Cows!

As has been mentioned in an earlier post, my family will be moving to Germany in a little over a month. When we do, our property will be transferred to our neighbours. I think it is an excellent arrangement for all concerned, because we are on good terms with our neighbours, and they are not complete strangers.

It has been decided that the neighbours' cows will already begin taking advantage of the upper half of our property. Accordingly, an electric fence was set up, and the cows have been visiting periodically. Some photos:

I like the cows very much. They are smaller than most cows, and the bull, in particular, has curly hair (especially around the head). Very endearing.

As for the garden, it has seen less overgrown days, but I rather like it as it is.

A Tribute to Brie

We recently had "Brie with fine herbs," a type of Brie that was so much to my liking that I felt it incumbent upon me to post about it.

First, a photo of the exact cheese we bought (taken from this website):

What I like about this variety is that it is soft (including the outside coating) and flavourful. This is in contrast to other Brie, which (while flavourful) tends to have a hard rind. I don't like having hard bits along with the soft inside, and it is too much bother to remove the rind entirely.

I haven't done anything particularly imaginative with the Brie. I've mainly eaten it with French bread and croissant (sometimes with lettuce added). For those of you who are more adventurous, or who have more Brie to work with, here is a recipe (from FoodNetwork.com, courtesy of Emeril Lagasse):

Delmonico's Smoked Salmon and Brie Crepes with Herbsaint Butter Sauce

For the sauce:
1/4 cup minced shallots
1 cup Herbsaint liqueur
1/4 cup heavy cream
Salt
Cayenne pepper
1 1/2 sticks cold butter, cut into pieces
1/4 teaspoon hot sauce
1/2 teaspoon Worcestershire sauce

2 pounds smoked salmon, thinly sliced
1 pound Brie, thinly sliced
12 medium crepes

In a saucepan, over medium heat, combine the shallots and Herbsaint. Season with salt and cayenne. Bring the mixture to a boil. Reduce the heat to medium low and simmer until the mixture reduces by half. Add the cream and continue to cook for 2 minutes. Remove from the heat and whisk in the butter, a couple of pieces at a time. Season with the hot sauce and Worcestershire. Strain through a fine-mesh sieve and keep hot.

Place a couple of slices each of the salmon and cheese over the bottom of each crepe. Roll each crepe up tightly. Place in a buttered casserole dish and bake in a preheated 350 degree oven for about 4 to 6 minutes, or until the cheese starts to melt.

To serve, spoon the sauce in the center of each plate. Lay a couple of the crepes in the center of sauce.

Note: It is nothing without the liqueur!!

I left out the parts about the "crispy" spinach. I don't really approve of frying spinach. It's just not right!

Square Root of Two Proof

My father and I recently discussed one of many proofs that sqrt(2), the square root of two, is an irrational number. By irrational number, of course, I mean a number that cannot be expressed as the quotient of two integers. Here is the proof, as I understand it:

Let us assume that sqrt(2) is a rational number. That means that it can be expressed as p/q, where p and q are integers.

So we get:

  sqrt(2) = p/q

Using simple algebra, the above equation can be rearranged as follows:

  2 = (p/q)²
  2q² = p²

Now, according to the Fundamental Theory of Arithmetic (or Unique Factorization Theorem), "every natural number greater than one either is itself a prime number or can be written as a product of prime numbers" (wikipedia).

q and p are no exception to this rule. Accordingly, they can each be expressed in terms of one or more prime numbers. q² will have exactly twice as many prime factors as q, and p² will have exactly twice as many prime factors as p. That is, q² and p² will each have an even number of prime factors. The expression 2q² must, then, have an odd number of prime factors (an even number + one extra factor of 2).

This is where the contradiction comes in. The Fundamental Theory of Arithmetic also states that each number's set of prime factors is unique (i.e. there is only one way to express a number in terms of its prime factors). So, if p² is equal to 2q², then the two expressions must have the same number of prime factors.

Yet, we have just shown (two paragraphs above) that p² has an even number of prime factors, while 2q² has an odd number of prime factors. That means that p² and 2q² can't possibly have the same number of prime factors. In turn, this implies that p² does not equal 2q², so our original equation can't have been correct. sqrt(2) cannot be expressed as the quotient of two integers, so it cannot be a rational number; it must be irrational.

