Sunday, December 29, 2013

Merry Christmas!

... belatedly, (or not for it is still the Octave)!

Nothing much to say, no deep nor deeply flawed meditations on offer, just a friendly Halloa, and keep yourselves well and warm (wherever the ambient is cold) and why not drop in for tea or virtual-tea some afternoon? I'm here all week!

With prayers for blessings,
— Belfry

Monday, December 16, 2013

The Halting Problem of Evil

Because this is just what you always wanted to read as meditation for the First Week of Advent!

Of course you have heard of Gödel's theorems; they are:

  1. Any sequential programming language that can implement interpreters for arbitrary sequential programming languages also implements programs that, for some input, do not converge.
  2. In particular, for any sequential programming language $L$ (such as LISP) that can implement interpreters for arbitrary sequential programming languages, there is no convergent program in any sequential language that separates convergent $L$ programs from non-convergent $L$-programs.

What's that, you say? The LISP programming language is significantly younger than Gödel's theorems? Uncertain of the serializability of LISP itself? Not to worry! This is what happens when mutually-interpetable (or bisimulant) things get mixed up in a mathematician's brain. As it happens, what Gödel did, to prove his theorem, was to show that you could implement LISP (or some other sequential programming languge) in The Arithmetic of the Natural Numbers. I don't know precisely why he did that, though it might have something to do with everyone who cared at that point having a firm belief that they understood what the natural numbers were, and no-one anywhere had ever yet heard of a machine programming language (though they certainly DID have programmable machines, such as farmland and the Gutenberg press and the Jacquard Loom and the Player-Piano; what all these things lacked was recursion, but never mind).

Another way to read the theorem (as applied to programs) is that by far the best way to find out what a program does is to run the program, as naturally as possible. This is very much like (as Dr. Thursday reminds us) the way (as Uncle Gilbert remarked) the point of playing a game is to find out who wins! Now, with programs as with other games, there is definitely a risk involved, due to the halting problem and its corollaries, in running a program. You never know, for instance, that the thing will not chew up your whole machine (or try) before it stops unless you carefully run it within a tiny virtual machine; but on the other hand, unless you have an arbitrary quantity of free space to build a virtual machine in (or a working copy of your working machine), you may never know if some insidious program is going to behave in surprisingly different ways, given the space to do so in.

Of course, God Himself knows what every deterministic pattern of any size looks like at the edges, in exquisite detail; but this should be thought quite something else from creating a living thing that plays within the pattern for His delight. And how much more fraught than running a program, a deterministic thing in a deterministic piece of the universe (bar radioactive decay — and we know Who has ordered radioactive decay) is it to give life to a free and willful thing? But how else could anyone, ever, anywhere, in any way, be good? It is, of course, impossible, to be good without first being, and furthermore being free and willful; the dumb or speaking dead machines are useful or nuissance at times, but not (in themselves) good or evil. And never mind that he cannot be saved who will not be saved, still more can none be saved who is not at all.

Of course, this is all just an infinitessimal slice of the way the “problem of evil” isn't so much a theological problem as it is a natural hazard (and an intrinsic one) within any creation sufficient for containing moral life. [Although C. S. Lewis may have expressed it more eloquently, he certainly never invoked the mathematical certainty of Gödel's theorems, which nonetheless seem suprisingly a-propos; I think we may guess he also never had to program a computer, and it's neither a surprising nor deficient omission.] I also have to admit that this sort of analytical precision has a very cold feel to it, out of proportion with the fact of suffering; the recurrently strange H.H. F. Pp. I recently remarked on the especially poignant case of suffering children — Stilwell excerpts here.

It would seem that those things God has allowed are permitted for some end; and it further seems that suffering, especially suffering in children, does induce its witnesses to charity, and that is indeed a very good thing. Suffering makes the sufferer more lovable. In some cases this is through a change in the sufferer, but as often as not it is by a change in the rest of the world. And this effect, that suffering ordinarily leads to charity, is not a mathematical necessity (I'm sure), but rather a sign of God's goodness, the stamp of part of His character in the world.

Monday, December 2, 2013

A Cautionary Tale

I was going to put up a mathy-philosophical post, with the grand-frivolous title "The Halting Problem of Evil"; it's already quite long, though I've no clue how to finish it, and something rather jarring has occurred since I started that, so this is what we have instead.

Thanks be to God for his most graciously and gratuitously preserving me (and everyone else) from some of the more adverse possible effects of my own stupidity; because, for silly reasons, I was not standing in front of the stove when the glass pie plate exploded (I thought I was steaming the broccoli …), covering the room with thousands of beautiful glittering pointy slivery shards; and for reasons unknown I was already wearing slippers, and standing next to the broom, and the door to the next room was closed. Alas, the pie was inextricably burned onto its own broken shards at that point (and starting to smoke, on the erroneous burner), and the stew was littered with them, too. But no serious injuries were there, just a brief alarm and some hours of scrupulous sweeping.

Saturday, November 16, 2013


In addition to their practises of exposure and sewering and Molochian sacrifice of “useless” babies, the hedonistic pagans of long ago (and of not so long ago) who had really more wealth than they could practically use, would also artificially extend the sense delight of savour and eating and all that, by means of the vomitorium, which is exactly what it sounds like (when not discussing theatre-in-the-round or volcanoes).

And the reason I bring it up with that lead-in, is to point out one gleamingly hopeful point in which we are, today, still a bit better than those pagans of the bronze-age: this kind of behaviour is still obviously abhorent. It is also still practised, but (in the West) most often finds its expression in an extreme form of plerophobia more commonly known as bulimia. I say this is a hopeful fact, because we actually do remember that a particular act which can be a great pleasure also has a purpose, a telos; we still know that applied engineering to subvert the purpose, to isolate or exaggerate the pleasure of it is actually a diseased and dangerous and literally disgusting game. The world that used to be Christendom is suffering reproductive bulimia, and can't get away from its hunger. Is it any wonder?

