Null Epistolary

The narrow way

2011-11-27T20:11:00.000-08:00

Dear Director,

Apart from the obvious things, I must admit to unhelpful habits of thought, around those obvious things. There are the maxims that float around, of the form "such is the cure for sich" --- and so I fall to thinking at God things like "See? You have to give me this-priceless-good, because otherwise I'll just keep falling into this-mortal-sin"; I become like the ersatz suicide holding himself hostage against God's mercy.

Each visit to God's Minister Through the Grille, I'm given an antidote against the deadliest part of this poison to which I seem to keep returning, and I'm prescribed a short course of purgatives --- or, sometimes, the chain of repeated forms makes me think of stitches; a row of sutures on my heart. I rejoice in the promise of health and healing. It hasn't, in the past, ever taken very long to play with the poisons again, to pull out the stitches. I read once that, outside the world of metaphor, if you DO need stitching in the same place twice in short order, it's better to use glue the second time, because the living tissues do something weird when they've been pierced mid-scarring. I wonder if that isn't somehow reflected in these human trials against temptation...

But today the stitching --- or however the patching is done --- today, it is fresh; I hear the echoes of temptations still, but now in this Day, let us rejoice. In this desert, my too-often too-parched soul, may I make a straight and level road for the Saviour to enter by; if I can see Him coming, perhaps then I shall see also the narrow way into Heaven.

in prayerful union

Random acts of apostrphe

2011-11-17T13:34:00.000-08:00

O Steam,

where hast thou gone?
I see from my windows
your hoarded dews ---
the chill echoes
against graded blues
of shadows wan.

Thy heats escaped,
and pressures fled,
now contemplate
whither to shed
in snowy spate
what wind hath raped.

But here, 'tis dry:
no urging force
advanced my course,
made whistles cry;
the work day's done,
now sets the Sun.

Who calls you hobbits, though?

2011-11-03T18:39:00.000-07:00

"Hoom, hmm! Come, now! Not so hasty! You call yourselves hobbits? But you should not go telling just anybody. You'll be letting out your own right names, if you're not careful."

"We aren't careful about that," said Merry, "As a matter of fact I'm a Brandybuck, Meriadoc Brandybuck, though most people call me just Merry."

"And I'm a Took, Peregrin Took, but I'm generally called Pippin, or even Pip."

"Hm, but you are hasty folk, I see [...] I'll call you Merry and Pippin, if you please --- nice names. For I am not going to tell you my name, not yet at any rate." A queer half-knowing, half-humorous look came with a green flicker into his eyes. ...

Being a lazy reader (and I really ought to be trying to work out when and why there's a splitting in some queer long-exact sequence involving spheres... the answer is "in exactly those cases I want to ignore") it has taken me a long while to think about the flurry of names-as-such in the Epic; some of this is due to the rich linguistic history that Tolkien imagined for his subcreation. But I'm starting to piece together something more: even deeper than Tolkien's love of euphony (whether or not Greek!) there seems to be something of a philosophy of names for things that he is keen on approaching from several angles.

"Eh? What's that? Don't you know my name yet? That's the only answer. Tell me, who are you, alone, yourself and nameless? But you are young, and I am old. Eldest, that's what I am."

It is curious that Bombadil claims this title for himself, and Elrond seems to ackowledge it; while Gandalf and Celeborn seem to propose him we know as Treebeard, who opened the topic for us, as "Eldest", and "the oldest of all living things". Perhaps this grant should be informed by our knowing (from the Silmarillion) that Gandalf is actually akin to Saruman and Sauron and the Valar, who have their memory from before the making of Eä or Arda in it, or the shaping of Middle Earth within that. Whether Bombadil or Treebeard is of the same sort or something else I can't tell or guess: the histories are confused, or I am.

But even more: Bombadil echoes something of Treebeard's philosophy in asserting that, on the one hand it is difficult (if not impossible) to talk of specific people without having some word to use as naming them, yet there is often something in each person's Story that will pin down which person they are: and so, Eldest works for Bombadil. If you aren't likely to meet Bombadil (and most of us aren't), then Eldest may as well suit Treebeard --- not that you're much more likely to meet him than Old Tom.

"Mithrandir we called him in elf-fashion," said Faramir, "and he was content. Many are my names in many countries he said. Mithrandir among the Elves, Tharkûn to the Dwarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not."

To the East... there are hints that in the Lost Tales more is made of the "Rods of the Five Wizards" --- you'll note we only ever have names and colours for three! --- that two Blue Wizards got lost in the East; but here we learn that to some extent, names are things given us by those around us. In this sense none of my noms de dactylographe is really apt, least of all that I use most. Mind you, wherever I go on the internet, if the local service doesn't assign me a name, whatever name I do use is effectively one I'm claiming for myself.

About that, let's jump volumes:

But when Gwindor would tell his name, Túrin checked him, saying "I am Agarwaen the son of Úmarth," --- (which is "Blood-stained, the son of Ill-fate") --- "a hunter in the woods"; and the Elves of Nargothrond questioned him no more.
[...]

On the one hand, it may be perilous to play with names too recklessly. There are plenty of cautions out there against nicknaming your Guardian Angel, for instance --- it being sufficient to use the title "My Guardian dear", and difficult to be sure that some other word doesn't address something less holy, or less wholesome. Very perilous; though Tolkien is not univocal on Man's proper relation to Peril: "Indeed, [Gimli], you are beset with dangers, for you are dangerous yourself, in your own way" on the one hand, while on the other "Yet I am wise enough to know that there are some perils from which a man must flee." But let us see also what Gwindor later advises his dangerous friend:

Now when Túrin learned from Finduilas of what had passed, he was wrathful, and said to Gwindor: "In love I hold you for rescue and safe-keeping. But now you have done ill to me, friend, to betray my right name, and call my doom upon me, from which I would lie hid."

But Gwindor answered: "The doom lies in yourself, not in your name."

That is, there is a definite sense in which what I call myself (short of impersonation -- cf. Amlach from "The coming of Men into the West", Silmarilion) is less important than my character in deeds and in conversation, and certainly the one is easier to change than the other. Túrin is indeed seen to be a tragic figure in the old Greek sense --- for though the "weight of [Morgoth's] thought" (Narn i chin Húrin) oppresses him, yet it is by his own habits that destruction and despoliation is able to follow wherever he goes, and eventually overcome him with despair.

On the other hand, there is --- even beyond history, the things we've done --- a sense in which certain names are more apt, though they may have to wait some time come into their own:

And so the very name it was foretold at his birth that he should bear was chosen for him by his own people.

After all that nonsense

2011-10-24T20:18:00.000-07:00

Dear Hilary,

I have fluttered through annoyance, despondence, frustration, confusion, and possibly two or three others that didn't last long enough to identify (like those $Z^{0}$ particles before the Super Proton Synchrotron got warmed up).

The thing is, it isn't you, HJMW, from whom I wish to remain anonymous, nor any of the friendly folk who care to leave replies here, but from unscrupulous con artists, stalkers, grudge-holders, borderline personalities, spambots, marketers and any antipapal inquisitors who might be keen to leverage whatever irrelevantia are handy for the cause of annoying the neighborhood Christian. It isn't folk of good will I'm aiming to frustrate, but search engines --- for they are indeed stupid automata. Just ask Dr. Thursday (which is not his given name, btw). This is why I have an anonymous-looking email address, writing from which I sign the name I was given in Baptism.

I have publically noted elsewhere over the present signature that I have a middle name of Christopher --- and indeed this is true, while I don't usually draw attention to it in real life. So I suppose I could honestly sign "Christopher" at your 'blog and we'd all be more-or-less happy. But this puzzles me: what particularly would you gain by my calling myself Christopher? Surely there are some dozens of millions of Christophers out there, many using the internet quite happily (and many of them not Christians at all). Which of them would I be, unless you met me? I could call myself Raphael or Philip, and you'd know about as much about me, and have as much reason to believe these were names given me (they're not). I could even call myself "Choi Chu" and be reasonably sure of a well-formed Mandarin name (or several), but it could as well be a command in Klingon to "beam me up". I already write in many places using the present pseudonym, and it would be unnatural to arbitrarily write now within the same circle under a new name. (I've already acquired two others, quite inadvertently, just because of the way google blogger works, and it mildly annoys me, when it's not amusing me.)

And it's not as though pseudonyms were a new or even ill-seeming phenomenon in writing, publishing, or commentary. To take some self-serving examples, in maths there's the infamous "Bourbaki"; in fiction, John LeCaré and Lewis Carol come to mind; I don't know if Anne Landers is a real name, or why it shouldn't be several people --- Landers is notoriously suggestible when it comes to agreeing with conflicting advice written-in by readers, and so I wonder.

It makes perfect sense to me that Fr. Z, whose blog is an extension of his professional and vocational activities, writes under his own name; I understand that you are a professional writer, too, but the Orwellian Picnickers aren't reading or commenting there as your professional associates, but for joy and comfort on the internet. The insistence on "real" names simply doesn't make sense, because you've no way to check them, no way to avoid false negatives, and no advantage anyways.

On the other hand, I'm very glad you're recovering enough to feel noticeably more awake, as you say, and I pray for your speedy return to full health (and your perseverence unto salvation, too!), and otherwise wish you all the best.

A la prochaine,

Guy Street

Puzzlements: Terms.

2011-10-16T20:23:00.000-07:00

If I may be permitted to introduce

The Obscure Carnival Man

"But, We are the Great, the Amazing ...
Surely, you have heard of us?
The Twins are reknowned far and wide
As they look each exactly like ...
And --- and, this Wolf-... No, he is! ...
See his toes? And here's well-noted Side!"

His aim: my interest's raising.
The result: I long off to hike

"Surely, the strange tales of Gus?!"
Of course, though, I haven't --- nor Fizz.

There's more than just odd to his manner,
I can't seem to blot out their banner
Or turn aside from the *pitch*
Though it's causing my heels to itch...

In the end I was rescued
by a damsel with pigtails
who said she had icecream
and plenty of wild quails.

Which is meant, in some way, to include answer to the interogative phrase "And you are ... ?"
And, you can see, I also squished the word toes in, though you can further see there's another spot where it might have made more sense. I think I'm in a mood for linguistic perversity, today, which in fact is a neat reflection of the impression I mean the narrator to have of that subject he is relating to us. This doggerel is in no way autobiographical: I've never been accosted by an obscure carnival man, nor rescued by a damsel with pigtails. I don't think I'm even particularly taken by pigtails on a lass, though of course there's nothing objectionable to the style...

I hope you've been entertained, anyways.

Word & Question

Enthusiasm

2011-10-06T10:55:00.000-07:00

I had me a hankering for some Triumphalist Patriotic Blake (with stirring music) and so moseyed me on down to the UTubes, and there found a nice little clip from the "Last Night at the Proms 06" (not quite Patria mea, but, you know... ). And danged, but if the most visible hand-waved flag in the FRONT ROW at Royal Albert Hall isn't our beloved per-pale argent-and-or of the Vatican City State!

Take THAT! Cranmer!

Lux perpetua luceat eis

2011-09-11T13:34:00.000-07:00

Dear Neighbors,

We are all bereaved; I with you, ye all with me and with each other, together and separately. Some indeed more closely and keenly, but none of us are untouched. We mourn for the friends we are robbed of. We mourn the sense of graceful motion now lost --- for where once we had walked as on a tightrope of common neighborly trust, we are now enmired by the strange customs of strange men, the possessed of fear and of walking Death and of Office --- strange gods indeed. We mourn the blood we have shed in search of vengeance. If we are wise, we will seek God's justice and rejoice therein, and lament the souls lost, caught by the stumbling blocks we have scattered about us.

But, for the sake of those friends of whom we are robbed, we must remember to pray in hope, and we must take comfort that they all shall find beatitude who can; and we must not forget to live. We must dare to live in joy; on this memorial of Our Lord's Resurrection, let us live, looking towards and keeping ourselves for the life of the World to come.

one among you

A reply to a comment on a post of Fr. D. Longenecker

2011-08-25T23:56:00.000-07:00

cc. to Fr. Dwight.

Dear Steve,

I'm writing here, because it turned into what I think is a "blog post", not a comment, and the good Father has (iirc) requested generally that we blog these things rather than stand in his sitting room to rant at the world. So, here we are.

Certainly the words of scripture with which the Blessed Sacrament is confected are taken from accounts of the Last Supper, (Gospel and Epistle); I think in some Missals there is a heading "Commemoration of the Last Supper" to name the relevant section of the Roman Canon. But that section of the Canon is not the Mass, it's not the end of the Mass, it's not the purpose of the Mass. Maybe it's the peak, the perfection... But the purpose of the Mass is to offer the One Sacrifice of Our Lord unto Our Lord Father, and to feed and strengthen first the Priest celebrant for his sacramental works, and then to feed the members of the Body of Χρ. with the Body of Χρ. It isn't belittling of the Commemoration to acknowledge the primacy of other ends; rather, it belittles the Mass to inflate the Commemoration!

It even belittles the meaning of the Last Supper. One may recall a letter of Paul, covering the subject of eating meat sacrificed to idols; it is helpful to note that this was the fate of most sacrificed meat: it would be eaten. And if any was to be eaten, the priest making the sacrifice would always have a share; so notes St. Thomas (ST III.82.iv.Respondeo). The very pious and special sort of sacrifice called a holocaust was an unusual and exceptional thing --- and difficult! You may recall that God commanded a holocaust of captive Amalek, which Saul tried to spoil. But Jesus' self-sacrifice is paterned on the ordinary sort, after the Pasch (but becomes a holocaust in the eating!); but we cannot eat anything in the accidents of human flesh, and the apostles could not have done so. Whenever by a miracle the accidents of human flesh are restored in consecration, that host has been reserved, and not consumed. The Body of our Lord given at the Last Supper is how the apostles first partook of the One Sacrifice. Hence, to exaggerate the supperness of the Last Supper --- meats and fruits unspecified, e.g. --- is to ignore that even the Last Supper was a participation in the Body of Our Lord.

That is all.

In Christ's charity,
the undersigned

With deepening gratitude

2011-08-23T14:04:00.000-07:00

Dear Visitors,

Today we are prime! In four more years, I shall really have come of age; who knows if I'll still be 'blogging then? We cannot look too far ahead, afterall.

Have some cake!

who, of course, shall pray for you

Fragments, interruptions.

2011-08-19T20:46:00.000-07:00

I don't usually like sharing unfinished things, but this--- I think I wanted to, in my laconic mood.

Shall I bring thee roses, roses white?
Oh! That my heart were pure as these were bright.
In thy sight, shall I bring thee roses red?
Oh! Give me the joy in which martyrs bled!

For the kind light of thy soul's windows,
How short of enough, to bring thee rose?

Shall I bring thee lilies and irises gold?
Oh! Spoke I fair as my heart would be bold ---
With Lilies of ochre and irises blue,
Could I tell all my hopes? Would you know I was true?

Solomon's envy, van Gogh to inspire
What can they avail to assuage my desire?

... There ought to be more, and I'll have to tighten up the meter (or maybe not!) but it occasioned this next long-lost, long-awaited little verse--- which is quite insufficient, given how long it took, I'm sure; which also fits the preceeding theme.

A Short Verse

The neighborhood children make dandelion bunches
With interspersed clovers and shamrocks assorted
For innocent sweethearts and mothers seraphic,
While running the fields where they ate picnic lunches.

Anyways. Now that we've got that out of the way... !

Credit where due.

2011-08-18T12:47:00.000-07:00

It seems to be working, again. Hooray!

Thanks, Gmail!

the gadfly

Harumph... please don't kill my accounts?

2011-08-15T18:11:00.000-07:00

Dear Gmail Team,

I can't find your address, and you seem to have delegated the task of user support to supportive users, so... an open letter in the aether.

I don't know how or why you did it, but the physical keys ↑, ↓, Home, and End no longer produce any effect upon the gmail page, though mouse-fiddling the scrollbar does what it should. This is, as I'm sure you understand, annoying as an inaccessible mosquito bite. For reference purposes, I'm using a 6.0 Firefox browser within a linux-based X.Org environment -- not that those last two points should matter.

Please fix.

Thanks,
a user who tries to be knowledgeable

Enough Muddling

2011-08-13T07:32:00.000-07:00

Your Majesty,

--- and all ye younger majesties heir to the body, hearken and take note --- I don't often question your wisdom in matters of your own craft, but I weep to think whatever on earth can be holding your wrath in restraint at this moment.

Your civilian police are effectively on strike; your parliament and prime-minister are in revolt (and quite possibly have even lost their pragmatic get-re-elected sense), and an uncomfortably large segment of your subjects have gleefully lost all self-control. If the rain does not fall soon (rorate coeli desuper!) to quell these flames, it will be to your greater ignominy and imperial humiliation if you do not risk physical humiliation and lead your cavalry in containing the wanton burglary, theft, and destruction that are even now entertaining so many stupid and cruel urchins. They desperately needed their mother or grandmother to step in and give them a proper scolding! And since their natural mothers and grandmothers seem also to have quit, gradually we find the need devolves up to the head of the First Family --- the Royal family. That is, your majesty, you.

I see today the prime-minister has sought the counsel of a non-subject who says "thugs must be taught to fear the Police"; certainly that will be a necessary first step, but really, these thugs must be taught to love their neighbor. This means they must be taught that their neighbors are lovable; this they will not learn if you, their mother-in-figure, do not act to protect their neighbors from wild stupidity.

Humbly yours,
A colonial observer

Sanity is a wonderful thing, yes?

2011-08-07T20:35:00.000-07:00

Dear Gil,

Such a wonderful thing, that I'll not think too much about it, just now (it's too good to contemplate closely, if you know what I mean?) but celebrate a particular instance of sane writing, in this case by the authoring of one Rob Schneiderman. It has, as is (alas!) all-too-necessary, a tone edging on polemical; but it reads nicely for all that and is just so delightfully chock-a-block with common sense.

The thing is presented as a PDF, by the American Mathematical Society here, called "Can One Hear The Sound of a Theorem". This is a play, at the very least, on famous old analysis papers, titled "Can One Hear the Shape of a ..." --- "Bell" and "Drum" have both appeared, but there may be others. (In case you're interested, the answer in the "Drum" case is "Yes, if..."; such answers are annoyingly frequent in analysis.)

I can't help but wonder if the mischievous Hoftsadter isn't indirectly resposible for some of the nonsense fried up in the present article, what with his Crab reading squiggles as beautiful music (or bad) that Achiles thought were arrithmetic theorems (or wrong ... or nonsense); they were prevented by tea-house etiquette from playing the Goldbach Conjecture to see what it sounded like. I thought old Douglas had clearly meant it as a joke, you know? But, anyway...

Won't you drop by for tea, some time?

some sort of chap

An opposite limit theorem

2011-08-01T18:58:00.000-07:00

This is something that those who ought to know these things usually do know, and eventually figure out in any case. So if it isn't usually part of your work to know these things, don't fret; I really ought to have learned it much sooner!

Suppose $D$ is a category with a terminal object, say $z$, and let $F:D\to C$ be any functor. Then the natural transformation $F0 : F\to Fz$ is initial among the category of objects $x$ of $C$ with natural transformations $F\to x$.

That is all.

Samuel Clemens once quipped...

2011-07-24T21:08:00.000-07:00

So, I live in a region which is laughably called the "temperate zone". The name must have been invented in Southern England. Anyways, what this means is that we get all sorts of horrible for our weather (or we like to think so... or it comforts our frailty to 'brag as though that were so) whereas people in more "extreme" places only get one or two sorts of horrible --- desert heats, or monsoon half the year, or glaciers... A friend has reminded me that this means we don't get those noxious toxic tropical insects: it's too complicated for them. I might counter that Monarch Butterflies spend more than half their lives as tropical insects, but they're so pretty it doesn't matter.

