Advent: Week 1 Day 5

Two dreams: Jacob's and Joseph's...



Upper left: Jacob's Ladder (or staircase?)

Jacob (grandson of Abraham) has a dream - somehow I recall it as happening at a point where he was to make (or had just made) a critical decision in his life... And now he sees the Great Passageway, where even angels fear to tread! Why do I say this? Hey, any angel in Heaven has GOT to have a bit of trepidation thinking about going DOWN, whew! (Yeah, I know, angels don't get scared, though GKC had a very interesting speculation about angels and fear; I will post it below.) As a computer scientist, I find this vision particularly significant, for here we see that the communications channel is bi-directional: messages may travel in both directions. (The word angel is just the English version of the Greek word for "messenger"!) Jacob doesn't realize it at the time, but he himself will form part of an even greater staircase, by which not angels, but GOD HIMSELF will one day come down to earth.

Lower right: Joseph's Dream

Jacob had a big family. Joseph was number 11 among 12 boys (yeah they had sisters too; I forget the names - hey, talk about trivia, try to list the brothers!) Jacob liked Joseph and got him a coat of many colours (which gets translated differently in some versions), and the favoritism bothered the other brothers, especially when Joseph had a dream about how the sun and moon and eleven stars knelt before him - and then went and told his brothers about it! It was really a prophecy, and you remember what happened afterwards... Joseph became Number Two reporting to the Pharaoh, and by his Divinely inspired foresight, was able to save a whole nation from starvation. Not only that, Joseph saved his family, too, and they DID come and bow before him! The Lord made him ruler of his house ("Pharaoh" is ancient Egyptian for "great house", an honorific title of their ruler) and gave him charge over all His possessions... And thus Joseph foreshadowed another Joseph, a distant nephew, who would have charge over the Everlasting Bread: the Bread given into his charge in Bethlehem, the House-of-Bread. (We'll see more on this later on.)

Please note: all my other blogging is suspended, in order that I may focus on each image, and you may also. Do you not love the word "focus"? You should. It is the Latin word meaning "hearth"... and this season ought to remind us of the Family. GKC explains: "The truth is that only men to whom the family is sacred will ever have a standard or a status by which to criticise the state. They alone can appeal to something more holy than the gods of the city; the gods of the hearth." [GKC, The Everlasting Man CW2:275] This quote is a strong indication of the influence on GKC of Pope Leo XIII's document Rerum Novarum, which I mentioned elsewhere in this blogg (in the post on Subsidiarity).

And that reminds me, I said I would tell you about GKC and the angels who were fearful. Oddly enough, it was the GOOD angels, back when they were getting ready for the heavenly battle (or are they still?) Here's the quote:

"...what, for instance, can be the basis of objecting to peacocks' feathers?"
Crundle was replying with a joyful roar that it was some infernal rubbish or other, when Gale, who had quickly slipped into a seat beside the man called Noel, interposed in a conversational manner.
"I fancy I can throw a little light on that. I believe I found a trace of it in looking at some old illuminated manuscripts of the ninth or tenth century. There is a very curious design, in a stiff Byzantine style, representing the two armies preparing for the war in heaven. But St. Michael is handing out spears to the good angels; while Satan is elaborately arming the rebel angels with peacocks' feathers."
Noel turned his hollow eyes sharply in the direction of the speaker. "That is really interesting," he said; "you mean it was all that old theological notion of the wickedness of pride?"
"Well, there's a whole peacock in the garden for you to pluck," cried Crundle in his boisterous manner, "if any of you want to go out fighting angels."
"They are not very effective weapons," said Gale gravely, "and I fancy that is what the artist in the Dark Ages must have meant. There seems to me to be something that rather hits the wrong imperialism in the right place, about the contrast in the weapon; the fact that the right side was arming for a real and therefore doubtful battle, while the wrong side was already, so to speak, handing out the palms of victory. You cannot fight anybody with the palms of victory."
[GKC, The Poet and the Lunatics, "The House of the Peacock"; emphasis added]

Advent: Week 1 Day 4

Here we have Abraham in two different scenes:



Abraham and the Covenant (upper left)

Here is depicted the mystical vision in which God instructs Abraham to take certain animals and sacrifice them, dividing them in two, then God sends His light (a firey lantern) between the divided parts. That ritual enacted the covenant as an ancient contract sealed in blood; it hints at a future covenant to be sealed in God's own blood: blood of Abraham's perfect descendant. "More numerous than the sands of the seashore, or than the stars of the sky, so shall your descendants be: I swear by Myself; they will be My people, and I will be their God."

Abraham and the Sacrifice of Isaac (lower right)

God orders Abraham to go to the Mount of Moriah and sacrifice Isaac, his only son. At the very last moment, God stops Abraham from the actual sacrifice... The young Isaac, carrying the wood up the hill suggests another Man carrying wood up the hill called Skull-Place (Calvary, or Golgotha). As they go up the hill Isaac asks, "Where is the lamb for the sacrifice?" and Abhraham answers "God will provide it." And surely, in God's good time, He does. Only that time, the sacrifice is not interrupted, despite the best efforts of the jeering Pharisees: "if you are the son of God, come down from that cross, and we will believe." But God was not fooled: He did sacrifice His only Son.

It is said that Mount Moriah is an ancient name for the hill of Jerusalem.

Advent: Week 1 Day 3

Today we have Noah's Ark, after the flood, with the rainbow. The Ark is a very important emblem, and we shall see it twice more on our Tree...



"And the dove vanished, and Noah and his family and all the animals of the ark went out. And Noah built an altar, and offered sacrifice.... And God said, 'See, I set my bow in the sky, to remind you of my promise...'"

The rainbow. I know the arc of the rainbow is terrible, and I forgot to check whether the colours progress correctly. It's a curious question: had there never been a rainbow before, or had no man ever noticed, or what? Why was THAT rainbow remembered differently? Or was it simply because it appeared THEN, and from that point on, this particular meteor was to serve as a sign of God's promise?

The Ark. The great box-like ship, about which God provided rather specific details - its size, what to make it from, its three decks, a door and a window. We'll see the second ark, for which God again gave detailed specs, in a few days. We do not get to hear the details of the third ark, but they are summarized in a brief sentence, and we shall see that one later on - only in the last century and a half or so have some of those amazing details been learned! Does the ark still exist? There are stories and reports of something strange on Mount Ararat, and it is something still to be investigated.

The Flood. Another something to be investigated; I will not attempt to explore the data now. It is another (third?) appearance of the "water theme" which recurs throughout the Bible, and about which I have written at length earlier in this blogg. The water, even as symbol, has so many uses (just as St. Francis tells us in his "Canticle of the Creatures"!) Here it cleanses, and so in that sense also rescues - though that is paradoxical - for Noah would have perished as well, if he had not obeyed God and built the Ark - perished, not from the Flood, but from the evils of Man, which is far, far worse. Hmm. Do you hear a itinerant carpenter saying something: "Better for him to have a great millstone tied around his neck and thrown into the sea, then to be led astray..." But this good man - who was also a CARPENTER - cut down some trees, and built a big box and all but buried himself in a watery grave - and so rescued the whole world.

(Please remember I am paraphrasing, and not quoting; we are not doing a rigorous study but a kind of sketchy contemplation. Another way of looking at this schematic "Jesse Tree" is that these are the "mysteries" of an Old-Testament "rosary"...)

Sorry to digress just slightly, but this talk of the Flood suggests a hilarious Chesterton quote, which is not his own, but his good friend Mr. Belloc's, and I have to add it to give you something else to ponder, which the evolvers clearly haven't (or won't!): "...nobody needs to be told that in a flood fish live and cattle die. The question is, How soon do cattle turn into fish?" [quoted in GKC's The Thing CW3:310]

Advent: Week 1 Day 2

And the serpent tricked the woman... she ate of the forbidden fruit... and she gave it to her husband and he ate it.



