Friday, 29 November 2013

Aufklärung 2.0

Bertrand Russell (18 May 1872 – 2 February 1970) is one of those rare birds that belong not only to one flock but is at home in many. He is a man of the renaissance born centuries after, long-lived (his productive adult life spanned World War I to the Vietnam War!), and made academic contributions to almost every field of human endeavour. His pictures always have a mischievous, Mona Lisa smile.

I first came across his name in reading about set theory (the theory of infinite arithmetic) but he was a polyglot: philosopher, logician, mathematician, historian and social critic. He is famous in this set theoretic context for finding a paradox called - interestingly enough - , Russell's Paradox. It is popularly called "the barber of Seville" (the barber shaves all the men who do not shave themselves; who shaves the barber?). I think I've mentioned this paradox somewhere in this blog which I tried to "solve" linguistically (ie, the notion of a noun is not just proper names, things, ideas and places, but may also be a purely (unspecific) grammatical slot that holds the grammaticality of Aristotelian logic, say).

But it is his philosophical view that the "age of enlightenment" was "...was a phase in a progressive development, which began in antiquity, and that reason and challenges to the established order were constant ideals throughout that time" (http://en.wikipedia.org/wiki/Age_of_Enlightenment) that I want to talk about here.

There is an almost linguistic approach of Russell - the "wrong" kind as far as I'm concerned because it is distinctly Saussurean - in all that he does, which is not really surprising given that he made great contributions to mathematics and logic. For eg, in the Stanford Encyclopedia of Philosophy (which is a great source of synopses and introductory information to philosophy and philosophers):

...that moral judgments are neither true nor false, since their role is not to state facts or to describe the way the world is, but to express emotions, desires or even commands. This (despite some waverings) was Russell's dominant view for the rest of his life, though it took him twenty-two years to develop a well worked-out version of the theory. He tended to call it subjectivism or ‘the subjectivity of moral values’ though it is nowadays known as non-cognitivism, expressivism or emotivism. He came to think that, despite their indicative appearance, moral judgments — at least judgments about what is good or bad in itself — are really in the optative mood. (A sentence is in the optative mood if it expresses a wish or a desire.) What ‘X is good’ means is ‘Would that everyone desired X!’. It therefore expresses, but does not describe, the speaker's state of mind, specifically his or her desires, and as such can be neither truth nor false, anymore than ‘Oh to be in England now that April's here!’ If I say ‘Oh to be in England now that April's here!’, you can infer that I desire to be in England now that April's here (since absent an intention to mislead, it is not the sort of thing I would say unless I desired to be in England and thought that April was here). But I am not stating that I desire to be in England, since I am not stating anything at all (except perhaps that April is here). (http://plato.stanford.edu/entries/russell-moral/)

What is called "optative mood" in the above quote is now called "subjunctive mood", which Wikipedia says, in relation to the "indicative/declarative mood":

The subjunctive is a grammatical mood found in many languages. Subjunctive forms of verbs are typically used to express various states of unreality such as wish, emotion, possibility, judgment, opinion, necessity, or action that has not yet occurred – the precise situations in which they are used vary from language to language. The subjunctive is an irrealis mood (one that does not refer directly to what is necessarily real) – it is often contrasted with the indicative, which is a realis mood.

All fine and well, I suppose. It's just that, to me, a linguistics/algorithmic logical approach, especially to moral philosophy, is a doomed enterprise - doubly so since one is also at the same time trying to come up with general principles of moralistic perspective and behaviour. It is precisely that normative/legalistic statements are rarely practical let alone informative that this whole enterprise is doomed (tragic, really, because I like Russell). Morality, as the Aristotelian principle of "phronesis" states, is really about dealing with particular and unique situations that call upon one to decide on how to act:

Phronesis is concerned with particulars, because it is concerned with how to act in particular situations. One can learn the principles of action, but applying them in the real world, in situations one could not have foreseen, requires experience of the world.(http://en.wikipedia.org/wiki/Phronesis)

Judeo-Christian principles are more like exercises in phronesis in that they're, at their cores, based on the notion of free will, of experiencing humanity and the "teachable moments" it affords:

He has shown you, O mortal, what is good.
And what does the Lord require of you?
To act justly and to love mercy
and to walk humbly with your God. (Micah 6:8)

Evil is not evil because G*d says so; it is because the consequences of our decisions are unavoidable (in reality). Ie, in my own experience, I have come to realize that in potentia I have in me both the possibility for right and wrong action. The thing is, in morality, the notion of personal responsibility is existential and inherent and cannot be done away with by algorithmic logic/normative measures alone. It is said that there are no laws against agape, kindness and charity.