Anyways, all that is preface or context for

\begin{enumerate}
\item[21] Rain, in proportion
\item[22] Wind, with or without bicycle
\item[23] Electricity
\item[24] Devices that exploit [23] to effect [22]
\item[25] Night quiet.
\end{enumerate}

With all due deference

2011-07-16T20:48:00.000-07:00

Dear Prof. Zmirak,

I have not a whole lot to say, against Austrian Economics generally, or Roepke's writings specifically, or any of that; but I will raise my concern now about the well-foundedness of the "price system", what I'd prefer to call the Monetary Standard: as with all things democratic, it's only as smart as the average vote, and people both rich and poor can be terribly stupid. Not only is "the last whiskey you're willing to pay for" often much too late to stop buying whiskey. Furthermore, as with all things democratic, nobody really knows enough to make infomed judgments about what the next or last whiskey or mobile phone service plan or college application or mortgage really costs him, before he's had it and waked up again the next morning, or until all the peripheral missed opportunities and consequences have echoed around him again. So how can he tell if 5€ really is not too much?

As examples of things which would cost far too much even if you were paid to take them with you, which yet seem to move lots of money around, here is a very short list:

recreational opiates

pornography

idle speech

Anyways, there we are. As Churchill said of democracy, it might well be the worst system imaginable, except for all the rest.

A Subsidiarist

Totally Weird

2011-07-10T18:27:00.000-07:00

echo >& /dev/null <<eof

Poking, in a self-indulgent way, through recent blog visitor statistics, it seems that during the recent scribal torpor ("hiatus" sounds like something a TV network or production studio would plan--- planning is beyond me, on this blog) perhaps half of my visitors come from websites that sell useless and/or imaginary things. OK, so maybe I'm a bit rough with my sarcasm; sarcasm is easy, on the internet, after all! Nonetheless, I've a sneaking suspicion that someone is investing modest ammounts of website design and traffic redirection to collect the attention of lonely amateur blogifiers skimming through their traffic statistics... a new a subtle form of spam designed to prey upon the incautious and/or self-alienated-and-inclined-to-intelectual pride? Or is it just that the internet is alive and stupid? I don't know. It makes me wonder how many cloudy terminals out there have fake PhDs awarded by fake schools? And how many of those bought their dissertation essays from web-enabled "editing" firms using phfished-out credit card numbers?

If the internet could speak, would it have troche fixation?

anyways, sleep well.

eof

Let the battle be joined!

2011-06-19T16:08:00.000-07:00

The unwittingly opposed camps:

Dr. Thursday
and
Abstract Type.

confundituri te saluant!

a pilgrim programmer

Wild conjecture

2011-06-13T13:48:00.000-07:00

Dear Pundits,

I heard that The Trump Suit isn't running; some silly people thought it was because The Barak made nasty jokes about him at that commedy show, and the Trump Suit, like a grizzly bopped on the nose, ran off into the forest. I think he was paid off.

Some other silly people thought The Trump Suit would have made an exemplary incorrupt President, because he was already so absurdly wealthy that he couldn't be bribed. Behold how ridiculous the proposition is: The Trump Suit has, by his extreme wealth and conspicuous consumption, demonstrated that he is eminently buyable; the whole premise of The Apprentice is that The Trump Suit doesn't receive you into his employ: he hands you kick-backs, if you're the toughest publican in the bunch.

So, I'm willing to bet one cold potato's digital photograph that The Trump Suit figured it was a better deal to mind his own household, and enjoy the happenstance of whatever November next year may bring.

a foreigner

A World of Writing

2011-06-04T09:47:00.000-07:00

Dear Lindsay,

Inspired by your reported dreams and successes in the strange-pen world, I went to that famousest internet auctions clearinghouse to see what they might have in the way of glass pens; and I've come accross something very strange!

WHY, do you suppose, are there so many venetian-made glass pens in East Asia?

That is all.

God bless,
much too tactile for six words

Where does money come from?

2011-06-01T12:25:00.000-07:00

Dear Prof. Smith,

The most honest answer is, of course, that we made it up. In other words, it is a creature --- a creature of Man. As such, it certainly has no life: breath, nor sight, nor hearing --- though we may give it mouth and eyes and ears in the form of Her Majesty's likeness. And of course, we don't even pretend anymore that any money has intrinsic value. So, alright, there is paper backed by metal-stock, there are title deeds for plots of land, and so forth. But the primary business of "business" in the British Imperial Diaspora is usually conducted, measured, and reported, (for taxation purposes) in units of some local currency.

Last time I wrote, I alluded to professional and trade unions, strike and other pressure tactics, which have as final cause that "whoever has accepted responsibility for paying them [agree] to pay them more. Whatever that means." The charitable view of strike/work pressure is that for whatever reason, the workers of some trade or profession generally aren't able to live in "becoming dignity according to their state in life", and a re-negotiation of working/contracting terms is wanted so as to correct that. The charitable view of employers' not paying more than they do for needed labour would be that they honestly don't have the extra money to spend. But it's worth-while asking what does it mean to pay people more?

Odd Rumblings

I actually came to this question from the other end, asking a friend one day (years ago) where inflation comes from; and his answer was that people keep asking for raises. The answer surprised me, because I had thought it worked the other way around: you work at some decided wage, then inflation outruns you, so you ask for a raise. I literally hadn't worked-out the instability inherent in the system.

This funny chicken-and-egg story reminds me of the odd way blocks of currency get bartered on the international market. What exactly is meant by that I really still haven't figured out; but it highlights the placeholder nature of all currency, in what I find a sad way. I understand that the basic narrative has something to do with hypothetical Greek goatherds who want to buy Congolese coffee, and Congolese coffee growers who want feta for their salads... but it leaves me feeling remarkably unsatisfied; I think I must be missing some degree of complication, perhaps the Italian-Libyan shipping conglomerate that carries their stuff in both directions, and recently developped a penchant for cold-brewed American Sasaparilla? Anyways.

Debt Eternal

An idea most estranged from common speech, but which I think very true and even widely understood, is that all money is borrowed. In more detail, you might argue that some (even most) people are paid money for their labor, or for goods they produce surplus to their own needs, but that's begging the question: for who pays out of what funds? The only answer really available is that Private Banks borrow cash from a Central Bank, move around bits of paper (or nowadays, electrons) referring to cash, lend it to clients, collect it from them again, and periodically send damaged cash back to the Central bank to be decommissioned. That the volume of circulation can grow at all is ultimately due to general contentment to not check whether the books add up from one week to the next --- they couldn't possibly. But it "doesn't really matter" because it's not human persons who owe this money, nor are human persons owed it.

Of course, it hasn't always been this way --- at least, not everywhere all at once.${}^1$ No-one would have bought it from the outset, of course. Sometimes the paper referred to some number of goats, or quantity of grain, or weights of various alloys... you know, useful things; the things might or might not be there, but at least you could find out which! Some paper now-a-days still does refer to these sorts of things, but they aren't widely perceived as personally useful anymore.

Last letter I lamented that the Monetary Standard (the circular principals that money is worth what it will buy, and all else is worth what top bidder will pay for it) artificially flattens our notions of value. This time I'm going to throw in the related contention that, under the Monetary Standard Cash Economy, is is as though money serves two masters, and these are at variance.

Firstly, money is (as I have defined it) a medium for commuting the indebtedness of individuals to society; in this usage, the invariant is the owner of the debt --- who holds the cash, whose name on the bank account, is the person to whom "society owes" whatever debt.

Secondly, money is rented out, as it were; time spent with flexible expenses is, aparently, worth something; it is "of interest". That is, money is sometimes moved in order to put the holder in debt. This is the opposite of the other meaning of money, where the holder of cash is also the holder of debt. Now, instead of communicating indebtedness, money itself is the substance of a debt. Also, while the owner of the debt probably does hold paper recording it (a loan or line-of-credit contract), neither the weight of the debt nor on whom it rests is really fixed, for the borrower probably pays the interest by obliging himself to people around him --- it's entirely possible that he is a good to society.

Worm-in-Can

These thoughts, of course, have been bugging me for some time. They're also clearly unfinished, and I can't see a good way to wrap-up now. But I'm allarmed to learn that the 3rd Nobel Laureate Symposium quantify poverty in a dollars-per-day language. These are supposed to be smart people, and instead they're using an expression that would have suggested extreme wealth to King James I of Scotland, for example, for to describe extreme poverty. In charity, I should acknowledge that they're writing to a club of contemporary bankers' friends and hoping to provoke particular actions within the year.

Anyways, clearly, I shall have to write again.

All the best,
the armchair philosop... oh, that's, like, all of them!

${}^1$ I had an amusing read about a Pharaonic Egyptian system of grain-backed currency (an update of the cuneiform record-tablets?) with built-in depreciation to model the tendency of stored grain to gradually spoil. The same webpage criticised Catholicism for suppressing the "Great Mother" Jungian archetype; I suspect this is a sorry debasement of Jung's philosophy (whether that is any good itself I don't know), to say nothing of how it misses pretty much the whole nature of the Catholic Faith...

Who is your audience?

2011-05-07T12:17:00.000-07:00

Dear Self,

I think you're mostly writing for yourself. Indeed, I can't think of anyone who more enjoys reading your various silly notes than you do yourself. (Cf. Michael Flanders, introducing his Mozart without an horn). The only thing, then, to wonder is whether that's really quite proper? Is it cricket?

I'm sure most bloggers, of the ammateur sort at least, reach some point of wondering whether they are writing only for themselves or for their readers. But, if I may say so, you've fallen into the particular habit of writing not for anyone. Sure, that's the "gimick", the blog-line "letters to ... no-one in particular". Even if the address is to various and no-one in particular, the writing ought to be for someone. It needs both an ad and an ut. You might do well for ad now and then, but the ut needs more focus!

I hope this has been helpful. In any case, I remain, in friendship,

thee.

Vere surrexit!

2011-04-24T13:47:00.000-07:00

Re. Daffodils

Dear Folk,

Paul has been a gentleman, and on Vigil Day posted some stuff like this:

Of course, it's just right for Easter Season, so with that, Happy Easter to you all!

God Bless,

another one practising for sainthood

The Sci-Fi Coolness Test

2011-04-21T10:33:00.000-07:00

Dear Gene,

Don't correct me if I'm wrong, because you know I'm not... Does anyone --- can anyone possibly --- believe that, in a Star Trek future, anyone in The Federation would practise/use abortion?

I can hear McCoy --- or Dr. Hologram --- objecting "I'm a doctor, not a butcher."

Of course they wouldn't. There isn't an economy anymore (OK, there's a black market that hangs out at Quark's on DS9...) because it isn't necessary for universal prosperity; so there's no poverty, either. There's a marvelous array of non-addictive drugs that dull pain but won't interfere with motor-control or kinesthetic sense, so no-one's afraid of delivery. And the same super-fancified medical care available also means no-one worries about whether their kid is born missing an arm, or with trisomy-21, or... because they'll have what they need to care for and mittigate those difficulties. And let's not forget that babies are cool!. Not least cool are those klingon-romulan-human-bajoran-descended babies who give clear witness to the oft-ignored fact that all sapient life is made in the image and likeness of God, and that the salvation of all of them was purchased by God-made-flesh one Friday Afternoon some two thousand orbits since on a molten-rocky planet about a main-sequence star of 1/20 the mass of those stars bound for black-hole status.

OK, so perhaps ST hasn't always imagined a perfect universe of perfect people. That's OK, because people aren't perfect: they are fallen. Thoroughly Utopian visions are not science fiction, but userpers of Heaven. And, for sure, we don't see nearly enough of Riker's ill-gotten brood anywhere --- but, again, think of all the young'uns we do see!

You just know it's true.

With fond memories

On Man's First Office

2011-04-13T12:25:00.000-07:00

Dear Auntie's readers and nephews and nieces,

I am a Christian --- in fact, I hold to the universal and apostolic faith of the first Christians, which is to say I am a Catholic (from the Greek, in latin letters "kata-" and "holos"; think of "catastrophe"--- all tumbled about --- and "holographic" --- the whole picture); this has probably been made obvious before, but it bears mentioning.

For the record, I don't at all mind being (called) a Latin Rite Catholic, because I am. I'm also trying to shore-up my scant Latin.

My objection to the conjunction "Conservative Catholic" (or "Liberal Catholic") is that they start as lies. "Liberal", in the mouth of a "Coservative" is meant to be an insult synonymous with "libertine", and second cousin to "libertarian". "Conserative", spoken by a "Liberal" means "much-too-conservative" --- unimaginative and unforgiving. Making them names for mutually-opposed groups of people disguises the fact that the Church teaches all Catholics to conserve the sacred traditions handed on to us from our ancestors in the faith, and also to liberally share with our neighbors in need that wherewith God has blessed us in plenty --- e.g. in spiritual and coroporal works of mercy.

Understandably, it's helpful --- as Ms. White emphasizes --- to distinguish between the distinct; on the other hand, it is creatures that most need names, not delusions¹. And this is why, in the documents of the various Church councils up to Concilium Vaticanii I you will find

NOT FROM A REAL COUNCIL

Any who teaches that the Holy Trinity is made of chocolate LET HIM BE ANATHEMA.

Any who teaches that even moderate enjoyment of chocolate is inherently inimical to salvation LET HIM BE ANATHEMA.

That is, particular errors are first defined (described plainly) and then condemned.
The councils and creeds and canons and anathemas have a technical language, but it doesn't become a jargon --- the words are used to be precise, not to be obscure or lazy; and so we don't find anything like

NOT FORMAL OF A REAL COUNCIL

Pelagians are wrong.

ALSO NOT FORMAL OF A REAL COUNCIL

Anyone who agrees with Pelagius is wrong.

Instead, we would read of anyone who might teach that "men are saved and justified solely through their own personal good works or by the own merit", that such folk are teaching error, they are a scandal to the faithful, and for the good of their faith all faithful must have no dealings with such folk until they recant and correct their teaching.

Some years ago, a friend I haven't seen in a long time argued that the now-disused so-called Anti-Modernist Oath had been a mistake in the first place because it condemned a collection of errors that no person had ever held altogether --- that is, he saw it as defining a creed which as an assemblage was to be condemned --- and which had never had any adherents. This struck me as odd then, and now I can hypothesize that he was distracted by the parenthetical "modernist" label, and answer that modernism as a movement may never have existed in the form of adhering to all of such-and-such errors, but such and such errors had severally become fashionable, and in all cases motivated by a desire for modernitas, of wrongly wanting to update something that was inherently eternal. Because there had been found several ways for modernizing desires to fall into error, it was convenient in the Scholastic sense to condemn the several sorts of error. To say that the oath was to reject a belief called modernism is as much to mistake the Councils of Nicaea I and Constantinople I as rejecting Arianism as the errors of Arius. rather than as errors. Instead, the canonical form might have allowed Arius to repent and recant, had he accepted such grace.

That's all I have right now.

a taxonomist of errors

1: not being psychiatrists, we are not making a study of delusions; we are distinguishing them from creatures.

Interesting to note

2011-04-03T20:15:00.000-07:00

Dear Christian,

Fr. Homilist today remarked on Our Lord's revelation and veiling today --- acts of the Divine Goodness, appearing contrary, but each suited to our needs.

I think it's a nifty observation that in today's Gospel (EF calendar) in fact we see the fulfilment of two petitions from Our Lord's Prayer: give us this day our daily bread --- the feeding of the multitudes --- and lead us not into temptation, but deliver us from evil --- seeing they are in danger of a great sacrilege, He removes the immediate temptation of His presence.

Let us never give up hope that God fulfils His promises to us!

Your brother in Christ

At the gate.

2011-03-30T19:41:00.000-07:00

A spot in Middle Earth, eh?

Hmmm...

There might be much to say about Dor Firn-i-Guinar --- the "Land of the Dead that Live" a name that should resound in the hearts of all werewolves --- only we don't hear much about it as a place beyond that there are Ents living nearby at the time. I'd very much like to do a post about a spot I can only call Annon Torech Ungol, which I wrote about obliquely here, and Meredith here. Alas, I haven't got that volume handy just now.

So I'll have to try at two snatched hints at the texts... I've read it too often, but I can't be sure of memory!

`"Now where's that Gollum got off to? I used to think he was after food, but I don't think that can be the case here. Not unless there's some sort of rock he fancies." ...

`Frodo laughed; such a sound as had not been heard in that part of the world since ... Sam was suddenly quiet, worried almost as if the very stones had ears. But Frodo laughed again ...

... someone else will have to supply the precise words, if they like. Now, it's bad enough that the place would be lifeless in itself, But can you imagine? Somewhere no-one had ever laughed? And this is also a much-used highway. There are tales of doomed prisonners cheering eachother with jokes at Auschwitz and Dachau. In this place, it was Frodo and Sam.

That's my locus.

UPDATE

I've got my book back, and here are the proper texts:

In a dark crevice between two great piers of rock they sat down: ...
[Sam:] 'There's a wicked feeling about this place.' He sniffed. 'And a smell, I fancy. Do you notice it? A queer kind of smell, stuffy. I don't like it.'

'I don't like anything here at all,' said Frodo, 'step or stone, breath or bone. Earth, air and water all seem accursed. But so our path is laid.'
...

'... I wonder if we shall ever be put into songs or tales. We're in one, of course; but I mean: put into words, you know, told by the fireside, or read out of a great big book with red and black letters, years and years afterwards. And people will say: "Let's hear about Frodo and the Ring!" and they'll say "Yes, that's one of my favourite stories. Frodo was very brave, wasn't he, dad?" " Yes, my boy, the famousest of hobbits, and that's saying a lot."'

'It's saying a lot too much,' said Frodo, and he laughed, a long clear laugh from his heart. Such a sound had not been heard in those places since Sauron came to middle-earth. To Sam suddenly it seemed as if all the stones were listening and the tall rocks leaning over them. But Frodo did not heed them; he laughed again. ...

... 'You and I, Sam, are still stuck in the worst places of the story, and it is all too likely that some will say that this point: "Shut the book now, dad; we don't want to read any more."'

'Maybe.' said Sam, 'but I wouldn't be one to say that. Things done and over and made into part of a the great tales are different. Why, even Gollum might be good in a tale, ...

'Gollum!," he called. 'Would you like to be the hero---now where's he got to again? There was no sign of him...

'I don't like his sneaking off without saying,' said Sam. 'And least of all now. He can't be looking for food up here, not unless there's some kind of rock he fancies. Why, there isn't even a bit of moss!'

Goodness me! but it's quite a bit thicker, what with trying to keep enough of the structure/context. I particularly like the internal contrast with a cozy fireplace; you might think it made the present place feel more desolate, but I find it actually softens the mood. It is as if our hobbit heroes actually conjure up some coziness for themselves with these innocent diversions.

So, you're wasting time with the internet...

2011-03-05T13:58:00.000-08:00

(If you're here, you must be!)

... and this Batty fellow keeps intruding with things you tried to forget that you never learned because of how terribly dull your course on matrices in linear algebra was, or is...

So, yeah, I do topology. In fact, algebraic topology. One of the things I like about algebraic topology is that sometimes you get to draw nice pictures. OK, so I can't draw worth your trouble, but it's fun anyways. Maybe Emacs or someone will make better pictures.

One more nifty thing about the pictures you can draw in topology is that they're useful for other parts of math, too, like group theory. And this is a big deal! There are some Nice and Easy-to-Describe topological spaces that "know" how to calculate things that we can't calculate. This is part of what makes algebraic topology difficult, but also part of why it's exciting. And if we're lucky, sometimes they give us help understanding the things we can calculate. In particular, being able to describe a calculation by drawing a picture can help us lots.

That's my introduction to

For instance, if you ever had to do linear algebra with matrices, then you probably heard about their determinants; for instance, a two-by-two matrix $\left(\begin{array}{cc}A&B\\C&D\end{array}\right)$ has determinant $AD - BC$, and a three-by-three matrix has an even worse determinant expression with perhaps six terms in it, and a four-by-four... they would have given you, however, the clever abbreviation

$$ \left| \begin{array}{cccc} a_{00} & a_{01} & a_{02} & a_03 \\a_{10} & a_{11} & a_{12} & a_{13} \\a_{20} & a_{21} & a_{22} & a_{23} \\a_{30} & a_{31} & a_{32} & a_{33}\end{array}\right| = a_{00} \left|\begin{array}{ccc} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right| - a_{01}\left|\begin{array}{ccc} a_{10} & a_{12} & a_{13} \\ a_{20} & a_{22} & a_{23} \\ a_{30} & a_{32} & a_{33}\end{array}\right| + {} $$
$$ a_{02} \left|\begin{array}{ccc} a_{10} & a_{11} & a_{13} \\ a_{20} & a_{21} & a_{23} \\ a_{30} & a_{31} & a_{33}\end{array}\right| - a_{03} \left|\begin{array}{ccc} a_{10} & a_{11} & a_{12} \\ a_{20} & a_{21} & a_{22} \\ a_{30} & a_{31} & a_{32}\end{array}\right| $$

and more things besides; but if you were lucky they also mentioned that there was a group acting on the set $\{0,1,2,3\}$, and that this group had a representation $\sigma$ as multiplication by $\pm 1$... if you were even luckier, they would have told you why this is true, and so forth --- especially, that this representation $\sigma$ tells you which sign to use for which terms when you expand the determinant all the way down.

