A Mathematician, a Catholic - and a Witch

Recently I have been posting on the ACS blogg about GKC and mathematics. If today were Thursday, I might have posted the following discussion over there - as GKC has very interesting things to say about Catholicism and mathematics, and about witches. But the Witch I am referring to is not the Hogwarts type of witch, nor the "double-double" kind, nor the evil and dark kind. It is not even a human being! Ah, my title has mislead you? I will show you a picture of this Witch:


[image from the CRC Handbook of Standard Mathematical Tables]

This curve is called "witch" by transliteration from an Italian term versiera (which means the above curve). Fermat had written an equation for it in 1665, but the name "Agnesi" has come to be associated with it.

Who was this Agnesi?

According to the Dictionary of Scientific Biography, Maria Gaetana Agnesi (1718-1799) is "the first woman in the Western world who can accurately be called a mathematician." She was the oldest of 21 children; her father was a professor of mathematics at the University of Bologna, and encouraged her interest in scientific matters. She was brilliant at languages: "By age eleven, she was thoroughly familiar with Greek, German, Spanish, and Hebrew." In 1748, she wrote a massive work (over 1000 pages) on teaching mathematics to the young - it was in Italian but "won acclaim in academic circles all over Europe" and was translated into English.

It was she who gave this definition for the above "witch" curve:

If C is a circle of diameter a with center at (0, 1/2 a), and if the variable line OA through the origin O intersects the line y = a at point A and the circle at point B, then the versiera is the locus of point P, which is the intersection of lines through A and B parallel to the Y axis and X axis, respectively. The curve, generated as the line OA turns (Latin vertere, hence the name versiera), is bell-shaped with the X axis as asymptote.
[Ibid.; cf. the CRC reference. This explanation matches the above CRC diagram. The diagram shows the equation given in the usual cubic form, and also as a parametric in f by which it is easier to plot if you're all excited to make your own...]

But Maria was not simply a brilliant writer, linguist, and mathematician. She was also a very serious Catholic:

The recognition of greatest significance to Agnesi was provided in two letters from Pope Benedict XIV. The first, dated June 1749, a congratulatory note on the occasion of the publication of her book, was accompanied by a gold medal and a gold wreath adorned with precious stones. In his second letter, dated September 1750, the pope appointed her to the chair of mathematics and natural philosophy at Bologna. [Ibid.]

After her father's death in 1752, she retired from all scientific work, and devoted herself to religious work and study, making great material sacrifices to help the poor in her parish. Finally, a long-held desire for the religious life was satisfied: "after acting for some years as the director of the Hospice Trivalzio of the Blue Nuns in Milan, she joined the order and died a member of it, in her 81st year." [The Catholic Encyclopedia, 1907 ed.]

What an exemplary woman! I do not know if her Cause has been started, but given tomorrow's feast, it is not unreasonable to request her intercession for us: dear Maria of the witch-that-turns, intercede with our Lord for linguists, for mathematicians, for the sick, and for the young who are learning mathematics!

Located In Kenya!

It appears that The Map Guys have found a place for Ria's Chocolate Cake Farm.

So while they are making their plans, hopefully enjoying some non-native chocolate cake until their crops are ready, I will contribute a poem:

Kenya, Home of the Chocolate Cake Farm

Kenya, the home of the Chocolate Cake Farm -
May this dear country come never to harm!

For here we can grow in the warmth of the sun
The sugar and chocolate makes cakes such fun.

We grow on a fertile plain wheat for our bread,
Finely ground for our cake as the cake-cookbook said;

And nearby in a jungle grow orchids so sweet
Which give us vanilla for the cakes that we eat.

In a barn on our farm we have cows for their milk
We churn some for butter, far smoother than silk.

We also keep chickens for eggs that they lay
Their rooster awakens us, crowing each day.

The soda for baking we get from the ground
The salt at the seashore is easily found.

Our house has our oven, our sink and our table,
And all the utensils which baking enable.

So armed with our recipe, we blend mix and bake
But there's still one thing missing - so what's our mistake?