To the serpent, God said: "Therefore, you will crawl on your belly... I will put enmity between you and the Woman - 'she' will crush your head, and you will await 'her' heel..."

To the woman, God said: "You will have pain in childbirth..."

To the man, God said: "Cursed be the ground because of you! By the sweat of your brow will you eat... for you are dust and unto dust you shall return!"

Then God stationed an angel with a firey sword at the gate to Eden...

* * *

(A warning: yes, the quotes are paraphrased out of memory! Yes I am also aware that there is some debate about the gender of the pronouns in the Protoevangelion.)

Note that the serpent has wings and big eyes to stand for its cunning. It also has a little "arm" handing the "apple" to Eve - on the left. (If it had been a bigger picture, there would have been legs as well.) Two bites because both ate from it. Why is it an "apple"? My own guess is this is a Latin pun, for malum = "apple" but also "evil"! But I drew the traditional picture, for every Jesse Tree ought to have a (partially eaten) "apple" on it! Note also that the Christmas red and green appear in Eden - for there was the first revelation of Christmas. Hmmm.. It's funny to think that Christmas was revealed in the condemnation of the serpent... Oh happy fault! Oh necessary sin of Adam! that won for us so great a Redeemer! - how can we not think about Easter at this time of year???

Advent: Week 1 Day 1

In the beginning, God created the heavens and the earth...



and it was very good!

(This and subsequent images are from my "Jesse Tree" wall display, made way back in 1986.)

Note: You read this one starting at the top, and going clockwise. The seventh day is the day of rest and so is not pictured. Yes, the wedge for "Light" has three equations in its center; another version might use the Maxwell equations - no doubt both sets are needed, and probably several more, but that gets too cluttered. Someday, perhaps, we'll know more, and make a more fitting design. Also note, I did not choose these pictures to debate "how" it started but to proclaim that God indeed started it!

Alert - Longest Advent about to start!

Please be aware that this year we have the longest possible Advent - four full weeks!

The official start, of course, comes tomorrow evening with the First Vespers (Evening Prayer I).

Let us then prepare - and make sure we have some extra oil for our lamps! As GKC warns us:

"Let us first of all consider, my brethren, the value of Light."
-- GKC, Heretics CW1:46

A Little Symbol Crash

A Little Symbol Crash

Over on Love2Learn Blog there was an interesting photograph of some nice wooden cabinets. One of them had some Chinese pictographs, and I wondered what they meant, so I wrote a comment there.

I was particularly interested because Love2Learn Mom responded that it was her son's name (Matthew) in Chinese - for I was curious about how names are handled. I went on to ask for more details. (Note: I have revised this next part from both my initial comment on Love2Learn and also from my original posting here.)

That is:

(1) Do those symbols "stand for" the name "Matthew" - do those two symbols in themselves represent the name, and one must know directly from them symbol that it is pronounced "math-you"?

Or!

(2) Do those symbols "spell" the name "Matthew" - as these letters do when I here write in English? (they really have no meaning individually, or no more meaning than the M or the a or the t or the h... The symbols perhaps jammed together just in order to adapt Chinese to this foreign (Hebrew/Aramaic) word?

Or:

(3) Do they "spell" the sound "Matthew"? That is, those symbols are a form of "rebus" - that is, a pictorial pun, in which the words "spelled" by those symbols happened to "sound like" or "suggest" the name, or the sound of the name. (The two separate words meaning something merely coincidental but providing the requisite sounds.) For example, I might draw two pictures: a welcome mat and a man attacking a log with an axe - that is, hewing the wood: hence "mat-hew". Or, I could write a verbal pun in English as "math" - "you" - two words which are NOT the name, but together sound like the name.

(And there may be other ways... This is why I had to revise my posting!)

This brings up a whole very interesting topic - not just names, but symbols and forms of symbol. It is very important to computer scientists, to philosophers and theologians, and to many other fields of study - though even amng these I have named, very few care to consider this, because it gets very hard to talk about.

Let me show you an interesting joke I saw somewhere (I have long ago forgotten where!) and I just drew it over for the sake of this posting.

What does this say?



You would probably "read" it as "THE CAT" - but that is very strange.

For I have made the two letters which ARE the same (the T) to LOOK different.

And I have made the two letters which ARE different (the H and the A) to LOOK the same.

As a computer person, I have long known that what "everyone" calls the letter "A" is not really an A at all, but the number 65 - or, to be even more accurate, the pattern 01000001. That is because many current computers, printers, screens, keyboards, and other devices use a more-or-less standard code (not a SECRET code, rats!) which is called ASCII - the American Standard Code for Information Interchange. Just as this A is an A, and this A is an A, and this A is an A, and this A is an A, and so on - these pictures are all different, but all "stand for" the singular concept of the first letter of the alphabet (or the sixty-fifth entity in ASCII!) Of course, because of heritage, that symbol also stands for the first letter of the Greek alphabet, where it is called "alpha" not "ei" as in "weigh".

The long years we spent long ago, when we learned to read - for which we ought to always thank our parents and our teachers! - that time and energy, and perhaps agony, was spent building the habits into our brains, and perhaps even into our very eyes! to identify certain shapes as logical entities. That wondrous skill is called "the ability to read" - and there is even a more-or-less accurate tool called "optical character recognition software" (or OCR) by which a computer can accomplish the same thing.

Now when one examines Egyptian hierogylphics, as I did back in high school, one finds out that some of them form a kind of alphabet, which permitted the ancient Egyptians to "spell" even foreign names. (That was one of the clues which helped Champollion to "crack" the code on the Rosetta Stone!) But some names were (as far as we know) the elements which made up the symbols, so we could imagine them using the "welcome-mat" plus "man with axe and log" to write "Matthew" - as they did in their own language. And perhaps either "Love2Learn Mom" will get back to me with more about the symbols on the cabinet - or else I will find a book to explore more about how Chinese handles proper names.

But even if I do not learn the details for Chinese, the question - or rather the topic - remains for us to consider, and to explore. I do have off today (hurray!) but I do have several dozen things to do, besides my chores, and eating, and praying. But I want to get into this a little more, at least until lunchtime.

First, we have to discriminate another issue in our discussion. That is, the distinction between the visual aspect of a word, and the audible aspect - which is where the usual delight of the pun resides. (Man, am I glad there are parentheses! I use them all the time. There are other puns, like that "THE CAT" picture.) But linguists divide spoken words into elements called "phonemes" which have their own printed representations (so that they can write textbooks about their field!) and so in some sense these sounds are still a "spelling" of the spoken word, just as the letters "spell" the printed word. (I leave out all kinds of interesting discussions and digressions about how GKC's friend and enemy, George Bernard Shaw, managed to spell the word woman with the letters G-H-O-T-I, and so forth!)

But there again, we spent another veyr long period of time learning - a time so far back that most of us have forgotten - unless we are parents (or older brothers or sisters) and have seen how long it takes for the baby to begin to learn what we are saying! And that skill - the skill which identifies the phonemes and links them together into words - the skill of comprehension of a spoken language - can also be made into a computer program, but there the accuracy can be rather less good than that given by OCR. It's a strange lesson in humility.

To resume: the point I wish to get to, before my time runs out, is that there are mental abstractions which we use in an absolute sense, even when we acknowledge their paradoxical relativity. I would guess that I (and you too!) could identify among at least a hundred people, just by the pronouncing of the same short word - perhaps even just one letter, or one phoneme - which means that they and we both know a singular idea (the word) but also can discriminate the hundred or more varieties of its pronunciation - in fact, so well that the pronunciation in itself serves as a unique identifier to the person pronouncing it!

