Tuesday, March 28, 2006

Revealing an Ancient Secret in The Vatican Code

Well, actually the real name of the source is the "Codex Vaticanus". It is the complete Bible in Greek, and dates to the early fourth century. Wow. It is among the oldest documents in existence - yes, we have many texts which are older in the sense that they were written much longer ago, but those texts are preserved as copies, most often made by monks in monasteries. Sure, you can buy copies of Julius Caesar or Euclid in the original printed a few years ago. But this particular copy of the Bible is actually over 1600 years old!

I now have, thanks to the assistance of a good friend, a "typographical facsimile" of one of the most important parts. It is one of the handful of quotes from the Bible which most people know completely by heart. Even more curiously, it actually does reveal a major secret: a secret of communication. Much better than the telephone, or radio, or the ethernet - better than Morse Code, or ASCII, or even any human language (in itself) - because it tells us how to communicate with God!

Oh, good - I thought you would guess - I mean the "Our Father" also known as "the Lord's Prayer". You can find the English for it in St. Matthew's Gospel, 6:9-13. OK, that you know the English, now take a look at the ancient form in the Vatican Code:

Here is my transliteration, so you can try sounding out the words - first, without spaces. Note that I wrote the omega as ô (long O) and the eta as ê (long e).

epigês tonartonê
And now, with spaces where the words are, and broken into phrases corresponding to the English. (Note, this is not quite the same as the usual Greek version, if you are trying to compare them.)
Pater êmôn
o en tois ouranois
agielthêtô to onoma sou
elthetô ê basileia sou
genêthêtô to thelêma sou
ôs en ouranô kai epi gês
ton arton êmôn ton epiousion dos êmin sêmeron
kai aphes êmin ta opheilêmata êmôn
ôs kai êmeis aphêkamen tois opheiletais êmôn
kai mê eisenegkês êmas eis peirasmo
alla rusai êmas apo tou ponêrou
This facsimile is replicated from a very amazing book called The Lord's Prayer in 250 Languages where it is number LXXX of the CCL versions. I had a particular reason for showing you this facsimile: because here you can see how hard it was to learn how to read! Notice: there were no spaces between words! No punctuation either! Words were sometimes broken onto two lines, though they did not write a hyphen. They even had something akin to our "contractions" (you know, don't you?) which you can see at the end of the first line, where there is a line above the "omega", standing for a "nu" which was omitted. and though this version used what we call the "small" omega, there were no small letters - everything was what we call "upper case" or "capitals"! Those of you who are familiar with Greek letters will note that the capital sigma, usually written as S is here written as "C". (Hence the "s" sound of "c" in some words - but that detail would take to long to explore now.) Also, no accents, no "breathing" marks - they knew where those had to come. (after all, this is not a lesson in ancient Greek!)

So there you have it. An important secret, right out of the Vatican archives (well, almost!) Communication with God, as taught by God Himself! Now available with spaces for easier reading. So then next time you say this wonderful prayer, you can be grateful for a whole lot more, including the spaces between words.

Maybe it would be a good time to say it now?

Saturday, March 25, 2006

My Favourite GKC Quotation

I wrote this up back in 1997 and never used it - but today is the most fitting day for it to be posted.
--Dr. Thursday
What is my favourite GKC quotation? Well, I thought I would write this up, since it is a very hard question to answer. There's so much to choose from. My favorite GKC prayer is Father Brown's "The cross of Christ be between me and harm," though the line about Holy Communion in The Ball and the Cross is a close runner-up: "If you are sorry it is all right. If you are horribly sorry it is even better. You only have to go and tell the priest so, and he will give you God out of his own hands." Then there is that moving line in The New Jerusalem, referring to the Garden of Gethsemani, where GKC quotes the boy as saying "it is where God said His prayers."

The most dramatic scene is that beneath the water tower in The Napoleon of Notting Hill, which I will not elaborate on in case you haven't read it yet. And I will refrain from revealing details of the book with the most tantalising title, namely, The Man Who Was Thursday. And for a biographical scene, I choose the incident of the lighthouse at Christmas, with its hopeful line from the Salve Regina: "Yes: Nobis post hoc exsilium ostende..." - "To us, after this exile, show..."

Yes, there are large numbers of lines which are clever as well as true, humorous as well as noble, accurate as well as attractive. But you don't want to hear this computer scientist quote lines like Gabriel Gale's "I often stare at windows" or words from those fought by Aquinas who think there's a thing "which is both Yes and No" - perhaps they call it "Yo"; or the liturgical link to high technology Chesterton saw in France: the Catholic thing that's "some kind of perpetual process, going on all the time" though it is true that "I have often thanked God for the telephone" and also "we have to call electricity by the Greek word for amber, since" - yes, it's still true almost one hundred years later - "since we have no idea of the true nature of electricity."

But speaking as a computer scientist I see an awesomely powerful and overlooked quote in Chesterton's The Everlasting Man. Much is always made of the importance of the number zero - the value of which is apparently nothing at all. Though you might not be a computer scientist, you might find it interesting that there are other kinds of "zeros" in mathematics. One of these is called "the identity of the free monoid over an arbitrary alphabet" - but though that is the correct term, it sounds too pompous for daily use, so we simply call it the empty string, or epsilon, or "quote-quote" (because that's how it is spelled in some computer languages).

This sounds much more complicated than it is. I feel like Maria explaining how singing works in "The Sound of Music"... When you want to add numbers together you start with zero. But when you want to stick characters together, you start with the empty string.

Let me make it even easier - where's that guitar? Get a piece of paper and a pencil. I'm going to spell out a word for you, and you write it down.

"Doe: a deer, a female deer" - no no. let's start again. Are you ready? C, A, T. Ok, you've got "cat" written now, right? Good.