Here are some pictures relating to these absurd claims.

This is an abstract of expanding the determinant of a (permutation) matrix. It looks like a forrest of lollipops! First you draw the circles corresponding to the permutation and drop the stem to plant the lollipop. Then you fill-in the remaining spaces (including the circles) in each row from left to right alternating between $+$ and $-$, and you always start with $+$! Because that's what the determinant expression says to do. Then you count how many $-$s you circled, and if you get an odd number, your permutation is odd; if you get an even number, the permutation is even. Easy, yes?

Here's another way:

Here you just write out 1,2,3,4,5,6,7 and draw an arc from each number in the first row to its image in the second row. Be careful that each arc is always going slightly down, so it doesn't cross itself, and each time you draw a new arc, make sure it doesn't hit any crossings you've already drawn! (If you want to break this rule, you have to be very careful in a more complicated way, so I won't allow it). Then you count how many crossings there are. If there's an odd number of crossings, then your permutation is odd. If there's an even number ... this should sound familiar by now. The point is, though, that these two procedures give the same notion of odd/even! Although, one is much easier to work with.

See, the point of group operations is that you can compose them. If you've got permutations $g$ and $h$, there are more permutations related to them: $gh$ and $hg$ and ...
And both the matrices and the string pictures also represent composition; to compose permutations given their matrices, just multiply the matrices.

To compose permutations given their string pictures, just stack one string picture over the other!

And, finally, odd/evenness also represents (something of) the permutations: if $g$ and $h$ are even, then $gh$ is also even; the same if they're both odd: $gh$ is even again. If $g$ is even and $h$ is odd, then $gh$ is odd, and so is $hg$. It's easier to remember if you write it this way, though:

$\times$	$1$	$-1$
$1$	$1$	$-1$
$-1$	$-1$	$1$

Anyways, trying to look at the lollipops... what on earth are we to do!? The procedure for deciding between even and odd, it may be easy, but it obscures something of what's going on. In fact, I'd rather call it an obfuscation.

But in terms of strings, it's easy to check that stacking the pictures, as far as counting crossings is concerned, coresponds to addition.

It's that easy!
Even better, the string pictures suggest why we only care about even/oddness, and not about the full number of crossings.

Incidentally, while getting this sketchy little post into some sort of shape, I have figured out what I think is the right way to view the lollipop diagrams. You see, there is something it really is obfuscating. If you see it... !!!

... all that is stippled, flickered, (who knows how!)

2011-02-25T10:27:00.000-08:00

Some musings.

A while ago one of my pseudonyms signed under a comment at Dr. Thursday's, asking what he had to say about GKC's use of the words "type" and "typical", which I don't think I quite understand; and I don't really expect I'll get a suitable answer, but I thought I'd share some other English words which it turns out have a common root --- you will see a family resemblance, I'm sure.

dappled timbrel
thumping tambour
stump type
timpani tamp
stippled stamp

I'm half-wondering whether children of tango/-ere/tetigi/tactus belong on the list; Lewis says it belongs to [TAG-] while indicating tympanum as a Greek loan word.

Anyway, three of these are drums, and one is one way to deal with a drum. Two or three may be controversial (I'm all about the sounds; the history, not so much... but I *think* it works, poetically at least --- oh, can someone tell me if German «glück» "(good) luck" and Greek «γλυκυς» "sweet/sugary" are related at all?)

Approaching this family from the perspective of "type", I was rather intrigued by how active the rest of the set are. A type --- sometimes also called a figure in the Douay-Rheims translation --- can be both a form/pattern and the impression made by such. Whereas a figure, an appearance or face ("la figure" en français, des fois) can sensibly be an interpretation or an artistic rendering or schematic diagram, type by contrast emphasizes an active and tactile connection, contact between the cast and the casting, the press and the impression.

The other interesting news that came out of this particular word-wander was a contention that Guttenberg's most important contribution to the art wasn't so much movable type --- reusable bits of typeface --- as the hand mold, used to quickly cast new pieces of lead typeface (Does "type-cast" mean something else to you?). Someone else can look into "font" and "foundry". I've been typing enough, now, about it.

Ich verstehe das nicht

2011-02-07T20:07:00.000-08:00

Dear Advertiser,

Alas, I read none of pashtun, farsi, arabic, or syriac; never mind whether I could distinguish among them, or how different they'd look to you. You might also guess by my institutional IP address that I don't have much disposable income at the moment, however much folk like me may enjoy spending. Altogether, there's not much point. I shall be asking Mary to pray for you.

an urban scholar

... propter magnam gloriam...

2011-02-01T19:47:00.000-08:00

Most excellent Theophilus,

I submit for your diligent consideration

\begin{enumerate}
\item[16] safe travels
\item[17] safe returning
\item[18] familiar faces
\item[19] cozy blankets
\item[XX] all that tells God's glory
\end{enumerate}

a fellow pilgrim

On The Incarnation

2011-01-27T19:38:00.000-08:00

Probably (hopefully!) there's nothing new here. But I wanted to make a legible note of it, just because...

The text I'm considering is from Genesis (stick with me): "Let us make Man in our own image". Lots has already been said about this, for instance "God is King of all creation: what does a King do to signify conquest? He erects a statue of himself". I don't remember my source for that line of reasoning --- and it's a paraphrase, of course. There's also Chesterton's observation (again, paraphrasing) "Men are indeed all like pennies; for their value in each case is exactly that they all bear the likeness of the King". In other words, God has put Men in the world at least partly as signs of His own kingship.

My observation is that when God makes a sign, He also makes a real thing. (God creates by saying, His words become what they signify) Since God has made an image of himself, a sign pointing to Himself, it's a fair guess He's going to make good on the sign. All of which is just to suggest that the Incarnation was promised even from the sixth Day of Creation. So, that conversation was interrupted for a few generations, we all know the story.

So it would seem that the Incarnation was foreseen and intended by God, from Creation, and its promise was revealed to the holy scribe and recorded in Genesis. ... I think. I will gladly defer to better learning on this matter.

A brief lesson in Parliamentary Democracy

2011-01-10T18:27:00.000-08:00

Dear Saskatchewan Premier, Justice Minister,

The word you're likely looking for is "notwithstanding".

a Catholic living elsewhere

For the benefit of Mr. Moore

2011-01-05T12:19:00.000-08:00

Dear George,

It looks like it is snowing, but I'm not convinced.
You might even say, it is snowing, and I don't believe that it's snowing. But, then, you always were easily conviewsed. And that's you, not me. Maybe: it's snowing, but I don't think it's really snowing. There are ants and ants, after all. Here are the former.

Do you like my red herrings? As you can see, they are of mackerel dyed green.

he must be mad

hee!

2010-12-31T15:51:00.000-08:00

Dear Jack,

I was just poking around the wikipaedian's notes on your Chronicles heptalogue, and see that in the phrase "traditional British and Irish fairy tales," he has links to "British people" and "Irish mythology."

I always thought Ireland sounded a bit too-good-to-be-true!

wishing you'd swim the tiber already ...

A little bit of misdirection

2010-12-28T09:11:00.000-08:00

... wherein we reduce the classical Sorites Question to a problem of Hilbert...

The qeustion was "how many grains of sand are needed for a heap?"
I answer that four are enough, though ten thousands may not suffice.

Put another way, the question of "how many" is the wrong question. Heapness isn't about quantity but about geometry. You have a heap of sand on a table when some of the sand isn't touching the table, but only more sand. To stably hold one grain of sand off the table, a tripod of lower grains will do nicely. But if they're spaced, say each 1cm from the others, you can easily fit 10000 on a modest square table, and there will be naught of heap to the ensemble.

We suspect that other Sorites-type questions (how many voters make a democracy? How many roads must a man walk down?) have similar resolutions.

Home-visiting adventures

2010-12-27T12:10:00.000-08:00

Dear Interface Designers,

... So, I'm home for the holidays, and thus I've discovered the new laundry washing machine my parents bought to replace the one that flooded our basement. It does a lovely job of washing the clothes, and has all sorts of blinking lights, which are nifty (although I worry about all that implicit software... there are no hard-set dials or aught.) What bugs me, though, is that the machine seems to be permanently cheerful. It strikes me as the product of a segment of a generation who grew up with talking books and ignored books about talking machines.

And so, when you set the machine to a particular program and initiate its run sequence ("tell it what you want, and ask it to start"?), it sings a chipper little musical motif, and when it's done it pipes another happy little tune to signal its satisfaction and gratitude for being given a task within its measure, the joy of a job well-done.

So indescribably phoney.

Anyways, to say the unnecessary, it would drive me up the wall if I were staying here very much longer than I otherwise intended.

I hope this has been entertaining,

a confused non-customer

Deadlines? But it's holidays!

2010-12-22T20:40:00.000-08:00

and I just haven't got a good poem idea; the word and the question have been stewing for a couple weeks; but I've got boppquiche.

When I do come up with something versifiable, I'll put it here. I hope the remaining Advent days are fruitful for you.

"The most forgettable..."

2010-12-17T08:37:00.000-08:00

Dear P.D.Q,

Christmas is coming! Hooray! I don't know why (at least, I haven't thought about why), but that always makes me think of old childrens' movies, like the animated Peter Pan. And the best thing about the animated Peter Pan, of course, is the Crocodile. And the best thing about the Crocodile, of course, is his delightful musical theme!

Have you ever noticed that there is some music that just have to be sung, and others that seem more to suffer from the imposition of words and human voices? The former is definitely the case with, for example, any part of Mozart's setting of the Requiem propers --- I can say this with confidence because I heard a reduction of it for string quartet as I was looking through a local record shop. But I'm pretty sure the Crocodile falls into the latter category. I mean, the song is cute and all, but there's something inimitable about the bassoon's chuckling waddle. And the little rippling glimmers of string and flute... they sound like the dazzling sunlight reflecting in odd ways off the submerged croc's wake, oh so precious, and Oh! so alarming!

Hmmm... come to think of it, I can only find tenors (or mock-tennors) singing it, and very much poppishly, too. It really wants a bass voice... I'm looking for examples singing other stuff --- like a solid Sarastro maybe, but...

Anyways, thanks for the Panther Dance Quodlibet!
the frosted cyclist

Nothing to report

2010-12-10T21:03:00.000-08:00

Dear G.K.,

Maybe you have heard of the electronic aperiodical Caepe? They specialize in satire, of course; but then I discovered a particular article (append "articles/marriage-handled-amicably,18566/" to their address), which I must suppose they meant to be funny, along lines like those of the item "Report: Mom Just Locked Her Door", which is funny in how it describes in action-news-speak a moment of household tension many of us recognize. The thing is, though, "Amicably" just isn't funny.

Perhaps I might toss a lit.crit. word into the mix? Part of the humour in "Locked" is the dramatic irony present in many of the characters' statements, e.g.

"It wasn't me," Katie, 11, told reporters. "I was just sitting here. I didn't do anything."

Anyone who has grown up with parents and siblings will recognize that the disclaimer "I was just sitting here" identifies one of the many (small) things that lead to "Mom"s escapade.

The irony in the "Amicably" item is that it has essentially substituted "marriage" for "divorce", and an ordinary family in mundane settings for celebrities amidst artifice. OK, so maybe it's a satire of the celebrity gossip rag. It's still not funny. It's just a sad story of a marriage gone tired, and I can easily imagine in our modern culture that some will find the joke to be that these are "stupid bored married people! they should just split and have fun!" Here's the thing: altogether, the pretend couple described are actually doing the very thing (if not everything) they should do, given that neither seems to be a danger to the other. So we have an example of perfectly ordinary people being faithful in spite of trials, being held up for laughs?

I think the world needs more people alive with two legs!

your adopted nephew Bat

There's no end!

2010-11-29T14:33:00.000-08:00

In case my gloomy tone was getting contagious...

\begin{enumerate}
\item[11] Fresh baking.
\item[12] Thoroughly opaque curtains.
\item[13] Sunday brunch with friends.
\item[14] The voices of infants.
\item[15] That a dull job is really the worst of my troubles.
\end{enumerate}

Some Family History

2010-11-26T23:58:00.000-08:00

Against chanting voices, above the din of war hammers, amidst the bleating of scattered sheep, I cried out, "De profundis clamavi ad te..."

My great-grandfather (one of four --- most of us have four!) was a landscape painter. During the Great War the British Army paired him with pilots of those new-fangled biplane things, to sketch the German positions. In his spare time he sketched and painted the soldiers around him; he was not himself a soldier, and did not take part in combat. Being frequently at or even behind the front line, however, he knew the stress of battle, and was caught in "Mustard" gas at least once. When he came home he lived in a small appartment with his wife and their son and daughter. They had one bedroom, which he used at night alone, while the other three slept in the front room.

The reason for this strained arrangement is that he was not a safe companion when sleeping. If disturbed in the night, he'd thrash and throttle the first thing he could wrap his hands around: it was as though he no longer had a working triage mode, and went straight to panicked self-defence.

Now, among Men I was unthought-of before he died, and even his son my grandfather didn't survive to my birthday, I can't claim from any familiarity that the War or any particular part of it was torturous to him. Nonetheless, it's clear that this tale from one branch of my family is hardly unique, and the capacity for reason we all share speaks clearly that something broke the proper relationship between soul and body in him, and it seems likely to have been something he experienced during the War.

This is all by way of bringing both some context and some content to a disputation simmering in my real-world neighborhood.

If anyone suggests to you that "waterboarding" is essentially "a little water up the nose", you might point out that if it's harmless then it shouldn't change the cooperativity of any interrogation subject; you might point out that it's quite a different proposition from offering someone a neti pot (oh! the horror!) or a saline spray. If they admit "sure it's unbearably uncomfortable, but it isn't torture", you might ask how they distinguish between unbearable discomfort and torture. You might alternatively mention "not all is torture that is condemned". The terminology of Gaudium et Spes, quoted at length in Veritatis Splendor is quite broad: as inherently disordered it includes

quaecumque humanae personae integritatem violant, ut mutilationes, tormenta corpori mentive inflicta, conatus ipsos animos coërcendi

whatever violates the integrity of the human person, such as mutilation, physical and mental torture and attempts to coerce the spirit

It has been said that waterboarding might be favoured by interrogators owing to forensic difficulty in detecting it after the fact: unless the subject develops a suspicious bronchitis, it leaves little visible scarring. Note, however, that the text of the pastoral constitution explicitly distinguishes between mutilation (a direct violation of the body's integrity in itself) and torture of two sorts. We see, then, that our Church recognizes the possibility of a category of illicit act violating the integrity of the person while seeming to preserve the integrity of the body. Ultimately, this willful attempt on personal integrity is the objection to torture, whether physical or mental. Physical torture seeks to coerce by upsetting the primacy of the soul over the body; mental torture seeks to coerce by upsetting the primacy of reason (practical or moral) over will.

I should submit further that mental torture is in fact the more pernicious sort; for in seeking to invert will over reason in others, it acts as a mode of contagion: reason itself, guided by the natural law, should tell us that mental torments are reprehensible, and thus one who attempts it has permitted his will to rule over his reason.

Considering then the soul of the perpetrator, we see the longer-lasting evil done by any evil act; for while torture may scandalize its victim, it otherwise moves the victim closer to God's pity, while moving the toturer further towards God's avenging justice.

What shall it profit a man, though he save for a time the lives of the whole world, if he lose his soul?

Just Between Us Commoners

2010-11-23T17:24:00.000-08:00

Dear Fellow Subjects,

(and dear spectators, too, for all of you in republics and Hapsburg lands, &c.)

A modest much has been made recently of the announced engagement between His Royal Highness the Prince and Ms. Katherine. If you want, here's my two cents' worth on the hou-plaugh.

To get right into it, the office of the Royal Family has always been (this may be controversial) that of the First Family, within the realm; the Crown Monarch has always been the saecular head of the family called Britain. Other expressions have been used. For instance, Henry VIII likened (himself) the King of England to a tiger keeping the "wolves and jackals" (his vassal lords) in line. But as much as we may say that a father is as a king in his house, it's more truely the opposite: that a King is as a father to his people. The authority to rule, whether by direct decree or by assenting to the advice of the assembled lords and representatives... whatever the style of government, if there be a Monarch, his authority is of the same shape as a father's over his family.

But as the saecular head of his or her realm the crown carries (well or ill) the duty of also modelling headship in an ordinary family. And so the significance of a Royal wedding engagement inludes that it particularly reminds us of the nominal arrangement for the family's continuation; it reminds that the nominally-arranged family is the innermost and primary of social circles, the principal of community, the Earthly pattern of living in mutually charitable servitude.

Honesty compells us to acknowledge that the Britannic Royal Family has not always been nor always appeared as a successful model family: they are, after all, merely human. The same Henry VIII thought to make himself both saecular and spiritual head of his country, which really should have been too much for credibility, not to mention confusing greatly just who the Royal Family were; as late as the reign of George III the rivalries recurrent through generations between King and Heir Apparent were notorious abroad. Even in living memory, attempts to place some supposed common good above the good of the actual living Royal Family as a family have had disastrous consequences for the commonwealth's willingness to accede to their Royals; and the Royal Family's renewed endearment to its subjects has followed their living visibly as a family.

But enough of dodgy facts and history half-learned, let's get on with some speculation! There is at this time a great legal tension, a juridical dissonance, amongst British laws for the commonalty, the laws governing the Crown, and the shifting laws of the church which the Crown has arrogated under itself. While the English are legendary for "muddling through", and are masters of diplomatic compromise, it would be wrong to think or name them a willfully stupid or ignorant people (Never mind the chavs. There is naught that is peculiarly English about chavery, anyways). And as long as they have sufficient wisdom to both keep an icon of family life at the head of their Law, and insist that the embodied form of that icon be recognisably a family in the only living and enduring sense, it can only be a matter of time before they realize in what peril they have left the ordinary family whose purpose it is to produce new servants of God, new subjects and electors. I perceive that thence lead only two roads: the canker must be cut out of the law, or the law's head cut off. You all know which outcome I prefer.

God save the Queen!
Her Majesty's good subject, but ...

An Impromptu on Two Prompts

2010-11-15T21:32:00.000-08:00

I wonder if Dylan was hoping to read something like this?

Billions and billions;
And yet, if there's too much light
All ends in big crunch.

Anyways... let's see... it's a while since I tried that sprung meter thing; I like trimeter, so let's see, what can we do?

The Weight of Light

Hast seen the Sun's Anvil
The desert's deadliest plain
Where Lawrence's hard will
Bedouin led by night
To Aqaba, with Turks' blood
Sand so clean to stain?
Even i'the Sun's core,
Though packed, the ions hot
Know each the others not
Except that messengers of light
Amongst them swiftest soar.
Time they do not keep
--- Not unto themselves:
In this like Arda's Elves;
Around them still it seeps,
It ripples blue or red.
Ponder not too heavily
this I have here writ:
Yet if thou, underfoot,
Glass shards crunch to grit
Think of the light thus loosed,
Unlock'd windward or lee,
Or falls, to die, on soot.

I know most of the impromptuness is lost in the blog/post/read sequence, but trust me, I've not putting much editing into this. Or maybe my saying so is entirely superfluous?

Seeking Perhaps To Make Oneself Unpopular

2010-11-11T00:13:00.000-08:00

Dear unparticular people,

I understand that what I'm about to propose for your consideration isn't a cheerful thought, though I hope there may be hope to find in it. I think it is, fundamentally, informed by hope more than offering any novel hope.