Friday, October 18, 2013

A dead comment.

Dear Paul,

(btw, I don't at all mind not being one of your notable theologians! It would be quite a relief, had I ever thought so much as to worry about it, actually... )

Of course, I'm not about to invite you to partake of detraction; in fact I'm happy to remain ignorant of which proponents you mean.

I have, on the other hand, met a number of gnostics among the detractors of either form. To that extent, I hadn't thought about it, and my only conjecture now is that gnosticism is much too easy to fall into, and can end up looking like pretty much anything: it doesn't surprise me anywhere.

To Mr. Kerr I might reply, first: the issue of the Calendars is smoked pickerel; devotees of the E.F. as such are no more intrinsically schismatic nor judaizing than our brothers the Copts, or the Greeks, or the Armenians (or Anglican Use Catholics, for that matter). For the question of understanding, I should say that the internal consistency of a ritual and its language is more important unto understanding than is initial fluency in its idiom. I might put this another way: before I met the Extraordinary Form my Latin was entirely gathered from the musical tutelage of a number of protesants choral conductors (that and the Pange Lingua Gl. we sang every Holy Thursday). The transition from a purely sensual encounter with these ancient prayers and their classical settings (for which I should be aeviternally grateful to my sundered teachers) to an almost-continual living prayer in their ancient form has been something like the old sense of ekstasis — a standing outside what was so familiar as to seem oneself before — but without any of the really-gnostic so-called charismatic nonsense of a dull "esctasy".

To be sure, the Priest must, morally, know what each part of the Mass is when he is celebrating it (and not pray it "like a parrot", to allude to recent remarks), but asking one to understand what it means, from fluency in the words on up, is like asking Augustine to comprehend the Trinity. Mass is supposed to form us, and we to learn from it; that couldn't happen if we had some firm belief that we knew it already.

From the perspective of internal consistency, the current Ordinary Form is... well, I should say, it is much too rough and raw, and will need some centuries of mellowing before we can give it a fair comparison with the Extraordinary. I find the order of it disorienting in places, jumpy and disjointed, now; but as for having it in English, I would only complain that the translation is just too easy. And any translation of the Extraordinary (to follow along with, e.g.) will suffer the same difficulty.

Without being gnostics, let's rejoice in the Mysterious, anyway!


Sunday, October 13, 2013

The future King

Whatever you think of the fellow, Malcolm Gladwell certainly has an ear for an interesting story and fine delivery, not to mention a keen intuition for dissonance.

And so it was that he, somehow, began to open up the story of Goliath of Geth, and his death not quite at the hand of King Saul's servant the court musician, David son of Jesse of Bethlehem, a young shepherd. The battle of the Elah in the war of the Philistines and the Israelites was never joined, for neither force could find acceptable terrain from which to strike; and so to break this stalemate, the Philistines proposed a trial by single combat and sent forth the giant; none of Israel's army dared singly approach this monster, save David; and when David had toppled him, all the host of the Philistines fled.

I don't propose to tell you Gladwell's telling of the tale; rather, I found that it raises the interesting questions (which he doesn't address) of Why did they flee? and Why is this story recorded and remembered among David's accomplishments?

One of the key differences between King Saul and King David is the David's personal humility in the Kingship. Saul angers the Lord by turning the Kingship into a means for his own personal glory: trying to keep the king of the Amalechites as a pet, for instance; counting the Israelites so as to boast of how great his kingdom is; presuming on his royal authority to insinuate himself among the cohenim. David, in contrast, is humble. When David offers sacrifice, it is as King of Jerusalem, "in the line of Melchizedek"; in the household of King Saul he does not put himself forward, but awaits his assigned tasks, in which tasks Saul sees that the Lord is with David; even the way David does later fall into abusing his kingship — it is heinous, and yet it is done as privately as can be, doing nothing to advance David in glory; and in the Elah, facing Goliath, again it becomes clear (in my case, with Gladwell's help) that David, unlike Goliath, is not in this fight for any glory.

Goliath for the Philistines proposed a duel, a wrestling match, "pistols at dawn". His compatriots look up to him (not just that he's tall), and he is clearly eager to triumph over whatever champion Israel might send to him. He has no idea what he is getting into. He is the fruit of a culture that prizes a warrior skilled in his art, a culture that reads divine approbation in divinely appointed outcomes, and reads every battle as a battle of the little gods because it has no God. David, the shepherd, cares nothing for this nonsense, and gives no honour to battle for its own sake nor to warriors for war's sake; the Philistines (like the Klingons) would say he has no honour; in a twist of modern usage, today's bloodsport aesthetes would call David a philistine of the arena. David is not in the fight to triumph over Goliath, but merely to win for God's chosen people. He doesn't put God to the test, he doesn't seek his own glory or protect his warriors' honour, but only makes durn sure that he wins.

The Philistines flee because they see that these people fight dirty. These people have no fear of the gods who come and go for warriors' valour or to avenge poor sporting. They will keep on fighting however they can whatever befall, just to stay where they are. And clearly the little gods have no power over them, for here they still are in spite of all the bad luck and dishonour they're plainly heaping on themselves. What else can be done with them?

Friday, October 11, 2013

What we have here is an equivocation

Specifically, "Catholic" can (it really can!) mean two, quite opposite things. Of course, what Catholic is supposed to mean is also supposed to get skeptics really annoyed when we point it out.

