly libertarian groups that claim restrictions and stigmas of DDT have caused millions of deaths indirectly by preventing its use to combat malaria. In 2002, economist Ronald Bailey wrote in Reason magazine that the book had a mixed legacy:
The book did point to problems that had not been adequately addressed, such as the effects of DDT on some wildlife. And given the state of the science at the time she wrote, one might even make the case that Carson's concerns about the effects of synthetic chemicals on human health were not completely unwarranted. Along with other researchers, she was simply ignorant of the facts. But after four decades in which tens of billions of dollars have been wasted chasing imaginary risks without measurably improving American health, her intellectual descendants don't have the same excuse.
The weekly Human Events gave Silent Spring an "honorable mention" in its list of the "Ten Most Harmful Books of the 19th and 20th Centuries." British politician Dick Taverne asserted Carson was responsible for millions of deaths:
Carson didn't seem to take into account the vital role (DDT) played in controlling the transmission of malaria by killing the mosquitoes that carry the parasite (...) It is the single most effective agent ever developed for saving human life (...) Rachel Carson is a warning to us all of the dangers of neglecting the evidence-based approach and the need to weight potential risk against benefit: it can be argued that the anti-DDT campaign she inspired was responsible for almost as many deaths as some of the worst dictators of the last century.
New York Times journalist and author, John Tierney, wrote of Silent Spring in 2007: "For Rachel Carson admirers, it has not been a silent spring. They have been celebrating the centennial of her birthday with paeans to her saintliness. A new generation is reading her book in school - and mostly learning the wrong lesson from it."
In 2009, the Competitive Enterprise Institute, "a non-profit public policy organization dedicated to advancing the principles of limited government, free enterprise, and individual liberty", set up a website Rachelwaswrong.org, stating "Millions of people around the world suffer the painful and often deadly effects of malaria because one person sounded a false alarm. That person is Rachel Carson." (http://en.wikipedia.org/wiki/Silent_Spring)
Then, as now, misinformation and uncritical appeals to public and personal "safety" and "interests" were framed in such a way as to make all of us mutually culpable (thus, trying to negate and preclude any rational discussion and collective action). The Anglican Church's decision on Enbridge stock show what the true make up of the tiger is: paper.
This, then, is less a political issue than one of financial interests (many vs the few). We need balance, and realize that everything comes at a cost - it's a question of personal/spiritual and societal values and principles.
Equality or ecology?
The Feynman book I'm reading right now (well, as a hoarder of books I reread many of my books - my aippakuluk not knowing I already have the book bought me another copy) raises a very interesting question that as a humanist I've thought often about but couldn't quite articulate or formulate into something that I can think about productively: the question of "fairness" or "equality". This is a very important question to be sure but it doesn't seem to go very far because it is an emotional (or political) issue rather than a material one (where I think it rightfully belongs).
In the chapter entitled, Is Electricity Fire?, Feynman talks about having been invited to an "interdisciplinary" conference and not being about to make heads or tails of it, and about his frustration with the self-same problem I speak of above. Feynman talks about the "obsession" of the conference participants with "the ethics of equality", "the fragmentation of knowledge" and the vague emotional terms in which they try and speak of it. In the end he concludes that these people are just pompous fools who play word-games as if they're talking about meaningful stuff when they actually aren't.
The questions of "fairness" and "justice" is that these concepts must apply equally (at least in theory) to everyone, but not "equally" in the way these pompous fools Feynman talks about cannot accept. The "fragmentation of knowledge" and "ethics of equality" are just subjective words and not actual realities - the same way that unicorns and immortality are just words. In fact, though Feynman doesn't actually say it such terms, these words are words of hegemony and mindless abeyance to the law (ie, not people who actually make decisions) when, in fact, no one has been able to legislate morality and political correctness.
I agree with Feynman in many ways but he doesn't get much into why he thinks these people he speaks of as pompous fools.
I read many years ago now Gregory Bateson (a great thinker in my estimation but sadly someone Feynman would have probably classified as a "pompous fool"). Bateson was the husband of Mead, and a cyberneticist. He wrote this book called, The Ecology of the Mind.
Feynman got me thinking about the question of "equality" and "justice" in a new way, but it relates to the concept of "ecology" that Bateson wrote about. I don't think we can really talk about the notions of "fairness" and "justice" (nor can we avoid the "fragmentation of knowledge" problem) without thinking ecologically or socially in which these subjective terms rightly belong.
Let me clarify: our atmosphere is not just oxygen. In fact, it comprises mostly of nitrogen with a smattering of other useful gases including oxygen. Neither is pure, distilled water very healthy for us because we need those minerals and other matter suspended in water that our bodies need. We need nasty things also to survive and thrive in the environment. It is said of the bubble boy that he died because his immune system was never programmed to survive in our environment.
The notions of "fairness" and "justice" cannot be just theoretically derived; they have to exist and work within an imperfect system which necessitate their existence in the first place. The Kabbalah talks about "might" and "mercy" as requisites for "justice" (whether divine or human) - in fact, the long tradition of Jewish learning and the Talmud spend a good deal of time reflecting upon and struggling with these self-same concepts, for thousands of years.
I read a story once where in the concentration camps God was put on trial by a group of rabbis and Talmudic scholars facing their imminent deaths in the gas chambers. I think in the end they vindicate God because what is life but a gift from Him, and that we cannot be selfish in our deliberations of life which is a rich mixture of both good and evil - it is our freewill to interpret and act as if it were so (ie, our interpretations and actions define who and what we are, not what we think "good" and "evil" are). Labels of good and evil, in other words, are incidental features (so vulnerable to abuse); how we choose to live and act are more fundamental.
These people of great humanity in the face of great darkness chose reasoned interpretation and action over visceral reaction to labels of "good" and "evil" (the very labels imposed upon them and that which brought them to their present predicament). They chose an "ecological" interpretation of life rather than a particular instance of life. Such is the potential for greatness; understated, even small but not disengaged.
The rights to life, liberty and happiness (ie, thriving) in the American constitution are not guaranteed to be equally distributed though human life (and right to dignity) is created equal. Society cannot exist as one amorphous, hegemonous blob of physicists (or lawyers, or doctors, or welfare recipients or anything). We need all the strata and mixture to make society work. The question of equality is meaningless without the agglomerated, imperfect society in which it should exist - whether it is a just and enlightened society or one of mindless darwinian vision are human choices made by human minds. A life lived well is a life examined deliberately (ie, not dictated nor imposed upon us). This is the difference between ideals and principles.
A postscript on Barton's approach to teaching Math...
Is there a word for "mathematics" in English? (par...
"a different box of tools"