My time is just about gone, so I will conclude by hinting that this vast puzzle and interesting topic serves to motivate many avenues of human endeavor, from computing to the nature of prayer, from the diversity of human language to the instruction of the young - and, yes, even to humour!

More another day.

Thanksgiving

In one of the truly great modern paraphrases of the Bible which can be seen in the English version of the Liturgy of the Hours, there is this very short instruction from St. Paul:

"Dedicate yourselves to thankfulness."
-- cf. Colossians 3:15

It is one with that amazing beginning which we hear in the Preface of the Mass, which I do not have handy to quote, but I recall as sounding something like this:

"It is truly right and just, proper and helpful towards salvation, that we always and everywhere give thanks to You, almighty and ever-living God..."

And, for those of us who do strive to dedicate ourselves to thankfulness, especially for the amazing writings of Gilbert Keith Chesterton, this day, as much as Christmas, deserves to be celebrated in a thoroughly Chestertonian manner.

And therefore, I will give just a few of the most delicious and relevant phrases, ending with what I consider to the the most mathematical and most theological and most scientific (as well as the most practical) of all GKC's works - and it is only 12 lines long.

"Thanks are the highest form of thought,
and gratitude is happiness doubled by wonder."
-- GKC, A Short History of England CW20:463

"We should thank God for beer and burgundy by not drinking too much of them."
-- GKC, Orthodoxy CW1:268

"The great painter boasted that he mixed all his colours with brains, and the great saint may be said to mix all his thoughts with thanks. All goods look better when they look like gifts. ... It is the highest and holiest of the paradoxes that the man who really knows he cannot pay his debt will be for ever paying it. He will be for ever giving back what he cannot give back, and cannot be expected to give back. He will be always throwing things away into a bottomless pit of unfathomable thanks. ... For that is the full and final spirit in which we should turn to St. Francis; in the spirit of thanks for what he has done. He was above all things a great giver; and he cared chiefly for the best kind of giving which is called thanksgiving. If another great man wrote a grammar of assent, he may well be said to have written a grammar of acceptance; a grammar of gratitude. He understood down to its very depths the theory of thanks; and its depths are a bottomless abyss. He knew that the praise of God stands on its strongest ground when it stands on nothing. He knew that we can best measure the towering miracle of the mere fact of existence if we realise that but for some strange mercy we should not even exist."
-- GKC, St. Francis of Assisi CW2:75, 77, 132

"I have often thanked God for the telephone..."
-- GKC, What's Wrong With the World CW4:112

"Have you ever said some simple word over and over till it became unmeaning, a scrap of an unknown tongue, till you seem to be opening and shutting your mouth with a cry like an animal's? So it is with the great world in which we live: it begins familiar: it ends unfamiliar. When first men began to think and talk and theorise and work the world over and over with phrases and associations, then it was involved and fated, as a psychological necessity, that some day a creature should be produced, corresponding to the twentieth pronunciation of the word, a new animal with eyes to see and ears to hear; with an intellect capable of performing a new function never before conceived truly; thanking God for his creation."
-- GKC, "A Crazy Tale" in CW14:74

"Eternities"

I cannot count the pebbles in the brook.
Well hath He spoken: 'Swear not by thy head,
Thou knowest not the hairs,' though He, we read,
Writes that wild number in His own strange book.

I cannot count the sands or search the seas,
Death cometh, and I leave so much untrod.
Grant my immortal aureole, O my God,
And I will name the leaves upon the trees.

In heaven I shall stand on gold and glass,
Still brooding earth's arithmetic to spell;
Or see the fading of the fires of hell
Ere I have thanked my God for all the grass.
-- GKC, Collected Poems CW10:209

The Power of XOR

The Power of Xor

(No, this is not a science fiction story. Though maybe I'll write one called this someday...)

I decided to give a little example about the kind of math I am talking about when I say "discrete math". This example comes from the branch called "Boolean Algebra", named for George Boole, a 19th century English mathematician. All computer people ought to have a graph on their tee-shirts like this:



which, as I am sure you will recognize, is the equation for y = x(1-x). If you are a computer scientist and do NOT know this equation, shame. You had better take a good look at it - then maybe order Boole's book about it from Dover. (See sidebar for their address!)

OK, now - what is the XOR? All mothers know it, all children ignore it. After dinner, mothers ask, "do you want ice cream or cake?" and their children answer "Yes." (Some answer "Both" because they didn't read Mr. Boole's book yet!)

The mothers are using the English word "or" where they should be using the mathematical operation "XOR" - which we pronounce "ex-or". It's short for "exclusive or" - because the usual or is the "inclusive or" which is what the kids were using, because it includes the "both" case. (We could have called them "Mom's or" and "Kid's or", but some professor thought XOR up a while back, and the name stuck.)

The XOR function comes from Boolean Algebra, where the number-haters rejoice, because there are only two numbers: ZERO and ONE - and that's all! And the XOR function is a nice and very useful function, which can also be called the "not-the-same" function, for it gives an answer of ONE when you give it two DIFFERENT values, but ZERO when you give it the SAME values.

So, remember the multiplication table, that seemed to go on and on? All the tables in Boolean Algebra have only four entries, so let's set up the table for XOR. Here it is:


0 XOR 0 = 0
0 XOR 1 = 1
1 XOR 0 = 1
1 XOR 1 = 0


All done. Now, let's use it to do something very interesting.

Let's say we are holding an apple in our left hand, and an orange in our right hand. But we want it to be the other way around. So, usually we have to set one of the fruits down on a table - let's say the apple - then pass the orange from our right to our left hand, and then pick up the apple again with our right hand. That means we have to have a temporary holding area.

Either that, or we would have to juggle them, in which case the air is like the holding area.

What if we couldn't find any holding area at all?

Well, we cannot do that with fruit and our hands. But we can, inside the computer, with the wonderful XOR.

Now remember! Inside the computer we have ONLY two things: zero and one. OK, now watch the magic.

We have two storage places, A and B. For this example, we shall say they both should four bits - that is, four values which can be either zero or one.

Now, we want to reverse this, so that whatever is in A at the start will be in B at the end, and vice versa. I will show you how to do it, with just THREE repeats of the powerful XOR.

Step 1. Compute the value of (A xor B), and put that into A.
Step 2. Compute the value of (A xor B), and put that into B.
Step 3. Compute the value of (A xor B), and put that into A.

And now the values are swapped, just like the fruits were.

You don't believe me, do you?

OK, then I will go through it, step by step. You can follow along.

For our demonstration, inside A we will put this pattern: 0011
And inside B we will put this pattern: 0101

OK, here we go:

Before step 1: A= 0 0 1 1 B= 0 1 0 1

Step 1. Compute (A xor B) which is 0 1 1 0 and put that into A.

After step 1: A= 0 1 1 0 B= 0 1 0 1

Step 2. Now compute (A xor B) again: that is 0 0 1 1 and put that into B.

After step 2: A= 0 1 1 0 B= 0 0 1 1

Step 3. Now compute (A xor B) again: that is 0 1 0 1 and put that into A.

After step 3: A= 0 1 0 1 B= 0 0 1 1

Now look at what was in A and B back before step 1. You see?

Yes! they are swapped! And no extra storage, either!

Remember, you can use any values you like, and it will ALWAYS work. And we know that, because in our example we used every possible pattern in our A and B values - that's why I picked those two values to begin with! Because, as we said before, there are only two numbers. Another day we will see more.

Original source: from a library routine used by the old Control Data Corporation machine on which I learned (at an unnnamed school) back in the mid-1970s. (Thank you, Seymour Cray!)