Our chocolate cake's ready, so large and so sweet -
Let's call some friends over - C'mon gang, let's eat!

Kenya, the home of the Chocolate Cake Farm -
May this dear country come never to harm!


-- Dr. Thursday Oct. 29, 2006
(details courtesy of Ria, Gus, and their assistants)

Laughing at Latin

Just a quick note on something that made me laugh. A few days back I posted about the musical notes and how "C" was once called ut because of an ancient hymn to St. John the Baptist.

You may know that ut is a Latin conjunction meaning "that" or "as" or "in order that" and several other things. Well, I happened to remember that there are other Latin conjunctions which are very similar:

at = "but"
et = "and"
ut = "that"

then I remembered that the irregular verb eo, ire = "to go" has:

it = "he, she, it goes"

But no (alas) there is no Latin word ot.

There is, however, in English. Oh, yes. On a summer day in London one might hear: "Blimey, it's 'ot today." Hee hee.

Request for an Adventure

Our friend Enbrethiliel asked for a reference about Cervantes and his very hobbit-like attitude to adventure... hee hee. I don't really recall posting on this, but it is good in itself, and somehow fits in well with Ria's "Chocolate Cake Farm" idea. So here it is:

The signs of the resurrection of Spain, of which I think there are many to be seen lately, have turned my thoughts to certain subtleties in the tradition of that land. They are things so subtle that they always appear to be simple. One of them is the tradition of chivalry and the double attitude towards it which we connect with the name of Don Quixote. There is no more fantastic paradox in all history than the life and work of Cervantes. He is generally recognised as having written a book to show that romantic adventures are all rubbish and do not really happen in this world. As a matter of fact, the one man in this world to whom romantic adventures were incessantly happening was the author of "Don Quixote." He covered himself with glory and lost his right hand at the most romantic battle in history - when the Crescent and the Cross met in the blue Mediterranean by the Isles of Greece, [the battle of Lepanto] trailing all their pageants of painted and gilded ships with emblazoned sails. He was just about to receive public recognition from the victor, Don John of Austria, when he was kidnapped by pirates. He organised a series of escapes, each like the ideal adventure of a schoolboy; he organised supplies and comforts for his fellow-prisoners with the laborious altruism of a saint. As men go, he was really a pretty perfect pattern of the knight of chivalry; eventually he escaped and returned home to write a book showing that chivalry was impossible. At least, that is what three rationalistic centuries have taken it as showing. But I think the time has come to dig a little deeper in that stratified irony, and show the other side of Cervantes and chivalry.
[GKC ILN Oct. 18, 1924 CW33:425]

To which I cannot help adding:

"We don't like adventures around here. Nasty impractical things. Make you late for dinner," said Bilbo Baggins to the wizard.
[JRR Tolkien, The Hobbit quoted loosely from memory.]

Which of course leads directly back to GKC, and this amazing cross-reference:

It is the humble man who does the big things. It is the humble man who does the bold things. [cf Lk 1:52] It is the humble man who has the sensational sights vouchsafed to him, and this for three obvious reasons: first, that he strains his eyes more than any other men to see them; second, that he is more overwhelmed and uplifted with them when they come; third, that he records them more exactly and sincerely and with less adulteration from his more commonplace and more conceited everyday self. Adventures are to those to whom they are most unexpected - that is, most romantic. Adventures are to the shy: in this sense adventures are to the unadventurous.
[GKC, Heretics CW1:74]

Wow, if I wasn't busy with work, I would be torn between wanting to bake a chocolate cake or write an adventure story! (Probably I'll have to settle for eating cake and reading GKC tonight.)

A Farm for Chocolate Cakes

Over at Liber Parma "Ria" proposes an interesting puzzle:

Where on earth might a farm be situated so as to be able to have available all the ingredients to make a chocolate cake?

This gives rise to a large number of interesting questions about the recipe, the required ingredients and tools, cimate, growing conditions, and so on.

I have already commented on it on "Ria's" blogg; but I have a little more to add about the puzzle in itself.

This puzzle is a wonderful thing to ponder. It reminds me of Robinson Crusoe, or the Swiss Family Robinson, or the Danny Dunn story about living on a desert island.