Jay

Saturday, 23 November 2013

Strogatz's Joy of x

I bought a book recently called, The Joy of x: A Guided Tour of Math, from One to Infinity, by Steven Strogatz (First Mariner Books, edition 2013). I think it's a great introduction to mathematical ideas and I highly recommend it.

It is a very visual treatment of mathematics (if I may use the term, "visual"). It is very much in the tradition of Riemann, whom, it is said, believed that geometric demonstrations were key to understanding the equations and their implications (Riemann helped create differential geometry whose ideas Einstein used heavily in his relativity theories - Einstein, himself was a highly visual person).

Strogatz is masterful in his historical development pedagogy and his demonstrations are intuitive precisely because he marries equations so well with illustrations. I've never quite thought about the method of exhaustion tied to the name of Archimedes as Strogatz has done it: he lays out quarter sections of a circle into a scalloped shape, first into four, then 8ths, 16ths, etc., 'til he finally achieves a regular rectangle with r height and πr base - brilliant.

And this is not the only instance where he makes mathematical demonstrations come alive. He does a similar thing with a demonstration that all angles of a triangle equal 180 degrees by appealing to the existence of a parallel line. Everything is logically laid out so when he comes to calculus the ideas he speaks about earlier are recalled and retooled for other purposes.

Where I'd take issue is his treatment of "closed rings" (ie, how different types of numbers are called into existence by the requirements of arithmetical operations: natural numbers, integers, algebraic numbers, transcendental numbers, imaginary numbers) though he adumbrates how these types of numbers arise in talking about the fundamental operations of arithmetic and the rise of imaginary numbers. There are other books like this available so I'd grant him this.

I have always wished that Nunavut schools would use the narrative (historical development pedagogy) as a basic teaching tool. This book is another important case why we need such a thing for this type of teaching and learning introduces the notion of mortals discovering and creating mathematics from a problem-solving perspective rather than suggesting this seemingly otherworldly subject as having come from heaven already fully formed and without the need for human contribution.

Jay

Tuesday, 19 November 2013

The Ford factor

I don't quite know how to write this entry with sensitivity and compassion it requires in the context in which I want to discourse on the subject. So, I'll just write as I go along.

The slow-motion train wreck that is Rob Ford of Toronto may be something new to most of mainstream Canada but in power relations that define the very nature of aboriginal communities the Rob Ford saga is strangely something familiar if extreme and pathetic.

It is said that all power corrupts and absolute power corrupts absolutely. Without painting anything in broad-strokes (heaven forbid that all is black and white and two dimensional) if the legal system allows it and one can get away with questionable technicalities of power relations it is a certainty that some abuse is bound to happen. That is not to say that there are no people who see the temptations and choose not to act thusly - in fact, abuse of this type only requires one willing to go over the line and it is often only one that acts thusly. Take Rob Ford (or someone in power who's willing to overlook the consequences in the interest of the few) and the legal and ethical quagmire that the Toronto city council now finds itself in.

My aippakuluk bought me a copy of Joe Clark's book, How We Lead: Canada in a century of Change (2013, Random House Canada). There used to be a notion of noblesse oblige (roughly speaking, the notion that those in power (or have the power to influence) have a certain obligation to act within ethical (if not legal) constraints to act honorably and responsibly in the exercise of that power). Clark talks about this notion quite a bit though (as yet) never having mention it explicitly.

It is my understanding that Clark does not hide his disdain for Harper's approach to governance. Methinks it is the very absence of noblesse oblige that irks many statesmen/women like Clark and many others in the laity like me (ie, those who keep track of politics). It is not just Harper but the whole infected right wing movement including Ford that spurns not only the foundational noblesse oblige but aggressively dismisses the notion of "conventional wisdom".

"Elites" and "liberal media" catch phrases form a huge piece of the right wing narrative; the only problem is (for those opposed to the right wing mentality) the inherent ambiguities and all-purpose uses of such terms, and, depending on the context, the Supreme Court of Canada; the whole Senate; the public watchdog/regulatory functions of public governments; informative and thoughtful media all fall into these labels. When a ruling government declares open season on all the long-standing institutions of a democratic society such as Canada the only way to maintain a semblance of rational discourse is what the French call faux amis "false friends" where seemingly equivalent concepts which seem to logically follow in a given slogan and/or talking points actually imply or mean something entirely different under scrutiny. Doublespeak.

For eg, the repeal of "Navigable Waters Protection Act" affects not only public health and safety but also affects waters that occur in disputed and settled territories in aboriginal land claims areas, and have bearing on species deemed of interest and/or at risk. Going by people in the know this particular repeal is heavily favoured towards the interests of the oil and resource extraction industries and makes it now possible to completely forego "meaningful" consultation with affected community and aboriginal groups if such consultation stands in the way of the amorphous national economic interests.