Catholic can and is supposed to mean "Universal": the Catholic faith is good for everybody, and God whom we worship is God of all, though that's not what he has usually called himself.

But, on the other hand, Catholic can mean "Christian" — you know, those funny folk who talk about turning the other cheek and heaping coals behind your back and have that Nicene Creed thing... or even more weirdly, those Papist Romanizing so-called "Christians", with their surfeit of holidays and authoritarian reading of scripture and... you know, a tiny sect, and anything but universal.

In the latter sense, and in so far as the latter sense remains that understood by everyone who says it, no, God is not "catholic". God does not belong to sects, in either sense of "belong to". That "sect" belongs to Him, but that's another matter.

God is good for everyone; lots of people don't know Him yet, and a few actually hate Him. One Church knows of Him what He Himself has revealed.

Friday, October 4, 2013

Callooh, Callay!

Today the 'blogger internal tracker tells me that on 16061 occasions has something asked it for a page from this blog. I happen to know a few of those are me, and a lot are referal spam, but some of them might well have been you!

But, more than this, 16061 seems to be a prime palindrome, so I'm glad just to have caught the counter when it was at such a number. Whee!

a man of simple pleasures

Sunday, September 29, 2013


I put this together just for fun, back in March. It's about measuring the area under a cycloid: adjacent blue triangles add up to the same area as the white triangle between them; and the lot of them add up to the regular polygon, so the cycloid is three polygons; and also the length of its curve (That one is a surprise).

Saturday, September 28, 2013

Trying to understand the world

Dear Hans,

On the one hand, one should avoid careless stereotyping/cliché mis-tropes and such; and furthermore ad-hominem falacy is remarkably easy to fall into; nevertheless:

There are some … odd … stories … about Immanuel Kant. Such that, I really have to wonder: was the poor fellow autistic? On the one hand, clearly a prodigious and productive thinker, notably instigating Laplace's consideration of gravitational collapse of dust clouds into stellar-planetary sytems, as well as proposing that some of the fuzzy oval bright spots one could discern in a telescopic view of the night sky were hugely far away and composed of many stars, analogous to the bright band of nearer stars composing the Milky Way (in old Greek, γαλαξίας κύκλος); in which it turns out he was quite right, and for which reason these “oval nebulae” are now known as Galaxies.

And yet. For instance, his fixation on sameness: it is said he was more reliable than a clock in taking his walks. (Admittedly, the development of reliable precision clockwork was still a nascent project at the time). Dr. Marshner tells us he built a device to consistenly set the vertical extension of his stockings. The Categorical Imperative might well itself be an expansion of the criterion of sameness to a moral doctrine.

Small wonder it would be, being praeternaturally inclined to introspection, that one should be suspicious of the verity of external reality.

And he tore down the world of Western Philosophy. One has to be ever so careful in reading the thought of an unhealthy mind!

Well, I suppose we must nonetheless hope, and pray for the poor souls.

a student of pure reason

Tuesday, September 17, 2013


(The player should cue itself to 2:18; recommend adding a low-pass filter [ ~ 8kHz ] to your sound system if you want the rest, because the artificier she visits first seems to be attempting to compete electronically with a cave full of bats.)

Björk appreciating Pärt in English (in Berlin).

B: [...] because you give space to the listener [...]

P: Maybe it's because I need space for myself.

Sunday, September 8, 2013

"Defend" marriage? Defend marriage?

“The truth is like a lion. You don't have to defend it. Let it loose. It will defend itself.”
some say it was St. Augustine; doesn't really sound like Augustine. It might have been Spurgeon. Either way, it's a catchy phrase.

And marriage simply is the truth. It is a truth that every boy knows, who falls in love: that he was, in a personal and a univeral sense, made for marriage. Marriage is not something that, itself, needs defending, but is a gift, part of our very being, of the original Love that many waters cannot quench: He walked on the waters instead, and proved stronger than death. But we are certainly defending something as we fight "in defense of marriage": what, then?

We are defending our own minds against a kind of nominalism — the notion that there are not actual things which can be named, so that all names are movable. We are defending our language against senseless drift — because when a word is moved such that it refers to a non-thing, it does cease to name. We are certainly defending particular marriages (all present actual marriages), both from the neglect of obscurity and the abuse of transient will. We are defending civilization, which grows in the gardens of marriage. As Stilwell forcefully puts it, we are defending our children. And, what no Christian may forget for long: we are defending our opponents against The Enemy.

So, yes: defend "marriage: n.". But never forget what we are defending thereby!

Friday, September 6, 2013

A poor request

Of your kindness, would you good folk say a prayer for my Dad? He has been assigned for coronary bypass surgery within two weeks. We share a middle name of Christopher.

Again some News, 5th Sept. Well, he's through the operation, now. Five bad spots bypassed (urgh!).

Actual News The "Further", below, was actually out of date before I posted it. Operation is set for tomorrow sometime Friday? Maybe? They keep changing the news. I keep forgetting to say "Thank-you" to all you folk. Thank you.

Further Well, he's still waiting in the pipeline, as it were. I got here last Friday, and it's been very good to visit him every day; he gets lots of visitors, including local clerics, but very little in the way of fresh air, stretch of the legs, or scenery. And so we keep waiting.

I do beg your pardon...

=> nucleus N 2 1 NOM S M

nucleus, nuclei N M [XXXCX]

nucleus, inside of a nut, kernel; nut; central part; hard round mass/nodule;

Whitaker's Words v. 1.97Ed

... but how on Earth under Heaven did “nuclear” ever get attached to the word family? How did this combination ever attain any kind of currency as naming some ideal of family life? A cursory glance through google scholar turned up only nonsense; the phrase exists in about three books (none as old as I am).