Ok, here's another: G, K, C. Well, that's not a word, but we all know what it means.

One more, ready? Now what have you written so far? Nothing at all, right?

No, because I haven't started spelling the word for you. Well, that which you see before you is the zero-like "nothing" we computer scientists call the "empty string". In programming we use it all the time when we are putting words together - just like you do when you clear your calculator or adding machine. (You can see it next time you "log in" - just look at the "empty place" where you type your password - that's the empty string!)

Now that you understand the empty string, I will tell you my favorite quote. It is the empty string, (well, ok, the typographer in me insists that actually it is the paragraph break) which appears a few paragraphs before the end of part one of The Everlasting Man - and to emphasize it, I will put a "pause" there in my excerpt:
[Regarding pagan Rome in the last years B.C.] ... It was something in the sense of impotence and despair with which men shook their fists vainly at the stars, as they saw all the best work of humanity sinking slowly and helplessly into a swamp. They could easily believe that even creation itself was not a creation but a perpetual fall, when they saw that the weightiest and worthiest of all human creations was falling by its own weight. They could fancy that all the stars were falling stars; and that the very pillars of their own solemn porticos were bowed under a sort of gradual Deluge. To men in that mood there was a reason for atheism that is in some sense reasonable. Mythology might fade and philosophy might stiffen; but if behind these things there was a reality, surely that reality might have sustained things as they sank. There was no God; if there had been a God, surely this was the very moment when He would have moved and saved the world.
The life of the great civilisation went on with dreary industry and even with dreary festivity. It was the end of the world, and the worst of it was that it need never end. A convenient compromise had been made between all the multitudinous myths and religions of the Empire; that each group should worship freely and merely give a sort of official flourish of thanks to the tolerant Emperor, by tossing a little incense to him under his official title of Divus. Naturally there was no difficulty about that; or rather it was a long time before the world realised that there ever had been even a trivial difficulty anywhere. The members of some eastern sect or secret society or other seemed to have made a scene somewhere; nobody could imagine why. The incident occurred once or twice again and began to arouse irritation out of proportion to its insignificance. It was not exactly what these provincials said; though of course it sounded queer enough. They seemed to be saying that God was dead and that they themselves had seen him die. This might
be one of the many manias produced by the despair of the age; only they did not seem particularly despairing. They seemed quite unnaturally joyful about it, and gave the reason that the death of God had allowed them to eat him and drink his blood. According to other accounts God was not exactly dead after all; there trailed through the bewildered imagination some sort of fantastic procession of the funeral of God, at which the sun turned black, but which ended with the dead omnipotence breaking out of the tomb and rising again like the sun.

I am not sure that even Tolkien surpasses this Chestertonian retelling of the Eucatastrophic drama of our history! Indeed. When I read this, I felt, and I still feel, for a fleeting instant, the Great Amazement which many wise men sought (and still seek) to find, and have not found. For a moment, I feel as the ancient Romans must have felt. In the empty string between the paragraphs, the "if statement" succeeded and as we say, the "then-clause" was taken. By the nothingness of that empty string, Chesterton denotes the moment when God did move and save the world - the moment when "the Word was made flesh - and dwelt among us."

The Fulness of Time

But when the fulness of the time was come, God sent his Son, made of a woman, made under the law. (Galatians 4:4)

Jesus emptied himself, taking the form of a servant, being made in the likeness of men, and in habit found as a man. (Philippians 2:7)

Happy Feast of the Annunciation, the delivery of Mary's Fiat to the Eternal Father, the Overshadowing by the Holy Spirit, and the Incarnation of the Eternal Word!

And for those of you who (like me) have been to Middle Earth, it is the memorial of the day of the Downfall of Sauron.

This picture

is from a new project I posted over on the "SmallPax" blogg in which I am honored to participate. (The blogg, not the project! The project is just an idea at present.)

And if, like me, you can never seem to get enough of this most joyous and pivotal event, please click here...

Friday, March 24, 2006

Light and Darkness

Over at Unity of Truth another friend named "Hedgemaker" posts about the Dark Night and the ancient images of very distant galaxies now being photographed.

This brings up a very interesting question:

Why is the sky dark at night?

Yes, yes - the sun has set. But that's only part of the reason.

If the "universe is infinite" - and "there are always more stars" further out there somewhere - well then: why is the sky dark? Shouldn't the sky be light, all the time?

This question may sound like a joke. It is a very serious question - so much so that it is called "Olbers' Paradox" after the German physician and astronomer, Wilhelm Olbers (1758-1840) who explored the question.

Father Jaki has an interesting book - The Paradox of Olbers' Paradox - about the history of this topic, and how astronomers have both debated and avoided it.

But the paradox of the dark night sky is not the only curious idea which "Hedgemaker" has evoked. Far more compelling is the question about the light versus the darkness - and of course this idea immediately calls forth two of the most dramatic lines from all the books I know.