With the Rob Ford train wreck, the ostensibly "strong" law and order Harper gov't's lack of public statements has been weighed and measured and found sorely wanting - though the PMO and CPC has since put out a public statement that CPC is against drug-use while in public office and drinking and driving with some mention of Trudeau for good measure though no mention of Ford is to be found anywhere. In fact, the higher ranking cpcers have gone out of their way to make it absolutely clear that they won't pass judgement on Ford. Wow.

Jay

Saturday, 2 November 2013

Creativity and "education"

During the last Nunavut territorial elections campaign there was a young Inuk man who said that education was the most pressing issue as far as he was concerned, that without the practice of getting homework (K to junior highs school) Inuit students struggle unnecessarily when they get to the secondary levels. I tend to agree with him, but I'd go a step further and say that it's not just getting homework to do that is a problem; it is lack of engagement (and sense of achievement) that is the problem.

When I worked as a policy analyst for an Inuit organization I was often invited to participate in symposia and workshops on Inuit education and curriculum development exercises. I enjoyed every single invitation because I not only got to engage with Inuit elders but really smart teachers (both Inuit and non-Inuit) - I mean, besides being given the opportunity to discuss and explore technical considerations.

It was during that time I got to thinking about the notion of "education" - philosophical, technical, theoretical dimensions of pedagogy, and what the layman would assume education to be. Often I was struck by the "consumer product" regard of "getting" an education (ie, getting a diploma at the completion of going to school). To me this is an ersatz version of education, very bureaucratic, very Piaget.

In fact, I consider Jean Piaget along with Benjamin Spock as the demon duo of Disney's Hercules, Pain and Panic. I know less of Spock but I blame him for the misinterpretation and misapplication of Dewey's theories on education (specifically, student-centered pedagogy), and I consider Piaget the anti-Vygotsky of the humanities' cosmology (a hint that I'm an advocate for liberal arts education). (here is a link to Vygotsky's version of child development that a good introduction: http://www.simplypsychology.org/vygotsky.html).

I'm also informed in my views on education by Northrop Frye, especially a collection of his essays and speeches called, On Education (1988). Frye said that:

The university can best fulfill its revolutionary function by digging in its heels and doing its traditional job in its traditionally retrograde, obscurantist, and reactionary way. It must continue to confront society with the imaginations of great poets, the visions of great thinkers, the discipline of scientific method, and the wisdom of the ages, until enough people in the democracies realize that a way of life, like life itself, must be lost before it can be gained. (On Education, The Critical Discipline, p. 37)

-In the course of writing this blog entry I also came up with this excellent link on education: http://www.wideawakeminds.com/ that I think is worth checking out.

More than historical development pedagogy (as Frye advocates immediately above). more than socio-cultural approaches to education (as Vygotsky says we need), I think we need to celebrate that uniquely human ability to create. I'm not just talking about drawing pictures, writing essays, etc. but something more.

When I was asked by an educator what I meant about mathematics, I said that we should focus on the mechanics of arithmetic only from K to grade 3 but after that algebra and creative problem solving (working thru and formulating possible questions and solutions - ie, the conceptual emphasis that go beyond the textbook) should form the basis of the curriculum.

In Marcus du Sautoy's book, The Music of the Primes (2003), he describes a man named Wilhelm von Humboldt:

In 1809 Wilhelm von Humboldt became the education minister for the north German state of Prussia. In a letter to Goethe in 1816 he wrote, 'I have busied myself here with science a great deal, but I have deeply felt the power of antiquity has always wielded over me. The new disgusts me...' Humboldt favoured a movement away from science [the practical, the utilitarian] as a means to an end, and a return to a more classical tradition of the pursuit of knowledge for its own sake. (p. 59)

This view is contrasted with the "Republican arithmetic" of Napoleon's utilitarian philosophy of education serving the needs of the state:

Humboldt's drive from teaching science as a practical tool to the more aesthetic notion of knowledge for its own sake had filtered down to Schmalfuss's classroom. The teacher steered Riemann's reading away from mathematical texts full of formulas and rules that were aimed at feeding the demands of a growing industrial world, and guided him towards the classics of Euclid, Archimedes and Apollonius. With their geometry, the ancient Greeks sought to understand the abstract structure of points and lines, and they were not hung up on the particular formulas behind the geometry. (ibid, p. 61)

As most people of my ilk are stereo-typically fascinated by trains, I too have a deep fascination with gothic cathedrals and bridges. But it is less the engineering (though it is that to be sure) but the aesthetic geometries and combinations of abstract shapes that hold their magical sway. I've always been fascinated by structures - whether linguistics, maths, physical structures, orthographical conventions, rhetorical devices, etc. - for there I see the divine that which drives me yet onwards to seek knowledge further and test my ability to comprehend. This aesthetic appreciation has always served me well for it is the key (as I've figured out) to critical thinking and the ability to formulate original insight.

Jay