The poetry of it is all wrong: (healthy) families are not like nuts nor their nutty insides; they are not like small round masses (ballistae, anyone?) or lumps of mineral to be admired or crushed, etc. They are certainly not the chemical atoms, except perhaps in the barest of superficialities: a central lump of stuff tightly bound (the initial marriage) surrounded by a cloud of complementary, lighter, and fluffier stuff (children, I suppose). Such an image of family considers only a single generation: the husband and wife; such an image of family naturally saturates at an equal number of parents and children; such an image of family reduces family life to merely natural attractions and repulsions, makes similar-looking things identical in nature, leaves attachments at the mercy of external environment, radically isolates married couples from eachother except as mediated by their children (except when things go horribly horribly wrong), and is internally sterile.

The West hasn't lost marriage for having lost the nuclear family: “nuclear family” has irradiated Western notions of marriage. Having got tired of the particular wrongness of the nuclear model of the family, we have tried substituting other wrongnesses: totally amorphous families; marriage by "chemistry", where bonds are as changeable as in a test-tube, and if the chemistry is "wrong", you go looking for different reagents; sometimes something more zoological, and so "tiger moms" and "eagle dads". Have we forgotten, somehow, that our children are not eagles, or tigers, or electrons? That we are, ourselves, children?

The modern revolt against marriage isn't really against Christian marriage; it couldn't be, unless modernity had ever encountered a truly Christian marriage. But where it has, it is not in revolt! Rather than try to find another bad metaphor, why not talk again of happy and holy families? Human families are human and familial. Let them be holy, too, and it will be enough.

Jeremiah XXIV

Monday, September 2, 2013

Dear Sam Harris,

(no, I'm not going to buy your book).

I don't understand why the distinctions must be articulated again, but let us not be reluctant to do so.

But first, The Challenge:
Anyone who believes that my case for a scientific understanding of morality is mistaken is invited to prove it in 1,000 words or less. (You must refute the central argument of the book—not peripheral issues.)
And, like a good sport, there is the (very brief) actual central argument:
Morality and values depend on the existence of conscious minds—and specifically on the fact that such minds can experience various forms of well-being and suffering in this universe. Conscious minds and their states are natural phenomena, fully constrained by the laws of Nature (whatever these turn out to be in the end). Therefore, there must be right and wrong answers to questions of morality and values that potentially fall within the purview of science.

The difficulties (which, I suppose, if I wanted to buy your book and read it, might or might not then be cleared up, but I deem the details to be "peripheral issues"), may be simultaneously summarized by replying that
There already is a scientific understanding of morality: it is Catholic Moral Theology.
but to be somewhat more explicit
  1. there is no cause to accept your premises
  2. the challenge equivocates on "scientific"
  3. the challenge equivocates on "morality"
  4. the claims behind the challenge are circular

Let us proceed in order.

Premises ungrounded

You say "Conscious minds and their states are natural phenomena, fully constrained by the laws of Nature." Let us set aside the odd coincidence of the last hundred and fifteen years, that the best abstract model of observed physical reality vocally declines to constrain its systems in their behaviour.

Why should I agree with you on the nature, or the ordinariness of consciousness? As it happens, I do think you are wrong; will you not, please, attempt to convince me otherwise?

"Scientific" is equivocal

What, Mr. Harris, is accepted as "scientific"? Of course, the broadest view should be "that which is reliably known by experience". For instance, I know quite reliably that the bishops of the Church exhibit the visible end of a physical continuum of contact from the Apostles to this day (orders being confered by laying-on of hands etc.). It is, to my understanding, therefore a scientific fact; however, I don't know whether you would accept it as such. I particularly don't expect that you would accept (as I do) as similarly scientific the fact of Jesus' Life, Death, Resurrection and bodily appearing to those same Apostles.

However, if you will restrict "scientific" to mean "that which is reliably repeated in controlled laboratory conditions" (see "MRI at the beach") then you can't actually conclude "the existence of conscious minds" other than your own. Sleeping bodies, for instance, consistently fail to show signs of consciousness, while ELIZA has reliably fooled patients that it is conscious. There is no general reliability on this point. Presuming a conscious mind other than your own requires something of a leap of faith; but then why stop at one?

"Morality" is equivocal

Suppose, for now, that you have a consistent definition of "scientific" which admits the existence of multiple conscious minds and at worst remains silent on the Divinity (by Gödel's first Incompleteness theorem, it is unnecessary to suppose that one theory resolves all questions); in what, then, does morality consist? My best guide to your intention is that it has something to do with "the fact that such minds can experience various forms of well-being and suffering in this universe". Is it impossible that a mind suffering may nonetheless have perfect well-being? And what is suffering, anyway? Do you mean the fact of subjectivity? Do you mean the experience of physical discomfort? Do you mean the confusion of contemplating paradox? Do you, perhaps, mean the confusion that results from experiencing a pain whose sense or purpose is unknown?

I beg thee allow me to suppose (what I think charitable) that whatever you mean by "moral" is consistent with the proposition that minds ought to be given truth to know: then, as long as you are silent on the Divine while I believe I hold scientific evidence for Him, will you not concede it moral of me to teach, say, my own children to address and inquire of the Divine what His will is for them?

The proposition is circular, or vacuous

But to put a deeper problem somewhat more baldly: why not agitate for pain or confusion in other "conscious minds"? An empirical science may well indicate what will cause pain or confusion, and what will alleviate them, but that goes no distance at all towards suggesting that this is good. You may have settled on a definition to encompass your use of the word "good", but that doesn't mean you are talking about what we are talking about: you have instead redefined the question out of interest. Otherwise, even to state the proposition presupposes a real, accessible, goodness.