Fandom may be slavering like a Hutt at dinnertime for even a morsel of Star Wars: Episode IX news, but Luke Skywalker himself, Mark Hamill, has made it clear he won't be the one dropping any breadcrumbs.
Could this Teutonic punnery itself be a spoiler? Will everyone in a galaxy far, far away be speaking German next time we see them? Does his use of the word "avalanche" hint at a return to Hoth in Episode IX?
Almost certainly not, no -- but, if his Twitter warning stands, this is the last Hamill will have to say about the film for quite some time.
Directed and co-written by J.J. Abrams, Star Wars: Episode IX stars Daisy Ridley, Adam Driver, John Boyega, Oscar Isaac, Lupita Nyong'o, Domhnall Gleeson, Kelly Marie Tran, Joonas Suotamo, Billie Lourd, Keri Russell, Matt Smith, Anthony Daniels, Mark Hamill, Billy Dee Williams, and Carrie Fisher, with Naomi Ackie and Richard E. Grant. The film is scheduled to open on Dec. 20, 2019.


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Area animal shelters adopt more, take in less during pandemic
Erin Glynn, Manistee News Advocate
Homeward Bound Animal Shelter in Manistee County has many cats available for adoption. (Courtesy photo)
MANISTEE COUNTY — Local animal shelters have had fewer animals to care for during the coronavirus pandemic.
Shareen Edmondson, manager of the Homeward Bound Animal Shelter in Manistee County, said there's been an increase in adoptions in the past year, particularly of kittens and cats.
"I think it's because (adopters) wanted company while most people were staying home and kittens are playful," she said. "It's just something to keep them happy and entertained."
That doesn't necessarily mean people are being spontaneous about adoptions.
"It's a commitment," Edmondson said. "These people (who adopted in recent months) knew that at some point the pandemic would be over and they'll still have their new pet and they were happy about that."
The Benzie County Animal Shelter has also needed to care for fewer animals during the pandemic, though not necessarily because of more adoptions.
Animal Control officer Kyle Maurer said it's hard to say whether there's been an increase in people looking to adopt because the number of animals the shelter has taken in during the pandemic has been low.
Maurer thinks that's due to a combination of factors. With restrictions in place to prevent the spread of COVID-19, people are more wary about leaving their homes to do things like bring an animal to the shelter. As people have stayed home more this year, they're less likely to find stray animals. It also may be because the shelter has tried to return more animals to their homes rather than bring them into the shelter.
"We're trying harder to return people's animals because money is tight for people right now," Maurer said. "It's good for us too because the shelter has been shut down a couple of times."
The shutdowns have made it more difficult to care for the animals.
Currently the shelter has no animals, which Maurer said is common this time of year.
Homeward Bound has also noticed fewer animals coming in. It currently has 12 cats and no dogs.
"Usually we have way more dogs than we've had this year," Edmondson said.
Edmondson encourages people looking to adopt to check out other local shelters and online databases like Petfinder, if Homeward Bound doesn't have what they're looking for.
Homeward Bound has a high demand currently for bleach, laundry detergent and blankets. The shelter is allowing adoptions and visits by appointment only. Its ours are noon to 4 p.m. Wednesday through Friday and 11 a.m. to 3 p.m. on Saturday.
RELATED: Pet portraits fundraiser benefits Homeward Bound
Erin Glynn
Erin Glynn is a recent transplant from the Cincinnati area who graduated from Miami University with degrees in journalism and global politics. She loves reading and writing narrative nonfiction and drinking copious amounts of tea.