Christus Rex and Thanksgiving - and finite math

Almost the end of another year, and a time to be thankful - and the funny thing is that for the Church, we have a very computational - ah, perhaps I should say "discrete math" way of dealing with time. (Discrete math is the branch which deals with finite collections of numbers, like on a clock, where 3 plus 10 equals 1.) Ahem! In order to "represent" infinity during our lifetimes, the Church does what automobile makers do with their odometers, and computer hardware designers with their registers (you know, 32 bits, 64 bits, etc.) - they just "wrap around" when we get to the "biggest number". Like on a clock! That is why the Feast of Christ the King comes at the "end" of the year - it stands for the Last Judgement! and then there are another six days until we start all over with the first Sunday of Advent, and think (again) about preparing for the Coming. It's all about planning ahead.

My mother had this curious little button she would wear. It showed an angel pushing on (or holding back?) the hands of a clock, nearly at midnight. It read:

To have a nice Eternity: Plan Ahead!

And so, with these very profound thoughts as we contemplate the last leaves falling, up here in the Northern Hemisphere, let us look at a very reassuring comment from our Uncle Gilbert. When I asked AMBER about this quote, I was rather startled to find that it comes up in TWO places, for I do not recall that I knew there was more. And, as you will see, they are both very rich.

First, the one I had been contemplating:

Great men may make despotisms; but democracies make great men. The other main factory of heroes besides a revolution is a religion. And a religion again, is a thing which, by its nature, does not think of men as more or less valuable, but of men as all intensely and painfully valuable, a democracy of eternal danger. For religion all men are equal, as all pennies are equal, because the only value in any of them is that they bear the image of the King.
[GKC, Charles Dickens CW15:44, emnphasis added.]

Then, the one which AMBER also found, which adds a special depth to that thought:

when we say that all pennies are equal, we do not mean that they all look exactly the same. We mean that they are absolutely equal in their one absolute character, in the most important thing about them. It may be put practically by saying that they are coins of a certain value, twelve of which go to a shilling. It may be put symbolically, and even mystically, by saying that they all bear the image of the King. And, though the most mystical, it is also the most practical summary of equality that all men bear the image of the King of Kings.
[GKC, A Short History of England CW20:563, emphasis added.]

An observation: CD was written in 1906. SHE in 1917. In his 1922 WISIA he elaborates on this last point in a very important way:

America is the only nation in the world that is founded on a creed. That creed is set forth with dogmatic and even theological lucidity in the Declaration of Independence; perhaps the only piece of practical politics that is also theoretical politics and also great literature.
[GKC What I Saw in America CW21:41]

It is most wise, then, that America's great solemnity of thanksgiving comes during this end-of-time celebration. For that is what (as Chesterton says) is the "highest form of thought."

"Is Math Hard?" The answer - from Aquinas!

While I was working on my Ph.D., students and faculty at many schools were debating via electronic bulletin boards on the statement that "math is hard." (I think it was something said by some talking doll - and it started up a lot of chatter about math, women, education, and all kinds of things. But no one ever seemed to get to a definitive answer.)

Some time afterwards, I found the answer in a book called The Division and Methods of the Sciences which is a commentary by St. Thomas Aquinas on another book called De Trinitate by Boethius (the same guy who wrote The Consolation of Philosophy).

Aquinas answered that mathematics (considered as a subject) is easy: it is a simpler subject than "natural philosophy" (which includes physics), which in turn is simpler than "divine science" (or theology).

In fact, the subject is called "mathematics" which is Greek for "the learning" because it is learned - someone can teach it to you, and then you know it! And, though any given individual may find any given aspect of mathematics to be "easier" or "harder", it is still possible for a good teacher and a diligent student to work together - and for the student to acquire a COMPLETE understanding of that topic or principle.

However!

One must go to nature to learn something about it, and even then one might only know very little - or even be fully misled. For many many solid things, it is true that when they are warmed, they become liquid. Like ice, or lead, or glass - or even rocks. But when an egg is warmed, it becomes solid. And for iodine and "dry ice", there is NO liquid - these two materials "skip" the liquid and go right to gaseous form - which is called "sublimation"!

And that is just some simple physical materials. When one looks at living things, or when one gets very precise about measuring, one finds some very difficult questions. And one can sit and think for a very long time before proposing a solution, which may STILL not be correct.

And the matters of the supernatural - I mean in the sense of human beings, and angels, and God - these are even more difficult, for these do not admit of direct observation. One does not experiment on an angel. But this, perhaps, is where I will do best to direct you to Aquinas for more details.

(I would do a SWQR of the book, but do not have the time to do a good condensation. Maybe next week. Anyway, Nancy over at Flying Stars had been asking some interesting questions about math, so I found this above comments from a larger essay. Maybe I will post the whole thing later.)

One more note I must append, as I re-read this before posting. I used the word "diligent" to describe a student. This word (as a Latin verb) is used by Aquinas in his song Adoro Te devote, and it means "love". In order to succeed at aquiring knowledge, the student must LOVE that subject. And that means it would be best for the teacher to also love it, and communicate that love.

(You may laugh at my crazy uniting of topics, but this is why Chesterton says there is no such thing as a different subject!)

Subsidiarity (a sample)

The following is a sample of the work I have been doing. It may form an appendix to the main work, which is of a rather different - ah - kind of writing.

The Modern Era: "Catholic Social Teaching"

Rerum Novarum
The idea of subsidiarity was first sketched by Leo XIII in his famous encyclical, Rerum Novarum, published in 1891. He founded the idea upon the family, setting it in logical opposition to the State – and thereby inverting the hierarchy which puts the State ahead of its components. Chesterton uses this inverted, upside-down view to indicate the correct perception of reality:

...you remember that he [Peter] was crucified upside down. I've often fancied his humility was rewarded by seeing in death the beautiful vision of his boyhood. He also saw the landscape as it really is: with the stars like flowers, and the clouds like hills, and all men hanging on the mercy of God." [GKC The Poet and the Lunatics 21-22]

Indeed, Leo XIII's work seems dematically linked to Chesterton's, in showing the impoortance of distinguishing things which need to be kept separate. As Jesus said "Think ye, that I am come to give peace on earth? I tell you, no; but separation." [Lk 12:51] and Chesterton's insightful inversion of Mt 19:6: "Those whom God has sundered, shall no man join." [GKC, The Common Man 143], Leo divided the social system into State and Family.
Now that Leo had effected the correct separation of the components in the social system, he restored order to it by lifting up the lowest part. This lesson, as Chesterton pointed out, "is the lesson of 'Cinderella ' which is the same as that of the Magnificat – exaltavit humiles. [GKC, Orthodoxy CW1:253. The Latin means "He has lifted up the lowly" Lk 1:52] Henceforth as Jesus predicted, the lowest was to rank ahead of the highest: "And behold, they are last that shall be first: and they are first that shall be last." [Lk 13:30] And we shall see this in even greater detail, because "That is the paradox of the whole position; that henceforth the highest thing can only work from below." [GKC, The Everlasting Man CW2:313. Also cf. Jn 13:2-15]
Here, then, is the kernel element of subsidiarity: The system is composed of parts, and the parts form a hierarchy – an ordered arrangement of layers – within the system. With this in mind, let us see how Leo proceeds:

