Why so many earthquakes?

Several people have asked this recently. But have we really seen an earthquake spike? The US Geological Survey keeps statistics for us:

Earthquake Magnitude	Annual Average Number	2001–2010 Rate	2011 Rate
8+	1	+30%	Average
7–7.9	15	−10%	+30%
6–6.9	134	+10%	+60%

Turns out we’re only slightly over our quota this year. So, tragic as earthquakes always are, perhaps the recent ones are not a “sign.”

Six classic opening lines

... because it’s essential to begin a story well.

“In a hole in the ground there lived a hobbit. Not a nasty, dirty, wet hole, filled with the ends of worms and an oozy smell, nor yet a dry, bare, sandy hole with nothing in it to sit down on or to eat: it was a hobbit-hole, and that means comfort.”

“Once upon a time there were four little Rabbits, and their names were – Flopsy, Mopsy, Cotton-tail, and Peter.”

“It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair, we had everything before us, we had nothing before us, we were all going direct to Heaven, we were all going direct the other way...”

“Our roof leaks. Drip! Drip! Drip! My daddy says there’s a hole in our roof. I know why there’s a hole. There’s a Hippopotamus on Our Roof Eating Cake.”

“Alice was beginning to get very tired of sitting by her sister on the bank, and of having nothing to do: once or twice she had peeped into the book her sister was reading, but it had no pictures or conversations in it, ‘and what is the use of a book,’ thought Alice ‘without pictures or conversation?’”

“CHORUS: Why do you cry out thus, unless at some vision of horror? CASSANDRA: The house reeks of death and dripping blood ... The primroses were over. Towards the edge of the wood, where the ground became open and sloped down to an old fence and a brambly ditch beyond, only a few fading patches of pale yellow still showed among the dog’s mercury and oak-tree roots.”

One night in a thousand years

“If the stars should appear one night in a thousand years, how would men believe and adore, and preserve for many generations the remembrance of the city of God which had been shown!” – Ralph Waldo Emerson

The constellation Orion: photo by “Mouser,” 2004

Genesis 1:14–19 describes the creation (or rather, formation, since the heavens had already been created) of the stars:

“And God said, ‘Let there be lights in the expanse of the heavens to separate the day from the night. And let them be for signs and for seasons [appointed times], and for days and years, and let them be lights in the expanse of the heavens to give light upon the earth.’ And it was so. And God made the two great lights—the greater light to rule the day and the lesser light to rule the night—and the stars. And God set them in the expanse of the heavens to give light on the earth, to rule over the day and over the night, and to separate the light from the darkness. And God saw that it was good. And there was evening and there was morning, the fourth day.”

Stars appear here as almost an appendage of the sun and moon, but the phrase “God saw that it was good” indicates that the primary role of the stars is to praise God (Psalm 148:3: “Praise him, sun and moon; praise him, all you shining stars!”).

Several passages in the Bible use the stars as an example of the greatness of God (e.g. Nehemiah 9:6, Job 9:7, Psalm 8:3, Psalm 33:6, Psalm 136:9, Psalm 147:4, Isaiah 40:26), and stars are often used as a metaphor for height (Job 22:12, Obadiah 1:4), brightness (Daniel 12:3), variety (1 Corinthians 15:41), etc.

However, the Genesis passage also hints at two practical purposes for the stars. The first is as a sign or mark, which seems to allow both for the role of stars in navigation and for portents such as the Star of Bethlehem. The second is as an indicator of designated times (“to regulate definite points and periods of time, by virtue of their periodical influence upon agriculture, navigation, and other human occupations, as well as upon the course of human, animal, and vegetable life,” according to Keil). This is, of course, the reason why Stonehenge, for example, was built. Nevertheless, the stars are not primarily practical:

“Worn out with this torture of thought, I rose to my knees. Night was come, and her planets were risen: a safe, still night: too serene for the companionship of fear. We know that God is everywhere; but certainly we feel His presence most when His works are on the grandest scale spread before us; and it is in the unclouded night-sky, where His worlds wheel their silent course, that we read clearest His infinitude, His omnipotence, His omnipresence. I had risen to my knees to pray for Mr. Rochester. Looking up, I, with tear-dimmed eyes, saw the mighty Milky-way. Remembering what it was – what countless systems there swept space like a soft trace of light – I felt the might and strength of God. Sure was I of His efficiency to save what He had made: convinced I grew that neither earth should perish, nor one of the souls it treasured. I turned my prayer to thanksgiving: the Source of Life was also the Saviour of spirits. Mr. Rochester was safe; he was God’s, and by God would he be guarded. I again nestled to the breast of the hill; and ere long in sleep forgot sorrow.” – Charlotte Brontë, Jane Eyre, Chapter XXVIII

The Milky Way: photo by Steve Jurvetson, 2007

Puzzle solution

In my last post, I quoted a puzzle about N×N grids of black-or-white stones (see below), and asked if a 5×5 rectangle-free grid was possible.