redpajama_set_name: RedPajamaCommonCrawl


Just a quick update to let you know that English Heritage – Shop have a Winter Sale with up to 50% off.
This English Heritage – Shop special offer is only available between Wednesday 28rd December 2016 and Sunday 08th January 2017 11:59PM. It looks like it's worth checking out either to stock up on birthday presents or to spend any money you were given as gifts for Xmas.
About English Heritage's online shop offers unique gifts inspired by Englands rich history. They have the perfect gift ideas for all ages and any occasion, many of them exclusive to English Heritage.
Gifts for her include traditional scented toiletries, Stonehenge and the First World War mugs, keyrings, cufflinks and more.
They also have original ideas for wedding gifts and christening gifts as well as an extensive range of traditional and wooden toys children love.
English Heritage protects and promotes England's spectacular historic buildings and archaeological sites, ensuring that they are researched, understood and accessible to all. They have over 400 sites open to the public, including the world-famous Stonehenge, the recently refurbished Kenwood House, Tintagel Castle and Hadrian's Wall. As a non-profit organisation, the proceeds from the sale of their products are used to maintain and preserve these properties.
Do you have any unusual Christmas traditions?
I hadn't seen this advertised anywhere else but just spotted it on one of the advertising networks we subscribe to. Marks and Spencer are running a Wine Clearance sale until the end of October with up to 40% off. I've always found them very reliable for wine and never had a bad bottle from them, so thought this worth sharing with you. Sounds like a good chance to stock up before Christmas. As far as I can see no voucher code is necessary, just visit the page below.
Their terms and conditions state: Up to 40% off wine clearance. Applies online at marksandspencer.com. While stocks last subject to availability. Discount applied at checkout. Offer does not apply to delivery charges.
Click here to see the Marks and Spencer wine sale.
If other relevant Christmas special offers catch my eye I'll share them with you on the blog. Do let me know if you find this helpful and also please share with me any site you find with great offers.
This Christmas will be a good time to enjoy a glass of Champagne.
Following on from my blog on Sept 16th about sorting out your Christmas travel arrangements as early as possible this weekend could be a good time to book a hotel room for the Christmas period. Martin Lewis – the Money Saving Expert today reported that Holiday Inn UK will start their Christmas room sale this Saturday (26th Sept 2009) at 00.01am selling rooms for the period Dec 17th to Jan 31st. They will be selling off Holiday Inn Express rooms from just £29 (usually £40-£60) and Holiday Inn rooms from £35 (usually £50-£80). It's not unusally for all the available hotel rooms to be booked within a few hours of these offers going online. So if you think you might want to stay in one of these hotels, it would be worth getting yourself organised to save a few pounds this Christmas. I highly recommend you visit Martin's site and signup for his weekly Money Saving Expert newsletter which is packed with similar excellent, timely money saving tips.


The co-curricular program ensures students are exposed to a variety of activities at St Michael's.
The co-curricular program at St Michael's is designed to introduce students to a broad range of experiences in the areas of Outdoor Education, Performing Arts (Drama, Dance and Music), Sport (competitive and recreational), Public Speaking, Debating and Chess.
Students also have an opportunity to participate in a number of coordinated clubs, which meet regularly throughout the year. These include Makerspace, Kitchen Garden, Robotics, Art, French, Hip Hop, COSMOS (Science), Chess and Environmental Defenders. Note: some clubs are available to certain year levels only.
The co-curricular program is divided into compulsory and non-compulsory events to ensure that students are exposed to a variety of different activities, and provided with the opportunity to be extended, in areas of their choice or passion, while also building relationships with others.