QED :o)

There are all sorts of other ways to prove that the sqrt(2) is an irrational number. One, for example, involves geometry (specifically, the 45-45-90 triangle with a hypotenuse equal to the square root of two).

Fixed Election Dates

According to this CBC article, Canadian Prime Minister Stephen Harper has promised to "introduce a bill next week to establish fixed federal election dates every four years." If the bill is passed into law, governments will be in power for four years (or less if they lose the confidence of Parliament). The idea is to prevent politicians from calling elections to suit themselves, while preserving Parliament's ability to kick out governments that aren't working.

On the whole, I support the initiative. The only conceivable downside (as far as I can see) is that fixed election dates tend to result in lengthy (and expensive) campaigns. Even if that downside is realized, however, the advantages of fixed election dates outweigh the disadvantages.

Edited to add: Since I wrote the above, I have discussed the matter with my family, as well as reading about it on the internet. I have come to the conclusion that fixed election dates are not really necessary. They may, in fact, be harmful.

For one thing, it is not necessarily undesirable for governing parties to call elections to suit themselves. Considering that majority governments are more stable and efficient, it can actually be better for the country if parties have a chance to gain seats early in their term.

Another point is that our current system allows for elections based on specific issues (like free trade or the sponsorship scandal). Canadians are, accordingly, able to directly influence public policy.

In general, our system has more flexibility, which is only a bad thing when it allows for abuse. In this case, I don't think there is much danger of abuse (at least not any sort of abuse that significantly impedes democracy in Canada). One could certainly argue that our first-past-the-post voting system is more damaging and more worthy of attention.

That said, several provinces in Canada already have fixed-term elections, as do most democracies. With that and the openness of the Canadian public, fixed election dates seem to be inevitable.

A Tour of the Alphabet

antiscorbutic

adj. & n. • adj. preventing or curing scurvy. • n. an antiscorbutic agent or drug.

bilge

n. & v. • n. 1 a the almost flat part of a ship's bottom, inside or out. b (in full bilge-water) filthy water that collects inside the bilge. 2 sl. nonsense; rot (don't talk bilge). • v. 1 tr. stave in the bilge of (a ship). 2 intr. spring a leak in the bilge. 3 intr. swell out; bulge. ¤ bilge-keel a plate or timber fastened under the bilge to prevent rolling. [prob. var. of BULGE]

calender

n. & v. • n. a machine in which cloth, paper, etc., is pressed by rollers to glaze or smooth it. • v.tr. press in a calender. [F calendre(r), of unkn. orig.]

disembogue

v.tr. & intr. (disembogues, disembogued, disemboguing) (of a river etc.) discharge (waters) into the sea etc. [Sp. desembocar (as DIS-, en in, boca mouth)]

ex silentio

adv. by the absence of contrary evidence. [L, = from silence]

frumenty

n. (also furmety) hulled wheat boiled in milk and seasoned with cinnamon, sugar, etc. [ME f. OF frumentee f. frument f. L frumentum corn]

gingerbread

n. 1 a cake made with treacle or syrup and flavoured with ginger. 2 (often attrib.) a gaudy or tawdry decoration or ornament. ¤ take the gilt off the gingerbread strip something of its attractions.

heeltap

n. 1 a layer of leather in a shoe heel. 2 liquor left at the bottom of a glass after drinking.

indubitable

adj. that cannot be doubted. ¤ indubitably adv. [F indubitable or L indubitabilis (as IN-¹, dubitare to doubt)]

jiggery-pokery

n. Brit. colloq. deceitful or dishonest dealing, trickery. [cf. Sc. joukery-pawkery f. jouk dodge, skulk]

koan

n. a riddle used in Zen Buddhism to demonstrate the inadequacy of logical reasoning. [Jap., = public matter (for thought)]

lese-majesty

n. (also lèse-majesté) 1 treason. 2 an insult to a sovereign or ruler. 3 presumptuous conduct. [F lèse-majesté f. L laesa majestas injured sovereignty f. laedere laes- injure + majestas MAJESTY]