20. It is a most sacred law of nature that the father of a family see that his offspring are provided with all the necessities of life, and nature even prompts him to desire to provide and to furnish his children, who, in fact reflect and in a sense continue his person, with the means of decently protecting themselves against harsh fortune in the uncertainties of life. He can do this surely in no other way than by owning fruitful goods to transmit by inheritance to his children. As already noted, the family like the State is by the same token a society in the strictest sense of the term, and is governed by its own proper authority, namely, by that of the father. Wherefore, assuming, of course, that those limits be observed which are fixed by its immediate purpose, the family assuredly possesses rights, at least equal with those of civil society, in respect to choosing and employing the things necessary for its protection and its just liberty. We say "at least equal" because, inasmuch as domestic living together is prior both in thought and in fact to uniting into a polity, it follows that its rights and duties are also prior and more in conformity with nature. But if citizens, if families, after becoming participants in common life and society, were to experience injury in a commonwealth instead of help, impairment of their rights instead of protection, society would be something to be repudiated rather than to be sought for.
21. To desire, therefore, that the civil power should enter arbitrarily into the privacy of homes is a great and pernicious error. If a family perchance is in such extreme difficulty and is so completely without plans that it is entirely unable to help itself, it is right that the distress by remedied by public aid, for each individual family is a part of the community. Similarly, if anywhere there is a grave violation of mutual rights within the family walls, public authority shall restore to each his right; for this is not usurping the rights of citizens, but protecting and confirming them with just and due care. Those in charge of public affairs, however, must stop here; nature does not permit them to go beyond these limits. Paternal authority is such that it can be neither abolished nor absorbed by the State, because it has the same origin in common with that of man's own life. "Children are a part of their father," and, as it were, a kind of extension of the father's person; and, strictly speaking, not through themselves, but through the medium of the family society in which they are begotten, they enter into the participate in civil society. And for the very reason that children "are by nature part of their father...before they have the use of free will, they are kept under the care of their parents." [Summa Theologica II-II Q10A12] Inasmuch as the Socialists, therefore, disregard care by parents and in its place introduce care by the State, they act against natural justice and dissolve the structure of the home.
[Rerum Novarum 20-21 (1891)]

One important aside: from this excerpt, Leo XIII might be said to be the "founder" of subsidiarity – but he did not use that word in Rerum Novarum.
I wish I had room to explore the extent to which this great document influenced Chesterton. It may be the substrate on which he built his What's Wrong With the World (1910) and The Outline of Sanity (1926), and he seems to have made occasional indirect reference to it (e.g. Illustrated London News essay for Nov. 17, 1923 CW33:216-217; The Everlasting Man CW2:186; St. Thomas Aquinas CW2:544), but it was so much in his mind that in 1926 he mentioned it in a mystery story: "The Oracle of the Dog" in The Incredulity of Father Brown.

Forty Years Later
But in the Roman Catholic Church, Rerum Novarum had a very significant effect. So important did this encyclical prove – the first of the "modern" studies of Church teaching on human society – that in 1931 Pope Pius XI wrote an encyclical, Quadragesimo Anno, specifically commemorating its fortieth anniversary.

It is indeed true, as history clearly proves, that owing to the change in social conditions, much that was formerly done by small bodies can nowadays be accomplished only by large corporations. None the less, just as it is wrong to withdraw from the individual and commit to the community at large what private enterprise and industry can accomplish, so, too, it is an injustice, a grave evil and a disturbance of right order for a larger and higher organization to arrogate to itself functions which can be performed efficiently by smaller and lower bodies. This is a fundamental principle of social philosophy, unshaken and unchangeable...[Quadragesimo Anno 5 (1931) emphasis added]

Here, Pius gives a succinct and general (though negative) form of the concept – yet we still do not have the term "subsidiarity." It is this encyclical, however, not Leo's, which most later documents give as a reference.

John XXIII Gives Us the Term
John XXIII released his Mater Et Magistra in 1961, seventy years after Leo XIII's work, examining the topic in ever greater detail, and with ever greater concern. Here, the idea proposed by Leo and discussed by Pius is finally given a distinguishing name.

52. But – for reasons explained by Our predecessors – the civil power must also have a hand in the economy. It has to promote production in a way best calculated to achieve social progress and the well-being of all citizens.
53. And in this work of directing, stimulating, co-ordinating, supplying and integrating, its guiding principle must be the "principle of subsidiary function" formulated by Pius XI in Quadragesimo Anno, "This is a fundamental principle of social philosophy, unshaken and unchangeable... Just as it is wrong to withdraw from the individual and commit to a community what private enterprise and industry can accomplish, so too it is an injustice, a grave evil and a disturbance of right order, for a larger and higher association to arrogate to itself functions which can be performed efficiently by smaller and lower societies. Of its very nature the true aim of all social activity should be to help members of the social body, but never to destroy or absorb them."[See excerpt from QA above]
54. The present advance in scientific knowledge and productive technology clearly puts it within the power of the public authority to a much greater degree than ever before to reduce imbalances which may exist between different branches of the economy or between different regions within the same country or even between the different peoples of the world. It also puts into the hands of public authority a greater means for limiting fluctuations in the economy and for providing effective measures to prevent the recurrence of mass unemployment. Hence the insistent demands on those in authority – since they are responsible for the common good – to increase the degree and scope of their activities in the economic sphere, and to devise ways and means and set the necessary machinery in motion for the attainment of this end.
55. But however extensive and far-reaching the influence of the State on the economy may be, it must never be exerted to the extent of depriving the individual citizen of his freedom of action. It must rather augment his freedom while effectively guaranteeing the protection of his essential personal rights. Among these is a man's right and duty to be primarily responsible for his own upkeep and that of his family. Hence every economic system must permit and facilitate the free development ofproductive activity.[Mater et Magistra 52-55 (1961)]

But "the principle of subsidiary function" was reduced, just two years later, to the simpler term "subsidiarity" – which appeared for the first time in John XXIII's Pacem in Terris, as he applied it to a system even larger than the Family/State of Leo:

140. Moreover, just as it is necessary in each state that relations which the public authority has with its citizens, families and intermediate associations be controlled and regulated by the principle of subsidiarity, it is equally necessary that the relationships which exist between the world-wide public authority and the public authority of individual nations be governed by the same principle. This means that the world-wide public authority must tackle and solve problems of an economic, social, political or cultural character which are posed by the universal common good. For, because of the vastness, complexity and urgency of those problems, the public authorities of the individual states are not in a position to tackle them with any hope of a positive solution.
[Pacem in Terris 140 (1963) emphasis added]

The idea, though not the term, was evident in Paul VI's Apostolic Letter Octogesima Adveniens in 1971, commemorating the 80th anniversary of Leo's work.

Similarly, John Paul II wrote Laborem Exercens a decade later (1981).

One hundred years after Leo's work, sixty after Pius XI's "negative" form, and nearly forty after John XIII's first use of the term, John Paul II gives this "positive" definition of subsidiarity:

Here again the principle of subsidiarity must be respected: a community of a higher order should not interfere in the internal life of a community of a lower order, depriving the latter of its functions, but rather should support it in case of need and help to coordinate its activity with the activities of the rest of society, always with a view to the common good.[ref to QA]
[Centesimus Annus 48 (1991)]

Getting in trouble with ancient Rome

I am no Latinist, and my connection with the ancient Romans is tenuous at best, even if I am in some sense an heir to the culture of Middle-Earth (No, it's not what you're thinking - it's just the English translation of "Mediterranean", sorry, my precious!)

But I have found something in my reading and have, after long thought and prayer, decided I have to blow the whistle - maybe I should say Pan-pipes? - on the ancient Romans.

It is well known to home-school kids, some Catholics, lawyers, and even some scientists, that Latin is what is called an "inflected" language. (No, that's not infected!) That means various words of that language require endings which indicate certain attributes or qualifications of the root meaning of the word. English is partially inflected - we have the "s" suffix for plurals, "-ed" and "-ing" but not much else - otherwise, we're periphrastic (that's a vocabulary word, kids, write it down.) On the other end of things, Vietnamese is completely UNinflected - it must use word order and additional words to handle tense, agreement, and the other mechanisms of meaning.

Latin, like ancient Greek, inflected just about everything - its nouns and its verbs, its pronouns, its adjectives and adverbs. (Not much left, then, is there?) So there are whole books listing the proper endings one must use to say things like "you (plural) (maybe) were being fortified" = muniremini. And there are all kinds of wierd irregularities - so many that there is even a special word for the words which are regularly irregular (the word is "deponent"). There are even strange anomalies, like the verb adolesco (= "I grow up") which has no passive, so it is not possible for a Roman to say "I am grown up" (which is perhaps why I don't say it either!)