The first is from St. John's "Prologue" to his Gospel:
And the light shineth in darkness: and the darkness did not comprehend it. [John 1:5]
The second was from Chesterton:
"The issue is now quite clear. It is between light and darkness and every one must choose his side." [Ward, GKC, 650]
It is light, and light alone, which brings us the knowledge of the stars, in a paradox far more Chestertonian than the one named for Olbers. For those nocturnal jewels which appear to be the smallest objects which we can see are indeed among the largest things in existance! Think about it - when you look upon the Andromeda Galaxy (which can be seen with the naked eye) you perceive directly some billions of stars. So - are the stars tiny or vast? But when you look upon them, they are just as much your own as they are great astronomers. Remember it was not that long ago I quoted Burnham on this? It's worth repeating:
"Considered as a collector of rare and precious things, the amateur astronomer has a great advantage over amateurs in all other fields, who must content themselves with second and third rate specimens. For example, only a few of the world's mineralogists could hope to own such a specimen as the Hope diamond... In contrast, the amateur astronomer has access at all times to the original objects of his study; the masterworks of the heavens belong to him as much as to the great observatories of the world." [p. 5, emphasis added]
Odd that he mentions jewelery:
I felt economical about the stars as if they were sapphires (they
are called so in Milton's Eden): I hoarded the hills. For the universe is a single jewel, and while it is a natural cant to talk of a jewel as peerless and priceless, of this jewel it is literally true. This cosmos is indeed without peer and without price: for there cannot be another one.
[GKC, Orthodoxy, CW1:268]
Yes, despite what you see in some science fiction, there cannot be more than one universe - by definition. The cosmos, remember, is the Greek word which is used in the Bible, but often translated as "world" - but really means "ordered creation" or "universe". You might try using "universe" for "world" in that famous line from St. John's gospel - it's verse 29 in chapter 1, and the priest says it during the Mass, just before Holy Communion. (I want you to do it yourself, so I won't quote it here!) See? Now think about those distant galaxies again...

And since we have now united all these dramatic and paradoxical concepts - on the eve of the Annunciation, nine months before Christmas Eve - how can I not fail to quote that most dear of all Chesterton's lines:
...the hands that had made the sun and stars were too small to reach the huge heads of the cattle.
[GKC, The Everlasting Man CW2:301]

A Debate on Science and Religion

I have decided to cheat while I am busy with several other things. I mean instead of writing I will post something Chesterton wrote. It is from his novel called The Ball and the Cross, and is part of a debate between MacIan, a Catholic, and James Turnbull, an atheist. Once you have read it, please consider the following question: Did Chesterton know of Pierre Duhem?
--Dr. Thursday

[MacIan said] "...You hold that your heretics and sceptics have helped the world forward and handed on a lamp of progress. I deny it. Nothing is plainer from real history than that each of your heretics invented a complete cosmos of his own which the next heretic smashed entirely to pieces. Who knows now exactly what Nestorius taught? Who cares? There are only two things that we know for certain about it. The first is that Nestorius, as a heretic, taught something quite opposite to the teaching of Arius, the heretic who came before him, and something quite useless to James Turnbull, the heretic who comes after. I defy you to go back to the Free-thinkers of the past and find any habitation for yourself at all. I defy you to read Godwin or Shelley or the deists of the eighteenth century or the nature-worshipping humanists of the Renaissance, without discovering that you differ from them twice as much as you differ from the Pope. You are a nineteenth-century sceptic, and you are always telling me that I ignore the cruelty of nature. If you had been an eighteenth-century sceptic you would have told me that I ignore the kindness and benevolence of nature. You are an atheist, and you praise the deists of the eighteenth century. Read them instead of praising them, and you will find that their whole universe stands or falls with the deity. You are a materialist, and you think Bruno a scientific hero. See what he said and you will think him an insane mystic. No, the great Freethinker, with his genuine ability and honesty, does not in practice destroy Christianity. What he does destroy is the Free-thinker who went before. Free-thought may be suggestive, it may be inspiriting, it may have as much as you please of the merits that come from vivacity and variety. But there is one thing Free-thought can never be by any possibility - Free-thought can never be progressive. It can never be progressive because it will accept nothing from the past; it begins every time again from the beginning; and it goes every time in a different direction. All the rational philosophers have gone along different roads, so it is impossible to say which has gone farthest. Who can discuss whether Emerson was a better optimist than Schopenhauer was pessimist? It is like asking if this corn is as yellow as that hill is steep. No; there are only two things that really progress; and they both accept accumulations of authority. They may be progressing uphill or down; they may be growing steadily better or steadily worse; but they have steadily increased in certain definable matters; they have steadily advanced in a certain definable direction; they are the only two things, it seems, that ever progress. The first is strictly physical science. The second is the Catholic Church."

"Physical science and the Catholic Church!" said Turnbull sarcastically; "and no doubt the first owes a great deal to the second."

"If you pressed that point I might reply that it was very probable," answered MacIan calmly. "I often fancy that your historical generalizations rest frequently on random instances; I should not be surprised if your vague notions of the Church as the persecutor of science was a generalization from Galileo. I should not be at all surprised if, when you counted the scientific investigations and discoveries since the fall of Rome, you found that a great mass of them had been made by monks. But the matter is irrelevant to my meaning. I say that if you want an example of anything which has progressed in the moral world by the same method as science in the material world, by continually adding to without unsettling what was there before, then I say that there is only one example of it. And that is Us."

Wednesday, March 22, 2006

Enumerating the rationals

Over on Unity Of Truth my friend Electroblogster asked about Cantor, a 19th century mathematician, and his demonstrations regarding "infinity". I do not have the books with me, and I only have a short between steps of my current work project, so I cannot talk about this at my usual length.

But first I must quote Chesterton, because once we start talking about infinity, there is a certain quote which we must always recall, whether we are mathematicians, computer scientists, theologians, philosophers, or just simple students:
Poetry is sane because it floats easily in an infinite sea; reason seeks to cross the infinite sea, and so make it finite. ... To accept everything is an exercise, to understand everything a strain. The poet only desires exaltation and expansion, a world to stretch himself in. The poet only asks to get his head into the heavens. It is the logician who seeks to get the heavens into his head. And it is his head that splits.
[GKC, Orthodoxy CW1:220]
So, perhaps I should write a poem, rather than explaining! (Maybe over the weekend.)

OK, the question (as I understood Electroblogster to ask) is: Are there as many RATIONAL numbers as integers?

Note: this is NOT the famous question answered by Cantor, but it leads up to that one, and if this seems hard to understand, the other one will be somewhat harder.

