Monday, December 22, 2008

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 bless├Ęd 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)

Sunday, December 21, 2008

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.]