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UK's extreme weather: Heat and fires in the south, storms and floods in the north this weekend
Fire crews continue to be under pressure, with stations up and down the country "planning for a busy weekend" of further fires fuelled by the ongoing dry conditions.
Saturday 13 August 2022 09:00, UK
Image: Firefighters battle a grass fire in the Leyton Flats, London. Pic: Associated Press
More extreme heat and drought conditions, and the potential for wildfires, are expected in the southern half of the UK this weekend - while the northern half is set to be struck by thunderstorms and floods.
The Met Office has issued an amber heat warning covering most of England and Wales, where temperatures of up to 34C (93.2F) are predicted for Saturday and Sunday.
On Friday, Wiggonholt, in the Horsham District of West Sussex, peaked at 34.5C (94.1F).
With an amber alert, heat-related illnesses including sunburn and heat exhaustion are "likely" among the general population, and delays to public transport are "possible".
Meanwhile, a lower-level yellow warning for thunderstorms is in place from noon on Sunday until 6am on Monday for most of Scotland and Northern Ireland.
This means there is a "small chance" of flooding in these nations and the potential for power cuts.
Image: A parched golf course is seen from a balloon at the annual Bristol International Balloon Fiesta
The highest predicted daytime temperature of 34C is forecast in the South East on Saturday, with 32C (89.6F) predicted in London and 27C (80.6F) in Edinburgh.
More on Drought
Thames Water hosepipe ban for 15 million people lifted
Hundreds of elephants and zebras die during drought in Kenya
Winter rainfall not enough to prevent spring drought next year, forecasters warn
Temperatures around the 30C (86F) mark are expected further north in England, while much of Scotland and Northern Ireland can expect temperatures in the mid-twenties.
This comes after an official drought was declared in eight areas of England on Friday by the National Drought Group, which comprises representatives from the government, water companies, the Environment Agency (EA) and others.
Image: Low water levels at Baitings Reservoir in Yorkshire have exposed debris long hidden
Three water companies - Welsh Water, Southern Water, and South East Water - have all imposed hosepipe bans, while Yorkshire Water has announced a ban will start on 26 August and Thames Water is planning one in the coming weeks.
Residents in the areas indicated in the map below can expect to see restrictions placed on domestic and commercial water use.
Meanwhile, fire crews across Britain remain under pressure from the high risk of wildfires following the prolonged dry spell.
Crews in Derbyshire were still tackling a huge blaze late on Friday night, with four fire engines at the scene in Creswell, Worksop.
Footage shared online showed flames filling the horizon and large plumes of smoke in the sky above a residential area.
Derbyshire Fire and Rescue Service also fought embankment blazes beside a railway in Matlock, and near Junction 26 of the M1.
The service said it was "planning for a busy weekend" of further fires, and echoing the pleas of fire services across the nation, asked people to refrain from starting garden bonfires or using portable barbecues.
With parts of the UK now in drought, Sky News brings you a special programme exploring the impact and causes
Hosepipe bans: What are the rules - and what are the exemptions?
What and where is the 'exceptional' fire risk - and how to avoid one
Some 35 firefighters were also deployed to tackle a two-hectare blaze at the Leyton Flats wildlife reserve in Waltham Forest, east London.
London Fire Brigade crews were captured beating back the flames at the scene.
The service said there were no ongoing fires in the capital at 9pm on Friday.
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England's drought could persist into the next year, according to the EA.
John Curtin, executive director for local operations at the EA, said after the driest summer in 50 years, it would take "weeks' worth of rain" to replenish water sources.
How the British landscape has changed during the summer's heatwave
Read more: What happens during a drought and how can you help?
The announcement could lead to more measures such as hosepipe bans, however, the EA has reassured the public essential water supplies are safe.


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Park and Float
With a kayak or canoe you can find yourself instantly transported to a world of serenity and beauty...where nature and fish await. Wild Side Guide Ken Tucker takes us to the water to find out more.
If you're like most of us the minutes and hours of each day are taken up with too many things to do. With work, errands and children, quiet time (what's that?) is getting more and more precious. But we've found a way to escape the daily pressures and routine.
In fact, it's easier now than ever, thanks to a program called Park and Float. With a kayak or canoe you can find yourself instantly transported to a world of serenity and beauty…where nature and fish await. Wild Side Guide Ken Tucker takes us to the water to find out more.
It's estimated that Park and Float areas will benefit approximately two hundred thousand anglers who fish Tennessee waters, all by creating access areas that require minimal construction. T-DOT and the TWRA hope to establish up to ten new Park and Float locations next year. But the success of their efforts will depend on the amount of cooperation received from communities, volunteers, and cities along our state's waterways. So if you know of a place near a bridge that would be a good site, contact your local T-DOT or TWRA office.