Boethius, Theta and Pi

I have just made my usual Thursday posting over on the ACS blogg - today I glanced at the very famous The Consolation of Philosophy by Boethius.

This book I first saw mentioned about 20 years ago, in a fraternity magazine from the 1950s or 60s, at a time when I was busy with - uh - fraternity matters. It is an amazing and powerful book, relevant to far more than even Greek college societies - or it should be.

Stored away in a mystical file in a little-used part of my disk, long forgotten and collecting e-dust, is a small collection of excerpts from this wonderful book. I e-blew off the e-dust, looked it over, and thought it would do good to give you a taste of this important book.

--Dr. Thursday

Excerpts from The Consolation of Philosophy
by Boethius, translated by W. V. Cooper.

Written by Anicius Manlius Severinus Boethius (480-524 A.D.) while in prison awaiting execution, The Consolation of Philosophy is a dialog between the author and the personification of Philosophy, treating such topics as the being and nature of God, providence, and fate, the origin of the universe, the freedom of the will and the transitoriness of earthly greatness.
[From the back cover]

(Philosophy approaches Boethius; the form of her appearance is allegorical.)

[In these first excerpts, the "I" is Boethius.]

While I was pondering thus in silence, and using my pen to set down so tearful a complaint, there appeared standing over my head a woman's form, whose countenance was full of majesty, whose eyes shone as with fire and in power of insight surpassed the eyes of men, whose color was full of life, whose strength was yet intact though she was so full of years that none would ever think that she was subject to such age as ours. One could but doubt her varying stature, for at one moment she repressed it to the common measure of a man, at another she seemed to touch with her crown the very heavens; and when she had raised higher her head, it pierced even the sky and baffled the sight of those who would look upon it. Her clothing was wrought of the finest thread by subtle workmanship brought to an indivisible piece. This had she woven with her own hands, as I afterwards did learn by her own shewing. Their beauty was somewhat dimmed by the dulness of long neglect, as is seen in the smoke-grimed masks of our ancestors. On the border below was inwoven the symbol P, on that above was to be read a Q.

[At this point a footnote reads: P and Q are the first letters of the Greek words denoting Practical and Theoretical, the two divisions of Philosophy.]

And between the two letters there could be marked degrees, by which, as by the rungs of a ladder, ascent might be made from the lower principle to the higher. Yet the hands of rough men had torn this garment and snatched such morsels as they could therefrom. In her right hand she carried books, in her left was a sceptre brandished.

... Then I drew breath again and engaged my mind in taking knowledge of my physician's countenance. So when I turned my eyes towards her and fixed my gaze upon her, I recognized my nurse, Philosophy, in whose chambers I had spent my life from earliest manhood. And I asked her, Wherefore have you, mistress of all virtues, come down from heaven above to visit my lonely place of banishment? Is it that you, as well as I, may be harried, the victim of false charges?

[in the following excerpts, the "I" is Philosophy herself.]

Should I, said she, desert you, my nursling? ...Should I not share and bear my part of the burden which has been laid upon you from spite against my name? Surely Philosophy never allowed herself to let the innocent go upon their journey unbefriended.

Think you I would fear the calumnies? That I would be terrified as though they were a new misfortune? Think you that this is the first time that wisdom has been harassed by dangers among men of shameless ways?

...it is no matter for your wonder, if, in this sea of life, we are tossed about by storms from all sides; for to oppose evil men is the chief aim we set before ourselves. Though the band of such men is great in numbers, yet it is to be contemned; for it is guided by no leader, but is hurried along at random only by error running riot everywhere. If this band when warring against us presses too strongly upon us, our leader, Reason, gathers her forces into her citadel, while the enemy are busied in plundering useless baggage. As they seize the most worthless things, we laugh at them from above, untroubled by the whole band of mad marauders, and we are defended by that rampart to which riotous folly may not hope to attain...

[Wow. This strongly reminds me of The Phantom Tollbooth. -- Dr. T.]

...It is not the walls of your library, decked with ivory and glass, that I need, but rather the resting-place in your heart, wherein I have not stored books, but I have of old put that which gives value to books, a store of thoughts from books of mine...

...Now I know the cause, or the chief cause, of your sickness. You have forgotten what you are... You do not know the aim and end of all things... You have forgotten by what methods the universe is guided... But let us thank the Giver of all health, that you nature has not altogether left you. We have yet the chief spark for your health's fire, for you have a true knowledge of the hand that guides the universe; you do believe that its government is not subject to random chance, but to divine reason. Therefore have no fear. From this tiny spark the fire of life shall forthwith shine upon you...