At the core of this idea's uncheerfulness is, in some ways, the motivating event for much of the past decade's news, popular debate, geopolitical reheaval, and particularized insanities. I refer, of course, to the Massacre of New York and Washington which took place in 2001 on the 11th of September.* It is my thesis here that the New York and Washington Massacre should not actually have changed much of anything.

Of course, some clearly visible changes must be acknowledged, in order from solemn to mundane: a few thousand people were murdered by a conspiracy of a few dozen, and some committed suicide quite visibly; several thousand connected people thus became quite publically bereaved survivors within scant hours. The operation of several businesses was interrupted or ceased entirely; several buildings were destroyed or severely damaged. Four airplanes were deliberately crashed.

The population of NATO, and most of Christianity I expect, indeed a large part of the world generally, were rightly angered by this public violence; and a large part of the world became understandably --- despicably --- smug. But more than that, a large portion of the world, meeting both smug and angered parts of it, seems to have gone somewhat insane because of the public bloodshed. And because you all know what I mean by this, I shan't detail the insanity.

My reply, however, is to point at several important constants, such as all folk aspiring to sanity should madly seize on and infect their neighbors with as soon as possible, if I may have aught to say about it; in order of fundamental to corrolaries, more-or-less.

The Divine

God did not change, did not change sides, did not change His mind about anything at the persuasion of the New York and Washington Massacre, or of its conspirators, or of its witnesses. In the mystery of His grace, he has permitted it for the good of all and for each; and all who in it departed this life were received by him in to Purgatory or Heaven, or relegated to Hell, even as He found them, according to His unchanging justice and mercy.

The Good

Even as God Himself did not change (He Is, unchanging), so the natures of right and wrong, good and evil, justice and iniquity, have not changed. In other words, the principles by which we order our lives, our comings and goings, our labours urban and wars and farms, how we ought to treat our neighbors and our friends and our enemies and our prisoners; these have none of them changed. It is true that various particular of the people we know we must prudentially re-classify among friends and enemies, but that in itself is not a new phenomenon. The acts themselves demand just retribution, if any of the instrumental conspirators survive; but the weight of retribution should be tallied exactly as it always had been.

Our Safety in This World

On the 12th of September 2001, we were none of us in more danger from terrorists than we had been prior to the Massacre --- indeed, many of us were safer in general, being on solid ground rather than in a plane twenty miles up hoping the engines and the flight surfaces and all keep working right. But the co-dependence of airline passengers on a very small number of well-trained professionals for their safety, on eachothers' well-behavedness, our dependence on them not to fall on or fly through us, these are old facets of any sort of travel; planes have been hijacked, have flown into buildings, have carried away unhappy victims many times over.

Neither is the scope nor speed of destruction we saw any new thing. In World War II *, Dresden was deliberately flattened essentially overnight, the harbor district of Hiroshima was transformed from city to a sterile ruin in seconds; and the holy city of Nagasaki burned for a few hours, ignited all at once --- the longer because the bombadier missed in poor weather, and hit neighboring forest. Looking further back, whole cities have been snuffed out by the very convulsions of our Earth. Indeed, we continue to live, as some have put it, by geologic consent, which may be withdrawn without notice at any moment. Are we all to live differently, now that America has fresh intimate reminders of these facts?

Because so many of the important things didn't change with the Massacre, we should have hoped that with somewhat more attentive police and espionage we might all live a little safer, while largely carying on as usual. We might even have contained a concerted will to evil, and helped better the world thereby. But here we are, now; I shall beg the latest Holy Catholic Martyrs of Baghdad to pray for the conversion of their homeland and all that dwell there. I even hope that we may, all of us, reach a better and more vigorous sanity than we have let ourselves slump into since the particular decadences of the last fifty years.

Now, let's all read some Tolkien!*

For President Never

* I think I shall henceforth refuse to call this event "nine-eleven". Aniversaries are marvelous things, and Bin Laden has unfailingly defered to the Christian Calendar when plotting his nefarities; but numbers are for everything, and as Mark Shea exhorts us, Man's first office is to name all creatures in this world.

* This also might want a better name. For instance, it's not clear to me if WWI is over yet...

* OK, the link is more of me, not Tolkien; it points to and quotes some Tolkien. Blargh!

Apocrypha Topologica I

2010-10-30T21:23:00.000-07:00

Dear Mathematicelli,

I should like today to introduce an apocryphal history of Topology, both as a phenomenon and as a field of mathematical study. It will necessarily be abbreviated, full of fictions, and other more innocent errors --- hence apocryphal. But it should be ordered to the truth so far as illuminating the modern study of topology itself.

Topology was imposed on the visible Creation by God at least as early as the Second Day, when He said

6 ... "Let there be a firmament made amidst the waters: and let it divide the waters from the waters." 7 And God made a firmament, and divided the waters that were under the firmament, from those that were above the firmament, and it was so.

This highlights the first introduction of a disconnected set, a "you can't get there from here" in the world: to reach the waters above from those below you must cross this firmament, whatever it may be. And this notion of separation, whether in the absolute sense of being mutually inaccessible, or the relative sense of inhabiting disjoint neighborhoods has been a puzzle and inspiration for topologists since before we even had the name topology to describe the field.

Some might argue that the temporal ordering of days already introduced an order topology (or the causal partial-order topology we learn from the Special and General Theories of Relativity). I reply that this is missing something of the point, but if you want to write your own paper on the history of Topology that's quite alright.

Other Biblical features of topological interest in denoting separation: the cherubim posted to keep Adam and Eve out of Eden; the Red Sea; the River Jordan; the Rivers Tigris and Euphrates, that separate the Land Amidst the Rivers from surrounding territories (I mean, you can get in and out of that without crossing either, but then you'd have to cross the ~40km line segment between Palu and Hantepe... a narrow road, as geography goes!)

The next great topological discoveries were knots and chains. Windows are a nifty invention too, I suppose, but knots and chains are much more tangible. The way these work, as I'm sure you've experienced, is that various strands of rope or metal, being extended in one direction, have new ways of becoming separated from conditions they might have liked to achieve: while it would take a wall to stop you, and you can walk around a rope quite happily, a string can get stuck by a rope in one perpetual wandering-around! By the by, I don't mean mechanical knots; these are fascinating, but the mechanical distinctions between various rolling hitches are much fuzzier than the topological fact that there are more ways to get tangled in a net than in a string tied in a single loop. Think of the "Gordian Knot" versus an undoubled slipknot bow as you might use on your shoes.

As another aside, there seems some discrepancy between my predecessors in mathematical apocrypha on the one hand vs. closer accounts of Alexander's encounter with Gordy's knot --- what the knot tied up, whether Alexander really sliced it in two or what, etc., are disputed points. One way or another, there were knots and mechanical facts emphasizing topological separations, and it became a point of proverbs through the march of time.

The Gordian Knot brings us to the relatively recent period and setting known as Greek Mythology, and there, for now we will interrupt our History. Next time: strings graduate from topological features to topological tools!

The Math Prof of Your Nightmares

PSA

2010-10-30T02:36:00.000-07:00

Dear Passers-by,

I noticed recently that the blogger profile for this persona didn't offer means of private communication, which was in fact the primary purpose of the /dev/null persona. This must have been the unintended consequence of some policy change within blogger, because other people have been surprised recently to not show contact info; in any case, I've changed that now.

And of course, it's easy to just write here, in Dumbledore Fashion, that mail addressed to qnoodles at gmail will find me. As a purely historical note, the q stands for Quincy, and no, I don't know anyone named Quincy. It just seemed to suit "Mr. Noodles" remarkably well!

your humble host

PS there really is only the one of me.

In deep October

2010-10-28T23:03:00.000-07:00

Enter Hamlet, reading (L.C.)
Pol. How does my good lord Hamlet?
Ham. Excellent well.
Pol. Do you know me, my lord?
Ham. Excellent well; you are a fishmonger.
Pol. Not I, my lord.
Ham. Then I would you were so honest a man.
Pol. Honest, my lord!
Ham. Ay, sir; to be honest, as this world goes, is to be one man picked out of ten thousand.
Pol. That's very true, my lord.
Ham. For if the sun breed maggots in a dead dog, being a god, kissing carrion,——Have you a daughter?
Pol. I have, my lord.
Ham. Let her not walk i'the sun: conception is a blessing; but as your daughter may conceive,—friend, look to't, look to't, look to't.
[Goes up stage.]
Pol. (Aside.) Still harping on my daughter:—yet he knew me not at first; he said I was a fishmonger. [Crosses to L.] I'll speak to him again.—What do you read, my lord?

I am told "Defiant" and asked "Are sparrows blithe?"

I've been having difficulty with this one, because all the words that come into my head are scripture, and it doesn't seem quite right to write a cento on the Bible --- that were only to diminish the worthiest poetry ever set down.

\begin{itemize}
\item "Are not two sparrows sold for a farthing? ... You are worth more than many sparrows."
\item "Consider the birds of the air: they reap not, nor sow, nor gather into barns..."
\item "How lovely are thy tabernacles! ... for the sparrow hath found herself a house, and the dove a nest for to lay her young."
\end{itemize}

What follows instead is an aliterative allegory of wishful thinking. Or something... yeah, I don't know what it is.

Butterflies and sparrows spin blithely by
My window, wonderous marvels in miniature,
Provoking contemplation, to ponder creatures
And Provident God, gracious in peace and plenty.
Against His coming Justice, fearing coldest Gaol,
We rightly cry repentance, and remission crave,
Converting to Love our lagging contrite hearts;
Even as I of Him, each evening,
Beg good grace anew to gain Beatitude
Before dying, as defiant before Death,
To thee would I this warrant of affection
Give; lest lacking love's greeting
We were parted by time's passing wave ---
O! to be so blithe as sparrows!

And, my friends dear, please don't worry. There's nothing more dire looming over me than that recurrent need of the sacraments --- that's sort-of the point, in fact. It's the kind of thing you want to get done *before* the rest looks dire!

Eeek! What a place!

2010-10-23T12:33:00.000-07:00

A locus focus, and Oh! what a scary place it is, too. For today we are serving

Detention with Dolores

Harry Potter and the Order of the Phoenix

[Harry Potter] had known this office under three of its previous occupants. [...]

Now, however, it looked totally unrecognisable. The surfaces had all been draped in lacy covers and cloths. There were several vases of dried flowers, each one residing on its own doily, and on one of the walls was a collection of ornamental plates, each decorated with a large technicolor kitten wearing a different bow around its neck. These were so foul that Harry stared at them transfixed, untill Professor Umbridge spoke again.

I'm already shivering!

I also thought about mentioning this locus back in September, for "educational" settings. Indeed, Harry learns much about the nature of evil --- as well as something of the heroic --- in this particular office room between his second and fifth year.

In its fifth-volume avatar, the Defence Against the Dark Arts Proffessor's Office shows us just how ugly good things like kittens can be made, with just the wrong sort of twist; in an interesting parallel, the same room highlights just how ugly such a good thing as devotion to the Truth can become when twisted into "devotion to what I say the Truth is" --- which is an idolatry.

I don't want to say too much more because I believe Enbrethiliel hasn't read this book yet.

That Bat also known as some guy on the street

WHAT ON EARTH?

2010-10-17T22:13:00.000-07:00

UPDATED

What has happened to Orbis Catholicus II??? Is the illustrious Mr. Sonnen in some strange unpublished need? Has his server been compromised? Or (weirder) has someone flooded a DNS cache with this sham site?

Bloggians! To the rescue!

UPDATE: it seems to be here now.

Whence 4?

2010-10-16T17:09:00.000-07:00

Time for some more math! At my (new! yay!) supervisor's behest I've been trying like a primordial lungfish to breath the fresh air called spectral sequences --- how they ever managed to acclimate to such thin and rarefied reference to anything tangible is beyond me; but then, the calculations themselves are thick as water to my more-terrestrial brain.

Today is not about spectral sequences, but back to geometric measure theory. Some time ago I got as far as to outline the proportion of surface areas vs. angles

$$ S(\triangle qrs):S(\mathbb{S})::\angle qrs + \angle rsq + \angle sqr - \pi:4\pi $$

for a spherical triangle $qrs$ --- although for reasons of presentation, that tale refered to the hemispheres $A,B,C$ described by the arcs $qr,$ $rs,$ $sq$ and containing the triangle $\triangle qrs$. (Do you see some ambiguity creeping into the tale? Don't worry: make your choices and then show that they aren't important!)

So, our task today is to improve the proportionality by establishing, for a unit sphere $\mathbb{S}$, an equality $S(\triangle qrs) = \angle qrs + \angle rsq + \angle sqr - \pi$, which by the complementary proportion will give $S(\mathbb{S})=4\pi$.

For simplicity, we'll assume the angle at $s$ --- that is, $\angle rsq$ is a right angle, also known as $\frac{\pi}{2}$, or half of $\pi$. (Not, btw, half a pie... half a pie is a whole $\pi$, and we're also trying to show today that half a unit pea has rounded area $2\pi$!). This means reducing our problem to the study of $\angle qrs+\angle sqr-\frac{\pi}{2}$, a form which should resonate in the mind of anyone who has thought seriously about right triangles in the more extraordinary, flat world.

A logician I once knew exulted in declaring that Man's office of naming things is also the mathematician's first tool: it does wonders to our reasoning to give a short name to otherwise clunky perilocutions as "the angle subtended at the spherical center by the arc $sq$" --- this angle I will call $\sigma$. The other arc's angle, that of $rs$ will be $\tau$. For similar reasons, the angles at $q$ and $r$ will become $\phi$ and $\theta$. One more angle needs a name, that of the altitude from $s$ to the hypotenuse, which I shall call $\zeta$. Its sole purpose is to simplify the formulae following our sketch of the situation thus far:

with this picture, we have the two equations

$$ \sin \tau \cos\theta = \cos\tau \sin\zeta $$
$$ \sin \sigma \cos\phi = \cos\sigma \sin\zeta $$

Incidentally, it's quickest to derive this formula if you already know ---as we do--- that great circles lie in planes through the origin, each of which is a set of points $(x,y,z)$ satisfying an equation like $x\cos\phi + y\cos\theta = z\sin\zeta$. By far the simplest situation to deal with is when you have some relation like $\cos^2\phi + \cos^2\theta + \sin^2 \zeta = 1$ --- and as I've described the angles $\phi,\theta,\zeta$ above, that's exactly the case here. Why? Hmm... it's more linear algebra. There ought to be auxiliary diagrams that clear it all up...

Anyways, The Trick, at this point, is to study the area of our triangle, and compare it to other things that are similar. For instance, when $\sigma<1$ we have

$$ \sigma - \frac{\sigma^3}{6} < \sin\sigma < \sigma < \tan\sigma < \frac{\sigma}{1-\sigma^2/2} $$

This means, for instance, that the area of a rectangle with sides $\tan\tau$ and $\tan\sigma$ is very close to $\tau\sigma$, which itself looks very close to twice the area of our spherical triangle --- how close? Well, in this case, it means if we fix $\theta$, and then imagine $\zeta$ decreasing to zero, then $\tau,\sigma$ also tend to zero, so that $1<\frac{\tan\sigma}{\sigma} < \frac{1}{1-\sigma^2/2}$ squeezes the middle ratio to $1$, sandwich-wise.The use of the accidental simplicity $\cos^2\theta+\cos^2\phi + \sin^2\zeta=1$ is that it can equally be written $\sin^2\zeta = \sin^2\theta - \cos^2\phi$, which if you remember your double-angle formulas, and your heterodyne equation, is

$$\sin^2\zeta = - \frac{\cos 2\theta + \cos 2\phi}{2} = -\cos(\theta+\phi)\cos(\theta-\phi)$$

What good is that? Well, it's handy that we can (again) just as well write
$\sin(\theta+\phi-\frac{\pi}{2}) = - cos(\theta+\phi)$...
oh dear, that's getting clunky, again... let $\alpha = \theta+\phi-\frac{\pi}{2}$. Note that this *is* the angle excess which we know to be exactly proportional to the area of our triangle.
Then $\sin^2\zeta = \sin(\alpha) \cos(\theta-\phi)$.
This is nifty, because on the one side we actually have $\tan\sigma\tan\tau \cos\phi\cos\theta$, which is proportional to our imagined rectangle, and the proportion only depends on $\theta$ and $\phi$; the other side is proportional to $\sin\alpha$ --- which is nearly $\alpha$ when $\alpha$ gets small, as it will --- so it seems we're left with comparing

$$ \cos\phi\cos\theta $$ vs. $$ \cos(\theta-\phi).$$

Now, you can't see --- because I skipped the step --- but what I've been writing $\cos(\theta-\phi)$ once used to be $\cos\phi\cos\theta + \sin\phi\sin\theta$. Oh! hooray! there's a $\cos\phi\cos\theta$! Oh! drat! there's another term! What is that other term?
Well, with the new name ($\alpha$) at our disposal, it's easily rewritten

$$ \cos(\theta-\alpha)\cos(\phi-\alpha) $$.

Compiling our results so far, we're at the point where we can say

$$ \frac{\tan\sigma\tan\tau}{\sin\alpha} = 1 + \frac{\cos(\theta-\alpha)}{\cos\theta}\frac{\cos(\phi-\alpha)}{\cos\phi}$$

In other words, the ratio of rectangle to angle-excess is $1$ plus that other thing --- that the other thing tends to $1$ as $\zeta$ tends to $0$ is yet more of these angle-sum and -difference rules, but as you can probably see, we're not far off.

The rough rectangle to roughly the angle excess is roughly 2, so the triangle to the angle excess is exactly 1.

We're done.

Fun with TeX and paper

2010-10-13T16:36:00.000-07:00

echo <<eof >>/dev/null

We have calling cards!

That is, these are the sort of card you leave on a silver tray under the eyes of a lady's Mother or their doorman, when said lady isn't home or disposed to receive you, to say that you did, in fact, come to "call" --- without the bother or nuissance to your neighbors of actually calling out with voice to see if she answers. Some folk call them business cards these days, what with the advent of the inescapable mobile phone, in principle allowing men to pester decent ladies with person-to-person "calls" at any hour of night or day. Since precious little business gets done here (thank goodness) to call these cards "business cards" would be farcical beyond even our usual fare.

The obverse face is a tweaked version of this TeX file --- it took some doing, too, may I say. I was quite worn-out by the end of it. The reverse are filled with a rhombic variation of those famous Penrose tilings, one of several impressively economical files here exhibiting the illegible efficiency of Adobe's postscript virtual machine.

Another picture:

eof

Is it scary here? Or is it just me?

2010-10-04T20:07:00.000-07:00

I seem to linger on one or two authors; this time I feel like another Tolkien spot, not far from last time's locus.

After stumbling along for some way along the stream, they came quite suddenly out of the gloom. As if through a gate, they saw the sunlight before them. Coming to the opening they found that they had made their way down through a cleft in a high steep bank, almost a cliff. At its feet was a wide space of grass and reeds; and in the distance could be glimpsed another bank almost as steep. A golden afternoon of late sunshine lay warm and drowsy upon the hidden land between. In the midst of it there wound lazily a dark river of brown water, bordered with ancient willows, blocked with fallen willows, and flecked with thousands of faded willow-leaves. The air was thick with them, fluttering yellow from the branches; for there was a warm and gentle breeze blowing softly in the valley, and the reeds were rustling, and the willow-boughs were creaking.

`Well, now I have at least some notion of where we are!' said Merry. `... This is the River Withywindle!...'

I suppose there's not much frightening about that, as far as it goes --- but you have to read the book! I love the way that "willow" note recurs, like an ostinato counterpoint. Or perhaps it's a flatted dominant? For myself, "willow" is one of my "cellar door"s, quite apart from how I admire willow-trees in person. But here...

... There were armies of flies of all kinds buzzing around their ears, and the afternoon sun was burning on their backs. At last they came suddenly into a thin shade; great grey branches reached across the path. Each step forward became more reluctant than the last. Sleepiness seemed to be creeping out of the ground and up their legs, and falling softly out of the air upon their heads and eyes.

Are you thinking what I'm thinking?

Go read the book, now, if you don't remember it. But it's worth noting that willows, while lovely and graceful, are not the trustiest of trees; their wood is rather too soft for structural uses, and they tend to fall apart as they get older. A venerable old specimen in one of my favourite boyhood parkly haunts was dismantled recently, to forestall it's falling down on unsuspecting visitors. Tolkien's rather more willful Old Man Willow character, who very much defines this place, is an alarming extrapolation of my poignant beloved trees.