All Chestertonians know GKC's answer to the question "What book would you want on a desert island?" is "Thomas's Guide to Practical Shipbuilding". But not everyone remembers GKC's discussion in Orthodoxy:

Crusoe is a man on a small rock with a few comforts just snatched from the sea: the best thing in the book is simply the list of things saved from the wreck. The greatest of poems is an inventory. Every kitchen tool becomes ideal because Crusoe might have dropped it in the sea. It is a good exercise, in empty or ugly hours of the day, to look at anything, the coal-scuttle or the bookcase, and think how happy one could be to have brought it out of the sinking ship on to the solitary island.
[GKC, Orthodoxy CW1:267]

It deserves serious consideration not only for itself, but for what it implies (see his next paragraph for details!)

GKC also has a great story in CW14 called "My Uncle the Professor" in which he tells the story (from a nine-year-old viewpoint) of how his "uncle" and he went to live in a tree. You will really enjoy it.

Finally, I will mention a famous science fiction story called Spacehounds of IPC by the exceedingly famous E. E. "Doc" Smith in which the hero has to build a high-tech device almost "from scratch".

Sean and the Professor: 1. How They Met

Sean and the Professor

Chapter 1: How they met

Dusty from his winning slide, carrying his bat and glove, twelve-year-old Sean Smith made a selection from the cold drinks, and sat it down on the checkout counter.
"That's ninety-five cents, please."
Sean pulled a dollar coin from his pocket, received his nickel change, nodded to the clerk, and popped open his soda. He went over to check the sports magazines - the new issue wasn't out yet. Then he heard the clerk tell the next customer, "That's two-oh-five."
The customer sighed, then in a deep, rumbly voice, said, "Oh, I have no change with me..."
With the speed that had just got him the winning homer, Sean was at the check-out. "Here, mister," he said, handing the clerk his nickel.
"A-hem! Why, thanks, young man," came the deep voice. "Very kind."
Sean looked up at the man - tall, rather fat, unkempt gray hair, worn brown suit over a white shirt and dark purple tie - nodding at him with a beaming smile and twinkling eyes.

"Your team win?" he asked as he followed Sean out the door.
"Yeah; 4-3. I got the winning homer."
"Great; good work. Then why so glum?"
Sean took a swig of his soda. "Homework. Our math teacher gave us a bunch of addition problems."
"Hmmph, addition!" The man chuckled. "You're probably in sixth grade, right?"
Sean nodded as the two walked along.
"What kind of addition - fractions, decimals...?"
"All kinds."
The man nodded. "Really? All kinds? Well, of course not all... A-hem! Say, if you're going up the hill, you can stop in my office, and I'll give you your nickel. It's just ahead, in Alsace Hall."
"You a professor at Howell?"
"Itinerant, son, itinerant. For a little while, anyway. I go where I'm needed."

Sean followed the professor up a few steps. At a large wooden door, almost hidden between holly bushes, the old man pulled out a big old-fashioned key, opened the door, and led the way into the basement of Alsace Hall.

"They put me down here this year," the professor explained as Sean walked with him down the hall, passing offices with students working quietly at desks. "Some don't like the basement, but I don't mind at all. Lots of students to talk to, learn from... and it's much easier to get to by this back door - and as long as I have a desk and room for my books, I'm quite happy." With a different key, he opened the door to his office, and Sean followed him inside.