Two to the two to the two

... is how many years ago this month that I took (and passed) the "prelims" - sometimes in other places called "quals" - the battery of tests which one takes as one enters into the "serious" part of the Ph.D. program. At that time and place and department, they were four evenings of VERY long exams, covering large swaths of the discipline.

And, by divine providence, hard work, and the support of good friends, I passed. Deo Gratias.

I mention all this because I have had to rummage back into my memories in pursuit of - er - perhaps a journal article. An article for a technical (scholarly) journal which will describe the work I did last weekend which I hinted at in a previous posting.

And, while I am at it, I would like to also mention another Ph.D.... that is, the comic strip called "Piled Higher and Deeper" by Jorge Cham, Ph.D. about the turmoils, tribulations, and triumphs of graduate school. It's uncanny how accurately he has described that life! Very good work, yes.

Ah - but you are wondering about the "prelims" - and why I mention such horrors here in a Chestertonian blogg? Because I wrote a poem about them, that's why. And yes, I wrote a poem for my dissertation, too, and it was published as part of that document. Hee hee. And now, the poem:

"Bruins"

"We must," said the prof, "your readiness gauge.
Please put your code at the top of each page.
You each get six questions, you must do four.
It's thought to be NP-hard to do more."

And so, with a heavy and sinking heart
I opened the test volume to its start,
Hoping the meager amount in my brain
Would be enough, and the PhD gain.

How fast this system? In this graph, how far?
State all the theorems which define A-star.
Show an expression to approximate sine,
And give the graphical form of a line.

What is a thunk? A deque? A stack frame?
What's call by reference, value, and name?
What is the debt that to Babbage is owed?
How do compilers produce object code?

Write CREW code to sort in big-O-log-n.
State the semantics of WHILE and IF-THEN.
List three movies where machines are a star.
Give object classes to model a bar.

What is third normal form? Define the terms
Trojan horse, viruses, time bombs and worms.
How do you prove that a grammar's type two?
How can k jobs share just one CPU?

If two jobs won't share, then one has to wait.
Show a routine so they'll co-operate;
Prove there's no deadlock, prove no starvation,
State your assumptions for termination.

Show in a table the groups of size four;
Three-address forms for LOAD, GOTO, and STORE;
The four types of grammars, and their machines,
Use formal notation, state what each means.

Compare and contrast Lisp, Prolog and C.
Pseudo-code functions to manage a tree
(AVL-balanced), a queue and a stack.
Give English equivalents for GREP, LEX and YACC.

State the advantages coming from RISC.
Why does cache memory speed up a disk?
Prove TSP has NP-completeness.
Show all your work; you get points for neatness.

I read it and thought, it will take a week
And it's just 1. (a) - so my outlook's bleak.
I swallowed and prayed, I went to begin...
Then I heard "Time's up! Please turn your test in."


[Made January 25, 1991. I was told by fellow CS grad students that this poem would serve as a useful study guide... Yes, indeed, for some of the questions in the tests I actually took are contained here! And if you are wondering why it is called "Bruins" that is another story for another time... ja? Hee hee.]

A Prayer Request - and Good News!

A dear aunt died last week - please remember her in your prayers.

As strange as it may sound, this has led to something interesting.

At the luncheon after the burial, I met a cousin-of-a-cousin - if I met him before, the memory is gone - but since he is on her side of the family (she was the widow of my father's brother) it is possible we had never met before.

In any case, he is working on his doctorate in physics, and we talked for a little while on tech matters. It was very funny since my work was in "string theory" the theory of "language", a branch of computer science, but his is in "string theory" the inner structure of elementary particles, a branch of physics!

He is still "in the hunt" for a dissertation topic, but was because of this remarkable - er - concurrence of our field-of-interest, he was curious about my own work, so I gave him a summary - the real short form is "I found fingerprints for bacteria" so you can think about that for a while.

He was somewhat surprised that such a cross-over of disciplines was still possible, and I explained that my work (in "string theory") not only helped with molecular biology, but actually began to reveal some odd things in my own field which hitherto had not been studied. "I think there's still some things no one has solved there - I know of at least one..." and he suggested that I resume my work.

So I did.

And so I can announce: this morning (Thanks Be To God!) I solved the extension of a popular algorithm when applied to DNA sequence analysis, known as ...

Well, now that I think about it, I do not think I should say more here in the e-cosmos.

