Thursday, January 25, 2007

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? 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...

Wednesday, January 24, 2007

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:


"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.]

Saturday, January 20, 2007

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
then often it is true that

(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)
(child-of-my-aunt-who-died) is a cousin of (phd-student-in-physics)
(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!

Thursday, January 11, 2007

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...