"Addition, eh? Have a seat," the professor gestured. "I'm going to make some tea; would you like some?"
"No, thanks; I've plenty of soda left," Sean said, staring around the office. Most of the walls were lined with rows and rows of shelves stacked thick with books; there were four-drawer filing cabinets with papers sticking out; a big wooden desk with more books and papers, spotlighted by a lamp on a complex little derrick clamped to its side; a computer on its own separate desk; and in a corner under a cupboard, a little table with jars, bottles, canisters and cups.
The professor soon had a steaming cup of tea, and put a plate of cookies on the desk by Sean.
"Have a cookie. Cheap at $2.05 a package. Oh, and here's your nickel."
"Thanks," Sean put it in his pocket and took a cookie. "What do you teach here?"
The professor took a sip of tea. "A little of this, a little of that; right now I'm, er, doing some research - on how addition works."
Sean wrinkled his face. "What?"
"Yes, " the professor smiled, "that's why I thought it might be interesting for you to come by. Of course, A-hem! if you have to get home..."
Sean checked his watch, fascinated by the office. There was a tall glass mirror-backed cabinet full of rocks, bottles and other strange things, and he wanted to ask what they were. "No, supper isn't till six today, and Mom knows I like to relax after a game. Sometimes I sit in the garden, up by the President's house..."
"Yes, very nice; I like that too."
"And besides I live just up the hill, in the Agnesi Apartments. Won't take me two minutes to walk home from here."
"Well, as long as you won't be late - because I have a tendency to talk on and on."
Sean took another cookie. "I'll keep an eye on the time."

The room was silent as the professor drank his tea. Sean kept glancing around at the books and glass cabinet. Almost without thinking he blurted out, "So many books... I have so many questions..."
"Yes," he nodded, "they have that effect on me, too. A-hem! But let us not get distracted right at the beginning of our journey." He finished his tea and put the cup on the corner table.

"Archimedes," the professor intoned.
"Yes master," came a voice. Sean's mouth dropped open.
"Where is my wand?"
"Your wand is in your desk drawer."
"Thanks."

Seeing the question on Sean's face, the professor smiled, shook his head, and murmured "I'll explain later." He opened his desk drawer and pulled out a clear red stick, just about a foot long. He waved it and the ceiling lights dimmed. "Ah, good," he nodded. "Let's start with the basics - integers."
"You mean whole numbers?"
"Even more basic - just the digits. Let's say," he flicked the wand, "Two. Plus. One. Equals." The numbers appeared in white, as if there was a ghostly blackboard hanging in front of the bookshelves.

2 + 1 =

"Three," answered Sean, bored. "First grade stuff."

2 + 1 = 3

"Are you sure?" asked the professor.
"Huh?"
"Why isn't it - twelve?" Another flick.

2 + 1 = 21

"That's twenty-one."
"That's because you're speaking English, and we read from left to right..."

1 + 2 = 12

"But that's not addition!"
"Sure it is. I started with a one, and added a two to it. One plus two is twelve."
"No, one followed by two is 12." Sean thought the professor was nuts. "If I have an apple and buy two more, I have three apples. Not twelve."

"Oh, I see," the professor said. "But I can't draw apples. I will just write little lines, though they will look like ones."

1 + 1 1 = 1 1 1

"That's right," Sean said, "but now it looks like one plus eleven is one hundred eleven."
"Yes, it does, doesn't it?" He waved the wand again and the lights went back to normal. "I told you I am studying addition. And all those things are just the beginning."
"So what do you mean by addition?" Sean asked.
"There are different meanings, and different - er - strengths - of addition. You've already seen two or three. And I will show you more." He waved the wand and the lights dimmed again.
"When you learn arithmetic, you first learn how to write the ten digits," and these appeared in a row,

+

0

1

2

3

4

5

6

7

8

9

"and then you learn numbers. Addition follows along. The first kind of addition in arithmetic is addition of the digits. That's so important you will have to have it as a basic skill, just like you learn how to stand - or you couldn't stand in right field." Sean nodded, all the while the professor had been waving the wand as if writing. Soon the following table was visible:

+	0	1	2	3	4	5	6	7	8	9
0	0	1	2	3	4	5	6	7	8	9
1	1	2	3	4	5	6	7	8	9	10
2	2	3	4	5	6	7	8	9	10	11
3	3	4	5	6	7	8	9	10	11	12
4	4	5	6	7	8	9	10	11	12	13
5	5	6	7	8	9	10	11	12	13	14
6	6	7	8	9	10	11	12	13	14	15
7	7	8	9	10	11	12	13	14	15	16
8	8	9	10	11	12	13	14	15	16	17
9	9	10	11	12	13	14	15	16	17	18

"So you learn this little table, but not as a table, but by memory - so when I say five plus eight, you can answer thirteen, quick as quick." As the professor said the numbers, the row with five at the left lighted in green, and the column with eight at the top lighted in red, making the 13 where they crossed light up in yellow.