Answer: no.

This is a result from Ramsey theory, but a simple proof from a colleague of mine goes like this:

• Assume there is a row containing three (or more) black stones (if not, there must be a row containing three or more white stones, so swap “black” and “white” in what follows).
• Let the column positions of these stones within the row be a, b, and c, and consider the 4×3 subgrid of those columns and the other four rows.
• If any row of three in that subgrid contains a pair of black stones, there is a black rectangle. Alternatively, let each of them contain a pair of white stones.
• Since there are four pairs of white stones, and only three possible pairs of columns (ab, ac, bc), at least one pair of white stones is duplicated, forming a white rectangle.
• Hence each 5×5 grid always has either a black or a white rectangle; quod erat demonstrandum.

Puzzle of the week

Consider N×N grids of black-or-white stones (in any combination), like these for the case of N = 4:

We say the grid contains a rectangle if there is a pair of distinct rows (a and b) and a pair of distinct columns (x and y) which combine (ax, bx, ay, by) to give four stones of the same colour.

The grid on the left has several rectangles, of which three are shown. The two grids on the right are rectangle-free.

Question: does there exist a 5×5 rectangle-free grid?

(Puzzle by Laurent Rosaz, from the EATCS Bulletin, #97, Feb 2009.)

The NZ Army Haka

Maori Battalion haka in Egypt, 1941

The NZ Army haka is less well-known than the haka used by rugby players. It runs in part:

... Tatangi nei ngā matā me te whewhio
Paku korara, ka mate, ka mate, auē taukiri e
Paku tāporepore auē, ka mau te wehi! ...
Moana Ngārimu ngā ū te wikitoria nui ...

... The bullets and ricochets sing
Bombs explode, ‘tis death, ‘tis death, alas the grief
Artillery rounds cartwheeling, oh, the fear! ...
Moana Ngārimu is awarded the Victoria Cross ...

This haka commemorates an action of World War II (and, by implication, all fallen soldiers): “On 26/27 March 1943 during the action at Tobaga Gap, Tunisia, Second Lieutenant Ngarimu, who was commanding a platoon in a vital hill feature strongly held by the enemy, led his men straight up the face of the hill and was first on the crest. He personally destroyed two machine-gun posts and owing to his inspired leadership several counter-attacks were beaten off during the night. He was twice wounded but refused to leave his men. By morning when only two of his platoon remained unwounded, reinforcements arrived. When the next counter-attack was launched, however, Second Lieutenant Ngarimu was killed.”

Winter Rose: a book review

Winter Rose (1996) by Patricia A. McKillip

I recently re-read this fairy tale for older readers by my favourite fantasy writer (after Tolkien), Patricia A. McKillip.

Once upon a time, there was a house by a Wood. Once upon a time, there was a winter – cold beyond mere ice. Once upon a time, there was a stranger who did not seem entirely human. Once upon a time, there were two sisters – Laurel and Rois. Once upon a time, there was an author who did with words what the Impressionists did with light:

“The well was one of the wood’s secrets: a deep spring as clear as light, hidden under an overhang of dark stones down which the briar roses fall, white as snow, red as blood, all summer long.”

Winter Rose by Patricia A. McKillip: 4 stars

Danger, Will Robinson!

The group of French mathematicians called Nicolas Bourbaki (active from 1935 until the early 1980s, and including among others André Weil, brother to Simone) has given us words like injective, surjective, and bijective. Another innovation due to them is the caution symbol (☡), which they used as a note in the margin for tricky passages:

Certains passages sont destinés à prémunir le lecteur contre des erreurs graves, où il risquerait de tomber; ces passages sont signalés en marge par le signe ☡ («tournant dangereux»).

[Some passages are designed to forewarn the reader against serious errors, where he risks falling; these passages are signposted in the margin with the sign ☡ (“dangerous bend”).]

The notation derives from warning signs on roads, like the following, which appears to mean “beware of snapped cables and falling cable cars”:

Photo by C. G. P. Grey, 2006

The book of Proverbs has a similar function. It marks tricky situations, where one risks falling:

Prov 23:1–2: When you sit down to eat with a ruler, observe carefully what is before you, and put a knife to your throat if you are given to appetite.

Photo by Phillip Capper, 2008

Prov 6:27: Can a man carry fire next to his chest and his clothes not be burned?

Photo by Peter Schäfermeier, 2005

Prov 6:10–11: A little sleep, a little slumber, a little folding of the hands to rest, and poverty will come upon you like a robber, and want like an armed man.

“Happy as a clam”

The phrase “happy as a clam” confuses people:

In fact, it’s an abbreviation of “happy as a clam at high-water” – a “common simile in New England” according to John Russell Bartlett’s Dictionary of Americanisms (1859).

Clams at high-water are safe, of course. Whereas at low tide:

O Little Town of Bethlehem

Bethlehem, 1898

“O little town of Bethlehem, how still we see thee lie!
Above thy deep and dreamless sleep the silent stars go by.
Yet in thy dark streets shineth the everlasting Light;
The hopes and fears of all the years are met in thee tonight.”

Bethlehem has been a largely Christian town from around 135 AD (when, after the Bar Kokhba revolt, the Romans expelled the Jewish inhabitants) until relatively recently.

Church of the Nativity, Bethlehem (photo by Wayne McLean, 2005)

Origen wrote around 200 AD that “in conformity with the narrative in the Gospel regarding His birth, there is shown at Bethlehem the cave where He was born, and the manger in the cave where He was wrapped in swaddling-clothes. And this sight is greatly talked of in surrounding places, even among the enemies of the faith, it being said that in this cave was born that Jesus who is worshipped and reverenced by the Christians.”

St Helena began the construction of a basilica over this cave in 327. The basilica was destroyed in the Samaritan Revolt of 529, but rebuilt. It was spared in the 614 Persian invasion, allegedly because of the mosaics showing Persian magi. Control of Bethlehem changed hands again in 637 (Muslim), 1099 (Christian), 1187 (Muslim), 1229 (Christian), and 1244 (Muslim), but the church remained (today, Bethlehem also has Lutheran and other churches).

Bethlehem in 1880

In 1867, when it was under Ottoman control, Bethlehem was described by Scottish Quaker missionary Ellen Clare Miller-Pearson (travelling with American Quakers Eli and Sybil Jones) as follows:

“Bethlehem has now 3,000 or 4,000 inhabitants, of whom only about 100 are Protestants and 300 Moslems, the remainder belonging to the Latin and Greek Churches, with a few Armenians.”

Bethlehem in 2006 (photo by “Soman”)

Originally intended to be part of the Jerusalem enclave, Bethlehem was annexed by Jordan in 1948, and an influx of refugees saw the town become majority-Muslim. Since 1995, urban areas of Bethlehem have been controlled by the Palestinian National Authority (except for the famous siege). Continuing conflict has resulted in considerable harm to both the buildings and the people, and a steady decline of the Christian population.

“O holy Child of Bethlehem, descend to us, we pray;
Cast out our sin, and enter in, be born in us today.
We hear the Christmas angels the great glad tidings tell;
O come to us, abide with us, our Lord Emmanuel!”

The Sewing Machine

Edward Hopper, Girl at Sewing Machine, 1921

In my previous post, I touched on the technology of sewing machines, one of a number of significant advances in textile technology since the replacement of the spindle by the spinning wheel in the High Middle Ages made spinning a little less tedious.

Thomas Eakins, Spinning, 1881

The sewing machine is the result of a series of inventions made between 1790 and Singer’s 1851 patent (with continued development since then). However, the sewing machine doesn’t stand alone: it relies on several other inventions. Thread of adequate consistency required the spinning jenny (1764), for example, while the sewing machine itself required case-hardened steel, and gears of at least moderate precision. And, of course, the machines had to be mass-produced in order to bring the price down to that of a cow – which means that east of the “Little House on the Prairie” there inevitably stand some “dark Satanic Mills.”

“Pa came hurrying back. He lifted the blanket away, and there stood a shining new sewing machine ... ‘I had to sell a cow anyway, Caroline; there wouldn’t be room in the stable next winter unless I did.’ ” – Laura Ingalls Wilder, These Happy Golden Years

Singer sewing machine

Technology

After reading The Dream of Perpetual Motion (which I’ve just reviewed), I’ve been thinking a bit more about technology. Technology, in its various forms, has been with us for a long time:

Much has been written about the sins of those who produce and use technology inappropriately – the sins of Isengard:

But there are also sins of technology consumption. One positive approach to technology is participatory acceptance, which includes self-manufacture of easier items, and the repair of more sophisticated ones. This relies, of course, on an engagement of both heart and mind with the technology in question, an engagement which can guide that technology in positive directions. Most cultures have a history of participatory acceptance of older technologies, although the level of participation is fading in many cases.

Edward Hopper, Girl at Sewing Machine, 1921; and Erik Hersman, roadside bicycle repair, Africa, 2007

Another positive approach is grateful acceptance – a positive, but more passive, attitude often reserved for music and literature.

What is dangerous is resentful acceptance, where people accept the benefits of a technology, while at the same time hating it and its creators. The Amish at times come close to this, since their culture is epiphytic on the surrounding steel-producing culture, which they shun. At the same time, they are wise to ban technologies which they cannot fully embrace, because they understand the social and spiritual harm which that produces. Back in the 1970s, Robert M. Pirsig famously explored the problem of resentful acceptance in the wider culture.