Metonic cycle

n. a period of 19 years (or 235 lunar months), after which the new and full moons return to the same day of the year. It was the basis of the ancient Greek calendar, and is still used for calculating movable feasts such as Easter. [Gk Meton, Athenian astronomer (5th c. BC)]

nuncupate

v.tr. declare (a will or testament) orally, not in writing. ¤ nuncupation n. nuncupative adj. [L nuncupare nuncupat- name]

otiose

adj. 1 serving no practical purpose; not required; functionless. 2 archaic indolent; futile. ¤ otiosely adv. otioseness n. [L otiosus f. otium leisure]

pule

v.intr. literary cry querulously or weakly; whine, whimper. [16th c.: prob. imit.: cf. F piauler]

quisling

n. 1 a person cooperating with an occupying enemy; a collaborator or fifth-columnist. 2 a traitor. ¤ quislingite adj. & n. [Vidkun Quisling, Norwegian Army officer and Nazi collaborator (1887-1945)]

rathe

adj. poet. coming, blooming, etc., early in the year or day. ¤ rathe-ripe 1 ripening early. 2 precocious. [OE hræth, hræd f. Gmc]

satyagraha

n. Ind. 1 hist. a policy of passive resistance to British rule advocated by Gandhi. 2 passive resistance as a policy. [Skr. f. satya truth + agraha obstinacy]

tracasserie

n. 1 a state of annoyance. 2 a fuss; a petty quarrel. [F f. tracasser bustle]

unctuous

adj. 1 (of behaviour, speech, etc.) unpleasantly flattering; oily. 2 (esp. of minerals) having a greasy or soapy feel; oily. ¤ unctuously adv. unctuousness n. [ME f. med.L unctuosus f. L unctus anointing (as UNCTION)]

vade-mecum

n. a handbook etc. carried constantly for use. [F f. mod.L, = go with me]

widdershins

adv. (also withershins) esp. Sc. in a direction contrary to the sun's course (considered as unlucky). [MLG weddersins f. MHG widdersinnes f. wider against + sin direction]

xiphoid

adj. Biol. sword-shaped. ¤ xiphoid process Anat. the cartilaginous process at the lower end of the sternum. [Gk xiphoeides f. xiphos sword]

yoicks

int. (also hoicks) a cry used by fox-hunters to urge on the hounds. [orig. unkn.: cf. hyke call to hounds, HEY¹]

zeugma

n. a figure of speech using a verb or adjective with two nouns, to one of which it is strictly applicable while the word appropriate to the other is not used (e.g. with weeping eyes and [sc. grieving] hearts) (cf. SYLLEPSIS). ¤ zeugmatic adj. [L f. Gk zeugma -atos f. zeugnumi to yoke, zugon yoke]

Note: All definitions are taken from the second edition of the Oxford English Reference Dictionary. I left out the pronunciation guides, and substituted or omitted some symbols and accents (e.g. I substituted the currency sign ¤ for a square).

Pride and Prejudice

What, after all, is a blog without a Pride and Prejudice post? :o)

In this case, my excuse is that I recently had occasion to watch Pride and Prejudice (the movie made in 2005). I had previously watched the BBC version several times, read the book several times, and watched the black and white movie version several times.

Here is my impression of each:

The book - I think that, to be honest, it is my favourite Jane Austen book. I say "to be honest" because it is such a common choice. I don't like being common. Still, I cannot deny that the book is readable and amusing. I cannot deny, either, that the main characters appeal to me, and that I greatly enjoy the spirit, style, and intelligence of the book. It is all exactly to my taste.

The Garson/Olivier movie - This version is more comedic than the others. In that sense, I think it works very well. The change in setting does bother me, though, as do the many changes in plot. Not to mention that Greer Garson seemed rather too old, and her humour rather too dry. As for Olivier as Darcy, I can't remember being much impressed with him. Perhaps his stiffness and pride are supposed to have that effect. Still, I prefer a more sympathetic and human hero.

The BBC mini-series - Here, as with the book and the earlier movie, I was amused, especially by dear Bingley and his smiles. I also greatly appreciated the length and the faithfulness to the book. I must say, though, that Darcy and Elizabeth were much too easy to laugh at in their emotional scenes, in which (depending on the character) they choked back tears, looked indignant and troubled, etc., etc. Perhaps I'm just unpleasantly cynical. Either way, I don't join those who go into raptures about Colin Firth's performance. Call it perverseness (or perversity) if you will.