+	0	1	2	3	4	5	6	7	8	9
0	0	1	2	3	4	5	6	7	8	9
1	1	2	3	4	5	6	7	8	9	10
2	2	3	4	5	6	7	8	9	10	11
3	3	4	5	6	7	8	9	10	11	12
4	4	5	6	7	8	9	10	11	12	13
5	5	6	7	8	9	10	11	12	13	14
6	6	7	8	9	10	11	12	13	14	15
7	7	8	9	10	11	12	13	14	15	16
8	8	9	10	11	12	13	14	15	16	17
9	9	10	11	12	13	14	15	16	17	18

"Wow, that's neat!" Sean said.
"Yes, isn't it? A friend of mine helped me with that."
"So - you need to know that, just like you learn your street address or telephone number - cold, by heart. No fingers!" he said, chuckling.
"OK, yeah, so I learned that long ago," Sean laughed. "How can there be other ways of adding?"
"I'll show you, but we're not yet finished with the first way, are we?"
"What do you mean?"
"That table is nice if all you wish to do is add digits." The table shifted over to the left of the room, leaving a large dark area. "But what if we have, say, 11 plus 11?"
11
+ 11
------
"Easy; twenty-two!"
"Yes... but how about 81 plus 91?" The numbers appeared, one over the other:
81
+ 91
------
"Uh... a hundred seventy two?"
"Right, but not as easy, right? How about this?"
478393
+ 48
--------
"Not as easy, no?"
"But professor, there's something wrong - we don't write it that way."
"You're right. I broke a rule - do you know what it is?"
"Uh - no. But the numbers have to be against the right side."
"Correct. After you learn to add digits, you learn the rules on adding numbers containing more than one digit. The first rule is to add like to like - units to units, tens to tens, and so on. Which means that the numbers must be aligned - each decimal point, even when it is not written, must be all in the same vertical column - so our problems must look like this:"

478393

+ 48

" And then?" the professor paused.
"We use the table..."
"Nine plus four..." As before, a row and a column lit up within the table. "Thirteen. Then three plus eight... eleven. So the answer would be..."

478393

+ 48

--------

1311

"One thousand three hundred eleven."
"No!" said Sean. "All wrong. The answer can't be between the numbers you're adding!"
"Very good. You have pointed out another rule. But I broke one as well, didn't I?"
"Yes. You have to start at the right."
"Correct, just as you always run counterclockwise, going to first base, then second..."
Sean smiled at the analogy. "But you also have to do the carry..."
"Also correct... that means we may have to add three digits at once! So that means..."

478393

+ 48

--------

141

"No, that's still not right. You have to bring the other numbers down," Sean stated.
"Why?" asked the professor. "Oh, you said the answer can't be smaller than either of the numbers being added. But I think there's a better explanation. We left out some zeros, because we don't really need them - but if I put them in, we'll be able to see the rule..."

478393

+ 000048

--------

"Oh! Sure," Sean said excitedly. "Now you just work from the right, column by column, each time using that table..."
"Ah, very good. You fielded that one nicely," smiled the professor. "So that gives us..."

478393

+ 000048

--------

478441

Sean nodded. "I know I could have done all that, but I didn't realize all the separate steps."
"Of course not," replied the professor. "You've just been doing it mechanically, because you were taught that way. Now you see, from just this one problem, you actually know two different kinds of addition already! The simple kind, where you add digits by knowing the table," and here he pointed to the glowing array of numbers hovering on the left side of the room. "You also know the series of steps - we professors call it an algorithm - to perform addition of two numbers of multiple digits."
"Wow. Sure, just like first I learned to catch and throw; later I learned field strategy."
"Yes, A-hem! So." He looked at his watch. "Well, it's getting close to six, so I'll just jot down the two ways we've looked at today:"

I. Addition of digits
a. can add any pair of numbers between 0 and 9
b. must use the "addition table":
c. pick row of first digit, column of second digit, and sum is at the intersection
d. have to learn the table "cold" (keep in memory)
e. Notice that the biggest result is 18!