Second note: I must remind you that this is NOT a matter of "belief" - it is just a bit of mathematics. You can probably find it explained better by somebody who does this for real, no pun intended!

Remember, a rational number is just what some of us call a fraction - you know, we say "something over something" - but we don't mind whether it might also be a WHOLE number, too: like say "six over two" which is really three. We just need the idea that there are two whole numbers, and neither one is zero (positive, nonzero integers).

Now, if we want to show that two things are the same size, we have to show that they are in one-to-one correspondence. A nice way is to make a list of the pairs of things. So that is what we'll do. We'll make a list of all the INFINITE rationals, and show that it's just as long as the INFINITE list of whole numbers!

Do you think God will mind us borrowing eternity just to do this? No, we don't need that long. And you won't have to buy a bigger disk drive, either!

Here's how we make the list. You can do this on your own piece of paper at home. (No, not an INFINITE piece of paper, silly!) Let's just go up to six for now, and you will understand the rest. Make a kind of big tic-tac-toe diagram, but with six columns and six rows. Then across the top, put 1,2,3,4,5 and down the side put 1,2,3,4,5. Hopefully you will have something like this:


Now, each of those boxes stands for a RATIONAL NUMBER - because there is JUST ONE pair of numbers, the row (on the left) and the column (on the top) which means that rational number for that box is (row over column). Here, I will fill part of it in, so you can see:


OK! so there we have our rational numbers. Now if we had that infinite paper, and God let us use eternity to fill it in, we would have them all listed. (But we don't have to bother. There is a good math reason for this, too, which is called "mathematical induction" and someday I will talk about that too. But again it is NOT about "faith" it is mathematics. You can trust me on this. ... wait, maybe it is about faith! So Chestertonian!!!)

OK, now we need to see that there are just as many boxes with all the RATIONAL numbers as there are integers.

And you throw up your hands and say HOW CAN THAT BE? There are LOTS more boxes than integers - if there are "infinite" boxes in one row, there must be "infinity squared" in the whole table!

And I say, no, there are just as many - because I can give you a list which links EACH box to JUST ONE integer, and none left over!!!

You get one chance to think it out for yourselves... and then I will tell you how to do it.

While I wait for you to try to get the answer, I'll just quote a relevant Chesterton poem, which is one of my very favourites:


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, CW10:209]

OK, here's the answer:

You start in the upper left with one. Then to its right put two. Go down one, and left one, and put three. Then, go back to the top row, and put four; then left-down, five; left-down, six. Back to the top: seven; left-down, eight; and so forth. Got it? OK, here is what the table looks like when you fill it in that way:


So! you see there is just ONE box related to every integer - OH! but that means "infinity squared" is NO BIGGER than infinity!!

Exactly. You need to do something a little more tricking if you want "a bigger infinity"!

Yes, this is funny to think about when one knows God - because He is real, and has all these other amazing properties, like love, and kindness, and justice and mercy, which no conceivable set of numbers can ever have.

So we have seen that the RATIONALS are "enumerable" - there are "as many" fractions are there are "whole numbers" - even if that sounds kind of funny. But there are lots of other numbers besides fractions, though some are very hard to talk about. But that's enough for today.

Tuesday, March 21, 2006

Cole's Paper on M67

As promised, here is the delightful story from 1903 of F. N. Cole and M67, that is, the "Mersenne number" M67 which is 267-1, and Mersenne's claim that it is prime. Not only does it show how persistence pays off, but it also demonstrates that knowing how to add and multiply can be very important!
Dr. Thursday

...In 1903 F. N. Cole (1861-1927) proved that M67 is not prime.
I should like here to preserve a small bit of history before all the American mathematicians of the first half of the twentieth century are gone. When I asked Cole in 1911 how long it had taken him to crack M67 he said "three years of Sundays." But this, though interesting, is not the history. At the October, 1903, meeting in New York of the American Mathematical Society, Cole had a paper on the program with the modest title On the factorization of large numbers. When the chairman called on him for his paper, Cole - who was always a man of very few words - walked to the board and, saying nothing, proceeded to chalk up the arithmetic for raising 2 to the sixty-seventh power. Then he carefully subtracted 1. Without a word, he moved over to a clear space on the board and multiplied out, by longhand,
193,707,721 x 761,838,257,287
The two calculations agreed.
Mersenne's conjecture - if such it was - vanished into the limbo of mathematical mythology. For the first and only time on record, an audience of the American Mathematical Society vigorously applauded the author of a paper delivered before it. Cole took his seat without having uttered a word. Nobody asked him a question.

[Eric Temple Bell, "The Queen of Mathematics" page 503 in The World of Mathematics Vol. 1.]

Saturday, March 18, 2006

An Interesting Mystery

If you are one of the bold ones who have read my lengthy essay on the Luminous Mysteries, you will recall that I made a kind of loose and poetic analogy between the 20 mysteries and the 20 amino acids which are coded by the genetic code of DNA. I'm not going to repeat that analogy here, but I need to mention it so you will have some background on the rest of this posting.

Last month when we did the novena for Pope Benedict, I concentrated on the Luminous Mysteries - and I thought how interesting it was that we could now meditate upon that wonderful scene "in the neighborhood of Caesarea Philippi" as we said the third Luminous mystery. [See S. L. Jaki's And On This Rock for some amazing details about this location, and its significance to the "Petrine Commission".] On another night, I spent the whole decade thinking over the scene which started "Lord teach us to pray... When you pray, say 'Our Father...'" Which is kind of interesting (especially for a computer scientist who has worked on compilers!) to pray one prayer while pondering another. Of course it's not that unusual - for we've all had that happen every time we start the Joyful Mysteries with the Annunciation - we're busy saying the Our Father while we hear Gabriel say "Hail Mary..." - or when we say the second Glorious mystery with its "in the Name of the Father and the Son and the Holy Spirit..."