Even if, say, we consider a more modest and laboratory-accessible question, on the health of a mind, try the analogy of health in plants: why should plants be healthy? The answer, for a farmer or ecologist, is that plants should be healthy so that they may beget healthy offspring, and that whatever naturally eats them will be healthy in turn. Half of this is actively paradoxical, and only the other half of this reason is admissible for wanting healthy humans. For healthy minds, neither seems to make sense. But if a healthy mind is only desirable for itself, why should I act (as I hope I do) so that your mind be healthy? It certainly isn't a scientific fact that this improves my well-being, or alleviates my suffering: I might never have heard of you and been just as happy and sane for ignoring it! I might indeed be taking more pains on myself than otherwise necessary, but would have me do less?

Well, I have done my short-worded best. No, I don't want the money, thanks.


Sunday, September 1, 2013

For your evening and nighttime

Who wouldn't like a little cello solo now and then?

Friday, August 23, 2013

Guess what!

It's the annual anniversary celebration! In honour of my being (once again) prime, everyone who says hello today will be awarded a random prime number of free points!

All the best to you,

the usual suspects

Thursday, August 15, 2013

Happy Feast Day!


And it is enough.

Thursday, July 25, 2013

From the beginning He made them

In the midst of contemplating how the immensely popular practise of self-submission to the-creator-and-destroyer basically fails to be a religion (at least under its presently-immensely-popular superstitious self-opposition to anything like reason), this in the midst of a f™ discussion confusing the relation between Man and reason in this immensely popular &.c. with, the relation between Men and Women in the same, and in other parts of the world; in the midst of all this, I say, the word came to me (not a new word, rather one you've heard every Easter Vigil)
And it shall be a lamb without blemish, a male, of one year: according to which rite also you shall take a kid.
You see, I'd been casting about in my memory to see if I couldn't recall if there were any sense in which attempting to apply the Sacrament of Holy Orders in any degree to nonstandard matter would be a violence to the nature of that matter. I don't think I found a real case for that conjecture, but never mind.

It isn't that female beasts were never used in sacrifice — peace offerings could be male or female, sin offerings for individual common folk seem to have been female, and a ewe was required for the cleansing of a leper (though I can't tell, in the ritual described, when if ever that ewe is killed) — but definitely they mean different things, and the male and female sacrifices are not generally interchangeable, or He wouldn't have bothered to be specific.

Come now to the New Covenant. The Sacrifice par excellence is also our passover. The Priest of our passover is also the Victim, and so it is with its daily re-presentation. The Lord has said that the passover victim is a male, even before the transposition of Levi for the Firstborn. I really don't want to be about "proof-texting" as it is called, I'm all about the poetry; but there it is. If the priest is the victim, and the sacrifice is the passover, then the victim must be a male, and so therefore must the priest be as well.

Saturday, July 13, 2013

A "recipe"

It isn't much, of course...

In a clean mid-size saucepan, combine
  • ½ lb chopped rhubarb
  • ½ lb strawberries
  • tbsp minced fresh ginger
  • sugar to cover (I didn't measure it. Don't be afraid: rhubarb is powerful tart)
  • water to wet sugar (< ½ c)
Apply medium heat, stirring occasionally. Bring mixture to boil, and reduce to simmer. Continue occasional stirring, until desired reduction.

I call it (for fun) “strawb’inger’barb’alade”, but, basically, it's spiced jam. What more does one need? Serve with breakfast pastries or icecream or cream tea or... The possibilities are, as Zombo says, endless!

Sunday, July 7, 2013

Attempting to distinguish well

Or, beware of smoked pickerel.

There is a study (oh, there's always a study, of course!) news whereof has been lately making the rounds, apparently demonstrating that, under carefully controlled laboratory conditions, men who exhibit one particular kind of reprehensible mental habit outside carefully controlled laboratory continue to show same habits, and even more so when contemplating pictures that gratify those habits. As Jolly Shea would summarize, water is wet.

Astounding, isn't it, that this kind of study was (apparently) approved by some ethics board?

There is another article entering the debate somewhere pointing out that modesty is an ambiguous word, being emblazoned with a Renaissance statue allegory of Modestia, the virtue whose opposing vice is vainglory. And they mention that many scriptural exhortations to "modesty" are corrections of excess in dress. The noted Shalit wrote a fascinating book richly woven on this ambiguity in modern (hmm) English, which does a much better job on their relation. I suppose it's just one of those funny things that the closest-sounding thing to "pudicitia" (lat) and later "pudeur" (fr) is the English prude, which is actually a contraction of a French contraction "prud-homme", which seems to be about prudence more than anything. In short, these are not the foxes you are hunting.

Recently, in advocating that people who live in civilization should be clad1, I pointedly declined to comment on swim-wear. There are a number of reasons for this; e.g. : there are severe engineering constraints on garb that both protects and is wettable, to the extent that what you could suitably wear to Church (say) would kill you if you tried swimming in it for more than ten minutes; e.g. : the popularity even of recreational swimming, at least on these shores (hee!) is a fairly novel thing; e.g. : there are or were places where undress is expected for swimming (and if one is there not to swim, he is effectively driven away); e.g. the second time we hear of Simon Peter leaving his boat at sea, a point is made that he was in some state of undress which he hastened to correct2.

The trouble with using the study to inform (or to deconstruct) choices of swimwear is that it replaces what seems to be a moral question (what reasonably can I do not to scandalize my brother and sister?) with one of instrumental reason (how can I use clothing to manipulate everyone else? whether to allure or to push away). The trouble with using this study to inform the genuine instrumental question (how does dress affect the beholder) is that it confuses use with the expressed desire to use.