II. Addition of two multiple digit integers
a. make sure numbers are aligned (units under units, tens under tens, etc) - push both to right side.
b. assume zeros on left if one number is shorter
c. working from the right, going column by column, add each pair of digits for that column. If that sum is more than 9, set down the units in that column, and write the carry above the next column to the left.
d. Notice that the sum can get bigger by no more than one digit, which has to be a one!
e. Also note that we can check that the answer is correct by seeing that it must be bigger than both of the numbers being added.

"Wow, that's a lot to know - but I learned all that in first and second grade," Sean said as he stood up.
"Yes, and that's just the beginning. There are ways of adding faster, and ways of adding different things... many other interesting things to talk about," the professor nodded, rising. As he put the wand down on his desk, the room's light returned to normal. "Maybe you'd like a copy?" He turned to the computer desk, picked up a piece of paper from the machine, and handed it to Sean.
"Thanks for a very interesting time, young man," the professor said with a smile. "Perhaps we can talk again another day."
"Sure, professor, thanks," Sean replied. "And it looks like some of my homework will be fun for once!"
Sean turned and went out of the office, down the hall, out the big wooden door and past the holly bushes out into the sun. He ran up the hill and reached his home just as the chimes of Old Main began to ring six o'clock.

(to be continued)

For Sarah as she is Confirmed..

Signed, Sealed, and Delivered

From a Holy Thursday morn
A fragrant oil bring;
Sound the organ, sound the horn,
The Spirit's anthem sing!

See the apostolic train
Mitered, with a crook,
In Peter the Key-keeper's, chain:
He opens now the book...

Name the Three Who shall inspire,
Call on Her who caused our joy,
Call on all from heaven's choir,
Their assistance to employ...

As the Dozen with their Queen
Once prayed for the Nine Days,
Fire True though now unseen
Consumes you with His rays.

Seven colors, seven stars,
Marked now with His gifts:
Bold in pondering the Scars
On the Tree which our hearts lifts...

May He hold you in His grace,
As onward now you go,
To run, at last to win your race:
Him face-to-face to know.

God bless you!
from Dr. Thursday
October 21, 2006

Notes from Brahms

A few days ago I happened to mention a GKC quote about musical notation, and promised a little more insight, both into GKC on music, and into musical notation. Both are deep, though not too deep to consider, at least in fragments. And while I proceed with today's work, hoping to get to my promised story about addition, I will entertain you with Brahms and GKC:

That all men are equal is a matter of abstract theory; that most men are equal is a matter of common fact. And as it is with altitude of stature, so it is with altitude in any one of the arts. At the one end there are a few who can do it perfectly; at the other end there are (I am told) a few who can only do it horribly or who cannot do it at all. Between the two stretch the interminable lines of that everlasting legion who can do it. There is such a thing as being able to read and write, being able to sow and reap, being able to play golf or read the Greek alphabet. And the difference between those who can do it and those who can't do it is much more absolute and abysmal (to a true philosopher) than any difference in the degree of value or vileness with which it is done. I know, as every man knows, the things I can, in this literal sense, do. I can swim: I cannot ride. I can play chess: I cannot play bridge. I can scull: I cannot punt. I can read Greek lettering: I cannot read Arabic lettering. In this strong, sound, fundamental sense, I can write literature; whereas I could not write music. Or, if you like to put it so, I can't play the piano, but I can play the fool. But the distinction is decisive. I can do it; and therefore I am a trader and not a thief. And I would sooner call myself a journalist than an author; because a journalist is a journeyman. He has a real working human trade; he even has a trade-union.
[GKC, Preface to A Miscellany of Men, emphasis added]

Now, to see some of the fantastically complex detail of real music, here is the first seven measures of the 3rd movement of Brahms' 4th symphony:



This is what a computer scientist might call "parallel programming" (I wonder whether it should be called CRCW or ERCW?) - but I will spare you the details. This is what the conductor uses as he conducts the orchestra. Here, you see sixteen lines of independent instructions (processes, in some systems). Actually, some lines are themselves executing parallel "threads", like the oboes... ah, but you need to know the German terms for the instruments. Here is the list of the required instruments:

Kleine Flöte = piccolo (little flute)
Große Flöte = flute (big flute)
2 Hoboen = two oboes
2 Klarinetten in C = two clarinets in C
2 Fagotte = 2 bassoons
Kontrafagott = contrabass bassoon
4 Hörner = 4 horns: 2 in F, 2 in C
2 Trompeten in C = 2 trumpets in C
Pauken in F-G-C = 3 timpani (kettledrums) tuned to F, G, C
Triangel = triangle
Violine I and II = first and second violins
Bratsche = violas
Violoncell = cellos
Kontrabaß = basses ("double bass")

Now, consider the "2 Hoboen" line, where we see two notes at the very first beat. An oboe can only play one note at a time, but Brahms wants two players, so one plays the top notes in the line, the other plays the bottom note. But if you study the score, you will see that there are other instruments also playing the same notes! Compare the upper notes in that line with the Violine I line, and its lower notes with the Violine II line - in the first measures they are the same - so the oboes are playing in unison with the violins.

There's more - much more excitement here - while these notes are moving downwards in pitch, the notes of the cellos and basses are moving upwards! Wow, high tech. And this is just a symphony, and just the first seven measures... If you really want some tech stuff, check out the counterpoint of a Bach fugue! And the classical artists are not the only ones who do this; even rock music does such things!

Well, I cannot give you an entire lesson in musical notation today, nor even begin to consider what implications this notation has for computing, or for more distant things like a university, or the Papacy - all essays for another day. But you might think a little, and hopefully I will have a story for you soon.

A belated thanksgiving - and additions.

I am chagrined to note that I did not inform my viewing audience of the successful completion of the doctoral defence of "Peter Terp" over at Catholicae Testudines. Thank God for this! May he do well in his future work, and truly be a doctor (teacher) in whatever work he does. And thanks for your prayers!

And while we're on the subject of prayer... there is a lot going on in the world, and around the e-cosmos, as you may already be aware. (For example, see here and here.) Besides these needs, I have a few very special intentions for friends ("R" and "J") who face difficult situations on Friday. Kindly remember them in your prayers; I will also remember your intentions at Holy Mass tomorrow.

And speaking of addition, perhaps I will have a new story soon, all about something really boring - addition! Just how many kinds do you think there are? Hee hee.

Musical notes, the Latin conjunction ut, and St. John the Baptist

I have, through much of my pi-over-two gigaseconds of life, had a great interest in music, along with many other curious interests in practical things like Catholicism, Computers, and Chesterton. Though I have dabbled with, er, let us say the "lower strings", in both bowed and electronic forms, I am hardly a performer, though I have played both Mozart and the Cars - not both on the same night, however.

How, then, you may wonder, does music fit into the hilarious collection of interests I have? Well, for a music guy, Chesterton might at first seem to be a real let-down, since he was rather tone-deaf, but he actually had some very important things to say about music. For example:

And the supreme and most practical value of poetry is this, that in poetry, as in music, a note is struck which expresses beyond the power of rational statement a condition of mind, and all actions arise from a condition of mind. Prose can only use a large and clumsy notation; it can only say that a man is miserable, or that a man is happy; it is forced to ignore that there are a million diverse kinds of misery and a million diverse kinds of happiness. Poetry alone, with the first throb of its metre, can tell us whether the depression is the kind of depression that drives a man to suicide, or the kind of depression that drives him to the Tivoli. Poetry can tell us whether the happiness is the happiness that sends a man to a restaurant, or the much richer and fuller happiness that sends him to church.
[GKC, Robert Browning]

And though music uses a large and clumsy notation (did you ever see a symphonic score?) music itself is not clumsy!

Another time I will quote more of GKC on music, but today I want to look at an interesting fact about the notation of music. Actually, this was something I promised to post about quite some time ago, and forgot all about it, until I had to look something up, and it jogged my memory. Specifically, I promised to explain the link between the names of the diatonic scale and St. John the Baptist.