Now, in reading a number of rather curious books, I have recently discovered a secret that the ancient Romans worked very hard to conceal. And you can look in the amazing "Lewis and Short" or in the handy "Wheelock" or any of the other very good books on Latin and you won't find it. For, I am growing more and more convinced, these writers knew this secret too, but they were in on the take, and decided to conceal it, in the forlorn hope that their support of this over two thousand year old conspiracy, a few more hardy souls might decide to learn Latin.

And now (brace yourselves!) here is the secret.

There are really SIX declensions in Latin.

The sixth one was called the declinatio secreta, and if you read long enough you will find it sneaking in here and there, even in popular writers like Cicero and Caesar - and even Virgil.

When the idea is raised, scholars usually try to divert suspicion by explaining the odd give-away endings as "copyists' errors" or other excuses. The poor monks of the 7th and 8th centuries get blamed for so much - and for what? To hide a rather dumb trick of some long-dead grammarians? How long did they think they could hide such a thing, anyway!

OK, so - about the secret declension. It actually occurs between the second and third declensions, but the Romans did such a good job in hiding it that EVERYONE thinks there are only five. The Greeks tried to do this same trick with their alphabet, but scholars have long ago been pushed into admitting the existence of digamma and yod.

(Man, like you can really hide letters of the alphabet! How would they have made computer keyboards back then? "Ok, then you press the secret letter key - no, no - not THAT secret letter, the OTHER secret letter!" Whew! Thank God we're not stuck with that kind of hassle in our modern era - we just have those squiggly letters to type into our bloggs if we want to add a comment... Then again, there is that confounded "any" key, which one has to press if one wants to continue...)

Anyhow, just why did they want to hide a whole declension, anyway? Well our best guess is that there was an ancient and long-running contest between Latin and Greek about this sort of thing. And the Greek of the Greeks had the Latin of the Romans beat as far as verbs were concerned: they both had active and passive, but Greek had the Middle Voice as well - big score, right there, a whole extra voice, that's one whole big chart of extra endings to learn - and then there was that wacky "Aorist" gimmick (for even more endings!!!)... and then they scored big by making the "negative" word ou or me, which both mean "not" in English) depend on how it was to be used!!!

So the Romans really had to struggle if they wanted to make their language really difficult to learn - and then they thought up the most amazing trick! What if there were a whole class of words that nobody knew how to decline? Behold! The Sixth Declension!

Now, I am sure you are curious to know just what words belonged to the Sixth Declension. OK, so let's see, here are some examples.

(pause)

But (ahem!) now that I think about it, I really like pizza. And spaghetti. And lasagna. And salami, and provolone, and mozzarella, not to mention the wine, and the bread...

OK, well (rats!) maybe there is some wisdom here. I mean, even Aquinas didn't tell! So I guess I will go along with my ancestors and the Latinists...

Non! Non dico! I won't tell. Won't! Yeah, threaten me as you will, I won't reveal any of those words... (Though it still amazes me how no one ever noticed before...)

Sorry to get you excited. Just press the "Any key" and go on to another blogg...

A fantastic piece of music

As I am part musician - which may account for my craziness - I often listen to music. (Alas, it is only part - and in some all-too-remote part of my being!)

And I like lots of different kinds, by which I mean I like "rock-and-roll" as well as "classical". I will not argue such points now, for that is like arguing how one likes tuna salad - (ahem!) for one might not want tuna salad today, even if one likes it... Anyhow, I want to tell you about one particular musical work, which is not at all like tuna salad.

One day some years ago, around about the time CDs started to become available, my friend who is a REAL organist (at a Cathedral, yes!) and I were visiting another friend who is also an organist in my town and a music teacher. He wanted to play a new CD he had gotten... He put it on and - WOW - were we blown away! An amazing piece of music - it starts with an orchestra, but soon adds organ - and the battle begins! Very excellent, dudes, yeah, really!

Now you want to know what this excellent piece is. It is called "Symphonie Concertante" and it was written by Joseph Jungen. I purchased mine from The Organ Historical Society. And though I cannot easily give you a sample of the music, I will here repeat their catalog comment:

"one of the most spectacular of a spate of late 19th and early 20th century pieces written to display the combatative possibilites of setting a full orchestra and a large concert organ at each others' throats."

Which may give you some sense of just how wonderful this music is.

Another great long word

I know it is not Wednesday - the longest day of the week - but it has been such a long time since I posted that I thought I would resume by posting something short.

So here is a nice little poem on a nice long Greek word from Homer:

Polyphloisboisterous Homer of old
Threw all his augments into the sea,
Although he had often been courteously told
That perfect imperfects begin with an e.
But the poet replied with a dignified air,
"What the Digamma does any one care?"

This was from a book I received long ago from my father: A Reading Course in Homeric Greek Vol II, page 184. Alas, I am not enough of a Greek dude to explain the various jokes, except that I do know about digamma. That is the letter that looked sort of like a capital F, but probably was pronounced "w" - and the Greeks gave it up long ago. (The Romans borrowed it, or perhaps kept it, for use in pronouncing the "f" sound.)

Perhaps someday I will study Greek. Ah! for the time to learn Italian, to read Dante, and Latin (to read Aquinas and Virgil, and the Vulgate), and Greek (to read Homer, and the New Testament)... and Hebrew, to read the Psalms! (and the rest of the Bible, too)

Oh, well, it was supposed to be a short posting. My mother always said I was vaccinated with a phonograph needle. (Does anyone even know what that is nowadays?)

Some more interesting quotations

A note: these are all from our Uncle Gilbert, and apply to technology, engineering, science...

"I have often thanked God for the telephone..." What's Wrong With the World CW4:112

"It may be easier to get chocolate for nothing out of a shopkeeper than out of an automatic machine. But if you did manage to steal the chocolate, the automatic machine would be much less likely to run after you." The Ball and the Cross

"No machine can lie," said Father Brown, "nor can it tell the truth." The Wisdom of Father Brown

"The rebuilding of this bridge between science and human nature is one of the greatest needs of mankind." The Defendant

"We have to go on using the Greek name of amber as the only name of electricity because we have no notion what is the real name or nature of electricity." The Common Man

"The Eastern says fate governs everything and he sits and looks pretty; we believe in Free-will and Predestination and we invent Babbage's Calculating Machine." (GKC quoted in Maisie Ward's Gilbert Keith Chesterton)

"I like the Cyclostyle ink; it is so inky. I do not think there is anyone who takes quite such a fierce pleasure in things being themselves as I do. The startling wetness of water excites and intoxicates me: the fieriness of fire, the steeliness of steel, the unutterable muddiness of mud. It is just the same with people.... When we call a man "manly" or a woman "womanly" we touch the deepest philosophy." (from a letter to Frances Blogg quoted in Maisie Ward's Gilbert Keith Chesterton)

I live in an age of varied powers and knowledge,
Of steam, science, democracy, journalism, art
But when my love rises like a sea,
I have to go back to an obscure tribe and a slain man
To formulate a blessing.
[CW10:30]

To the child the tree and the lamp-post are as natural and as artificial as each other; or rather, neither of them are natural but both supernatural. For both are splendid and unexplained. The flower with which God crowns the one, and the flame with which Sam the lamplighter crowns the other, are equally of the gold of fairy-tales. In the middle of the wildest fields the most rustic child is, ten to one, playing at steam-engines. And the only spiritual or philosophical objection to steam-engines is not that men pay for them or work at them, or make them very ugly, or even that men are killed by them; but merely that men do not play at them. The evil is that the childish poetry of clockwork does not remain. The wrong is not that engines are too much admired, but that they are not admired enough. The sin is not that engines are mechanical, but that men are mechanical.
Heretics CW1:112-113