No, indeed, I am not going to publish it here. After all, if no one has solved it yet, I may actually get to publish it in a JOURNAL. Guys with Doctorates do that from time to time. Hee hee.

This is absolutely hilarious, since the connection between us might be said to represent the complexity which defeats the original algorithm. That much I can tell you.

First, an "alphabet" is the set of symbols upon which some aspect of string theory is based. The usual DNA alphabet is {a, c, g, t} representing the four "bases" (adenine, cytosine, guanine, thymine) from which the strings (or "words") of the genetic code are built. (Notice I use small letters here.)

However, the "wild-card" alphabet for DNA has several other letters, representing more than one of the four bases. We still have A, C, G, and T (which are now the capitals!) but we have others like M which stands for either a or c, S which stands for c or g, and N which stands for any of a, c, g, t.

To help deal with these NEW characters, we have a NEW property, called "matches". In the wild-card alphabet, two characters are said to "match" if there is SOME character which they have in common: for example, A matches M, and A matches N.

Now, for the fun.

A matches M, and M matches C.

But!!! A does NOT match C.

Now, for many of the things you know about in math, when
x SOMETHING y
and
y SOMETHING z,
then often it is true that
x SOMETHING z.

(Like when SOMETHING means "equals".) Us math guys call that "transitive".

But there are some things, even in the NON math world, which don't work that way.

For example, "is a cousin of".

(dr-thursday) is a cousin of (child-of-my-aunt-who-died)
and
(child-of-my-aunt-who-died) is a cousin of (phd-student-in-physics)
but
(dr-thursday) is NOT a cousin of (phd-student-in-physics)

So now you know... stay tuned for more on this very exciting development.

And my sincere thanks to... uh ... x, y, and z.

PS: no, this is not some Fermat-like "the margin is too small to contain this marvellous proof". I have it in code, and it works. Next I have to prove a theorem or two, and there's no "back-of-the-book" to check if I get it right! And then maybe see if anyone did it already, and THEN see if there's still some journal that wants tech stuff like this... Hee hee. What a thrill!

an update

Just so you know - I've been busy. Work, writing, and other matters have cut into my day, and even my night.

You can still read my postings on Thursdays over at the blogg of the ACS.

Meanwhile, keep praying...

December 24, 2006 - "The End of It"

Dickens put those four words together as the title of the concluding Stave of his "Christmas Carol". And you may indeed wonder how, after the marathon technical textbook of the last 21 days how I might also make "The End of It". But God has also provided, yes, even for this, just as He provides us with the sunrise and sunset...

As we have gone through our 20 meditations pondering the 20 mysteries of the Rosary as well as the 20 amino acids denoted by the triples of mRNA, I have mentioned the "codes" by which each amino acid is indicated. This was the stupendous discovery made by Watson and Crick in the 1950s: the sequence of bases (the letters A, C, G, U) in the mRNA - the "working blueprint" used in building a protein - is "scanned" in triples, and each triple stands for exactly one amino acid. And, since there are four possible bases, and three positions for each base, there must be a total of sixty-four possible codes: ranging from AAA (which stands for Lysine) through CCC for Proline and GGG for Glycine, to UUU for Phenylalanine. The code AUG stands for Methionine, but it is also the special start code which begins the translation from RNA into protein.

Now, if you have been watching very carefully, you may have put all these 20 days of data together into a table, and listed all the names of the twenty...

The amino acids

J2	A	Ala	Alanine
L2	R	Arg	Arginine
S5	N	Asn	Asparagine
S2	D	Asp	Aspartic acid
S1	C	Cys	Cysteine
S3	E	Glu	Glutamic acid
S4	Q	Gln	Glutamine
L3	G	Gly	Glycine
G3	H	His	Histidine
J5	I	Ile	Isoleucine
J4	L	Leu	Leucine
L5	K	Lys	Lysine
J1	M	Met	Methionine
G1	F	Phe	Phenylalanine
G5	P	Pro	Proline
L1	S	Ser	Serine
L4	T	Thr	Threonine
G4	W	Trp	Tryptophan
G2	Y	Tyr	Tyrosine
J3	V	Val	Valine

Or, perhaps you will have collected the various codes together using the traditional alphabetical arrangement:

The Genetic Code

A A A	Lysine	C A A	Glutamine	G A A	Glutamic acid	U A A	?
A A C	Asparagine	C A C	Histidine	G A C	Aspartic acid	U A C	Tyrosine
A A G	Lysine	C A G	Glutamine	G A G	Glutamic acid	U A G	?
A A U	Asparagine	C A U	Histidine	G A U	Aspartic acid	U A U	Tyrosine
A C A	Threonine	C C A	Proline	G C A	Alanine	U C A	Serine
A C C	Threonine	C C C	Proline	G C C	Alanine	U C C	Serine
A C G	Threonine	C C G	Proline	G C G	Alanine	U C G	Serine
A C U	Threonine	C C U	Proline	G C U	Alanine	U C U	Serine
A G A	Arginine	C G A	Arginine	G G A	Glycine	U G A	?
A G C	Serine	C G C	Arginine	G G C	Glycine	U G C	Cysteine
A G G	Arginine	C G G	Arginine	G G G	Glycine	U G G	Tryptophan
A G U	Serine	C G U	Arginine	G G U	Glycine	U G U	Cysteine
A U A	Isoleucine	C U A	Leucine	G U A	Valine	U U A	Leucine
A U C	Isoleucine	C U C	Leucine	G U C	Valine	U U C	Phenylalanine
A U G	Methionine	C U G	Leucine	G U G	Valine	U U G	Leucine
A U U	Isoleucine	C U U	Leucine	G U U	Valine	U U U	Phenylalanine

And you will have discovered that there are three codes which haven't been mentioned. Ah, yes. Here we have an interesting lesson.

Remember the movie "Fantasia" where a young mouse is seen as an apprentice to a wizard? He is told to fetch water (no, it wasn't for a wedding feast this time!) and being a bit lazy, he thought he could get away with invoking his master's magic to assist him by commanding the broom to act as his servant... except that he does not know the word by which he can command the broom to STOP.

In one of the special topics of computing, we call this the "terminating condition": the way in which we "finish" or "complete" a certain kind of task. Astronomers (when they remember, or feel the need to be pedantic) do not say the words "sunrise" or "sunset" but speak of the "morning terminator" or "evening terminator" which mark the bounds of the day and the night...

Yes, this delimiting extends even to the depths of biology. We have already seen that AUG (besides standing for Methionine) marks the start point of translation. The three codes which were not yet mentioned, marked in the above table with a "?", are UAA, UAG, and UGA - the "terminators" of translation. They mark the place where the completed protein is detached from the ribosome (the protein-buiilding machine). It is now free to go about its business, to be useful for the work of the living cell.

In our analogy, we recall that the Rosary also has a special concluding prayer, the "Hail Holy Queen" with its "collect" (from the feast of the Holy Rosary, October 7). This prayer "completes" the larger prayer, and "frees" - not the prayer, but us - to go about our business, and be useful in the life of the Mystical Body.

Let us pray:

O God Who by the life, death, and resurrection of Your only-begotten Son has purchased for us the rewards of eternal life, grant we beseech You, that by meditating upon these mysteries of the Most Holy Rosary of the Blessed Virgin Mary, we may imitate what they contain and obtain what they promise. Through Christ our Lord. Amen.

December 23, 2006 (G5) Proline

Proline - the Coronation of Mary (G5)

December 23, 2006 - (Emnmanuel) - Tomorrow is the Vigil!

Ah, you have come back to learn the solution to the puzzle I mentioned yesterday! Yes, we have considered 19 amino acids and related them to 19 mysteries of the Rosary. But there is one more mystery, perhaps the most mysterious of all.

The mystery called "the Coronation of Mary" is, even more than the Assumption, only vaguely hinted at by any biblical writing. And yet we say that these mysteries are "the Gospel in miniature". How can this be?

The simplest explanation was given by Jesus, when someone in the crowd called out some quip of family-flattery: "Blessed is the womb that bore You, and the breasts that nursed You!" It may not have been meant badly, but it could have easily been misunderstood. So Jesus replied with something which might be even more readily misunderstood: "Rather, blessed are those who hear the word of God and keep it."

This is no contradiction, but a correction. It was not in a physical relation that Mary was Mother-of-God, but in her obedience to the will of God. Yes, this obedience had its completion on Calvary, the offering Jesus made of Himself to the Father - but an offering which Mary had to ratify. But there was another completion, which (because we are created) had its stages. Those stages are the first four Glorious mysteries.

But there was one more stage. And this stage was to involve US, our work, our obedience - that is, our OWN roles in this Great Work. There is no more profoundly perfect representation to be given to this stage than the "event" of Mary's crowning. This crowning, which is the perfect recognition and true completion of her work, clearly cannot be done until her work is complete! Which means, in some sense, this event is NOT in the past - it is only to occur at the end of time. And that is only fitting, for all the subjects of the Queen should be there to pay her homage and rejoice with her as she is crowned - since they (in some sense) ARE her crown.

And so, this mystery is very much of a difference from all the others. Whether it is simply a matter of the "eternal" character which is so much a part of it, or my own speculations, or simply the occurence of G5 after the Assumption (G4), somehow we need to have some strikingly different symbol if we are to propose this mystery in its truly unique setting.

And God, the Master Designer, has given us that most suitable symbol in Proline.



Proline, you see, is NOT an amino acid, though it always ranks as one of the 20 "amino acids" from which proteins are built. Proline is technically an imino acid, because it does not conform to the arrangement of an amide, a carboxylic acid, a hydrogen, and a side chain, all attached to the central (alpha) carbon.

No, in Proline there is a link from the side chain back to the amide. This form is termed an "imino" - it has an -NH- or imide group rather than an -NH₂ amide group. The loop is called a "pyrrolidine ring"; it is not chemically reactive, but its unusual shape changes the larger structure of the protein - Proline "puts a kink" or bend into the protein where it appears.


Proline (abbreviated Pro or P)
RNA Codes:


C C A
C C G
C C C
C C U


Proline has four codes, all of which begin with CC, the third is the "wobble base".

(Every so often I see eighteen-wheel trucks with trailers labelled Proline; I've never seen any of the others.)

So, Proline (the amino acid, er, imino acid, not the trucking company!) has a ring, hinting of the eternal character of the Glorious mysteries. By its being an imino acid, its "side chain" might be considered to contain the nitrogen of its own imide, but that same nitrogen is also part of the underlying structure - this preserves the essentially Marian character, but also hints of a larger topic for meditation, which we may never really grasp until (please God) we come to stand in attendance at the great ceremony, where the good wine will be served...

O Mary, our queen and our mother, pray for us, and guide us to your Son, the Emmanuel.

December 22, 2006 (S5) Asparagine

Asparagine - the Crucifixion (S5)

December 22, 2006 - (Rex Gentium) - Two days to the Vigil!

Today, the last Friday in Advent, we come to Calvary and the mystery of the dying God. As I mentioned earlier in reference to Dickens' "Christmas Carol" we must first understand that Jesus was born, and grew up - that He actually lived - and then grasp the mystery of today: He died - died in a horrible and shameful way, enacted by the conniving of the truth-preserving monotheists and the justice-proclaiming pagans... And the Roman centurion, so skilled in killing, verified the finality of the death with a sword-thrust to the heart; no coroner, no physician, would have quibbled; for the centurion's own life would be forfeit if he had been wrong. Strange echoes sounded then on that hill, that late afternoon in spring: "I too know the meaning of obedience..." Well for us that someone did.

The crib of Bethlehem and the cross on Calvary are not very distant at all: only a few miles (five, perhaps?) and about 33 years (maybe a little less, maybe a little more?)... same wood in each... as a sign to recall the First Sin which involved a tree as well. And it involved food, it involved will - or lack thereof. And so the solution to its puzzle had to involve all those things too, but adjusted, and completed, and restored.

And when the characters in the story have made a royal mess of things, it's up to the author to make the revisions which can bring the story to the conclusion which was originally intended...

The mystery of Calvary, then, is not an end. That guess at its explanation only lasted into the morning of the third day afterwards - at which point it was discovered that the book hadn't finished, because a new chapter - no, a new volume - had begun.

But as we prepare for our own new chapters, let us remember how this chapter came to its completion.

And so today, we come to the last of the amino acids, which, mysteriously, is not the twentieth.



Asparagine (abbreviated Asn or N)
RNA Codes:


A A U
A A C


Asparagine has only two codes, both of which begin with AA, followed by a pyrimidine (C or U), thus splitting the AA codes with Lysine.

Asparagine has a hydrophilic side chain, indicating the Public Life, though it is nonpolar. As Glutamine is derived from Glutamic Acid by substitution of an -NH₂ or amide group for the -OH, so Asparagine is derived from Aspartic Acid. That is, the side chain of Asparagine is the amide derived from acetic acid. The acetic acid hints at the vinegar given to our Lord on the cross; as before, the nitrogen indicates the Marian component, for St. John tells us how he was there beneath the cross with the Mother of Jesus, and heard those words to her: "Woman, behold your son" then to him "behold your mother" - and so the Family began to grow.

This is not simply history any more. This is our Family we're talking about and remembering... it's up to us to live now so as to join our relatives eventually. So much do they look forward to that reunion! Let us do the same.