It's kind of like that piece for two violins by Mozart (I think it is called "Table Music") - clever, and very interesting - yes - but the intellectual counterpoint of two prayers at once was not what I am getting at.

Tonight, I noted something curious about the third Luminous mystery, which may be denoted by the title "The Proclamation of the Kingdom". Sometimes I review the various "occupations" our Lord performed during His public ministry, sometimes I choose one or more particular scenes, as I mentioned earlier. But tonight I let the mental "focus" widen to span the entire public ministry, from just after the Wedding at Cana (in Luminous Mystery 2) up to the Transfiguration (in Luminous Mystery 4) - and when I did so, I was struck by the fact that all the "mystery" is a continual "theophany" - sometimes very low-key - but nevertheless distinct.

Remember a theophany is a "revealing" of God: the visit of the Kings, the Baptism in the Jordan, the Miracle at Cana - all these are theophanies, and recalled as such by the Church. Clearly, the Transfiguration is also one; the msytery of the Eucharist requires a deeper study which I may try to consider another time.

But the idea that this ONE mystery - the third Luminous - could touch on so many aspects of the life of Jesus - the multiplication of the loaves and fishes, the walking on water (and Peter's too!) the parables, the lessons, the argumentation with the Pharisees and the Saducees, the healings, the journeys, "Consider the lilies of the field..." "Martha, you are worried about many things..." "Whoever does the will of my Father is brother and sister and mother to Me..." and the prophecies and predictions and warnings... I thought it was the most complex of the mysteries.

Then I saw I was wrong.

It is the simplest of mysteries, for it is the commonest. It fits so many things of our Lord's life: public or intimate, tender or bold, active in clearing the temple, asleep in the storm-tossed boat, feeding, healing, teaching, arguing, defending, accusing.... revealing Himself as true God and true Man.

And I realized that there was a resonance with my analogy from the Rosary to the amino acids. For there is a very simple amino acid called "glycine" - like the other amino acids, it has the carboxylic acid group (HOC=O) and the amino group (NH2) and a hydrogen connected to the central carbon - but where the so-called "R" group would be attached, there is just a simple, lowly hydrogen.

Glycine is the simplest amino acid, and so can fit where others would be too big or bulky, or have special properties which might get in the way at that point...

Obviously, such a strange analogy can only go so far. But I was startled by this parallel, and so I will think some more about this.

A Partial Index

For your convenience, here is a partial index to some of the items on this blogg. I hope it is useful.
If you have any suggestions for improvements or additions, please let me know.
--Dr. Thursday


The Call
Three Calls
The QWERTY Parable
For Best Results, Set The Volume To Max
The Only Begotten
The Shape of Water
Why Mary Wears Blue
The Legend of Lance the Bird
Secret Arts
Playing Saul's Spot
Playing Saul's Spot (part II)
The Great Discovery
HalloweE.n coli
Ass, Ox, Sheep
Books, Ancient and Modern
Words (and) Knock Knock
Does Anyone Care About Poetry?


A Family Matter
Experienced Armies
Green, Green and Green


What Happened Then
The Meeting of GBS and GKC


The Division of the Waters
Part 1
Part 2
Part 3
Part 4
Part 5

Light From the Rosary
Part 1
Part 2
Part 3
Part 4
Part 5
Part 6
Part 7
(back cover)

Excerpts from On the Nature of the Papacy: Exploring Some Secular Parallels
Part 2
Part 3
Part 4
Part 5
Part 7

Some other short entertainments

Clock Day
Getting in Trouble with Ancient Rome

Friday, March 17, 2006

A Prime Example

The other day something a young friend posted something on his site, The Map Guy. Actually he was posting something about Egypt or Alexandria or something, and mentioned Eratosthenes.

Eratosthenes was an ancient Greek scholar, who did some amazing things, but one thing in particular leaped out in my memory, so I posted a long comment about it. Since then I decided I had some more to say about the matter, so I will take the liberty of reproducing most of that comment, and augmenting it with some more interesting items.

First, I must point out something very funny about our favourite Uncle Gilbert. Most people think that because he was a writer, he only did "literary" things, which if you are from England you must say "lit'ry" things, and then quickly sip some tea. I am not from England. Ahem. But you see our Uncle Gilbert was interested in everything, which means he even talked about...

(shh, come close to the screen and be quiet so I can whisper it!)

... math.

Yes, I mean mathematics, like 2+2, and x over y, and that sort of thing - and of course he immediately related it to much larger and more dramatic topics, like martyrdom, and belief in the Trinity. You are surprised? You should not be. If you won't beliege me, a lowly computer scientist, then believe Mr. Chesterton. Here's what he said:
[People have] the common idea that mathematics is a dull subject, whereas the testimony of all those who have any dealings with it shows that it is one of the most thrilling and tantalising and enchanting subjects in the world. It is abstract, but so, to all appearance, is theology. Men have hurled themselves on the spears of their enemies rather than admit that the second person of the Trinity was not co-eternal with the first. Men have been burned by inches rather than allow that the charge to Peter was to be understood as a charge to him as an individual rather than to him as a representative of the Apostles. Of such questions as these it is perfectly reasonable for anyone to say that, in his opinion, they are preposterous and fanatical questions. And what men have before now done for the abstractions of theology I have little doubt that they would, if necessary, do for the abstractions of mathematics. If human history and human variety teach us anything at all, it is supremely probable that there are men who would be stabbed in battle or burnt at the stake rather than admit that three angles of a triangle could be together greater than two right angles.
[GKC, Lunacy and Letters 58-59, emphasis added]
At first, when you read the particular topic that I posted over on the Map Guy's blogg, you may also think it dull. But I will show you that it is actually kind of fun, and also then I will tell you the thrilling part, which is what I forgot to post in my comment, because I was playing hookey then, and waiting for some dull thing to finish while I was at work. Now I am playing hookey from some other things I ought to be doing, and so I have decided to write about something thrilling, just for a little while. OK. So first, I will give you the comment, which is a nice fun project, with a little more detail, and then go on to the thrilling part.