The recent movie - I liked it very much, despite the shortness. One of my only objections was that Bingley was made out to be rather idiotic (pffff!). Having established an overwhelmingly favourable opinion, I began to wonder what other people thought of the movie. Accordingly, I looked it up in the IMDB (Internet Movie Database). Being more interested in opinions different from my own, I ended up reading almost exclusively negative reader comments. It was depressing! There was, after all, merit to the reviewers' objections. Many of the characters (including Elizabeth and Darcy) were significantly altered in the movie — to the point that one could dispute the aptness of the movie's title. The setting was unlikely, and many key elements of the story (e.g. Wickham) were passed over. (Just to name a few of the apparent offenses . . .)

In the end, though, I decided that none of the above negates the fact that I thoroughly enjoyed the movie (especially the lovely music, the lovely countryside, and the portrayals of Elizabeth and Darcy). If some people prefer to be "most seriously displeased" with the movie, they may suit themselves.

More Games

Apropos of the Hase und Igel post, here are some more fun games for all ages.

First, Mille Bornes, a French card game:

The objective is to be the first to get a thousand milestones ("mille bornes"). Players start out with six cards, and begin each turn by picking up a card from the centre pile. From there on, players have several options. They can deal an accident card to another player, add to their store of milestones, counter other players' attacks, etc. The idea is to gather milestones as quickly as possible, while making it as difficult as possible for others to do the same.

The second game is a board-game called Europareise (or Journey through Europe):

I haven't played it in years, and I don't remember the rules, so here is a brief description from BoardGameGeek:

"A travelling game. Each player has a home city and draws cards for other cities that they must visit. The first player to visit all their cities and return home wins."

I have great memories from playing all three games. I only wish my siblings would play with me more often. :.o(

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Note: The first photo is from Timewarp Vintage Toys, and the second is from BoardGameGeek.

Hase und Igel

Gnomey, Grimsly, and I have rediscovered a classic board-game called Hase und Igel (or Hare and Tortoise).

A picture of the game in play (from Billabong Boardgamers):

The objective of the game is to be the first to cross the finish line. Rather than relying on dice, however, players advance by "eating" carrots. Each player starts out with a certain amount of carrots, and can gain more by landing on certain squares. Players also receive three lettuce cards, which must be "chewed" (in exchange for carrots) before reaching the finish line.

It is a fun game of strategy, in which the trick is to find a balance between speed, caution, and luck.

Detailed rules and some hints are available here (pdf file).

A Spot of Maths

I felt like doing math problems last night. They are a convenient alternative to puzzles or games like Sudoku and FreeCell, because there is so much variety to be found (calculus/geometry/linear algebra/etc.). Endless and useful fun! :o)

In hopes of maximizing the useful aspect, I decided I would brush up on some parts of math that I didn't learn properly the first time around. I ended up starting out with linear approximations, because my understanding of approximations and error calculations has always been a bit sketchy. Not sketchy enough, in truth, to warrant this review, but one must begin somewhere.

A sample problem from the fifth edition of Single-Variable Calculus, by Robert A. Adams:

"The acceleration a of gravity at an altitude of h miles above the surface of the earth is given by a = g[R/(R + h)]², where g ≈ 32 ft/s² is the acceleration at the surface of the earth, and R ≈ 3960 miles is the radius of the earth. By about what percentage will a decrease if h increases from 0 to 10 miles?"

It's not a particularly interesting or difficult problem, I admit. I will try to find a better one and post it later on. In the meantime, here is my solution to the acceleration problem:

s = 0 miles = h at surface of the earth
a'(x) = derivative of a with respect to h at h = x
L(x) = linear approximation of a at h = x
Δa = decrease in a between h = 0 miles and h = 10 miles
P = percentage by which a decreases between h = 0 miles and h = 10 miles

a'(h) = [gR²/(R + h)²]'
     = gR²[-2/(R + h)³]
     = -2gR²/(R + h)³

a'(s) = a'(0) = -2g/R

a(s) = gR²/(R + s)² = g

L(h) = a(s) + a'(s)(h - s)

Δa ≈ L(h) - a(s)
  = a(s) + a'(s)(h - s) - a(s)
  = a'(s)(h - s)
  = -2gh/R

P = (Δa/a(s)) × 100%
       = ((-2gh/R)/g) × 100
       = -200h/R
       = -200(10)/3960
       ≈ 0.5%

I had some trouble with the derivative of a, because I treated R as a variable. Tsk, tsk! In earlier problems, I found that I had forgotten the derivative of tan(x), and that my memory of the quotient rule and the 30-60-90 triangle was indistinct. Oh well. Those are all things that can easily be looked up and recommitted to memory.

