I want to introduce a concept to some who won't be familiar with it, and then use it to illustrate a constructive way of thinking. For those who have had a course in linear algebra, please skip to the second part while ignoring my clumsy mathematical explanation in the first.

Spans and Bases

Points on a two-dimensional plane can be expressed by ordered pairs such as (4,5), where the first number is an x-coordinate and the second a y-coordinate. In three-dimensional space, we can use (4,5,2). This extends up to any number of dimensions (although once we …

There is general agreement that a world food crisis is occurring. Biofuel (especially ethanol made from corn) has borne a large part of the blame. I'm not convinced that it overshadows other factors — speculation, water scarcity and the effect of the price of oil — but it certainly allows for the most vivid imagery.

Once again I am reminded of a passage from Dune. The titular planet is mostly desert, dry to the point where water is currency and windtraps are constructed to harvest airborne moisture. Two characters talk about trees planted brazenly outside the mansion of the ruling Duke:

The …

Agitating to lower "unfair" gas prices isn't something I would ever be caught doing; I like the idea of expensive gas forcing the stiff-necked to actually use public transit. Regardless, I'm attentive spectator on the way to peak oil, so I came up with a little game:

When will crude oil cost USD 150 per barrel?

So far we've got:

• 1 July 2008 — Konrad P
• 15 August 2008 — Matt M
• 1 November 2008 — Greg T
• 1 January 2009 — Paul K
• 14 February 2009 — Amy J
• Never — ??

Feel free to leave a guess in the comments, or to revise your initial …

Chirruping brightly (through dusty, long-closed windows) Spring comes, insistent

     —an exile driven on by Fate, he was the first to flee the coast of Troy, destined to reach Lavinian shores and Italian soil, yet many blows he took on land and sea from the god above— thanks to cruel Juno's relentless rage—and many losses he bore in battle, too, before he could found a city, bring his gods to Latium, source of the Latin race, the Alban lords and the high walls of Rome.

At the University of Toronto Bookstore yesterday, I discovered I had been too hasty in buying the David West prose translation of Virgil's Aeneid …

The prepared text of a speech given at the Engineering Science Alumni Dinner, Friday 04 April 2008.

Good evening. I have been asked to speak briefly about my personal experience, and about student development and leadership in the Division of Engineering Science. This is an extraordinarily difficult assignment. Not only do I follow Prof. Cheng and others of intellect and stature, but you, my audience, are a variety of Engineering Science undergraduates and alumni. If the Registrar's office is correct, at least three quarters of you are smarter than me. So though I resolve to avoid truisms about the Division …

As part of the excellent course APS501 Leadership & Leading for Groups & Organizations, we were offered leading (ha) questions and guidelines for writing a personal mission statement. Before you scream "Flake!" you should know our professor did more or less the same in his mid-20s, and considered it instrumental in attaining his eventual position as president, CEO & chairman of DuPont Canada.

That's not easily dismissed.

Here's what I came up with:

To become a balanced, thoughtful & serene person, so that I may always approach life and people with care and respect, and through doing so become a model of goodwill for …

Carrying on from the previous post…

Though we can't simply dismiss Carl Sagan's universe-architects in Contact by saying 'a π is a π is a π,' it's still true that the task of creating a universe is inconceivable, given that we hardly understand what our universe is and how it came into being. Another inconceivable endeavour is the building of a Dyson sphere—a structure completely enclosing a star so as to capture all its radiation on the inner surface.

But of course as soon as 'inconceivable' is aired, someone's going to bring up that Princess Bride quote: "You keep …

I was trolling (in the conventional sense) through Wikipedia today, reading about the Oort cloud, cosmology, and various superstructures and -voids in the Universe.

I also read about the shape of the Universe. For anyone without a math or science background, this is should be as baffling as I found it to be at first. More easily grasped is Gauss' Theorema Egregrium, which has to to do with curved surfaces, for example the surface of the Earth. The Theorema describes a characteristic of flat maps that anyone can observe: when displaying geographical features, flat maps distort shapes, distances, or both …

I missed Nuit Blanche last year, so I had a great time this Saturday and Sunday wandering around with some teammates from the Iron Dragons. I won't say more, but you can view some photos at Torontoist or on Kim's Flickr account. Also, I have to go back to Bau-Xi sometime for a less hurried look.

Around 1 AM we were passing through Yorkville and squeezed into the packed Bay & Cumberland Starbucks to get some java (Disclaimer: I'm still a Second Cup nut! A friend passed me a $20 Starbucks card he was given but didn't intend to use). I …

"Either way, it takes up too much space in your mind. It's not what you should be thinking about. "You should be thinking about how good the cup of coffee you're drinking tastes. Everything figures itself out from there. At least it has up to this point. And I assume it'll keep figuring itself out without too much bother." —Will Butler of Arcade Fire V. Wagner. "The Heat Begins To Rise." Toronto Star (Feb. 11, 2007), sec. C p. 4.

I'm reading Jean-Jacques Rousseau's The Social Contract (Goodreads, Penguin, Wikipedia) and really enjoying it. Either translation from French to English is a perfected art nowadays, or the originally writing is good. Both is more likely both. Whatever the reason, the prose is very clean and many good points are made simply and strongly in every paragraph.

The book clarifies one's thoughts on the roles and authority of citizens and governments. Of particular usefulness is the distinction between the general will and the will of all. The former is the opinion of the whole civic body, whereas the latter is merely …

Contrary to popular advice, I often sweat the small stuff. Today, cups.

Coffee shops generate litter. Ideally, we should each tote around a mug to whip out whenever we need a caffeine fix. I try and do this as much as possible, but the paper cup is unlikely to be obsoleted.

Paper cups are not terrible because they can be recycled or composted, unlike (in most locations) styrofoam. Second Cup (my favourite coffee chain) uses cups by Dover Cup in Brampton, Ontario. Tim Horton's and several other shops and use a cup branded Conference Cup, made by Dopaco. I wonder …

After reading this, I've installed several Drupal modules:

• Comment Info
• Captcha and Form Store
• Spam

Now anyone should be able to comment without logging in by answering a simple math question. If you have cookies enabled, your user information can be saved for future use. The system should be familiar to users of Blogger and similar sites.

After another long hiatus—five months—I now have a list of topics on which I have concrete ideas, which might be enough to start regular writing. Writing six or seven items in quick succession will hopefully establish a habit.

Apropos the long delay, a discussion of writer's block, for the delay testifies to a lack of confidence in the value of my writing. I address the various aspects of this doubt in turn.

What authority can I claim? The cliché "the more I learn, the less I know" is painfully relevant. It has become habit, as I form an …

The Earth Challenge (Wikipedia) was announced, an occasion for some hand-waving math.

What if you simply planted trees? They act as a carbon sink, sequestering carbon dioxide as biomass. One statistic says that one million trees will sequester 0.9 teragrams over their 40 year lifetime. That is:

0.9 Tg = 9×10¹¹ g

9×10¹¹ g ÷ 106 trees ÷ 4×101 a = 2.25×10⁴ g·tree-1·a-1

That is, one tree will fix 22.5 kg of carbon dioxide in one year. The Earth Challenge requires removal of 1 billion tonnes (10¹⁵ g) annually …

Weather in Toronto has recently taken a cold turn. Given the recent release of the First Working Group / Fourth Assessment Report of the IPCC, the joke du jour has become "What's all this fuss about global warming?" This bothers me for two reasons.

First, I feel it's heedless to joke about what is, by general consensus of the scientific community, a serious problem. It betrays a simplistic, "out-of-sight out-of-mind" naïveté. By analogy (here I corroborate Godwin's Law), consider how foolish they felt in 1945 who said, in 1940, "Holocaust? What Holocaust?"

Secondly—humour me for a moment while I indulge …

For the LazyWeb: After wasting over half an hour searching for a free, simple Windows utility to clone a CD for my mother, I gave up and used Ubuntu. With the disc in my recorder, I opened a terminal and typed:

cdrdao copy --device /dev/cdrw

CDRDAO prompted me to insert a new disk but otherwise ran unattended.

I subscribe to Harper's Magazine, which comes monthly and is always a good read. Wikipedia describes it as

a monthly general-interest magazine covering literature, politics, culture, finance, and the arts from a progressive, moderate left perspective in a fashion often not found in the ordinary news-media. It is the second oldest continuously-published monthly magazine (the oldest magazine being Scientific American) in the United States…

In the December 2006 issue, there's an interesting piece on thousands of scavengers living on an enormous garbage dump in Manilla, the Philippines. The phrase "economic Darwinism" is used, and the whole thing strikes me as …

Each month and year, I become a more rabid cheerleader for public transit. Where once I was simply delighted by the cheap, eco-friendly idea of having one person drive scores of others around, I'm now enraged by the attachment of the average Torontonian to his or her automobile. I'm even more incensed by quixotic city-dwellers who aspire to saving for and buying a car as a mark of adulthood. Such a waste of money!

I allow that using Mississauga Transit or its 905 equivalents is a horrendous experience. Even more horrendous is getting anywhere by bicycle—a tiring, if not …