B.t.w., if there somehow is a question as to propriety around swimming, the most I will actually venture to say is that swimwear is excellent wear for swimming, so long as it really is good for swimming (and I have my doubts about lots of it). More generally, the meaning of particular garb is, of course, dependent on context (which is why carefully controlled laboratory conditions are about as silly as taking an MRI to the beach).

A former school colleague, in conversation about obvious things, asked whether deleterious behaviour that happens to find biblical condemnation should again be condemned also in our Criminal Code; the fishy point in this question is that you don't need the bible to tell you that deleterious behaviour is deleterious.

You need the Bible to tell you that God is to His people (indeed, to every created rational soul) as Husband to Wife; that is, you need the Bible (or authentic living tradition, but this is a tradition attested in ancient Holy Writ) to tell you that, if you get Marriage wrong, you also get yourself in relation to God seriously wrong. That is, you might just need the Bible to tell you that getting marriage wrong in this kind of way is itself a grave sin.

You do not need the Bible to tell you that [effacing the distinction between dwelling in common vs. establishing a productive, living family] is [the state spending itself on society killing itself]. Do not in any argument accept the premise that the marriage question is only a religious question.

1 : Allow me to remark that clothing the naked is classified as an act of corporal mercy, along with feeding the hungry, comforting the sick, and consoling prisoners; to be short of clothing, in our fallen world, is a misfortune and a poverty.

2 : This, I think, lends more support to the beautiful theory expressed by Miss Sabatina; namely that if Peter has learned to swim then he has also learned that it's boat-loads easier without the coat; so, given that he put his coat on, it's even more likely that he isn't swimming!

Tuesday, July 2, 2013

Borrowed from a real poet

JUNE 26, 2013

By parody of Holy Mass
A building made of steel and marble
Has been altered into paper
Let the lawful tremble

So that the rain that soon will come
Will cause it to disintegrate
A sodden mass instead of stone
Starting from this date

When marriage was allowed to be
Celebrated by the demons
He and he or she and she

We have become the little gods
And parodies of holy priests
Who revel in the sullied flesh
And turn themselves to beasts

Pavel Chichikov


Have I mentioned before? I rather think I must have, for I know it occurs to me most every year, of late...

It's just funny the way the Church has decided to celebrate the Visitation about a week after the Nativity of St. John The Baptist. Clearly, the placement of this feast (celebrating an event which must have actually take place about two or three months ago) is not about chronology, while in contrast the Annunciation and John's Nativity and Christmas are very carefully coordinated with eachother.

It must be an echo of how Time means something different in Heaven; a different reflection of how, every Sunday we witness anew the Passion, and commemorate the resurrection in the veiled presense of The Resurrection. Ours is a profoundly poetic Church.

Happy Feast Day!

Saturday, June 29, 2013

All kinds of stupid

I'm in a mood. So... I dunno, ... pray for me?

If he that breaks a thing to find out what it is has left the path of wisdom, what shall we say of him who breaks a thing because he has forgotten what it was?

JRRT fan

Wednesday, June 26, 2013

There is no joy in Mudville

My dear neighbours,

As much as I am annoyed by the erroneous majorities delivered today, I am even more saddened to think of whatever ways the Superior Court of my own native Crown Realm, and its Prime Ministers and parliamentarians, have served poor example and made the day's transpirations at all easier.

frater tuus in fide

Tuesday, June 25, 2013

Homotopy Type Theory

Out in the strange world beyond the pseudonyms (or, actually, the realm of different pseudonyms, used by other people) there is noise surrounding a new book, a collaborative work, titled Homotopy Type Theory, to which I can (quite unreliably and unverifiably) claim to have made at least a moral contribution (and one blog post contribution --- no, I'm not telling you here!). And I don't at all mind that my name appears nowhere in the text, because really this sort of thing is more about the fun than the credit (also, two or four dozen other people made much-more substantial-and-original contributions anyway).

The text is subtitled “Univalent Foundations of Mathematics”, which is really a much more interesting notion than “homotopy type theory” as such, and it is about this Univalence that I'd like to sing for just a little while.

Now, for a long time, mathematicians of a certain kind have been competing with eachother to compose a sort of abstract semantics which might conceivably give an underlying meaning to all the abstract nonsense ordinary mathematicians do for a living. This might sound like a funny thing to worry about, but it's had immensely practical results in the realm of computer science and such, whether the dear fellows and dames intended it or not. It also might sound like chasing one's tail (indeed this is a danger that competitors of the sport learn early on to avoid), which is probably why Foundations is so emphasized in the name of the specialization.

Anyways, lots of people have composed such schemes of abstract semantics, and so modern mathematicians have lots of variety to choose from whenever they worry about if they're spouting absolute nonsense or merely incomprensible sense; and these do have some interesting distinctions among them — the best foundations are perfectly able to talk about all of the other foundations, and find some interesting things the other foundations say, and explain why they are all wrong. This is part of the sport, you see. Great fun! What settles a mathematician on one foundation or another (some never do settle!) involves a combination of aesthetics, pragmatics, and intuition.

Homotopy Type Theory is, roughly, a language for discussing (and perhaps describing) objects made of stuffs that are put together, somehow. This sounds vague, I know; but it isn't that the words “objects”, “stuffs” or “put together” are intrinsically vague, it's that the rules for using them haven't been made explicit here. They aren't the usual words (except “objects” might be!) but that's immaterial. But there are words, and rules, and the rules let you do enough that one can call the result a language, and even think it versatile; and that's half of what one has come to expect of a foundation these days. The other third and the final quarter are, respectively, some assumptions about what you can assert without comment, and how you decide what follows from which assumptions. (If you're worried that ½ + ⅓ + ¼ is ¹³⁄₁₂, you're paying too much attention).