[The following is from my comment...]

In computer science, we learned about a thing called the "Sieve of Eratosthenes" - it is a way of finding prime numbers. A prime number does not have any divisors except for itself and one. (13 is prime, 12 is not prime, because 2 goes into 12.)

The "Sieve" is easy to do, and even kids can find prime numbers with it - and what's even more fun, you do NOT have to learn how to divide in order to use it!!!

I will tell you how to do it, so you do not have to go looking around. Take a blank page, and write the numbers, starting at one - go as high as you have room to write. To be tidy, you might just write them in ten columns. Let's say you go from one (at the top) to one hundred at the bottom. Then, sit back and enjoy the nice table of integers! (ah.)

OK, now when you are ready to do the sieve: get a new color pencil (it's not really necessary, but helps make for a nice design). Now, make a circle around your TWO, and then go through the table, putting a slash ("/") through every SECOND number - so you slash four, six, eight... etc until you come to the end of the table.

Now, go back to the top, and circle THREE, and slash every THIRD number (yes, you slashed SIX again - well, six is two times three, remember?) and so on down the table.

Now, back to the top, and circle FIVE, and slash every FIFTH number. ...

Now, back to the top, and circle - what? and then slash - what?

Now you see what happens? You keep going until there is nothing left to do.

The numbers with circles are prime. You can check, there ought to be 25 circles between 1 and 100 (check - one is neither circled nor slashed!) All the others are crossed off.

Hurray! No dividing, no sticky fingers, no crying, no crumbs for the dog to lick up. Lots of ancient math fun for the whole family.

[end of excerpt from my comment]

Now for a couple of thrilling parts.

First, there are ways of saving some work for yourself. Once you do this for numbers from 1 to 100, you will quickly see that you do NOT have to write any numbers which end in any of the following digits:

because ALL of them will be crossed off (except, of course, for the very first row, which has two and five circled!) So the only columns you really need are those ending in one, three, seven and nine, but then of course you have to remember to skip the missing columns as you count.

Second, there are lots of very interesting things about prime numbers. Primes are one of the very important topics in the branch of mathematics called "number theory". One of the very important workers in this area was a French mathematician by the name of Marin Mersenne. There are a special kind of prime number called "Mersenne primes" which he studied. They are numbers which are prime, and have the form
where p is a prime number. But the really interesting part about Mersenne, who lived from 1588 to 1648 and talked with people like Descartes and Galileo is this - he was a CATHOLIC PRIEST. He also did work in physics and astronomy.

Now for another thrilling thing. When I was doing my doctorate in computer science we had a funny little saying. It's sometimes just as important to find funny things to say as it is to find interesting things to study - and it's even better when the two are connected. This time they were connected. Here is the funny thing, which we made up because we listened to another student talk about how he was studying a new way of working on numbers to see if they are prime. We said:
Spies like big prime numbers.
That's because one of the ways in which one can encrypt messages - that means, turn into a SECRET CODE!!! - is to use a really big prime number. It is complicated, and spies and government agents or even credit card companies like secret things which allow information to be hidden in a code - so of course they like big prime numbers.

But there are other things one can use prime numbers for which are not so secret. One of them is also a lot of fun to talk about. It is called "hashing" and it is a way of storing information in a computer. But that will take some time to explain, so I will have to talk about that another day.

Tuesday, March 14, 2006

Why I am busy

Just to keep you informed of my situation here - yes, thank God, I am quite busy, with both work (that means employment) and work (that means the various projects I undertake for others). But you might be wondering about what that work is. Obviously I am not at liberty to go into my employment at present - though it usually means moving files, or having the machinery move files according to my orders. And I am not at liberty to go into all my projects either.

But I will give you just a little insight into WHY I do them - the projects, not the employment. I do that for money, and because there are others who depend on me, though not in the sense the IRS uses that term! It is good to acknowledge, in this posting, how much I depend on others, too - for food, writing, laughter, and all kinds of things too long to list here. As Chesterton said, "The greatest of poems is an inventory." [Orthodoxy CW1:267] And in telling you why, I may give you a clue to what it is I am doing. I found this quote in a book by S. L. Jaki - it is his "intellectual autobiography":
In that essay I spoke, of course, of Duhem, partly to illustrate the duty of a Catholic intellectual to drop everything else once he spots a topic of great moment for Catholic culture.
[Jaki, A Mind's Matter, 222]
Pierre Duhem, as you may know, was a brilliant French physicist, Catholic, hiker, artist, mathematician, and also an amazing historian of science (1861-1916). Jaki has three books on him and his work, as well as a book on his daughter; he refers to Duhem many times in his other books, in particular Duhem's 10-volume Systemè du monde which I think I mentioned on March 7. Alas as yet it has not yet been translated into English! Another day, perhaps, I will post more about the importance of that work.