--Some Guy on the Street, for

The River Withywindle
The Lord of the Rings: The Fellowship of the Ring
J.R.R. Tolkien

Something a little more Aedifying?

2010-10-03T21:26:00.000-07:00

Dear Exegete,

I gave myself to LifeChain for an hour today; and whilst standing there the hymn occurred to me that, for no good reason, I know best in the Russian chant setting. Not that I could tell you which words mean what, nor how they fit together...

Anyways, I thought it made a nice contrast to the more commonly-referenced De Profundis; which is apposite, of course, but has so many other uses, as well. The latter is good for commemorating those lives already cut short; but Save, O Lord, Thy people is looks from the present to the future, and recalls souls that thrive still on Earth and for whom there is hope.

awaiting your reply,
he would be more sad, if not for life

Parce Domine populo tuo
et ne des hereditatem tuam in obprobrium
ut dominentur eis nationes
quare dicunt in populis "ubi est Deus eorum"?
zelatus est Dominus terram suam et pepercit populo suo

I need to fill my horrid writing fix somehow!

2010-10-01T19:29:00.000-07:00

Dear Strongbad,

Its seems to like be a long tim you hasnt write email ansers. why is that? do you not get emailz anymor? Are you cant think to smart way of write back them? when do you write agane?

yores truly
guido quiscumque
INTERNETS.

The Good God just keeps on giving

2010-09-24T19:40:00.000-07:00

Dear Fellow,

For future reference

\begin{enumerate}
\item[6] Intercessors.
\item[7] The moon one night past full.
\item[8] Sanctifying frustrations.
\item[9] An internet's worth of crafty artists.
\item[X] Glue.
\end{enumerate}

That's all for now.

one who would exhort you to rejoicing

Someone asked, and I say...

2010-09-18T14:55:00.000-07:00

It's quite short, this time around. The question seemed so sad, I had to give the whole thing a sing-song feel, from LOL-Cat silliness to many amphibrachs, just to keep myself cheerful. I think I'll call it "Fluffball".

Fluffball

Our poor little fluffball, she's limping! You see,
The silly cat pounced on a candle (what lark!)
Which we had set out against vesperal dark
And now she's got wax on her paws. (goodness me!)

How not to bake croissants

2010-09-16T18:35:00.000-07:00

Dear Self,

That need for speed? Yeah... it doesn't get you anywhere.

Cheers!
silly cook

From FDR to "W" et alii

2010-09-11T08:13:00.000-07:00

Dear Loathed Successors in Office,

It seems that you have taken my first inaugural in entirely the wrong sense. And so you tread fearless before the Lord, you walk in dusty shoes over holy ground; making yourselves fools. For the fear of the Lord is the beginning of wisdom. Instead of the Lord, you would have us fear the market, the collapse of the market, the Islam of swords, appearing to fear any Islam, our children in their very numbers, our parents in their aging, airplanes, bottles of water and shoes on airplanes, talcum powder, coughs and sneezes.

The only thing we have to fear is Fear itself. The fear of the Lord is holy; O America, O Christians, let the Lord be your Fear and your Love, and you need fear nothing in this world.

From a wheelchair

Liber Generationis Jesu Christi

2010-09-07T23:09:00.000-07:00

Epistula nullibus a nullibus...

From centuries past our Holy Mother Church has prescribed for Masses of this Feast of our Holy Mother Mary the Gospel text Mt.1:1-16, which runs between

The book of the generation of Jesus Christ, the Son of David, the Son of Abraham.
...
and Jacob begot Joseph the husband of Mary, of whom was born Jesus: who is called Christ.

It might seem a bit ... odd... that this Marian feast is honoured with Joseph's genealogy.

The fact is, however, that all the attention paid Joseph adds up to a rather backhanded compliment if that were the whole tale. Joseph is remembered in this account and Luke's Gospel precisely because of his relationship to Mary, Maria mediatrix gratiarum, Maria radix et porta, Maria mater Dei. Joseph, patron saint of the Universal Church, unborn children, fathers, immigrants, workers, against doubt and hesitation, and of a happy death, &c.; it is through Mary that Joseph first came to know Christ.

Something to think about.

Alter nullus

Unbearable Beauty

2010-09-02T15:54:00.000-07:00

Dear Ms. Argerich,

We wuv you! Can you play at our respective wedding receptions? I don't think either of us can pay you much, but you'll be welcome to stay for dinner!

some guy, and a friend

The Inquistors' Campfire Song

2010-09-02T08:05:00.000-07:00

There's a hole in your favourite heresy!
There's a hole in your favourite heresy!
There's a hole, there's a hole, there's an epistemic hole
There's a hole in your favourite heresy!

There's a kludge to fill the hole... (x2)
There's a kludge, there's a kludge, there's a loud rhetoric kludge
To fill the hole in your favourite heresy!

There's a madness to the kludge... (x2)
... a most inhuman madness,
about the hole in your favourite heresy!

There's a Mob that live the madness... (x2)
... a loud and angry mob
fell in the hole in your favourite heresy!

There's a WAR against the Mob...
... a cruel and unjust war
and all because of your favourite heresy!

Interrogative vocabulary $\mathrm{I}$

2010-08-25T08:12:00.000-07:00

Enbrethiliel delivered a word and a question quite some time ago. Lots seem to have come up with something, but I'm having a hard time. So I got lazy and banged out this accrostich. It seems to me that the elementary-school nonsense of long-cue accrostichs might well be responsible for much of the unreasonable unmetric word-presentations (like that "Mouse" abomination). My fourth-grade teacher taught us Limmericks. I don't see why we couldn't learn sonnets (or triolets) in grade three. Anyways, the question is "What was your reaction?" And, so far, my reaction is this ... whatever it is. It is, largely, about reaction, but what the prompts are, I don't even begin to fathom.

Perhaps unthinking revulsion, poisonous laughter echoing?
Possibly --- unless recalled pain laconically eschews
Potential understanding. Returning, personalized light errors
Parting urged ritual passages, lengthening entertainments:
Passionfruit, Ulster royalist peasantry, lollypops, ermine.
Partly, upon reading portents, localized enuie
Pursued us rearwards, pressaging loxodromic escapades.
Pikestaves, up! Royal portage, leave. (Exeunt)

I think I want another try, so I'll see if I can't make-up something more... coherent? Rythmic? Rhymy? Anyways, have fun! (Btw, the word is the obvious one that doesn't appear as a word in the text).

Round and round...

2010-08-23T18:03:00.000-07:00

For the past year I've been little more than a cube. As of about today, I'm *perfect*! ... or slightly-over, but not when rounding down!

$ 28 = 2*14 = 4 * 7 = 1 + 2 + 4 + 7 + 14 $

oh, ha-hah

2010-08-21T10:17:00.000-07:00

Dear Cousin Bilbo,

Yes, very witty.

Milo

PS. Rory's quite cheerful of late.

Hic sunt raptores

2010-08-07T13:24:00.000-07:00

Dear Dr. Malcolm, I thought you'd be entertained by a case-in-point, maybe one of your accolytes could make a good study of it. A couple months ago, I noticed that some recent acquaintances of mine particularly enjoyed talking about houses; and so the principal instigator decided to say something like "let's do that deliberately!" setting a time and place(ish) for the discussion, and then at the last-ish minute, switched the theme to family homes. I don't quite recall how that worked out, but anyways, as my intended presentation was about a house which wasn't a family home, some scrambling ensued --- I still haven't quite got 'round to that, either... and of course, quite notably, there are plenty of family homes that aren't quite houses either. ...

The grass under their feet was smooth and short, as if it had been mown or shaven. The eaves of the Forest behind were clipped, and trim as a hedge. The path was now plain before them, well-tended and bordered with stone. It wound up on to the top of a grassy knoll, now grey under the pale starry night; and there, still high above them on a further slope, the saw the twinkling lights of a house
[...]
They were in a long low room, filled with the light of lamps swinging from the beams of the roof; and on the table of dark polished wood stood many candles, tall and yellow, burning brightly.
[...]
He opened the door, and they followed him down a short passage and round a sharp turn. They came to a low room with a sloping roof (a penthouse, it seemed, built on to the north end of the house). Its walls were of clean stone, but they were mostly covered with green hanging mats and yellow curtains. The floor was flagged, and strewn with fresh green rushes.
[...]The guests were commanded to sit quiet, and were set in chairs, each with a footstool to his tired feet. There was a fire in the wide heath before them, and it was burning with a sweet smell, as if it were built of apple wood.
[...]
Frodo stood near the open door and watched the white chalky path turn into a little river of milk and go bubbling away down into the valley.

Ahah! Yes, this is (in case you don't recognize it yet) from the Lord of the Rings, describing one of the most quietly magical places in all Middle Earth, the house of Tom Bombadil. And it clearly won't do for the present weekend theme, but I thought it would make an interesting comparison to the camel-breaking straw I'll describe next...

Things went on, and some houses crept in again, one of the latest just after the next thematic conference was announced on Nature Settings, this particular house underground, which I remarked on, and then mentioned another it reminded me of; and I wrote also (silly me), pointing-out the fitting nature-ness of my recollection, whereat our flighty captain decided "that's it! Not nature settings, underground settings!" and here we are, again.

He shuffled on in front of them, carrying the light, and they followed him, nudging each other in an anticipating sort of way, down a long, gloomy, and, to tell the truth, decidedly shabby passage, into a sort of a central hall; out of which they could dimly see other long tunnel-like passages branching, passages mysterious and without apparent end. But there were doors in the hall as well—stout oaken comfortable-looking doors. One of these the Badger flung open, and at once they found themselves in all the glow and warmth of a large fire-lit kitchen.
[...]

This is the Badger's home. Some marked differences from Bombadil's: the one is old and shabby, dark, and winding, and the other has an almost eternal freshness to it, is comfortably compact, and well-lit inside (until it's time for sleeping).

The floor was well-worn red brick, and on the wide hearth burnt a fire of logs, between two attractive chimney-corners tucked away in the wall, well out of any suspicion of draught. A couple of high-backed settles, facing each other on either side of the fire, gave further sitting accommodations for the sociably disposed. In the middle of the room stood a long table of plain boards placed on trestles, with benches down each side. At one end of it, where an arm-chair stood pushed back, were spread the remains of the Badger's plain but ample supper. Rows of spotless plates winked from the shelves of the dresser at the far end of the room, and from the rafters overhead hung hams, bundles of dried herbs, nets of onions, and baskets of eggs. It seemed a place where heroes could fitly feast after victory, where weary harvesters could line up in scores along the table and keep their Harvest Home with mirth and song, or where two or three friends of simple tastes could sit about as they pleased and eat and smoke and talk in comfort and contentment. The ruddy brick floor smiled up at the smoky ceiling; the oaken settles, shiny with long wear, exchanged cheerful glances with each other; plates on the dresser grinned at pots on the shelf, and the merry firelight flickered and played over everything without distinction.

Again, though, we find within the branching warren a cozy and welcoming place. It is significant that both of these homes are found by our protagonists as places of refuge; and both our authors have clearly done their best to make them fitting as such. (Of course, the four wandering heroes at Bombadil's will encounter a great many more such places, offering varying degrees of comfort; one of the ways we see them grow is in how readily they finally will make-do with much less.) And so we have many common elements between them: the places themselves have a solidly-built quality (flag-stone and brick flooring), they are filled with comforts (deep settles/soft chairs with footstools), good food --- simple and yet copious --- and both feature a warm fireplace.

Now, about subteraneanity --- it is a Hobbit's preference, but Bombadil's isn't; it's also much to the liking of a Mole or a Badger:

... 'Once well underground,' [Mole] said, 'you know exactly where you are. Nothing can happen to you, and nothing can get at you. You're entirely your own master, and you don't have to consult anybody or mind what they say. Things go on all the same overhead, and you let 'em, and don't bother about 'em. When you want to, up you go, and there the things are, waiting for you.'

The Badger simply beamed on him. 'That's exactly what I say,' he replied. 'There's no security, or peace and tranquillity, except underground. And then, if your ideas get larger and you want to expand—why, a dig and a scrape, and there you are! If you feel your house is a bit too big, you stop up a hole or two, and there you are again! No builders, no tradesmen, no remarks passed on you by fellows looking over your wall, and, above all, no WEATHER.

and Badger does go on a length about that. There is a curious thing, though, about Badger's place, in that it hasn't always been underground. But I suggest reading the book, about that.

... I suppose it isn't really a question of strange attractors or unstable dynamics, but I suppose I will have to be careful what I suggest, if I'm to be flitting about with this sort of crowd, won't I? Anyways, here's to your eventual recovery. Take care of that leg, now! a paleophile

Frivolous optical heroics

2010-08-04T15:54:00.000-07:00

Now as refraction dominates Rayleigh to colour our evening
Light giving witness to rarified are 'round our Earth at high altitude
Soon will their contrast show points of light 'gainst darkness deepening
Stars are some, nebulae other: too big to see, lost in similitude
...

the internet's irony

2010-08-01T23:58:00.000-07:00

Dear Ray,

this internet: it's a wonderful place, eh?

It's full of friends. They tell me things. I laugh. They laugh. And the colours!

feedburner bookworm

sewing

2010-07-23T11:30:00.000-07:00

Dear Mr. Bat,

I'm feeling terribly frustrated... but I thought of another metaphor of sewing in mathematics, and that is assembling ideas. The trouble is that, when it comes to communicating mathematical ideas, it is, for me, an awful lot like sewing in the dark: you have access to the needle and thread (that's words you can string together) and can maybe feel the cloth --- if you have any notion of what ideas are common to your audience --- but you can't necessarily see how the patches are stitched together; that is, without some decent back-and-forth, you (I) can't tell how your (my) readers are holding their patches, where the seams end up, what's the shape of the final product, how neat the stitches are...

Sometimes I really fear I'm not that good a tailor afterall. Back to the candle-lit space that is my own head, for now; but I'm told there's nothing for the rest but practise.

the sidewalk apprentice teacher

Poetics, primes, and $\pi_n$.

2010-07-14T14:57:00.000-07:00

Dear Elsa,

I'm not today writing so much to say anything particularly mathematical, but to describe something of what it is like to study mathematics, and something of what my own mathematical interests are.

I'm not a historian, but I get the impression that the way maths are studied today is quite different from they way they were studied in, say, 1828, which is in turn different from what you'd have found in 1687, and so on, back to the lovely compilation of surveying tools and book-keeping tricks known as "Euclid's Elements of Geometry". Mathematics also has its fads and fashions, which come and go in various times and places.

Euclid, of course, studied plane geometry, starting from intuitive propositions and building towards elaborate consequences; and that at least has remained as a consistent motif in mathematics. It's an awful lot like building life-sized castles out of toothpicks and paste --- only at some point you don't really see the toothpicks anymore, just the bricks and framing you weave them into. Once you get really good at bricks and framing, you might not notice the toothpicks at all until you start thinking about patterned wallpaper, and realize you need something that isn't a brick, a beam, or a joist.

In fact, a lot of research in mathematics proceeds in a way a lot like saying "something proceeds in a way a lot like something else" --- mathematics is not only about building elaborate things from simple things, but it's also about building elaborate things until they remind us enough of simpler things; again, there is a tendency to build competeing elaborations until they look broadly similar, but with visibly variant elementary bits. To put it more poetically, mathematics is the precision study of analogy, largely motivated by appealing analogies.

Now, as any poet knows, metaphor and simile are litterary, not litteral, and that's part of what makes them beautiful. Chersterton's slipper hunt is only as fun as it is because we know slippers don't really run away on their own, as much as we may imagine so trying to find them the rest of the time. Similarly, as other mathematicians have written (Baez and Connes come to mind), the more provocative analogies pursued by mathematicians are those that don't reduce to strict equivalence.

Just to illustrate, I'd like to describe a (very mathematical) analogy that doesn't approach any kind of precision, but still keeps me entertained. To do that, I'll have to tell you two stories, and, well ... we'll see how it goes.

There are several popular ways to name a natural number. One dull way is just to give your friend a bag with that many pepper imps in it; this method has its obvious limitations. Another way is to describe the number as a sum of fibonacci numbers, for example

$ 82 = 1 + 5 + 21 + 55 $

which gets every number; you can even insist that you only use each fibonacci number once (or not at all), and never use consecutive fibonacci numbers, and then there is still exactly one way to describe any natural number. So a number can effectively be named as strung together from bits chosen from $'fs'$, $'s'$; $'.'$ and $'f.'$: if you write $'.'$ or $'f.'$ you stop; then the number you know as $82$ looks like $'fsfssfssf.'$. Here, the last $f$ or $s$ says whether the fibonacci number $1$ is needed; the one before says whether $2$ is needed, then $3$, and so on. It's even very simple to figure out which of the fibonaccis you need: just find the biggest fibonacci that isn't bigger than your number (in the case of describing 82, it's 55), and work out what you need to describe the difference${}^1$ $(82-55)=27$.

Another way to describe a natural number is as a product of irreducible numbers --- commonly known as primes. In this system, we have (for instance) $82=2\times 41$. This system has properties very useful for lots of algebraic nonsense (group theory, cryptography, ... ) but it's also got a fair ammount of difficulty to it; for instance, one needs to know what the primes are. Another way the primes versus the fibonaccis are different is that the primes are a great deal thicker than the fibonaccis, because multiplying numbers makes them get big much quicker than does adding them. They do both thin out as they get larger, but the primes are definitely weirder. (And this does help for the cryptographic application described above). Notably, it takes much longer to factor a generic natural number into its primes than it does to write it as a sum of nonrepeating nonconsecutive fibonacci numbers.

That's one of my two stories. The other one is about... well, I'd say it was about spaces, but that's both too broad a word and yet also doesn't quite suggest how weird "spaces" can be. A better word would probably be "geometric figures", where we don't mind how wobbly our drawing is --- and we also pretend we can draw arbitrary-dimension objects.

Perhaps a more descriptive metaphor for my kind of "spaces" would be "sewing projects". One can, for instance, treat both armchairs and tire inner-tubes as elaborate sewing projects, involving three-dimensional things (chair stuffing, or compressed air for inner tires, although sometimes...) and two-dimensional things (the sheets of cloth/leather you need) sewn together along one-dimensional things (seams, held together by thread) which come to a terminus at zero-dimensional things (knots in the thread, usually, but here we may be stretching the analogy a bit much...). So you're already used to four steps (or gradings) in the ladder of dimensions for our figure-sewing projects.

Now, as you know chairs and inner-tubes are rather different shapes. You will recognize this when I tell you that chair-shapes incorporating inner-tube shapes fall into two distinct categories: those for people without practical use of their legs, and those made out of porcelain.

But on a more fundamental level, they have different topologies. Now, in the poetic and vague mathematical I'm setting up, I've only got so far as describing the analogue of numbers and fibonacci numbers. OK, I now admit that the fibonacci numbers were kind of silly... powers of $10$ will do nearly as well --- but they do rather emphasize that while there may be many ways to write a number as a sum of fibonaccis (we can, of course, consider $55+55=110$), but that some are better than others ($55+55=55+34+21=89+21$) and the best way have special properties. In the numbers and fibonacci case, this means we don't even need consecutive fibonacci numbers; in the sewing project case, it means we can always suppose that a 3-dimensional thing is sewn (stuffed or glued) along its boundary to a 2-dimensional thing; and so on up or down the ladder.

This very nice and convenient way of describing sewing-project figures in fact corresponds to a handy algebraic gadget --- named $h_n(X)$ for natural numbers $n$ and sewing project $X$ --- which helps classify our spaces, at least so far as putting them in the right chapters of a dictionary (oh my, how mixed up our metaphors are getting!); and the possible chapters of our dictionary are called the homology coalgebras. (This in turn is related to one of Dr. Thursday's FSA board games, which maybe I'll write about another time.) There is, however, a different way of describing a sewing project, very different indeed, which is much trickier to get any handle on from a visual point of view, but which in many ways is more fundamental, and are even called so.