The Univalence Hypothesis belongs to the third part, assumptions to be quoted without comment, and specifically makes assumptions about some particular objects one can mention, and specific details about how they are put together. In just a little more specificity, it supposes there to be a family of particular objects, called $\mathrm{Type}_j$, that the stuffs each $\mathrm{Type}_j$ are made of are themselves objects, and that every object is party to most of them, and (most importantly) each $\mathrm{Type}_j$ is put together in such a way that equivalence of objects-as-stuffs-put-together is equivalent to objects as parts of $\mathrm{Type}_j$.

That's still vague, because I still haven't written here what the things mean, nor do I intend to, but an illustration might help.

Suppose a pair of twins shared a pair of identical bicycles. Now, the twins know eachother apart from themselves, and the bicycles certainly aren't in the same place, but in our imagination “identical bicycles” really does mean the twins can't distinguish the bicycles by sight, and because they're good detached Catholics they also have no inclination to fight over who is on which bike, and so There Are Two Ways for twins to mount and ride their bikes. The left-hand supposition of Univalence (and our experience in the world of the senses!) is that there is a path, or choreography between these two configurations: twin first-to-breathe and twin first-to-say-“ma!” (if this lists them all two) can dismount and walk around and effectively trade places. The right-hand supposition of Univalence is that there is, effectively, exactly one way to do this and one way to not; and this is where Univalence and the world of sense part ways, because there is no way to exhibit such a simple figure in our paltry three-space-less-one-time dimensions. But the key idea — having exactly one way to switch and one way to not-switch — generalizes in a beautiful and poetic way, and leads to all sorts of other beautiful and poetic equivalences, to say nothing of many subtler rhymes it gives rise to. For instance (one of my favourites!), there is a circle of ways to be the order of the integers. This notion of equivalence, identified with “identifiability”, is the key novelty proposed in Univalent Foundations, is the organizing principle of the book, and makes for some fun thought exercises too.

There's lots lots more (of course! we'll never be finished) and this wasn't ever meant to be a math 'blog, however fun maths is; so I'll leave off there, and if you want to go read more about it elsewhere, perhaps we'll meet again by other names and in other guise.

à bien-tôt!

Tuesday, June 11, 2013

To The Editor, or Worth doing? Then, even badly...

Dear Sir,

Oh, how the spheres do buzz some time; this cannot have been what Pythagoras had in mind...

Disclosures perhaps relevant to your weighing of what follows: I, a gent in hope if not indeed, have sometimes been described as "dapper", yet I own but two pairs of trousers and just enough of the other things to get through a week between launderings.

On the subject of appropriate garb: it is my considered opinion that civilized folk should wear clothes. That is, they should be clad. Beyond that, being dressed is all well and good in moderation and if suited to the job in hand. Being merely ornamented or sculpted are not at all the thing, should you be not actually made of maple or marble. Let's just leave the subject of swimming well alone.

a poor maths student

Sunday, May 12, 2013

Something that has lately amused and puzzled me

Why is it that, after The Man is received into a cloud, "behold two men stood by them in white garments"? Continuing,
"11 Who also said: Ye men of Galilee, why stand you looking up to heaven? This Jesus who is taken up from you into heaven, shall so come, as you have seen him going into heaven." Not that it is unusual for "men" to appear and disappear, in the Inspired Record of Salvation History (it might have been unusual in an absolute sense, but the Bible isn't about business-as-usual), and yet... Is it, for instance, possible that the eleven were in danger of lingering by the mount untill they sequentially keeled over for hunger and exhaustion? Why, for this very practical nudge, is it so conveniens that it be delivered by angels and not Our Lord who, really, was just right there. And what about their non-question interjection: "[he] shall so come, as you have seen him going"; is this advice to them, and how is it not the answer to their own question, "why stand you looking up to heaven"? I presume they were angels, for Peter and James and John would recognize Moses and Elijah, and Luke would have said so if it were them again.

These are some things that lately have puzzled and amused me.

Any thoughts? (please limit your comments to less than 1 megabyte in size)

Wednesday, May 8, 2013

Troubles with Scientism and Antiscientism

Oh, for the good old days that never were...

Have I ranted here before about the silly slogan "gravity is just a theory"? To sum-up (too much to explain), it revolves around (hee!) a confusion of "theory", "hypothesis", and "observation".

Today in my book of faces arises a photo impression of a "science" "quiz" titled "Dinosaurs: Genesis and the Gospel"; the keeper of the books of faces have tried to make it difficult to circulate this thing, and the circulator (not circulants) is doing her darndest to get around (are we talking in circles, yet? It's not intentional) such frustrations.

The trouble with the Scientist is that, while fighting the antiscientist, she thinks she is fighting something to do with "religion". But religio ("I bind together", man to God, men to men) has very little to do with the D:G&G "science" "quiz"; it is rather a work of superstition (on which the OED says that its etymology is confused, but may have something to do with a soldier pointlessly standing over a defeated enemy).

The particular superstition of the Book-Literal antiscientist is that God's Creation ought to fit in a book; there is a similar kind of scientistic superstition as well that the Universe ought to fit within Creation, but... why, under Heaven, anyone would take the name of Christ and insist that God made Creation a small thing, a humanly brief and fleeting thing... as though He wouldn't be large enough anymore if the Past and Future didn't fit within human history... For instance, it is abundantly clear that the people we hear about who breathe the air and speak and sing to the Lord a new song do not flee, as it were a shadow, neither is alles Fleisch es ist wie Gras, und alle Herlichkeit des Menschen wie des Græses Blumen — das Gras ist verdorret, und die Blume abgefallen. We are (in a litteral sense) rather more long-enduring than grass and flowers, if not more permanent in body. But that's not the point of the Book!