But you may wonder about how this fits together with Chesterton. Obviously for a Chestertonian, all topics are interesting, but there is something extra exciting when one sees the convergence of several of one's own delights.... Jaki, Newman, Chesterton... here, check this out:
By then I had twenty or so years of intensive writing behind me, which taught me the truth of a saying of John Henry Newman: "Nothing would be done at all if a man waited until he could do it so well that no one would find fault with it."
[Jaki, A Mind's Matter 103]
Compare that with this:
...if a thing is worth doing, it is worth doing badly.
[GKC, What's Wrong With the World CW4:199]
Or this, perhaps even more amazing:
Would, today, a "progressive" theologian repeat with Newman that we know much more about angels than we know about brutes, or the animal kingdom?
[Jaki, A Mind's Matter 213]
compared with:
A turkey is more occult and awful than all the angels and archangels. In so far as God has partly revealed to us an angelic world, he has partly told us what an angel means. But God has never told us what a turkey means. And if you go and stare at a live turkey for an hour or two, you will find by the end of it that the enigma has rather increased than diminished.
[GKC, ILN Jan 4, 1908 CW28:21]
This is so exciting - and I would like to tell you more, but the machinery needs to be burped, so I must resume my other work now.

An Update

I found the first Newman quote! Courtesy of www.newmanreader.org:
At least they expose their inherent imperfections, if they incur no other penalty; for nothing would be done at all, if a man waited till he could do it so well that no one could find fault with it.
[Newman, Newman Reader (page 403)
Present Position of Catholics: Lecture 9:
"Duties of Catholics Towards the Protestant View"]
Now, the question before us is: Did Chesterton read this book before he wrote his What's Wrong With the World in 1910?

Friday, March 10, 2006

blink bloink blarp bleap

blink bloink blarp bleap

That's another cue-tone!

(And it's not even the "witching hour" - that is, xx:28 or xx:58 for television...)

And so we interrupt our usual blogg-writing for


Hey bloggist! Has all your blogg-reading - and writing - left you feeling tired and irritable? Why not...

(Ahem! Wrong script, just like last time... hee hee. Let's try this again.)

Attention, nephews and nieces of Aunt Frances and Uncle Gilbert! We're at war. But you knew that already. Ever since the Fall. And I don't mean autumn!

Yes, ever since the Serpent did his dirty work back in the Garden, we've been at war. It was succinctly put in one of Chesterton's most important lines:
"The issue is now quite clear. It is between light and darkness and
every one must choose his side."
[Maisie Ward, Gilbert Keith Chesterton 650]
I sincerely hope you've all chosen the side of Light, and are fighting hard. But the battle is fierce, and we tire easily, and get bored, and distracted....

However! There's a guy I know - he's a really hard worker - who is known as the "Terror of Demons"... You probably already know (and love) his wife - a humble Jewish Mother - and her Son. Yeah - you guessed it - I mean St. Joseph.

Well, it's time to do something practical. Like I said, there's this war. And there are people who need regular employment, and others who need stability, or new homes, or peace in their families... all kinds of things. I am sure you know of lots of people in such situations, or other difficulties...

So, starting tomorrow, March 11, for nine days, you can do the most practical thing to assist (you know - it's subsidiarity!) with all these various needs - by simply joining with your host, Dr. Thursday, in saying a rosary in honor of St. Joseph, asking him (1) to squash the infernal pests who attack us, and (2) to assist with all our needs, especially those which deal with employment and with families.

That's it. No coupon to clip. No form to fill out. You don't even have to double-click. And no credit card bill either! You can't beat that price anywhere else!

But now I gotta read the fine print: Please note - you need not post a comment in order to join. That's between you and God. I would have preferred not to have to post this at all - but even an occasional commercial break has its uses in the Divine Economy. (Oh, you don't think so? Just wait... you'll see.)
Don't forget - it's just nine days - synchronize your calendars... get practical...

We now return you to our regularly scheduled posting...

A Correction!

I have forgotten that, because this year March 19 falls on a Sunday, the feast day is transferred to Monday, March 20. (You know, it's so tech-cool - St. Joe is so important, his feast day cannot be suppressed, even by Sunday... not even by Holy Week! Really cool.)

So that means this year the novena will start on Sunday March 12. Please join us.

As an added feature, I will offer my intentions at daily Mass for all bloggers who join - remember, you need not post to join. (God's network takes care of all underlying protocols, and most efficiently, too.)

Tuesday, March 07, 2006

March 7 - the "Birthday of Science"

According to the older calendar, March 7 is the feast day of St. Thomas Aquinas, the day he entered into Life.
But today is also the Birthday of Science - science, that is, in the modern sense.
I learned this from a most amazing book, about which you will be hearding more in the not distant future. That book is Science and Creation by Stanley L. Jaki.
So I will quote the relevant parts for you, and then (after Holy Mass) depart for my lab to join the festivities...

--Dr. Thursday

Effective reorientation could not come about except through recourse to the deepest resources of faith. This had to imply something dramatic if the guideposts of faith for reason were to be planted with a historic impact.

The dramatic event took place on March 7,1277, when a list of 219 propositions was condemned by Étienne Tempier, bishop of Paris. The wide spectrum of questions over which a firm judgment was passed clearly indicated that the claim about the perennial recurrence of everything in every thirty-six thousand years (Prop. 92), and about the various aspects of the alleged eternity of the world (Prop. 83-91), represented only a most revealing part in a far broader and deeper issue. What ultimately was at stake was man’s rather newly acquired awareness of the contingency of the world with respect to a transcendental Creator, source of all rationality and lawfulness in the macrocosmos as well as in the microcosmos. Even a cursory review of the condemned propositions can show that what philo-sophy needed was not an "autonomy" based on the exclusion of some very real experiences, religious as they could be in character. The true need of philosophy consisted in vistas pointing far beyond the confines of pantheistic monism, however ancient its pedigree could be in the history of man’s speculations about the universe and his destiny in it.
The vindication of the Creator’s attributes opened up far-reaching possibilities for the interpretation of the cosmos. The recognition of the possibility of several worlds (Prop. 27); the rejection of the superlunary material as animated, incorrupt-ible, and eternal (Prop. 31-32); the admission of the possibility of a rectilinear motion for celestial bodies (Prop. 66); the rejection of their actual motion as if sparked by animal desire (Prop. 73); the rejection of the celestial orbs as organs equivalent to the eyes and ears of the human body though not as parts of a celestial machinery (Prop. 75); the rejection of the deterministic influence of stars on individuals from the moment of birth (Prop. 105); the rejection of the necessary production of the "first matter" from the celestial one (Prop. 107); all these de-cisions followed intimately from the effort to safeguard the abilities and exclusive rights of the Creator against any compromise dictated by a narrow rationalism. Those decisions also shaped the state of mind and conceptual groundwork for a revolutionary new approach toward the understanding of the workings of celestial and terrestrial bodies alike.