Given any sewing project figure (suppose it's a chair), we can make a new one by just sewing in a sheet along its edge --- and the edge is just a circle. Being mathematicians (I hope youu don't mind being called one?), we're interested in what two ways of sewing-on a sheet look different. For that context I'm most curious about, two such ways of sewing a sheet to a chair are "the same" (or "equivalent") if you can
\begin{itemize}
\item connect their seams by a curve on the chair and then
\item glue a patch onto the chair so that it's edge follows one seam, the connecting curve, the other seam, and then backwards along the connecting curve again.
\end{itemize}
I won't get into details here, but we've just described the basic ingredients for the fundamental functors $\pi_0$ and $\pi_1$. $\pi_0$ considers the same any two spots you can join with a curve, and $\pi_1$ considers the same any closed curves you can fill-in with a patch --- although there are a few more rules and wrinkles --- and the story also continues up the ladder, so for each sewn figure $X$ and each natural number $n$ we have an object $\pi_n(X)$.

The homologies $h_n(X)$ are like an abbreviation of how our project is sewn from sheets of different sizes; the fundamental functors $\pi_n(X)$ describe how the same project can be combed out${}^2$ with "simple" projects as typical strands. Of course, "simple" here means something quite complicated --- except as seen by $\pi_n$! The "simple" projects are usually called $K(n,G)$ where $G$ is a sufficiently nice, easily-understood thing --- never mind that now --- and $n$ is a natural number. The defining characteristic of a $K(n,G)$ (there are many, but they're similar enough) is that $\pi_n(K(n,G)) = G$ and otherwise $\pi_m(K(n,G))=\{1\}$ whenever $m\neq n$.

Anyway, in the poetic analogy I'm imagining of late, combing-out is very like factoring numbers, and the sort of threads you get, the $K(G,n)$s, are very like prime numbers in this regard --- not only in that there's not much combing left to be done on them, but also that it takes some work to understand them and pick them out from among all the other objects that might interest us. (I wonder if we ought to look for a Riemann hypothesis of homotopy types?)

I've been writing this for five days, now, and I seem to have lost something of my rhythm, and I don't know how to wrap up... but that's about all I wanted to say. Well, I hope you've enjoyed it, anyways.

an awkward fellow

${}^1$ this sort of "greedy" algorithm, to find the best simple fit you can and then make it better, is another common trick of the precision study of analogy.

${}^2$ this is somewhat like combing out a jaguar pelt. There will probably be some twists/tangles to undo, and it might not look spotted afterwards!

verba quaesitaque

2010-07-13T07:13:00.000-07:00

There are few things as compelling of poetry as being stuck in a bus for seven hours. And thus comes this blank novena.

In fields of purple vetch and goldenrod
I asked my Lord "Is't here?" He answered "No."

In time the wood was turned to red and gold;
"An unconsuming Flame? Now surely, here?"
In turn my Lord: "Not here, though not far-off."

Deep in the darkest month, the snows without
Could not have chilled my joy. "Is Heaven here?"
"Not here, Sir King; here lies the road thereto.
Keep on as now begin'st, thou shalt there come."

It's admittedly laconic --- a hint for who doesn't already know the allusion, the last person speaking is the Bishop St. Remigius. The earlier replies are meant to be the voice of God, speaking through the natural law which is, of course, written on all our hearts.

Anyways, the given word is "Month"; the question... you can figure it out, I'm sure.

some guy on the street

Burrowing around familliar loci

2010-07-11T20:37:00.000-07:00

It's me, in persona Chiropteri, writing to tell you about a fictional setting which also happens to be a family home, at the instigation of Enbrethiliel (who seems to blame me in some way for the particularity... ). This family home, invented by that most notorious waitressing-to-rich-author personality, J.K.Rowling. (And, yes, I'm claiming fair use for all excerpts.)

Here is our first view:

It looked as though it had once been a large stone pigsty, but extra rooms had been added here and there until it was several storeys high and so crooked it looked as though it was held up by magic (which, Harry reminded himself, it probably was). Four or five chimneys were perched on top of the red roof. A lopsided sign stuck in the ground near the entrance read `The Burrow'. Round the front door lay a jumble of wellington boots and a very rusty cauldron. Several fat brown chickens were pecking their way around the yard.

`It's not much,' said Ron.
`It's brilliant,' said Harry happily, thinking of Privet Drive.

The Burrow is of course the home of the Weasley family --- and what a family they are! In the recent round, Enbrethiliel has remarked on how houses are like reflections of the people that live in them. J. K. Rowling makes explicit use of this idea for most of the homes through the series, and The Burrow is an excellent example: it is as diverse and varied as its family, partly due to it's conjectured patch-work construction, partly through the active efforts of the family members themselves. Take, for instance, `Ronald's room':

Harry stepped in, his head almost touching the sloping ceiling,${}^1$ and blinked. It was like walkin into a furnace: nearly everything in Ron's room seemed to be a violent shade of orange; the bed-spread, the walls, even the ceiling.

(Imagine an orange that looks violent next to a born Weasley's hair!)

For much of the series, the Burrow also becomes like Harry's second real home (the first one being Hogwarts, of course), although for magical reasons he is forced anually to reside with his beloathed muggle relatives.

`It's a bit small,' said Ron quickly...
But Harry, grinning widely, said, `This is the best house I've ever been in.'

I'd say more, but I've a poem to write (dang it!)

some guy on the street

${}^1$ Does that remind you of somewhere else?

Ever we fall, ever we get up again...

2010-07-07T14:08:00.000-07:00

Dear Maurits,

I've recently been staring at a book of your prints, moved to sorrow for all those folks who have to keep climbing nowhere for all eternity. I almost fool myself that I feel some sympathy for them; and maybe they some for me. But the truth is that they don't really feel anything, being static, and I'm not stuck on a twisted bundle over $\mathbb{S}^1$; I'm not always climbing, because I keep falling. However much it might feel like an ongoing upward trudge, that feeling only persists so long as I forget having slid down that well-worn slope by the fascinating little rocky outcrop that you have to clamber through the briars and nettles to get at... and the rocks really aren't so nifty-looking up-close. It's just a heap of dead rocks.

Some people call your strange prints "illusions"; but that's really not right: they're properly paradox, a contradiction in pictures. What I occasionally suffer is illusion. You're just weird, and fascinating because of it.

I don't recall if you're the sort, but I'll ask you anyways, pray for me!

a sinful geometer

In words like some ascribed to the Blue-eyed Shogun

2010-06-27T18:44:00.000-07:00

Reports of my arrest/tear-gassing/vandalism/robbery/inundation are greatly exaggerated. Not that anyone is likely to have invented or repeated such reports... I'm just the Belfry Bat, after all. There were some brief, amusing-to-me questions from a polite police officer.

Metropolitan University looks more-or-less as it always did.

I'd tell you more, but that would give everything away.

All is well!

I'm feeling paradoxical today

2010-06-22T07:27:00.000-07:00

Dear Albert,

As you are, of course, intimately and immediately aware, there's a strange universe out there. I was recently reminded of your remark, "The most incomprehensible thing about the universe is that it should be comprehensible". I recently had occasion for some metaphysical musing, and was struck by a strange intelectual discord among modern antitheists and so forth.

My remark arose from considering various sorts of metaphysical mythologies --- anyways, I'm going to suggest that there are, broadly, three categories of attitude to the Metaphysical Problem, and suggest that it just might be worth-while to consider each of the options, and that we can reason about which is the best.

But before that, I suppose I ought to explain what I mean by the Metaphysical Problem.

The Metaphysical Problem

To start with what I hope is an informative contrast, the Physical Problem, which underlies all the natural sciences, is the question of "how does everything we see fit together". To be sure, this is a vague statement of the problem; unwrapping things a little, we set out from the object of your incomprehension: that the universe appears to be comprehensible. That is, we see broad patterns, widely similar behaviour among the various bits of the observable universe --- some famous examples, wood and iron canonballs obey the same ballistics (up to terms arising from air resistance); electrons and various shapes of atom all obey intimately related statistics, a close cousin of which also describes the colour of hot iron, and says why it should be the same as that of equally hot coals; and so on.

Physics, our concerted attack on physical problem, is about giving these relations mathematical precision, and has been hugely successful. In Thomistic/Aristotelian language, we have been able to understand the various natural substances we encounter in the large world as accidental arrangements in various patterns of other, finer substances, each having various rules-of-thumb on the accidental patterns they will allow. In fact, this has been accomplished two or three times already, although the number of substances and rules hasn't often simplified. We're still looking for yet another, hopefully a more poetic itteration of the process. That's what Strings and Ms (LOL) and, alternatively, generalized spin-foams are about; maybe some day we'll find out how they're getting on.

Now, you might have noticed that one thing remains in common between our world-picture from step to step in the physics process: we always have substances, and we always have rules describing the possible accidents the substances can exhibit. There may well be dreams of finding a "basic" substance with rules so elegant and indecomposable that it might as well be a Platonic Ideal. In some ways we already possess such a picture with sufficient expressiveness, but it's rather involved and elaborated, making lots of people queasy; and that's why foundational physics is still a live field of study. But there's no need to ever finally hit upon the right rock-bottom substance, or the right basic rules. Consider an analogy: a bit of poetry will be the same poem whether it is written down in ink on paper, in chalk on a blackboard, graven in copper, or cast in moulded plastic with "Made in Taiwan" stamped on the reverse. At some point the particulars of underlying substances don't matter as far as the real-world applications are concerned.

The Metaphysical Problem, as I mean the phrase, is what's left of inquiry into the nature of what is after you recognize that physics itself --- observation and organization --- won't ever get underneath the physical universe. So, once we've figured out that we can't read beyond $\omega$ turtles downwards, it is a mute point to argue whether there is an $\omega$th turtle, whether the turtle tower is a countable ordinal or uncountable, or it might not cover the entire ordinal hierarchy. Instead, I believe we should skip all that unfathomable nonsense and, if still interested, talk about what it means for any of the turtles, or indeed the whole stack, to be there at all. This, I feel safe in saying, is the same as asking "Why is there any stack of turtles? Why is the Universe here?"

Three Responses

The range of possible reactions to the metaphysical problem can be put into three categories, which I'll outline in my arbitrarily chosen order:

"Nihilist fortuity"

You might be a Fortuity Nihilist if when I ask "Why is there anything at all" you answer any of
\begin{itemize}
\item "Who cares?"
\item "That question makes no sense,"
\item "It just is; deal with it."
\end{itemize}
It has the advantange of dealing with a problem of no obvious immediate practical application simply and straight-forwardly. It is subject to Chesterton's objection to atheism that, to really adopt this position, you can't ever think about the question again (unless someone asks; and even then... ). It's like agreeing to play The Game. The nihilists don't say much, and I've rather little else to say about them.

Various Platonisms

We hear from Plato's commentators (I don't trust myself to recall enough of Plato himself) the proposition that ideals of things have a real existence to them; thus, there IS a perfect circle, a perfect line, a perfect friendship. From the Cave dialogue, we also inherit the notion that the things of sense experience might well be less real than the ideals they suggest to us --- but I don't think this is necessary, either. The idea that I'm calling Platonism is the strengthened proposition that the internal consistency of an ideal is itself sufficient to confer some kind of existence to its subject: the mathematical consistency of Euclidean Geometry is enough to satisfy us that there IS a mathematical Euclidean Geomtry with its own perfect lines and perfect circles. (Mathematically, there ought to be MANY distinct Euclidean Geometries, but that's another matter)

There's an interesting ambiguity in this notion of Platonism, in that it's difficult to decide how elaborate of an ideal gets to be real: If it's mathematical, does it have to be in a first-order language? Does it have to be finitely expressible?

There's a joke warning against computing digits of $\pi$, because it is conjectured (conjecture still open) to be a normal real number, thus incorporating all possible digit strings, a vanishing fraction of which are still under copyright. Of course, one in between about $10^{30}$ and $10^{400}$ of these will come with appropriate copyright information attached, and a smaller fraction will have convincing documentation of licensing.

Adopt a sufficiently slippery Platonism (and I can't see good reasons to put the brakes on anywhere) and you will believe that there IS a constellation of red projective planes; a triune Godhead who creates a world into which He Himself enters and takes on Himself the form of a Man; another self-contained world that looks exactly like the created world just described, but without the God to create it; another self-contained universe containing only film footage of Regis Philbin leaving his house every morning.

The Expansive Platonist will --- must! --- believe in worlds he cannot ever see or touch, about which there are no general rules, and that in general will not follow any concise or poetic system of rules themselves. Some of them might look like they do for a space and a time, and then surprise you. And so, if we are expansive platonists, we cannot trust that the rules we have enjoyed in our own world for the last five hundred years or so (or throughout the history that we can see in our Telescopes) will persist long into the future; there IS a world in which the rules can fade away (I've just written about it, and are we Platonists or not?!), and there's litterally nothing to guarantee that we don't live there!

And it is that whereof I feel most paradoxical today.

Deo Volente

The third category of response supposes a Personal Deity --- the uncaused Cause, The Prime Mover, Who Is, Who Wills, Who Loves; and that whatever else is exists by His will.

The mathematician Laplace is said to have suffered an audience with the King of France, who remarked to him after a lecture on planetary motion "Tu n'as rien dit de Dieu en tout celà" (or words to that effect), to which Laplace replied "Je n'en ai pas eu besoin de cette hypothese". The rules are sufficient for describing whatever follows the rules; this is a truism. Modern thinkers with aversions either to God or to Science seem to imagine that this squeezes God out of the picture; and they respectively caricature this as a good or a bad thing about Science. Both such extremes miss the point: the Christian God is not only Who Is, but is also Truth. Science --- that is to say, experimental Knowledge --- certainly belongs to the Truth, and --- trusting that the Christian God indeed Is --- it is only by Divine gratuity that Science can hope in the ongoing success of the scientific endeavour.

The sufficiency of rules to describe what follows the rules moves our need to trust away from trusting ourselves, away from trusting the rules, and away from the trusting the universe to follow them, back to trusting in the Divine, who gave the rules in the first place, that He will uphold those rules for all time. Squeezing God out of any picture is a bad feature, not of Science, but of shoddy philosophy about science.

Is that everyone?

I think you'll discern from my shifting style which of these positions I personally hold to; I'm sure restrictive platonists could argue the consistency of their cases fairly well. I'm sure the nihilists won't much care except to be annoyed at my brining it up. But there is actually a fourth category of people, who ordinarily wouldn't much count, only there's rather a lot of them. These would be the people who don't get what I'm getting at --- who don't grasp the distinction I'm trying to articulate between prediction and explanation; between substance and matter.

Just last month I read a headline (always risky!) "Scientists Discover why universe exists". But that's not what they meant; the scientists in question had measured a trend in particle/antiparticle generation at an accelerator/collider to produce slightly more of the easily detectable "particles" of conventional experience than the easily detectable of their "anti-particles". They hadn't discovered this trend, because it has long been conjectured; nor is it why the universe exists; it's just an interesting and significant feature of the mechanisms --- the rules, as I've called them --- underlying the persistence of the kind of universe we see around us already.

I wrote privately to an atheist how I don't trust in physical theories themselves to keep the world running as it ought, and he thought my distinction between description and explanation to be "hogwash", asserting that it were just a matter of time before science finds "the explanations". It makes me sad.

It makes me sad that there are people who are prevented from forming trust in God because they don't understand what Science is.

I suppose, Albert, that it's a bit late for you yourself to do much about this confusion, publically at least; but, as I pray for your soul, don't be surprised if I hopefully ask for your prayers for the public understanding of Science and its place within all knowledge.

some mathematician on the street

More Evidence of God's Goodness

2010-06-18T17:11:00.000-07:00

Dear Self,

For future reference

\begin{enumerate}
\item That strawberry.
\item Roses that look --- and smell --- like peaches.
\item Whoever it was thought to breed the previous item.
\item Tchaikovsky
\item My mountain bike --- and my survival in spite of that.
\end{enumerate}

That's all for now.

a grateful sinner

Questioning Words

2010-06-14T13:55:00.000-07:00

Dear Miss Q,

In the anticipated commemoration of a lovely daydream of unrealized circumstances,

A picnic

"What is our picnic-lunch?" asked me the fair
Young lass (she far out-dazzles clear Sun-rays
In my poor eyes) "and where that magpie stays,
Marks he our place to sit, by Spanish Stair?"

"For you, dear friend, poached eggs and Camembert ---
Some millions love meringues, some Holandaise:
Most swear by devil'ds on these hot Sundays.
For you, they're poached --- wool picnic-blanket. There!"

Tall stood a shady poplar overhead,
Great lions' hand-fed vestige prowled about.
My cara's hat upon the blanket set,
Earth's turning turned 'till Sunlight her locks met;
No amber shot with gold so rich shone out!
As her's, glory is all God's, reflected.

I dare to hope you might have had as lovely a time as I surely would.
northern morpheus

Part of Word and Question

A friendly circle

2010-06-11T07:34:00.000-07:00

Hello, all!

It seems to be about

My own circle is quite narrow; I've been reading these 'blogs for many times longer than attempting to write this one. So it's a genuine surprise to me when a friend found only through her 'blogging so far tagged me in a "pick-five" game.${}^1$

There also seem to be rules:

1) Save the image above so you can upload it on your own blog without direct linking.
2) List 5 things you absolutely love to do
3) List 5 friendly bloggers, and comment on their blogs to let them know they've received an award!

...

Five things I absolutely love to do

(I) I love learning new things; whether it's isolated words in a foreign language or Thomistic good sense or beautiful new maths, it's a real joy. It happens with maths more often than the others, for obvious reasons... thank goodness I'm not trying to earn my keep by philology; it looks like fun, but I couldn't keep my categories straight, I'm sure.

(II) I love cooking and baking. This reminds me that I should eat something, soon, today... but you can really derive a sense of accomplishment by it when you mess about in the kitchen a while (I like to make a mess, too, in a little way, by-the-by), and you end with something pleasant and filling to eat! (And if other people are there to enjoy it, that's even better!)

(III) I love following in my missal the ceremonies of the Extraordinary Form of Mass. The meditative psalms and the prayers that accompany every gesture... they're thick as raisins in a pie! (did I mention I enjoy cooking?) and manifoldwise juicier for the soul!

(IV) I love listening to musical art. That may seem an odd expression: but I propose there is a great quantity of stuff out there you could call music, possessing melody, rhythm, and harmony in various proportions, but which remain flat, artless, and heartless. I don't mean those, I mean the stuff that's written to sound beautiful, performed with care and appreciation, that draws you in rather than driving you away. I dare to include in this the time I have spent playing chamber music myself with other (better) musicians, under the excuse that at least we could all hear and immagine what it was supposed to sound like; and that was good. I might also include poems and paitings with musical subjects, e.g. this one;

(V) In the remaining spot, I really love having a good chat with dear friends --- a leisurely talk, quiet and thoughtful. There are one or two friends I see almost daily who are always good for such a chat. It will usually about not much of anything, but nontheless refreshing. Enbrethiliel has conjectured that 'blogging is like a performance art; I'm inclined instead to think it a kind of conversation, and I include that sense here. You who generously share your insights and take the time to consider my meandering musings, in voice or text, are a great comfort to the soul. For you, and for those times, I thank God.

List 5 friendly bloggers

Thinking back, the two most-referenced fellow 'bloggers here are Enbrethiliel, who reminded me about apostrphes recently, and Meredith who reminded me of the other meaning of apostrophe the *first* time she linked here. They've both already been tagged, and now here we all are!

So... I wonder if I can think of five new 'bloggers... I can't say any of them seem the sort to play these 'blog games, but that's OK, I don't mind. In no particular order,

1) erev; he plays dress-up as a latin trad like me sometimes (but with much shorter hair). He's not-so-secretly actually a Greek Catholic! (It's all true, and he's super friendly, ~~but now he's quit blogging... :P~~ False alarm! He just moved and turned tacks. hmmm... doesn't seem to be a commenty-blog... but no worries!)

2) OYTIΣ --- says of nobody "Just a nobody. But by the grace of God I'm a Catholic nobody." Nobody's blog is dedicated to highlighting the little treasures of a relatively young archdiocesan Cathedral. In the light of the faith and illuminating the faith, pictures are accompanied by intriguing passages from scripture, Patristics, and the writings of later saints.