Some interesting quotes

"One of the severest tests of a scien­tific mind is to discern the limits of the legitimate applications of scientific methods."
-- James Clerk Maxwell, "Paradoxical Philosophy" 1878

"Much is spoken today about the power of science, and rightly. It is awesome. But little is said about the inherent limitations of science, and both sides of the coin need equal scrutiny."
-- Vannevar Bush, "Science Pauses" in Fortune May 1965


"It's about as likely that an ape will prove to have a language ability as that there is an island somewhere with a species of flightless birds waiting for human beings to teach them to fly."
-- Noam Chomsky, Time March 10, 1980

[The widespread taking of mechanistic physics for the truth of a mechanistic philosophy proved to be] "a superstition far more dangerous than the one about the existence of witches: It leads to a general spiritual and moral drying-up which can easily lead to physical destruction. When once we have got to the stage of seeing in man merely a complex machine, what does it matter if we destroy him?"
-- W. Heitler, Man and Science

"I have no practice in abstract reasoning, and I may be all astray."
-- Charles Darwin, letter to W. Graham, July 3, 1881

[The female pine cone, with its airfoils which set up spiral air currents, guiding the pollen between its scales... ...the work of a] "coniferous air traffic controller deliberately bending the flight paths of the pollen grains to its aerodynamic will..."
--B Fellman, "An Engineer's Eye Helps Biologists Understand Nature", Smithsonian July 1989

[quoted in "The Heuristics of Purpose", chapter 6 of The Purpose of It All by S. L. Jaki]

Light From the Rosary (Conclusion)

Light From the Rosary (Conclusion)

Light From the Rosary (Part 1)
Light From the Rosary (Part 2)
Light From the Rosary (Part 3)
Light From the Rosary (Part 4)
Light From the Rosary (Part 5)
Light From the Rosary "back cover"


Conclusion: Ten and Twenty
Since I am occasionally a poet as well as a lunatic, I mean a computer scientist, I would like to show you a nice little limerick I once found. (Note: I did not write it!)

(12+144+20
+ 3·Ö4)
÷ 7
+ 5·11
= (9^2) + 0

Which, like the limerick on "Salisbury" which Chesterton enjoyed, really has to be translated to be appreciated:

A dozen, a gross, and a score,
Plus three times the square root of four
Divided by seven
Plus five times eleven
Is nine squared and not a bit more.

[Note: Here is the limerick as reported by Maisie Ward:]

There was a young curate of Salisbury,
Whose manners were halisbury-scalisbury:
He went cycling to Hampshire
Without any pampshire,
Till his Bishop insisted he walisbury.

To construe the verse, you must know that the Bishop of Salisbury, by an old medieval usage, still signs himself Sarum, and that the postal version of Hampshire is Hants.

There was a young curate of Sarum
Whose manners were too harum scarum:
He went biking to Hants
Without any pants,
Till his Bishop insisted he wear 'em.
[Maisie Ward, Return To Chesterton, 144]

I mention this because one of the very strange things about English is that it has synonyms for certain numbers. We call the ten Hail Marys a decade, which of course is from the Latin, and so is "dozen" for 12, and even "gross" for a dozen dozens. But "score" for 20 is English. And there does not appear to be very much numerological use of 20, at least in the Bible. Obviously it is twice ten, and ten has its own special significance. To the Greeks, ten was mystically enshrined in the word pistiV meaning faith or trust, and it also has Biblical significance in the ten Commandments and the ten plagues of Egypt. Moreover there was a strange mathematical connection which our Lord hints at in His comments about the fruitfulness of the Word of God, which yields fruit in one hundred or sixty or thirty fold (Mt 13:8) – for these numbers are ten times 10, 6, and 3 which are all triangular numbers (look at the arrangement of bowling pins to understand this word!)
Now people that like to play with numbers like to look for patterns – this does NOT make them numerologists, just as people that like to look at the Zodiac are not therefore astrologers. And of course there are four Gospels and four Living Creatures in the Apocalypse (Rv 4:6-8) and now there are four sets of mysteries of the Rosary.
But there really is something interesting in seeing a certain repetition of this three in odd places. And one of the oddest has just been revealed, now that there are twenty mysteries. For there is an interesting place where the number three is related to the number twenty – and it has been known for only about fifty years.
That relation is hidden within a very sophisticated code. The code is arranged to reduce the likelihood that an error will corrupt the message. It is also arranged so that the frequency of use of symbols in the message is paralleled (when possible) by the number of symbols used to encode that message. And there is this curious fact: the coding symbols come in groups of three, and, except for a special "punctuation mark," there are exactly twenty message symbols.
What is this code? It is called the genetic code, and it is the way in which DNA sequences are translated into proteins (which are sequences formed from the collection of twenty amino acids). A sequence of three DNA components (which are called "bases": A, C, G, T) stands for one of twenty specific amino acids (or else it is the punctuation mark indicating the end of the sequence).
Now, as I mentioned at the beginning of this essay, there is this verse in which Jesus links the words light and life:

Again therefore, Jesus spoke to them, saying: I am the light of the world. He that followeth me walketh not in darkness, but shall have the light of life. (Jn 8:12)

To follow Christ – to study Him – will result in the possession of both Light, the ultimate message-carrying entity of nature, and Life, which is the ultimate message incarnate. With the addition of the mysteries of light, John Paul II has revealed the Rosary to be based on an "alphabet" of twenty mysteries – paralleling the twenty amino acids which constitute the "alphabet" of life.
It is thus, in the Twenty Mysteries of the Rosary, at the junction point of molecular biology, computer science, and Catholicism, that we get the first faint hint of the profound earthquake of truth from the Eternal Poet, Who inspired John to write:

"The Word was made flesh."
`O LogoV sarx egeneto.

Light From the Rosary (Part 5)

Light From the Rosary (Part 5)

Light From the Rosary (Part 1)
Light From the Rosary (Part 2)
Light From the Rosary (Part 3)
Light From the Rosary (Part 4)
Light From the Rosary "back cover"


Up another level – Tertiary and higher structures

In the chemistry underlying molecular biology, other connections or linkages may occur as the properly linked molecule folds and makes new contacts with itself – or even with other molecules. The amazing apparatus called the ribosome is made up of three separate strands of RNA and several dozen small protein molecules, all folded and linked together. From the molecular viewpoint, it is large and complex: so large it can be seen as a tiny dot under a microscope! (I mention the ribosome in particular because it is the cellular machine which actually "reads" the message obtained from DNA and builds a protein corresponding to it – and we will see more of this protein building later.)
Again the Rosary can be seen to have more complex links – both with itself and also with other prayers.

The Rosary in the Rosary
Yes, it is indeed possible to contemplate the Rosary itself in praying it. This sounds like some kind of liturgical pun – a prayer which contains itself? But like two mirrors placed across from each other, the Rosary has a self-referential character: the image both refers to, and is referred to by, its original. This character always existed, but it has also been strengthened by the Johanno-Pauline mysteries.
One of the marvellous self-referential aspects of the Rosary concerns the "Hail Mary": the prayer which is the "backbone" – the ostinato or drone music – on or over which the meditation is woven. [The musical analogy is apt, and deserves a longer treatment which probably ought to be done poetically, or better, musically. Another musical analogy, even more apt, is a passacaglia – "a slow dance with divisions on a ground bass in triple rhythm." A ground bass is a musical line consisting of "a few simple notes, intended as a theme, on which, at each repetition, a new melody is constructed." This seems clear enough.] The prayer itself is formed (at least its first half) from the words of the Angel Gabriel: "Hail, full of grace, the Lord is with thee: blessed art thou among women." (Lk 1:28) and of Mary's cousin Elizabeth: "Blessed art thou among women and blessed is the fruit of thy womb." (Lk 1:42) Hence, the meditations for mysteries J1 and J2 contain (or refer to) the prayer itself as a starting point, a means, and also an ending point.
Likewise, another mystery contains part of the formula for the "Glory Be," which has been said for centuries as the Trinitarian Doxology in psalmody and other forms of prayer. In G2, we recall our Lord's final words before ascending to Heaven: "Going therefore, teach ye all nations: baptizing them in the name of the Father and of the Son and of the Holy Ghost." (Mt 28:19)
By some stretch of the mystical imagination we might claim the introductory Apostle's Creed to be linked with G3 (Pentecost) or even (with the new mysteries) with L5 for it was at the last Supper that Jesus told them: "But when he, the Spirit of truth, is come, he will teach you all truth. " (John 16:13) And we might also link the concluding "Hail Holy Queen" to the Magnificat in J2, for as Luke records Mary's words: "for behold from henceforth all generations shall call me blessed." (Lk 1:48)
But in the traditional 15 mysteries we do not find the Lord's Prayer. Hence, it is a truly satisfying fact that, with John Paul II's addition of L3, we can now also meditate on the words we were taught by our Lord Himself, in which we dare to say "Our Father." For included within the meditations of the "Proclamation of the Kingdom of God" we may surely spend the whole decade in pondering Luke's report on how the disciples came to Jesus saying "Lord, teach us to pray, as John also taught his disciples." (See Lk 11:1-4)


The Rosary and the Office
We have already mentioned the "Glory Be" and the Lord's Prayer, both of which are important elements of the Divine Office. The three great Gospel Canticles are found in the Joyful Mysteries: the "Benedictus" and the "Magnificat" in J2, the "Nunc Dimittis" in J4. The Psalms appear in many places, quoted even in the Magnificat itself – but perhaps it might be well to see a few examples of their other appearances in the Gospels. The following, appearing as they do in various discourses of our Lord, obviously relate to L3:

Mt 5:4 Blessed are the meek: for they shall possess the land.
Ps 36:11 But the meek shall inherit the land, and shall delight in abundance of peace.

Mt 5:8. Blessed are the clean of heart: they shall see God.
Ps 23:3-4 Who shall ascend into the mountain of the Lord: or who shall stand in his holy place? The innocent in hands, and clean of heart, who hath not taken his soul in vain, nor sworn deceitfully to his neighbour.

Mt 5:35. [Swear not] by the earth, for it is His footstool: nor by Jerusalem, for it is the city of the great king.
Ps 47:3. With the joy of the whole earth is Mount Sion founded, on the sides of the north, the city of the great king.

Mt 7:23. And then will I profess unto them, I never knew you: depart from me, you that work iniquity.
Ps 6:9. Depart from me, all ye workers of iniquity: for the Lord hath heard the voice of my weeping.

Mt 16:27 For the Son of man shall come in the glory of his Father with his angels: and then will he render to every man according to his works.
Ps 61:13. And mercy to thee, O Lord; for thou wilt render to every man according to his works.

This next, however, is at the Transfiguration (L4):

Mt 17:5. And as he was yet speaking, behold a bright cloud overshadowed them. And lo a voice out of the cloud, saying: This is my beloved Son, in whom I am well pleased: hear ye him.
Ps 2:7. The Lord hath said to me: Thou art my son, this day have I begotten thee.
The Sorrowful Mysteries are also involved, as there are psalm references during the Passion as well:

Mt 26:38. Then he saith to them: My soul is sorrowful even unto death. Stay you here and watch with me.
Ps 41:6. Why art thou sad, O my soul? and why dost thou trouble me? Hope in God, for I will still give praise to him: the salvation of my countenance.

In particular, we should recall that on the cross Jesus quotes the beginning of Psalm 21: "O God my God, look upon me: why hast thou forsaken me?"
Also on the cross He utters the first phrase of the beautiful Night Prayer responsory: "Into thy hands I commend my spirit: thou hast redeemed me, O Lord, the God of truth." (Ps 30:6)

Perhaps the most dramatic of all references to the psalms is this one, because Jesus acted it as is indicated (Mt 13:34-35) rather than only quoting it:

Ps 77:2. I will open my mouth in parables: I will utter propositions from the beginning.

Indeed, this single verse might be considered a Psalm commentary on the Third Luminous Mystery.

Another, and much more complex, point to examine is the way in which the entire liturgical year is mirrored and mirrors the chronological structure of the twenty mysteries. If the cosmic plan for the astronomical bodies that God specifed in Gn 1:14 ("let them [the sun and moon] be for signs, and for seasons, and for days and years.") has its ultimate implementation in the Canonical Hours of the Day and the Liturgical Year, then the Rosary (true to its origin in the Office) is its microscopic – or perhaps we might call it the "handheld" (palmtop?) version. In a little over an hour, one can "celebrate" all the major events which the Liturgy recalls in a whole year, spanning the whole life of our Lord!

The Way of the Cross
Clearly, S4 contains the first nine Stations and S5 contains Stations 10 through 12. The final two may either be included in S5 or in G1.

The Holy Sacrifice of the Mass
Since the Mass is the "unbloody" re-presentation of the Sacrifice of Calvary, the Mass was always intimately connected with S5. With the addition of L5, the connection between the Mass and the Rosary is brought to a deep intimacy. We have already discussed the connections to the Trinitarian formula "In the name of the Father..." (G2) and the Lord's Prayer (L3). But there are other, less obvious, links to the Mass – some of which we will indicate.

Gloria
The Gloria, now sung on solemnities and most Sundays, clearly has its origin in the song of the angels which the shepherds heard (Lk 2:14) at Christmas (J3).

The Gospel
The proclamation of the Gospel itself spans the entire Rosary (or at least all the mysteries from J1 to G2; G3 is in Acts, and appears in the other readings). As the Liturgical Year proceeds, the Scripture readings associated with every mystery will be encountered. Hence, there is a very strong link here, and one to which the rituals (of the Rosary or of the Mass) have yet to take into account.

Water Added to Wine
There is a more subtle link with J3 in the prayer which is said as the water is added to the wine at the Offertory:
"By this mingling of water and wine, may we come to share the divinity of Christ Who humbled Himself to share in our humanity."
This prayer is, according to the liturgists, derives from an old Collect for Christmas. But this might also link to L2, in which we see the water changed into good wine.

Commemorantes
In the Canon, the name of Mary is always mentioned, thus fulfilling her prophecy in the Magnificat (J2). The Apostles are also mentioned; this might be linked to our Lord's call (L3) or even to Pentecost (G3).

Unde et memores
Immediately after the Consecration, the "memorial" being accomplished is stated: this includes the Passion (S1-S4), Death (S5), Resurrection (G1) and Ascension (G2).

Agnus Dei, Lavabo
The triply repeated "Lamb of God" is an echo of the words of John the Baptist the day after he baptized Jesus (L1): "The next day, John saw Jesus coming to him; and he saith: Behold the Lamb of God. Behold him who taketh away the sin of the world." (Jn 1:29) These words are also echoed by the priest as he shows the Host to the people. Another link to L1 might be seen as the priest washes his hands, and the innocence of baptism is recalled.

Domine non sum dignus
I always like to ask people what part of the Mass is based on a pagan prayer. Of course it is unknown whether the centurion (Mt 8:5-13) really was a pagan – though it is rather likely. Also it is unknown whether he actually spoke in Latin and had an interpretor, or if he was speaking the common Greek, or even if he had managed to acquire some Aramaic. But it is a very comforting thing to think of how Jesus praised the faith of this Roman, and we might ask for the same faith, whether we are meditating on L3 or saying "Lord I am not worthy" just before receiving Holy Communion.

Ite, missa est
As the Mass is completed, the command "Go" (ite in Latin) recalls the "great commission" our Lord made just before ascending to His Father (G2). We have a job to do; so we "go forth."

(to be concluded...)