Having said that, I am sure you will think I must be a musician - or at least a poet! to link such strange things together. But I did not link them. That was done by Guido d'Arezzo (990-1050), who introduced the names of six musical pitches based on the first syllables of the ancient hymn "Ut queant laxis" which is a prayer to St. John! This hymn was written by Paul the Deacon (720-799); St. John is considered a special patron of singers (see Luke 1 for why!)

Here is the hymn in the Gregorian notation:


[from Elson's Music Dictionary, 21]

And an English translation:

That thy servants [this choir] may be able to sing thy deeds of wonder with pleasant voices, remove, O holy John, the guilt of our sin-polluted lips.
[Britt, The Hymns of the Breviary and Missal, 256-7]

Yes, "doe - a deer, a female deer" used to be "ut - a conjunction, a Latin conjunction" but that was deemed hard to sing. Hee hee. Actually, according to Elson's Music Dictionary, "the change of ut to do is attributed to Buononcini about 1700." The seventh or "leading tone" was called "si" but to avoid confusion with "so" it was changed to "te".

Just to make things even more curious, the note ut was also called "gamma". So to go through all the notes from "gamma" to "ut" is to "run the gamut"...

Another time I will talk a little about the mathematics of the notes, and how the powers of two are important to musicians as well as computer scientists. Stay tuned...

Update

A bit more detail:

"The French changed ut to do which was more sonorous to them; ti is the European si formed from the first letters of the last two words Sancte Ioannes. To avoid confusion of the sol-fa si with the alphabetic "C" we [English] changed si to ti."

[Klarmann, Gregorian Chant 126]

Novena for J. K. Rowling

Nancy Brown has started a novena of prayer for the great author J. K. Rowling, who is presently writing the seventh and final episode of the Harry Potter story.

When there are so many evils, difficulties, and problems in our world, it may seem rather strange to think of praying for an author - especially one who is writing what most consider a "children's story" and "a fantasy". But in God's amazing world sometimes such simple things will have more profound effects on the future than any number of scientific discoveries or civic actions - or even the media.

And then there is the debate over the "goodness" of the Potter story - an evaluation which obviously cannot be completed until the story is complete:

"Are you working?"
"No, I was reading a detective story."
"Oh. Is it - is it good?"
"I don't know. It's reasonably well written. But I can't tell whether it's good until I've finished it."
"Oh."
[John Dickson Carr, The Dead Man's Knock, p. 2]

Alas, far too often I have been reading detective stories rather than working, though a good deal of my work is often spent in detecting the errors in my own work, or the work of others. GKC pointed out this remarkable link between the ultimate "progress" of an individual and the nature of a "story":

Another example might be found, not in the problem of evil, but in what is called the problem of progress. One of the ablest agnostics of the age once asked me whether I thought mankind grew better or grew worse or remained the same. He was confident that the alternative covered all possibilities. He did not see that it only covered patterns and not pictures; processes and not stories. I asked him whether he thought that Mr. Smith of Golder's Green got better or worse or remained exactly the same between the age of thirty and forty. It then seemed to dawn on him that it would rather depend on Mr. Smith; and how he chose to go on. It had never occurred to him that it might depend on how mankind chose to go on; and that its course was not a straight line or an upward or downward curve, but a track like that of a man across a valley, going where he liked and stopping where he chose, going into a church or falling drunk in a ditch. The life of man is a story; an adventure story; and in our vision the same is true even of the story of God.
[GKC, The Everlasting Man CW2:377-8]

And the same holds true for Mr. Harry Potter of Godric's Hollow - an adventure which hints of Tolkien, but also of GKC's Thursday and all the great detective stories of the past.

Hence it is a good thing that we pray for Joanne Rowling, for like Harriet Vane and Dorothy Sayers, "...she writes detective stories and in detective stories virtue is always triumphant. They're the purest literature we have." [D. L. Sayers, Strong Poison, p. 127]

Indeed! May virtue be triumphant for Harry and for J. K. Rowling!