3) the sober sophomore. I suspect she isn't really a sophomore; but then, I'm not really a bat ... while you're over there, stop and listen to Bruckner's Os Justi setting. She also makes a point of intermitently counting out five blessings in thanksgiving: a fine example for all of us in life!

4) the fallen sparrow. From his 'blogging, all I can say is he is intense, and I feel ashamed at times to be so comparatively lukewarm. Also that he seems friendly. He's the only one on this list I've neither met nor e-mailed.

5) Dawn Eden. God bless her! God sustain her work! She's more famous for The Dawn Patrol and her book The Thrill than her occasional column at the Bistro, but as the latter has a better chance of being updated, there 'tis to whither I'm linking.

There you go, five friendly 'bloggers.

I think that's about it.

some guy on the street

${}^1$ Some people call it a "meme". That means there's a funny meme running around distracting people from what memes are about. Or maybe it's a funny mime! I think we can enjoy playing without trying not to call it a game ;-)

a mysterious impromptu

2010-06-10T22:57:00.000-07:00

Miracles

Like dewy grass under sunrise
To bare feet, as infants' smiling faces,
Or a book long unread closed around traces
Of letters written long since: surprise!
God's graces startle awake sleepwalkers;
They arise and shake us, but quietly! shine;
All-deftly moved. No edge is keener, no shade too fine
God knows its tincture, directs its line
'Twixt joints and marrow while we stand like gawkers
Drunk on sweet wine: the heart was glad.
Were we mere talkers? For yet quiet as grass,
Dewy grass at morning, were God's miracles:
as leaf's budding and leaf's fall.

It was softer than I could name,
more than I could hold, all the same
in my heart too-narrow. Praise God!

Did anyone notice?

2010-06-04T21:08:00.000-07:00

Dear 'blogger folks,

Thanks! I'm glad this is working, now!

I'm quite sure it still didn't do much about one month ago; still, it took less than a year from my first noticing. I suppose that's a good job, given all the other stuff that's going on.

an appreciative ambulator

Just what I've always wanted

2010-06-04T16:15:00.000-07:00

Scandals and Converts

2010-06-02T08:55:00.000-07:00

Dear Friend,

Some thoughts, unsolicited. Let's start with the bad news we all know, and then move to something more hopeful!

Through this Year for Priests, some folks have, for reasons of their own, struggled mightily to slander the whole Priesthood of Christ, by inflating crimes committed by a tiny fraction of all priests into an imagined problem endemic to the Priesthood itself. At the same time, the people who make money by estimating phenomenon frequency (insurance companies) inform us that Catholic Priests are among the least likely to commit such crimes. There are other, related problems to deal with --- tightening up vocation discernment on the part of seminaries, episcopal discipline and response protocol, etc. And I want to emphasize that no-one is suggesting the crimes themselves to be negligible, or that anyone should be less outraged than they are; the outrage we hear is indeed just, and suggests our fallen world to be capable of redemption still! It is the direction of the outrage that dismays me, even if it does not surprise. For many folk, children and adult, Christian and pagan and heathen, have been scandalized and led to stumble, perceiving the crimes of far-too-many, though thin and scattered.

Indeed, you should know the apostasy and the despair that follow from such scandals are a deeper and more lasting wound than the scars of abuse: in the resurrection, the hurts of abuse shall be comforted and redressed; but some may have so fallen away that they cannot appeal to God's mercy, and may suffer His justice for eternity. All the more heavily will it weigh on those who did cause these to stumble.

The scandal of such evils among the Priesthood may cause some to stray from the Faith. I promised at the opening to speak of hope, and it is this: the converse is also true, the holiness of the Priesthood can convert souls. Let me repeat for you some of the story of Alec Guinness:

... Then came the film Father Brown ... and on location in Burgundy I had a small experience the memory of which always brings me pleasure. ...

Night shooting had been arranged to take place in a little hill-top village a few miles from Macon. Scaffolding, the rigging of lights and the general air of bustle caused some excitement among the villagers and children gathered from all round. A room had been put at my disposal in the little station hotel three kilometers away. By the time dusk fell I was bored and, dressed in my priestly black, I climbed the gritty winding road to the village. In the square children were squealing, having mock battles with sticks for swords and dustbin lids for shields; and in a café Peter Finch, Bernard Lee and [the director] Robert Hamer were sampling their first Pernod of the evening. I joined them for a modest Kir; then discovering I wouldn't be needed for at least four hours turned back towards the station. By now it was dark. I hadn't gone far when I heard scampering footsteps and a piping voice calling, `Mon père!' My hand was seized by a boy of seven or eight, who clutched it tightly, swing it and kept up a non-stop prattle. He was full of excitement, hops, skips and jumps, but never let go of me. I didn't dare speak in case my excruciating French should scare him. Although I was a total stranger he obviously took me for a priest and so to be trusted. Suddenly, with a `Bonsoir, mon père', and a hurried sideways sort of bow, he disappeared through a hole in a hedge. He had had a happy, reassuring walk home, and I was left with an odd calm sense of elation. Continuing my walk I reflected that a Church which could inspire such confidence in a child, making its priests, even when unknown, so easily approachable could not be as scheming and creepy as so often made out. I began to shake off my long-taught, long-absorbed prejudices.${}^1$

Think about that.

When it is clear that Christ's Priests are trusty folk, little Catholic children can convert strangers, melting their "long-absorbed prejudices."

your friend in hope

${}^1$ Blessings in Disguise Alec Guinness 1985, Hamish Hamilton London

Oh, Heck, let's try another!

2010-05-29T09:49:00.000-07:00

Dear GK,

Happy Birthday!

You may have read that last week I reported some of your notes about Beacon House; this week, I think I'll return to Manalive, if that is allowed, and repeat some of your remarks about Cambridge. A copy of the notes is attached bellow

Your child in orthodoxy

Here is Cambridge as described collaboratively by "Wilfred Emerson Eames, Warden of Brakespeare College, Cambridge and Innocent Smith".

A celebrated English university backs so abruptly on the river, that it has, so to speak, to be propped up and patched with all sorts of bridges and semi-detached buildings. The river splits itself into several small streams and canals, so that in one or two corners the place has almost the look of Venice. It was so especially in the case with which we are concerned, in which a few flying buttresses or airy ribs of stone sprang across a strip of water to connect Brakespeare College with the house of the Warden of Brakespeare.

The country around these colleges is flat; but it does not seem flat when one is thus in the midst of the colleges. For in these flat fens there are always wandering lakes and lingering rivers of water. And these always change what might have been a scheme of horizontal lines into a scheme of vertical lines. Wherever there is water the height of high buildings is doubled, and a British brick house becomes a Babylonian tower. In that shining unshaken surface the houses hang head downwards exactly to their highest or lowest chimney. The coral-coloured cloud seen in that abyss is as far below the world as its original appears above it. Every scrap of water is not only a window but a skylight. Earth splits under men's feet into precipitous aerial perspectives, into which a bird could as easily wing its way as--

"As" what? Well, you will have to get the book. You see, about a third of Manalive is effectively a court record --- the proceedings of the High Court of Beacon --- and all letters etc. must be read-in. At this point the opposite advocate interrupts with an objection, which is duly noted, debated, and judged. But I think we have enough to be going on with. I rather like the "coral-coloured cloud", not only for its alliteration, (c's and l's!) but also because it is evocative of particularly peaceful sunset or, as the case may be, dramatic sunrise.

I don't feel any need to go on as I did last week. It's all there, really, and to say too much would rather spoil it!

Friends, Romans, Compliments...

2010-05-27T13:59:00.000-07:00

Dear Earlendings,

"... I come not to bury Sancta Sanctis but to braise her... "

I think I shall probably have to interrupt my lecture to Adam Smith (it's not really addressing anything of his per-se; he just stands-in for practical economics) so that I can expound some nonsense in appologia pro cultus personalis. Because, while Enbrethiliel may have disabled comments at her own blog, she Can't Stop Me Commenting Here at Mine!

'Brethil' opens by sumarizing her intent in recent musings thus

"When it comes to being Catholic, there is no ideal individual, no ideal parish, no ideal culture, no ideal country, and [...] no ideal period of history."

And I should whole-heartedly agree, so far (;->) as the intention of "no ideal" is to acknowledge the basic facts of the fall and of unique individuality --- another way to say this is that the negated existential here ("there is no ideal...") should be understood as a negated instantial --- I've just coined that word for myself, though it may be in use elsewhere. Saying it somewhat differently, of all Mortals two are without sin, and everything that depends in some way on any of us individually --- parish, culture, country --- is subject to sin and will in somewise fail of God's temporary purposes for them.

On the other hand, being a mathematician and thus constantly battling with a kind of Platonism, I should uphold that there are in an appropriate sense perfect ideas of individual, parish, culture, and country. (Periods of history are inventions-in-hindsight, so I won't argue about them.) To be more explicit, Creator God creates according to His own perfect design${}^1$ from which since the Falls of the rebel angels and of Man all of creation has declined --- but His perfect design for each of us, each parish, every culture and every country, while ineffable to all of us, is the proper ideal${}^2$ to which everything of each kind ought to strive. Furthermore, as soon as we recognize that Man is a species of being, we can understand that there are elements common to God's perfect design of every man and woman --- similarly, for all parishes, all cultures, all countries.

(I'd also like to emphasize that by highlighting these things, I don't mean that 'brethil' has negelected to recognize them; it simply seems to me important that they be mentioned fully)

We have two further paraphrases of 'brethil's thesis next. First,

"What any given person has right now, in his home and in his parish, is already all he needs to follow God all the way to Heaven"

This may well be true --- the contrapositive of "`must' entails `can'" is that the impossible is not compulsory. Spelling things out, in the absence of a parish, we have all we need insofar as God can be known by the light of reason; with a parish, insofar as the sacraments themselves communicate grace ex opere operato; in a healthy, well-tended parish, of course, we meet other trials. Except that God almost always calls us to something more. Some muslim arabs have visions of Jesus, and feel compelled to seek out the Church even risking their lives; the children of escapees from Cuba may study art and Church history, and feel compelled to design beautiful new Church buildings; women like you (or, well, slightly different) join cloistered communities like the Summit NJ Moniales OP. All of us, of course, are called to be saints. God gives us more than we need; still, we need to do something.

The second paraphrase, the one

"Catholic blogs--all of them, including this one--are, therefore, a problem, inasmuch as they make it seem that other Catholics in the world or in history have [had] it better than the person reading the blogs . . . because that simply isn't true."

In one sense, it may be quite plain what Enbrethiliel is getting at here.

There are a number of 'blogs whose speciality might be construed as the triumphalist vainglory of pastors and artists who "get it", the "in set" congratulating eachother on their snobby aesthetism in the service of The Lord, deriding and decrying the drab stuff imposed on and celebrated by the uneducated sheepfolk in other parishes' pews.

In another sense, the 'blogs I read that might be perceived this way I find to be general quite charitable and full of humility. Their concern for beauty and right worship is founded in reasons both catechetical and medicinal; and since when has it been unseemly to rejoice in what is truly beautiful, and the deep poetry of not being sick?

On the one hand there certainly is potential for an element of pride in any sort of artisan, and so that the quick publicity of 'blogging may be an occasion of pride for bloggers. But even 'bloggers with proper humility can write exciting and compelling articles; it is inevitable that some of these should cultivate their own quirksome style: so, on the other hand, the occasion of sin that some readers find certain 'blogs to be (whether to presumption, despair, pride, envy, ...) is in no small way attributable to those readers' particular vices.

This brings us to what I think is the meat of Enbrethiliel's concern. In particular, she writes against a perceived tendency in the Catholic 'blogging community to develop the odd cult of personality. Now I must say this is an odd thing to lament in a medium which consists largely of a person establishing a personal setting for publishing their own personal reflections, and collecting in boxes the odd comments of his or her very odd readers.${}^3$ Be that as it may; Enbrethiliel makes the perfectly sensible observation that this may develop into an occasion of sinful pride in the 'blogger and an occasion for idolatry in some readers (and occasions for wrath in others... or in the same, if the 'blogger ever goes apostate). Nonetheless, I should say it is incorrect to summarily dismiss the whole thing as idolatrous or proud. It is, in fact, a natural continuation into modern technology of a long and honourable Catholic tradition of public discourse; and the potential for cults of personality that naturally develops out of this is itself nothing new, nor entirely a bad thing.

I should spell the remainder more fully, but I have the feeling of having rambled-on rather too much, so the rest is in point form:

1) The recording the fruits of contemplation to be read by others is an ancient practise, pre-dating the Resurrection, joyfully taken up even by the Apostles themselves practically from the very beginning of the Church.

2) The Cult of Personality should properly be seen as a trial sent to test and strengthen its subject; and there are among the Saints several who suffered such a following, who strove mightily to dissuade their adorers, and whose cult survived their death even through their successful canonization --- Ss. Augustine of Hippo, Dominic, and Philip Neri at the very least come to mind easily.

3) There are (or should be) plenty of good writers out there with a solid grasp of the Faith, and it would seem extremely odd if none of them were positively called to preach the Gospel to the photosphere${}^4$, now that it's here.

Those are my thoughts on the matter. I hope I haven't mistaken anyone too horribly, nor confused the matter any more than necessary.

no rhetor for Aurelians

${}^1$ No, I'm not talking about the Evolution Debath.
${}^2$ Not to be confused with "proper ideals" --- nontrivial kernels of nontrivial ring homomorphisms.
${}^3$ I use this construction only to express how odd it is for visitors to leave comments. For instance I know that this week I have had some 31 visits, mostly to a single post, but only some six new comments from other readers; and this has been an unusually good week for both comments and visitors.
${}^4$ Technically, the shell of circular photon orbits around a critically-dense spherical mass; usually a black-hole, but surprisingly this is not quite necessary; here used by analogy to describe the fiber-optic internet backbone network etc.

Home to the Dukes of Beacon

2010-05-21T21:15:00.000-07:00

Dear Enbrethiliel,

It's Belfry, here.

This may seem an odd choice, given what others have complained of as "GKC's predilection for splashing purple moons and peacock skies about and calling it scenery" ( --> ). But in fact he was also a man keenly interested in family and holy homes, and being also a writer of vivid imagination, in Manalive he builds for us a diverting holiday house indeed, though it takes a while.

A wind sprang high in the west, like a wave of unreasonable happiness, and tore eastward across England, trailing with it the frosty scent of forests and the cold intoxication of the sea.
[...]
The flying blast struck London just where it scales the northern heights, terrace above terrace, as precipitous as Edinburgh. It was round about this place that some poet, probably drunk, looked up astonished at all those streets gone skywards, and (thinking vaguely of glaciers and roped mountaineers) gave it the name of Swiss Cottage, which it has never been able to shake off. At some stage of those heights a terrace of tall gray houses, mostly empty and almost as desolate as the Grampians, curved round at the western end, so that the last building, a boarding establishment called "Beacon House," offered abruptly to the sunset its high, narrow and towering termination, like the prow of some deserted ship.

Welcome!

From relatively scant readings, it's my impression that in Chesterton, perhaps stemming from his dramatic interests, Scenery is usually dynamic in the sense that he'll tell you about a thing or a place because something happens there; this is in contrast to Tolkien, say, who will write about inns and castles, vast stretches of field, forest, and mountain, to impress upon you the vastness of Creation in space as well as time, and even more because in some way he saw them and they beautiful to behold. And for these reasons Tolkien will then tell you of things that happened there.

We are brought to Beacon House by a great wind against which people, houses, and even hats stand only by the grace of God; and Beacon House meets the wind looking at first very much like a "deserted ship" --- think of an empty sailing ship, stalled with her prow to the wind's eye. She'll feel the wind, that wind ordinarily her life and strength, and though this wind won't move her, it feels not a little precarious for all that! (On the other hand, does anyone else think of Minas Tirith and the Tower of Ecthelion to read that?)

But our ship is not quite deserted:

And there were actually five inmates standing disconsolately about the garden when the great gale broke at the base of the terminal tower behind them, as the sea bursts against the base of an outstanding cliff.

There is indeed a garden; every house should have one.

... All day that hill of houses over London had been domed and sealed up with cold cloud. Yet three men and two girls had at last found even the gray and chilly garden more tolerable than the black and cheerless interior.

Oh! alas, the house is dark and dull; they have left it, while the garden remains drab and cool.
But let's follow that breeze a little more:

When the wind came it split the sky and shouldered the cloudland left and right, unbarring great clear furnaces of evening gold.
[...]
Grass and garden trees seemed glittering with something at once good and unnatural, like a fire from fairyland. It seemed like a strange sunrise at the wrong end of the day.

Alright, Chesterton's had his "peacock sky" --- never you mind, my dear --- about this time, two (young ladies) of the five leave the other three (young men) in the suddenly colourful garden, running back inside, where

the sunset breaking more and more from the sundering clouds, filled the room with soft fire and painted the dull walls with ruby and gold.

Something is coming to light the beacon in Beacon House, I think!

On some sides our garden is not fenced, but walled (very sensible on windy heights), for soon we see "a disappearing hat .... like a white panama ... settling in the centre of their own lawn as falteringly as a fallen leaf."

"Somebody's lost a good hat," said Dr. Warner shortly.

Almost as he spoke, another object came over the garden wall, flying after the fluttering panama. It was a big green umbrella. After that came hurtling a huge yellow Gladstone bag, and after that came a figure like a flying wheel of legs, as in the shield of the Isle of Man.

It's a tall wall, too; we have now met the notorious Innocent Smith, who is not a small man, but his arrival is as sudden and unexpected as the brightening evening. At the close of the Enigmas, Smith revisits this garden wall, playing at alleycat stray (no House can hold him: he holds himself to his House).

As we go on, we find the house doesn't seem the same, anymore: given a room, "Smith went up the stairs four at a time, and when he bumped his head against the ultimate ceiling, Inglewood had an odd sensation that the tall house was much shorter than it used to be." His room also seems small for him, a "dwarfish room, with its wedge of slanted ceiling, like the conical hood of a dwarf." But it suits him:

"I love these pointed sorts of rooms, like Gothic. By the way," he cried out, pointing in quite a startling way, "where does that door lead to?"

"To certain death, I should say," answered Michael Moon, staring up at a dust-stained and disused trapdoor in the sloping roof of the attic. "I don't think there's a loft there; and I don't know what else it could lead to."

Naturally, certain death requires closer inspection, so we do that, and find the
"long gray-green ridge of the slate roof, ... gutters ... chimney-pots", and an evening tea party more lively than any of Mary Poppins'. (I do object to how Moon fligavit ampullam... sure it's a lovely sound, but breaking glass in the streets is a stupid violence.)

There's lots more, but now at least we've seen our House's salient points from ground to roof-top; later, blue railings will become javelins, the dining room will become a courtroom, where Mrs. Duke the Landlady, the Duke of Beacon will sit in judgment, and we'll get a close look at the strangest sorts of vandalism and attempted murder. I will spare you my hash of the details, and instead let Chesterton do all the speaking.

You can find the text in various forms here, though my personal preference is to find it solid, in a library, which works well whenever they have a copy.

the pedestrian reader

The Root of all Evil

2010-05-21T11:47:00.000-07:00

Dear Prof. Smith,

There's a facebook status meme going around, asking people to set this slogan as their status for the day

No one should die because they cannot afford health care, and no one should go broke because they get sick.

It also asks for "politicians to get this right".

The gap between getting it right and the current state of affairs differs, of course, from place to place and across demographics. Nonetheless, whatever partial solutions are implemented in Italy or the Phillipines or the United States of America, there are common and basic problems that the perfectly-sensible appeal to justice above highlights.

People get sick

As a fact it is simple enough. For instance, the very earth we tread is riddled with opportunistic critters more than happy to eat you alive; those we encounter most often do this on a miniscule scale at snail's-pace so that you usually won't notice. Enough, however, have truly debilitating side-effects, or progress with such rapacious speed, that (ordinarily) a relatively small portion of our society is in some state of general incapacity or bodily peril, and it behoves those of us who are able to help them in some practical way.
And there are other woes that may befall us --- injuries mechanical and chemical, from carelessness, abuse, or innocent mishap. Some people regularly poison themselves --- sad, but true.

This raises the question of what, in general terms, should society do about it? And I say "society" should do something about it because those who are sick or injured are often themselves least capable of properly treating their ills.