If I actually stick to this, I may soon have a look at Taylor Polynomials, differential equations, partial derivatives, and proofs. Not particularly likely, I'm afraid. :o( I am a fickle creature.

Runbot

I have been watching Daily Planet (the TV show) lately, and was intrigued by their report on RunBot (a speedy two-legged robot).

Here, for more details, is a quotation from NewScientist.com:

"A two-legged robot that walks at record-breaking speed has been developed by researchers from Germany and Scotland.

'RunBot' is the fastest robot on two legs — for its size. At 30 centimetres high, it can walk at a speedy 3.5 leg-lengths per second. This beats the previous record holder — MIT's 'Spring Flamingo' — which is four times as tall but manages just 1.4 leg-lengths per second."

If you wish to see RunBot in action, here is an mpeg video (can be viewed with QuickTime — possibly also with Windows Media Player/RealPlayer/etc.). May you find the video as amusing as I do.

Note that the video is nothing without the sound, so turn up the volume! :o)

Edited to add: The blog has been loading very slowly lately, and it is getting annoying. In hopes of speeding up matters, I have chosen to link to the video above, rather than embedding it in the post. I have made other (significant) changes to the post as well.

A Tribute to Gouda

My family — long time consumer of cheddar cheese — has recently (and, perhaps, temporarily) switched to Gouda cheese.

A picture from this site:

In my non-connoisseur opinion, Gouda is like a delicious cross between mozzarella and cheddar cheese. It has an excellent consistency and texture for cutting and eating, a mild taste, and the capacity to melt perfectly. Speaking of which, here are some melted Gouda recipes for lazy folk:

Chili with Gouda

• make canned chili (or homemade, if you must)
• put warm chili on tortilla
• roll up tortilla, cut into pieces
• put pieces in baking dish (I use the aluminum pans that pies come in)
• cover with Gouda slices
• heat at 200°C or 390F until the cheese has melted

Spaghetti with Gouda

• make spaghetti and peas in separate pots
• cut spaghetti into pieces, put in baking dish with peas
• cover with Gouda slices
• heat at 200°C or 390F until the cheese has melted

"Anti-graffiti crackdown"

A recent CBC article states that London, Ontario, has passed a bylaw "banning the sale of markers and spray paint to anyone under the age of 18."

The article cites the following statistics:

"Police records show that in the last two years in the city, 25 of 42 people arrested for making graffiti were under 18.

As well, 126 people were seen but not caught. And, of them, 92 were minors."

I wonder what the statistics are concerning the number of minors who buy spray paint or markers and use them for something other than graffiti.

In any case, I think the bylaw discriminates against minors; it violates their rights based on stereotypes and unconvincing statistics. It isn't right to penalize people for crimes they may or may not commit in the future.

It is an entirely different matter for the city to "provide outlets for minors to express themselves creatively and artistically." Such measures are positive and constructive, and they don't assume guilt on the minors' part.

Combatants for Peace

I recently came across the following video on youtube. In it, a group of Israelis and Palestinians — most of whom have committed acts of violence in the name of Israel or Palestine — meet to discuss their roles in the conflict and their campaign for a non-violent resolution. Two of those present, in particular, provide an account of their actions and the experiences that led them to reject violence. One is an Israeli major, and the other is a Palestinian who spent over ten years in jail after attacking Israeli soldiers.

There are several things about the video that appeal to me. To begin with, I appreciate the lack of generalities. It isn't often that one hears first hand accounts from those involved in the conflict or sees Israelis and Palestinians as individuals. I also appreciate the hopefulness of the video, and the humanness of the setting. The video is, admittedly, relatively short, but it gives you a valuable and unusual perspective of the conflict in Israel and the Occupied Territories.

But, please, see for yourself. :o)

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Note: See http://www.combatantsforpeace.org/ for more information. You will find, among other things, written versions of the personal stories (here and here).

Photos Again

A moth outside the little house:

Flowers on a silver dollar plant: