Happy Holidays

All of them -- Christmas Eve, Christmas, St. Stephen's, St. John's, and Holy Family. I'm off to see family. I'll be back around the New Year with some blogging on James Boswell's Christmas in 1764. December of that year saw Boswell on the Grand Tour, visiting early in the month with Rousseau and spending the Christmas holidays with Voltaire. In the meantime, God bless.

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.

For Christ is born of Mary, and gathered all above,
While mortals sleep, the angels keep their watch of wondering love.
O morning stars together, proclaim the holy birth,
And praises sing to God the King, and peace to men on earth!

How silently, how silently, the wondrous Gift is giv’n;
So God imparts to human hearts the blessings of His Heav’n.
No ear may hear His coming, but in this world of sin,
Where meek souls will receive Him still, the dear Christ enters in.

Where children pure and happy pray to the blessèd Child,
Where misery cries out to Thee, Son of the mother mild;
Where charity stands watching and faith holds wide the door,
The dark night wakes, the glory breaks, and Christmas comes once more.

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!

--Phillips Brooks (1867)

Whitehead on Learning Mathematics

The study of mathematics is apt to commence in disappointment. The important applications of the science, the theoretical interest of its ideas, and the logical rigour of its methods, all generate the expectation of a speedy introduction to processes of interest. We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it--''Tis here, 'tis there, 'tis gone'--and what we do see does not suggest the same excuse for elusiveness as sufficed for the ghost, that it is too noble for our gross methods. 'A show of violence,' if ever excusable, may surely be 'offered' to the trivial results which occupy the pages of some elementary mathematical treatises.

The reason for this failure of the science to live up to its reputation is that its fundamental ideas are not explained to the student disentangled from the technical procedure which has been invented to facilitate their exact presentation in particular instances. Acordingly, the unfortunate learner finds himself struggling to acquire a knowledge of a mass of details which are not illuminated by any general conception. Without a doubt, technical facility is a first requisite for valuable mental activity: we shall fail to appreciate the rhythm of Milton, or the passion of Shelley, so long as we find it necessary to spell the words and are not quite certain of the forms of the individual letters. In this sense there is no royal road to learning. But it is equally an error to confine attention to technical processes, excluding consideration of general ideas. Here lies the road to pedantry.

[Alfred North Whitehead, An Introduction to Mathematics. Oxford University Press (New York: 1948) pp. 1-2.]

'Get a Life' Meme

I saw this at Evolving Thoughts; it's a list of 219 movies, with the suggestion that if you've seen more than 85 you have no life. My count is 119, and even that is generous because I only counted movies I've seen all the way through; for several of those not marked I've seen most of the movie, just not part of it (usually the beginning or the end, of course). I had originally put my number at 114 but going back over the list I realized that there were several I had seen but simply forgotten.

( ) Rocky Horror Picture Show
(x) Grease
(x) Pirates of the Caribbean
(x) Pirates of the Caribbean 2: Dead Man's Chest
( ) Boondock Saints
(x) Fight Club
(x) Starsky and Hutch
(x) Neverending Story
(x) Blazing Saddles
(x) Universal Soldier
(x) Lemony Snicket: A Series Of Unfortunate Events
(x) Along Came Polly
(x) Joe Dirt
( ) KING KONG which version?
( ) A Cinderella Story
(x) The Terminal
( ) The Lizzie McGuire Movie
( ) Passport to Paris
(x) Dumb & Dumber
( ) Dumber & Dumberer
(x) Final Destination
(x) Final Destination 2
( ) Final Destination 3
(x) Halloween
(x) The Ring
(x) The Ring 2
( ) Surviving X-MAS
(x) Flubber Orignial version only
( ) Harold & Kumar Go To White Castle
(x) Practical Magic
(x) Chicago
( ) Ghost Ship
( ) From Hell
(x) Hellboy
( ) Secret Window
(x) I Am Sam
(x) The Whole Nine Yards
(x) The Whole Ten Yards
(x) The Day After Tomorrow
( ) Child's Play
( ) Seed of Chucky
( ) Bride of Chucky
(x) Ten Things I Hate About You
( ) Just Married
( ) Gothika
(x) Nightmare on Elm Street
(x) Sixteen Candles
(x) Remember the Titans
(x) Coach Carter
(x) The Grudge
( ) The Grudge 2
(x) The Mask
( ) Son Of The Mask
(x) Bad Boys
(x) Bad Boys 2
( ) Joy Ride
( ) Lucky Number Sleven
(x) Ocean's Eleven
(x) Ocean's Twelve
(x) Bourne Identity
(x) Bourne Supremacy
( ) Lone Star
(x) Bedazzled both versions
(x) Predator I
(x) Predator II
( ) The Fog
(x) Ice Age
(x) Ice Age 2: The Meltdown
( ) Curious George
(x) Independence Day
( ) Cujo
( ) A Bronx Tale
( ) Darkness Falls
( ) Christine
(x) ET
( ) Children of the Corn
( ) My Boss's Daughter
( ) Maid in Manhattan
(x) War of the Worlds
(x) Rush Hour
(x) Rush Hour 2
( ) Best Bet
(x) How to Lose a Guy in 10 Days
(x) She's All That
(x) Calendar Girls
(x) Sideways
(x) Mars Attacks
(x) Event Horizon
( ) Ever After
(x) Wizard of Oz
(x) Forrest Gump
(x) Big Trouble in Little China
(x) The Terminator
(x) The Terminator 2
(x) The Terminator 3
(x) x-Men
(x) x2
(x) x-3
(x) Spider-Man
(x) Spider-Man 2
( ) Sky High
(x) Jeepers Creepers
( ) Jeepers Creepers 2
(x) Catch Me If You Can
(x) The Little Mermaid
(x) Freaky Friday
(x) Reign of Fire
(x) The Skulls
(x) Cruel Intentions
( ) Cruel Intentions 2
(x) The Hot Chick
(x) Shrek
(x) Shrek 2
( ) Swimfan
(x) Miracle on 34th street
(x) Old School
(x) The Notebook
(x) K-Pax
( ) Kippendorf's Tribe
(x) A Walk to Remember
(x) Ice Castles
( ) Boogeyman
(x) The 40-year-old-virgin
(x) Lord of the Rings Fellowship of the Ring
(x) Lord of the Rings The Two Towers
(x) Lord of the Rings Return Of the King
(x) Indiana Jones and the Raiders of the Lost Ark
(x) Indiana Jones and the Temple of Doom
(x) Indiana Jones and the Last Crusade
( ) Baseketball
( ) Hostel
( ) Waiting for Guffman
( ) House of 1000 Corpses
( ) Devils Rejects
(x) Elf
(x) Highlander
( ) Mothman Prophecies
( ) American History
( ) Three
( ) The Jacket
( ) Kung Fu Hustle
( ) Shaolin Soccer
( ) Night Watch
( ) Monsters Inc.
(x) Titanic
( ) Monty Python and the Holy Grail
( ) Shaun Of the Dead
( ) Willard
( ) High Tension
( ) Club Dread
(x) Hulk
(x) Dawn Of the Dead
(x) Hook
(x) Chronicle Of Narnia The Lion the Witch and the Wardrobe
( ) 28 days later
( ) Orgazmo
( ) Phantasm
(x) Waterworld
(x) Kill Bill vol 1
(x) Kill Bill vol 2
(x) Mortal Kombat
( ) Wolf Creek
( ) Kingdom of Heaven
( ) The Hills Have Eyes
( ) I Spit on Your Grave aka the Day of the Woman
( ) The Last House on the Left
( ) Re-Animator
( ) Army of Darkness
(x) Star Wars Ep. I The Phantom Menace
(x) Star Wars Ep. II Attack of the Clones
(x) Star Wars Ep. III Revenge of the Sith
(x) Star Wars Ep. IV A New Hope
(x) Star Wars Ep. V The Empire Strikes Back
(x) Star Wars Ep. VI Return of the Jedi
( ) Ewoks Caravan Of Courage
( ) Ewoks The Battle For Endor
(x) The Matrix
(x) The Matrix Reloaded
(x) The Matrix Revolutions
( ) Animatri
( ) Evil Dead
( ) Evil Dead 2
( ) Team America: World Police
(x) Red Dragon
(x) Silence of the Lambs
(x) Hannibal
( ) Battle Royale
( ) Battle Royale 2
( ) Brazil
(x) Contact
( ) Cube
( ) Dr. Strangelove
( ) Enlightenment Guaranteed
( ) Four Rooms
( ) Memento
( ) Pi
( ) Requiem for a Dream
(x) Pulp Fiction
( ) Reservoir Dogs
( ) Run Lola Run
( ) Russian Ark
(x) Serenity
(x) Sin City
(x) Snatch
( ) Spider
( ) The Sixth Sense
(x) The Village
(x) Waking Life
( ) Zatoichi
( ) Ikiru
( ) The Seven Samurai
( ) Brick
( ) Akira

The Good Princess

By the example of my lord St Nicholas she will secretly send gifts to these good people by her almoner, without even the poor themselves knowing who is sending them the alms....She will speak to the poor and to the sick; she will visit their bedsides and will comfort them sweetly, making her excellent and welcome gift of alms. For poor people are much more comforted and accept with more pleasure the kind word, the visit, and the comfort of a great and powerful person than of someone else. The reason fo rthis is that they think that all this world scorns them, and when a powerful person deigns to visit them or to comfort them they feel that they have recovered some honour, which is naturally a thing that everyone desires.

Christine de Pisan, The Treasure of the City of Ladies, or the Book of the Three Virtues. Penguin (New York: 1985) 53.

Antiphons for Advent

We are approaching Christmas, of course, so here's an article on the O Antiphons. (This webpage is also a good source.) The Advent Antiphons, which date back at least to the ninth century, are probably best known from the fact that in the twelfth century they were reworked by an anonymous source as a French hymn, which was put into Latin at some point between then and the eighteenth century, which Latin version in turn was translated in the nineteenth century by Neale into the lyrics "Draw Nigh, Draw Nigh, Emmanuel," which time and much singing has altered to the following (with some variations):

O Come, O Come Emmanuel

O come, O come, Emmanuel,
And ransom captive Israel,
That mourns in lonely exile here
Until the Son of God appear.
Rejoice! Rejoice! Emmanuel
Shall come to you, O Israel!

O Come, our Wisdom from on high,
Who ordered all things mightily;
To us the path of knowledge show,
and teach us in her ways to go.
Rejoice! Rejoice! Emmanuel
Shall come to you, O Israel!

O come, O come, our Lord of might,
Who to your tribes on Sinai's height
In ancient times gave holy law,
In cloud and majesty and awe.
Rejoice! Rejoice! Emmanuel
Shall come to you, O Israel!

O come, O Rod of Jesse's stem,
From ev'ry foe deliver them
That trust your mighty pow'r to save;
Bring them in vict'ry through the grave.
Rejoice! Rejoice! Emmanuel
Shall come to you, O Israel!

O come, O Key of David, come,
And open wide our heav'nly home;
Make safe the way that leads on high,
And close the path to misery.
Rejoice! Rejoice! Emmanuel
Shall come to you, O Israel!

O Come, our Dayspring from on high,
And cheer us by your drawing nigh,
Disperse the gloomy clouds of night,
And death's dark shadows put to flight.
Rejoice! Rejoice! Emmanuel
Shall come to you, O Israel!

O Come, Desire of nations, bind
In one the hearts of all mankind;
Oh, bid our sad divisions cease,
And be yourself our King of Peace.
Rejoice! Rejoice! Emmanuel
Shall come to you, O Israel!

The usual music to which it is sung appears to be Gregorian chant adapted to French plain song adapted to nineteenth century hymnody (often adapted to twentieth century tastes). From generation to generation, from nation to nation, from language to language, from culture to culture, people young and old, rich and poor, have carried forward the Advent message, adapted in words and music but never changed in point: Christ our Lord comes, the Star who brings light to those who live in the darkness and shadow of death.

Benevolence Is the Greater Part of Justice

Democracy, it seems, is the rule of the merciless. Thomas Kostigen argues that we should do away with Presidential pardon:

Why, oh why, should one individual be able to gain favor (and freedom) over another in a democratic system such as ours? No. The pardon system should be done away with, and along with it the ethical controversy that it portends.

Yes, why, oh why, don't we punish individuals as if they were all exactly the same! Oh, that's right, because sometimes, as James Wilson puts it, people "may be unfortunate in a higher degree, than that, in which they are criminal." And because sometimes, due to particular circumstances of the case, we can make a reasonable judgment that we would all benefit more if the person involved were given a second chance. And sometimes, perhaps just a little, because we need some clear symbol that laws are not perfect, that courts are not flawless, that mistakes are not unforgivable, and that compassion is essential to the health of justice.

P.S. Ruckman, Jr. notes that Kostigen's argument is based only on a few cases that make it into the papers:

And that is too bad. Kostigen should consider writing down the names of the 179 individuals who have received pardons and commutations from President Bush. Each name should be placed on a separate card. Kostigen should then place the cards in a bag and draw names randomly, until he comes up with one that he knows.

And President Bush is notoriously stingy in his the pardon power (Ruckman has a good post on that, too); a more reasonable use of the pardoning power would increase the names on the list. We should not just casually dismiss something that reaches into so many lives, so many families, so many communities.

Tom's Algebra of Logic and James's Boundary Calculus

I have been toying around with ways to represent propositional-logic forms of Carroll's literal diagrams in a notation that could potentially allow for clarification of complicated instances (many terms) and yet would still preserve something of the diagrammatic character of the diagrams. And the most promising was a version of notation borrowed from Jeffrey James's version of boundary mathematics (PDF). Such a notation has three key features:

instance ()
abstract []
inverse <>

Out of these you can build number systems. But you can also do any sort of Boolean algebra with them, which means you can do standard propositional logic. So, for instance, this can be the disjunction (p v q):

(pq)

This would then be conjunction:

([p][q])

To negate anything, we take its inverse, which, as noted above, is done with angle brackets:

<p>

Then rules for doing things with these brackets make it possible to handle all the transformations of standard propositional logic.

In toying with this a bit, I realized that it seemed a bit familiar; and indeed it was. It's closely related to Tom's algebra of logic. Here are Tom's types applied to propositional logic with their boundary counterparts:

[+a+b] : (ab)
[+a-b] : (a<b>)
[-a+b] : (<a>b)
[-a-b] : (<a><b>)
(+a+b) : ([a][b])
(+a-b) : ([a][<b>])
(-a+b) : ([<a>][b])
(-a-b) : ([<a>][<b>])

The brackets are reversed, but of course that's arbitrary. Of course, one would expect similarities in notations; but it never would have occurred to me offhand that Tom's algebra of logic was in the same family as boundary mathematics and so it was a bit of a surprise. (Surprise, I find, is almost the essence of logic.) But it means that one should be able to adapt boundary mathematics to do categorical syllogisms; and, vice versa, Tom's algebra of logic to do a hefty amount of mathematics. A smarter person wouldn't have been surprised by that, either; but I am very slow about these things. Something for me to think about, in both directions.