Passive voice

Speaking vaguely, it is easy to recognize that, when possible, treatment should be applied, suitable to the patient and her condition, in such a manner as to alleviate the debility caused by her illness, so far as this is reasonably possible. I say "reasonably", not to invite slitherisms, but simply as recognition that in some cases there really is nothing that can be done.

History has shown us that there is a degree of both natural aptitude and learned skill that help to improve the success of this process: that is, doctoring requires ability and training. In other words, most people aren't suited to be doctors, and it takes a large investment of time to become one. On top of that, the doctor has to pay attention to his present task, which may require extended operation or periodic observation. As such, it's impractical for a surgeon or physician to also, say, tend his own farm, or opperate an independent taxi service. Doctoring will have to be his profession, even the core of his vocation. "The labourer is worthy of his hire", so he should, and worthily can, make his living by his medicine.

The Root

In modern terms, this means that the doctor has to be paid. That means, money has to change hands. We have all heard tales of odious clever folk with steady hands who have decided to squeeze the medical profession for every drop of gold they can manage; it's not blood-money, perhaps, but these tales do give doctor's bills some of the smell of ransom. And that's too bad, really, because as people doctors really do need to bring in a living, and we really do need them.

Something akin, but much more abstracted and impersonal, has happened to the chemical design/engineering industry, particularly the pharamceutical sector, wherein publically traded companies are required by market fiat to collect as much money as can be managed from production and sale of carefully-packaged medical substances, with the effect that chronic health maintainance, especially against rare conditions, can easily become hugely expensive on a per-capita basis even when the total resource cost of treating all cases of any given illness is negligible in comparison to the needs of all people.

Something of this love of money has infected pretty much every necessary profession --- police, firefighters, doctors, nurses, sanitation crew, infrastructure maintainance, tutors --- and it shows up most whenever one of these groups bands together in professional solidarity and does whatever they reasonably can to make the rest of us uncomfortable, until whoever has accepted responsibility for paying them agrees to pay them more. Whatever that means. Unfortunately, there are places where no-one has particularly made it their responsibility to care for doctors; (the apothecaries take care of themselves). In such places, while a doctor may not withhold treatment when the patient can't pay, there will be sick folk who just won't see a doctor, fearing the long-term financial cost. Getting medicines you need, or an extended stay in hospital, can be even more daunting.

The injustice, the cracks that spread from this one hurt, the love of money when it infects medicine, are that a sick person can be thought of as a burden --- it's not clear on whom --- and even may think themselves too much of a burden. In truth, the burden is the sickness itself, and the patient bears the worst of it! A person who is successfully treated of an illness is then able to work again, and will generally prove to be a positive good for all those around her.

Hacking away at that root.

I will have more to say about this in another letter, I think, but for now I want to just remember that the love of money is the evil here, and there's not much we can do if most-everyone stays attached to it.

There are plenty of reasons it's silly to love money --- money won't say nice things to you, keep you warm, bandage your scraped knees, or feed you: it's only good when you replace it with other things. Put another way, money is a medium for communicating gratitude, or indebtedness. It's a rather indirect medium, too, and it's probably not the best --- except perhaps for many of the rest.

As a medium of gratitude it wields the two-edged sword of simplicity: most everything that can be got can also be given a rough money-value, so we don't have to argue about how many bushels of loganberries are the value of a *goat*, versus their repsective values in raw stilton: we just ask how much does *each one* cost money-wise, sell our thing for cash and then buy what we want out of the rest of the market; so that's handy. It's a *standard measure*, more or less.

But actually, that's not quite how the real world works. Certainly, the materials and labour that go into making stilton and getting it from the dairy to your dinner table are reflected in the farmer's asking-price, and the grocer's. But then there's that thing about scarcity and demand; and demand varies not just between products, but also between buyers, and in any one buyer from day-to-day. In some ways, that is as it should be, but in others... In brief, many independent considerations get added-up to fix the price of a thing, which is, I expect, a misfortune subject to a form of Arrow's Impossibility Theorem. More fully, the process of making things is a multi-dimensional phenomenon, but when we decide between making and buying various things, largely the question becomes one-dimensional: will it fit my budget? I propose that this artificial flattening of reality is conceptually one of the first real pitfalls of econo-centric politics. Later I hope to write more properly about why that is, and perhaps make some suggestions on what to do about it.

So, expect to hear from me again, soon. I'm curious of your reactions, but keep in mind that I'm not finished!

Chester Jones

Unintended Consequences

2010-05-12T22:06:00.000-07:00

Dear Buddy,

It's really *weird*. I've noticed that, since I got into a habit of keeping my cellular on "vibrate", two strange and conflicting things happen:
\begin{enumerate}
\item It's a commonplace for me not to notice the phone actually ringing.
\item I frequently mistake other disturbances for phonecalls.
\end{enumerate}
I don't know what to make of it! It's like, I've got phantom phone rings that sometimes fall asleep.

What is up with that?

bemused

If pigs had wings...

2010-05-10T20:57:00.000-07:00

... would they be kosher?

Dear Thomas,

I hope you'll forgive the indirect ribbing.

non nobis

[...]

Dear Enrico,

It occurred to me recently that several fabulists have pondered the potential consequences of history-changing time travel. I don't myself believe it possible any more than the many-worlds interpretation of Quantum Mechanics. Goodness knows there's enough weirdness that just comes from classical dynamics in at-least three dimensions! (anyone up for a game of chaos?) In any case, lots of people have wondered about that, and the general consensus seems to be that it's a bad idea to try playing with, as everyone's attempts to fix various things that have gone wrong in our personal lives or politics or S.T. Colleridge's kite-high poetry... but I digress... they all invariably go wrong and produce something much worse.

At the same time it occurred to me that many people also agree that the 20th Century has been one of the Worst Times Ever. Sure, we all live in obscene comfort now (only, we don't all ...) and now is (as ever) one of the best times to be alive, also some of the most horrendous things have been done almost as soon as they got sufficiently easier to do. And that's easier just from a technological point of view.

So, many agree that Time Travel to Change History will lead to Bad Things, and also the Recent History is full of Bad Things. So, to answer your question "where are they all?" if there were any, (ok, not space aliens, but time tourists) I'd suggest they're probably at odd moments between 1910 and 1978, give or take, with plenty of arbitrariness thrown-in.

luke skywalker

Lies! Vicious Lies!

2010-05-10T16:07:00.000-07:00

Dear Ms. Welch,

Fr. Longenecker noticed and pointed to your recently published opinion letter, and I noticed at the end this most insulting editorial flourish:

The opinions expressed in this commentary are solely those of Raquel Welch.

Of course, this a patent falsehood! There must be millions of people who agree with what you write here --- several thousand of these surely must be compatriots of yours. Possibly they meant to say "the opinions expressed in this commentary are not intended as indicating any policy of ours," or "... do not carry any dogmatic weight," or some such slitherism; but to suggest that your notions are totally unsupported by anyone else's wisdom is at best linguistic carelessness of the worst kind! I'm even inclined to suspect that they have agreed to publish your letter largely as a lightning rod for negative reaction, and are more than happy to keep happy those you critique as wanting in discernment, while suggesting that you've basically become a reactionary kook! In the attention-getting business, no publicity is bad publicity, right?

Well I for one am not fooled. I might have to think carefully about how close you get to the Truth, but basically I agree. And be assured also of my ongoing prayers for your salvation!

God Bless,

the author; he is entirely responsible for the opinions expressed in this commentary; he doesn't give two cent's worth of worry for what blogger or your ISP thinks about them.

Yo, /dev?

2010-05-08T12:26:00.000-07:00

echo <<eof >>/dev/null

Have an eye out for this series. I think it's going to be a keeper.

eof

<--!
addenda:
Our Father,
Who art in Heaven,
Hallowed be thy name.
Thy kingdom come,
Thy will be done
on Earth as it is in Heaven.
Give us this day
our daily bread,
forgive us our trespasses
as we forgive those who sin against us;
And lead us not into temptation,
but deliver us from evil.
-->

(insert incoherent grumbling noises here)

2010-04-29T20:34:00.001-07:00

Dear Editor,

I have more linguistic points of contention to bemoan; in this missive I will only perturb your restful contemplation of other things with one category:

Excessively derived redundant words
Why oh why oh why?
\begin{itemize}
\item Orient (n) --- the East; derives Orient (v) --- Acquaint with or inform of East; derives Orientation (n) --- how an object with shape occupies space (so far so good, all new ideas); aparently derives "orientATE" --- See Orient (v).
\item Demolish; Demolition; DemolishionING?
\item Ironical, adj. : a shortening of "ironically", the adverb derived from "ironic", the adjective derived from "irony". I've only ever seen it used meaning "ironic".
\item Thusly: a demonstrative adverb meaning precisely the same as the demonstrative adverb "thus".
\end{itemize}
Note I have deliberately omited, e.g., "typical" --- here the order of derivation is "type, typical, typically" --- no redundancy, no ugly obscurity. On the other hand, if "ironical" were used as meaning "pointing to/indicating irony" instead of "marked by/notable for irony", then I'd concede it wasn't an offensively redundant word.

And it's not the redundancy alone I object to; it's the obsessive elaboration of known words in such a way as to say less instead of more. These are constructions that make our speach uglier by way of obscuring a clearer way to say exactly the same thing, while tying up constructs that could have been used for other, newer things!

the impatient reader

Alarming mathematical thought for the day

2010-04-28T06:51:00.001-07:00

echo << eof >>/dev/null

It seems some people don't like remembering History. There are certainly plenty enough people who will gladly ditch all things ancient as "out of fashion". I don't know why that should be, but ... anyways. My alarming mathematical (and also historical) thought for the day is to remark that the past, History, is the thing that is grow, among past and future. We like to think of the future opening up before us, spreading out ever new and increasing possibilities, but this is an illusion. What grows in this direction is our imagination of the future, not the future itself; and this is built, of course, on the growing past. Each of us, gradually, is running out of future, and one day all that's left for each of us will be Eternity.

That's my thought for the day.

eof

A Gospel Redux

2010-04-26T11:53:00.000-07:00

Dear Neighbour,

It's not how I'd have put it, but sometimes, amidst the Dark Night of the Soul, it should be helpful to remember what our Dear Auntie expresses in the sixth comment here.

a meandering soul

Fourth Glorious Mystery

2010-04-05T13:54:00.000-07:00

Dear JR${}^2$,

I was wondering if you might have any insight a conjectural thought I had regarding various Traditions --- actually, I thought of asking your friend Jack first, mostly because of his ocasional motif: "no-one is told what would have happened". Then I started to worry because these specific Traditions are particularly extrascriptural, and remembering his reticence which I hear troubled you also, I figured it'd be better to ask a fellow Roman. On the other hand, I then remembered how you once mused that Men were from the first given a new gift, to "seek beyond the world, and find no rest therein", so I wondered if maybe we were thinking along similar lines. But enough digression!

From of old we celebrate both the Immaculate Conception and the Assumption to Heaven of Holy Mary the Theotokos; and also it is clear that these points are importantly interlinked. What I started wondering was whether the latter honour accorded to Mary should not have been the destined state of all Men had our first parents not fallen? To flesh out this notion, so to speak, while Mary indeed finally fell asleep, it would seem that she did not suffer the same sundering of body and spirit which is the fate of all Men marked by original sin.

And so, to phrase the question as I might ask it to trouble Jack, does Mary's Assumption show us "what would have happened" to us had we not sinned? I do expect he'd say "no-one is told", meaning that it is a distraction to speculate on such counter-factuals, but it seems to me that his other proscription doesn't apply here: we are told her story --- if not in full, still at least with these important highlights.

A distantly-related thought that occurs to me in this connection is that we often speak of Purgatory as having its own sort of time --- it works a process, gradually --- which suggests to me that it's tightly linked to the world we inhabit in our beginning, and I might even guess that purgatory was created after the fall, an invention as it were to make up for the defects we adopted in sinning. But it's also an important fact of purgatory that our souls pass through it without our bodies; even that our bodies would, echoing Jack's notions, "get in the way" of the cleansing flame. One might say that Mary could keep her body because her soul didn't need such cleansing, but I think it would be more proper to say we must lose ours for half of Time specifically because our souls do need it.

In the back of my head, at the same time, I've this notion that Mary's assumption holds an important confirmation of the Easter Promise: Specifically, Easter promises that death is not the terminus of our existence, but a new birth; but in the assumption we see that this new life isn't a "new thing", rather it's the promised return to us of our proper nature as seen in the entirely human Mary, lost under our sins, and liberated through God's merciful and gratuitous forgiveness.

Of course, this doesn't give the least inkling of the real mystery in Easter, or the Assumption; I'm keen to learn what you make of my nonsense?

Sincerely,
an avid reader

PS. Now I've learned to count...

An astonishingly short proof

2010-04-01T09:20:00.000-07:00

That right! I've discovered an astonishingly short formal proof that ZFC is inconsistent! It's been thoroughly checked by two different proof-checkers on various hardware, and they all agree that Math As We Know It Is Insane!

The Astonishingly Short Proof was initially produced by genetic tree-searching algorithms with success measured by a heuristic "inconceivability index" for strong sentences. It is conjectured that this index is only one of an infinite family --- indeed an $\infty$-groupoid of such notions is expected to exist!

Our specific index --- a real number --- is also known to imply falsehood whenever it exceeds 3/31, and our algorithm this morning arived at a formal proof from ZFC of an index 4/1 (=4)!

For more, proceed "below the fold"!

OK. It's not true. For help, try to see what's happened to gmails vowels.

the fabulist again

Aetymology

2010-03-21T13:04:00.000-07:00

My dear Puffin,

You may have noticed The Poetess a couple of weeks back published her ripening metrically-faithful interpretation of Horace's Soracte ode. The particular meter used here is known as "Alcaic", whereon wikipedia absurdly declares

"The Alcaic stanza is a Greek lyrical meter, an Aeolic verse form traditionally believed to have been invented by Alcaeus, a lyric poet from Mytilene ... ".

That may all be well and good from a literary-historical point of view, but it doesn't come anywhere close to the True Meaning of Alcaic!

My own research has shown that the latinized "Alcaeus" was in fact a nick-name (much as Plato was so-called for his broad, flattened face), sprung from the multiple inspirations of his fondness for an adopted and very lost Thick-Billed Murre --- no doubt blown off-course during a late Etruscan-Era hurricane --- and his own odd waddling gait, which so resembled that of his bird, and which was mirrored in some of his more-forgotten verses. (compare the suggestion that Beethoven's rhythmic experimentation was partly driven by the sound of his own irregular heart-beat, due to his undiagnosed lead poisoning).

The name his fellows gave this bird and the poet was initially "alkon", which resounds in our present day "awkward" (fr. O.E. "aukgard"), while murres and relatives are nowadays known collectively as alcidae. Anyways, it's a charming meter, and none the worse for its feathery origins. After all, all of creation declares the greatness of the Lord!

the unapologetic fabulist

Some notes

2010-03-07T16:55:00.000-08:00

Dear Bat,

I've been thinking.

Our beloved Mother Church, last Sunday, in the words of Paul, reminded us that coveting is a kind of idolatry. Of course, coveting can be incited by another's gloating, boasting, or immodesty.

I have usually tended to think that immodesty was the visible counterpart of pride. After all, a proud person may well tend to gloat and boast, and such; but since I started considering modesty of dress, I've tried to put together how modesty and modesty might be akin. And while there is certainly a great deal of immodest dress out there, and more than in relatively recent history, it's not clear to me that there's so much more pride w.r.t. our individual forms except in rather narrow circles.^*

Today, I'm inclined to describe immodesty seemingly by its effects, instead of its motivations: specifically, I'd like to say that the virtue of modesty is the habit of encouraging proper reverence in others by discouraging their distraction. That is, the defect of immodesty is its invitation to remove another's (or one's own) due reverence for God, by drawing that attention to oneself, whether by boasting, or ostentatious costume, or over-gladly receiving undue praise.

This doesn't mean it is necessary to conceal one's talents or natural beauty, but rather it leaves them in their proper place, and uses them to glorify God; which is only fitting as they are His works.

I'm curious what thoughts you might have, or any of those you will share this with.

Sincerely,
the philosophophile

* PS: of course, I may well be wrong about any of these anecdotal generalities.

An exercise in geometric measure theory

2010-02-05T13:53:00.000-08:00

echo <<eof >>/dev/null

I was given a math paper to read over that includes, in its introduction, the assertion
"the length of an algebraic curve of degree $d$ in the unit disc is less than $4d$". I don't think I'd seen this before, so I've decided to try proving something like it, and got a smaller constant than $4$, but not much smaller. (If you've not seen this problem before, can you guess?!)

The proof involves the following ideas:
\begin{itemize}
\item The length $l(s)$ of a line segment $s$ is given by

$\displaystyle l(s) = \frac{1}{2}\int_0^\pi |p_\theta(s)|\,d\theta $

where $p_\theta$ is the orthogonal projection onto a line $L_\theta$ at angle $\theta$ to the ordinate axis (or what you will), and $|X|$ is the length of the set $X$.
This boils down to the identity $\int_a^{\pi+a} |\sin(\theta)|\,d\theta = \int_0^\pi \sin\theta\,d\theta = 2$.
\item The length of a measurable curve is approximated by the length of a fine polygonal approximation to the curve.
\item An algebraic curve $\gamma$ of degree $d$ (in the plane) meets any line $L$ at most $d$ times, or else $L$ is a component of $\gamma$
\end{itemize}

The practical upshot of these ideas is that you can measure the length of a decent bounded curve $\gamma$ by
\begin{enumerate}
\item for each $\theta$ and for each $x\in L_\theta$, counting the number $n_\theta(x)$ of points on $\gamma$ that project to $x$ orthogonal to $L_\theta$ --- that is, the number of times the line through $x$ and perpendicular to $L_\theta$ intersects the curve $\gamma$.
\item for each $\theta$, calculating the integral $\int_{L_\theta} n_\theta(x)\,dx $.
\item integrating the results of the last calculation:

$\displaystyle l(\gamma) = \frac{1}{2}\int_0^\pi \int_{L_\theta} n_\theta(x)\,dx\,d\theta $

\end{enumerate}
Because of the caveat about $L$ perhaps being a component of $\gamma$, we note that the definition of $n_\theta(x)$ needs a little refinement: strictly speaking, there may be countably many $\theta$ and $x\in L_\theta$ such that $n_\theta(x)$ as described should be $2^{\aleph_0}$, and it's not clear how to define the integral in this case; but these $x$ and $\theta$ correspond to a line segment projected to a point, so that it actually contributes $0$ to the length estimate described by polygonal approximation. This might be a good example to have in mind when carefully discussing what happens when you try to change the order of limit operations...

I should point out that all the integrals are unordered integrals of positive things --- basically, this is still measure theory. Consequently, we are still within the realm of convex analysis, so we can get estimates on $l(\gamma)$ by finding estimates for the numbers at any of steps $1,2,3$. In the present example, we want an upper bound on $l(\gamma)$, and we are given an upper bound $n_\theta(x) \lt d$

This lets us write

$\displaystyle l(\gamma) \lt \frac{1}{2}\int_0^\pi \int_{p_\theta C} d\,dx\,d\theta $

where $C$ is the unit disk (or circle ... ). The length of the projection $p_\theta C$ of the unit disk is simply $2$, which gives the estimate

$\displaystyle l(\gamma) \lt \pi d $

Since $\pi \lt 4$, we're done!

Of course, with an upper bound, it's useful to have examples to compare it to. The unit circle itself is a curve of degree $2$, with length $2\pi = \pi 2$ within the (closed) unit disk; more generally, the curve $(a\cos(n\theta)+b\cos\theta,a\sin(n\theta)+b\sin\theta)$ is algebraic of degree $2n$, with length within the unit disk as close to $2n\pi$ as you like (choosing $a,b$ carefully). I'm having difficulty thinking of a curve of degree $2n+1$ with length in the disk more than $2n\pi+2$.

That's all!

eof

My silly question for the day

2010-02-02T07:45:00.000-08:00

Dear Phil,

Does this mean that Johannesburg gets six more weeks of outdoor cricket weather? Or do we have to go there and ask the meerkats?

definitely in the Northern Hemisphere