One may, therefore, look with Duhem [52] at the decree as the starting point of a new era in scientific thinking, provided it is kept in mind that the decree expressed rather than produced that climate of thought which Whitehead once rightly presented as the most crucial ingredient for the eventual creation of modern science. His views were expressed in a long passage which, because of its classic Whiteheadian stamp, deserves to be quoted in full:

I do not think, however, that I have even yet brought out the greatest contribution of medievalism to the formation of the scientific movement. I mean the inexpugnable belief that every detailed occurrence can be correlated with its antecedents in a perfectly definite manner, exemplifying general principles. Without this belief the incredible labours of scientists would be without hope. It is this instinctive conviction, vividly poised before the imagination, which is the motive power of research: – that there is a secret, a secret which can be unveiled. How has this conviction been so vividly implanted on the European mind?
When we compare this tone of thought in Europe with the attitude of other civilisations when left to themselves, there seems but one source for its origin. It must come from the medieval insistence on the rationality of God, conceived as with the personal energy of Jehovah and with the rationality of a Greek philosopher. Every detail was supervised and ordered: the search into nature could only result in the vindication of the faith in rationality. Remember that I am not talking of the explicit beliefs of a few individuals. What I mean is the impress on the European mind arising from the unquestioned faith of centuries. By this I mean the instinctive tone of thought and not a mere creed of words.
In Asia, the conceptions of God were of a being who was either too arbitrary or too impersonal for such ideas to have much effect on instinctive habits of mind. Any definite occurrence might be due to the fiat of an irrational despot, or might issue from some impersonal, inscrutable origin of things. There was not the same confidence as in the intelligible rationality of a personal being. I am not arguing that the European trust in the inscrutability of nature was logically justified even by its own theology. My only point is to understand how it arose. My explanation is that the faith in the possibility of science, generated antecedently to the development of modern scientific theory, is an unconscious derivative from medieval theology. [53]
Half a century has passed since these words startled a distinguished audience at Harvard University and indeed the whole intellectual world. The magnitude of the shock merely corresponded to the impenetrable density of a climate of opinion for which the alleged darkness of the Dark Ages represented one of the forever established pivotal truths of the "truly scientific" interpretation of Western intellectual history. Not being a professional historian of science Whitehead could not be blamed for not having perused the first five volumes of Duhem’s Système du Monde. Its extraordinary wealth of documentation might have very well raised in Whitehead’s mind some doubts about the validity of the concluding phrase of his long statement. At any rate, the spectacular flow of studies An medieval science touched off by Duhem’s monumental work provided among other things ample evidence that the medieval faith in the scrutability of nature had its logical justification in the medieval theology about Creator and creation, and that the faith in the possibility of science is a most conscious derivative from the tenets of medieval theology on the "Maker of Heaven and Earth."


[52] Le système du monde, vol. VI, p. 66. Duhem offered the last five volumes of his monumental opus as proof of the proposition that modern science "was born, so to speak, on March 7, 1277 from the decree issued by Monseigneur Étienne, bishop of Paris." By this Duhem meant that the decree decisively reinforced, mainly at the University of Paris, a train of thought leading ultimately to the formulation of a new (classical) physics.

[53] Science and the Modern World: Lowell Lectures, 1925 (New York: The Macmillan Company, 1925), pp. 17-18.

[quoted from Science and Creation by S. L. Jaki pp 229-231]

Thursday, March 02, 2006

March 2 - The "Feast Day of Subsidiarity"

Before everyone gets concerned that I have forgotten it is Lent - this is not an official designation. Yes, I know it is Lent. No, you did NOT miss an important announcement from the Vatican.

But for me, while I live, I will always consider this day as the "feast day" of Subsidiarity. For on Thursday, March 2, 2000, the machinery at the place-where-I-used-to-work went "live" and began officially running.

What was that machinery? Well, as much as it may horrify you to learn, it had to do with playing commercials on cable TV.

But there was a computer called HOME (there's no place like it) and on that computer was the heart of the machinery - a program called PUMP (hee hee, love these puns!) and the innermost part of that program contained a file called "subsid.c" - for it performed the complex task of controlling spot delivery to the Field - the task that everyone at the company knew was called "subsidiarity".

That file of "C" programming started with a very unusual quote. Good programming practice (and indeed justice!) suggests that when one uses ideas invented by others, one gives that person credit and acknowledgement in the comments...

The principle of subsidiarity:

A situation is always dealt with at the lowest possible level.

"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."

John Paul II: Centesimus Annus, 48

excerpted from a version of PUMP dated January 14, 2000

The machinery ran - and ran well - for just over 2000 days, round the clock. Because of this, a lot more people know about "thirteenth century metaphysics" which (as GKC noted in CW1:46) we resorted to, "inspired by the general hope of getting something done." And they know about subsidiarity too.

And, since today, six years later, it is again Thursday, I express my thanks to all those who worked hard to implement and maintain the amazing achievement we accomplished.

Yes, the world changed since then... but the principles have not.