How often have I lamented (in other words) that the difficulty in talking with the world is that the world has forgotten how to talk? And there's something about that in The Last Battle...

Anyways, this is, I suppose, one of those letters-to-nobody... I wonder who will open it?

a Christopher

Thursday, May 2, 2013

Brief and Minimally Considered

  • I have this hour run across MyJetpack
  • There are many ways to work stale bread into sweet pudding. At least two involve eggs.
  • The american robin, it seems, is a relative of the thrush. I haven't seen them eating snails; but then it's been a while since I saw wild snails. Perhaps in later in the season.
  • Have you before considered use of "the" to treat as gramatically definite a fictitious generic creature, as in "The american robin..."? These things amuse me!
  • I'm starting actually to get tired of this friendly web-logging thing; the gimmick isn't holding up and very few people ever say hello; and that's OK. At the tmbl (which I'm using in a most-untmbly fashion, it seems) there is still the fresh focus of my academic speciality, which might keep me going there longer in spite of even fewer people saying hello, but this... One of my early inspirations-unto-blogging did recommend it as a way to make acquaintances, but I've made more from reading than from writing, and that one also doesn't 'blogg any more that I know of. And that's OK, too...
  • TeX-setting diagrams is tricky, but you can do it incrementally. One day MathJax will pick up XYJax and then we'll all be that much more impressed with everything.
  • Six is enough, I think. Don't you?

Sunday, April 21, 2013

Who has seen... ?

Fr. C. gave an awesome sermon today, on the Lord's being seen and not seen
Modicum, et non videbitis me...
This is what happens on the Third Sunday After Easter, in the Extraordinary Calendar. Fr. brought out something of the mystic sense of see and shall not see: already before the third hour, one of the twelve is in spiritual despair and ten more have fled, unable to see the Present Divinity.

It brings to mind one of the recurring motifs in John's Gospel: from time to time, one or another heap of people sought to stone Him or make Him king-of-the-narrow-land, “... but Jesus hid himself... ”; and now He is telling the Twelve that something like that is about to happen to them, if only for “a little while”. Hearing this, they do not hear.

There is far too much here to say, so I shan't. Take a break and read the thing. Start early: context is like a good neighbour.

Saturday, April 20, 2013

Natural Law really is prior law and superior

First Things is, of course, a mixed bag, as are well-nigh all human efforts; but this one seems solid and sound, easily up to its cautious aspirations.

The thing reminds me of a moment at... actually, I'm not sure when. Something to do with Halbardiers and English clerics or would-be-such of some sort... Guy Crouchback in something of a lightened state urges the other fellow "... but surely, wouldn't you say the supernatural is actually the only really natural thing there is... ?" to which the other responds "Up to a point...", which is funny both if you've also read Scoop and also because Guy really is closer to true things here than he usually is elsewhere.

Anyways, have-at-'em; Happy spring to you, from a land of blowing snow and hail.


I'm sure it's terribly amusing; 'twas 22℃ just yesterday

Saturday, March 30, 2013

Happy Easter!

D'you all remember that about a merry Lent? On review, there's plenty more I could have done with this Lent, and been happier for it, but right now it is Easter and I feel as happy as a fellow can who also feels as weary as... goodness me, there isn't really a good reason for my feeling weary (none but that one of you good friendly folk will know better), so I shan't complain, nor brag. Must get to sleep now, or my voice won't have recovered from Vigil enough to be any use to the schola at noon.

Happy Easter!

Thursday, March 28, 2013

Let it be recorded

... that on this day, your humble anonyblogger tossed aside Shakespeare and his own advice, and wrote and pasted a poste intending to make mockery of ... well, something silly and stupid and intending evil and having its origin in unreason. On its own terms. I now doubt me of the advisability of this kind of disputation, and will instead wish you all a blessed Holy Triduum. May the Passion of O.L.I.C console and ædify us all.

Friday, March 15, 2013

A Moment of Philosophy

Dear Benvolii, dear Benvolia,

There's a certain something... I don't know how it gets into any particular heart or head, but it certainly drags one to that hole out of Creation that started with the Fall... and when things Momentous or Important or Notable or even just Noisy occur it can bring the tendency to the foreground in many of its sufferers...

Some people just don't want to be happy. That is the only explanation I can think of for it. I pray they may not suffer this unwill forever, but there it is. The unwill to be happy meets occasions and expressions of joy with excuses against becoming cheerful, with false praemonitions of madness and delusion in their fellows; as it were, the unwill to be happy seeks to be contagious, except that unwill cannot properly be said to seek, as it is not a thing but an evil, a lack.

Not being one of these, and fervently wishing that none of you reading this will become such for having read me, I shan't display any particular examples of these cracks-in-what-is, and I'm sure you all can think of what I mean anyways. Rather, I will recall that oft-sung, most singable Will, that you may know what to do when you come accross such gloomy folks:
Sigh not so, but let them go,
And be ye blithe and bonny!

May I have the honour to remain,

yours in mirth and no matter

Wednesday, March 13, 2013

This One Is Different.

Do You Realize??? It's the very first time from æternity that, D.Nos. Georgius S.R.E. Cardinalem Bergoglio has ever been elected Pope. And I don't believe it'll ever happen again!

I think it's also the first time the Cardinals have elected anyone baptised under the patronage of St. George.

Ad multos annos! Hooray!

Sunday, February 17, 2013


It is a fascinating thing that the introit, gradual, tract, offertory, and communion verse for this* First Sunday are the psalm sifted by the Devil at the second temptation in today's Gospel text; indeed the tract has almost the whole thing (which some tell us used to be the norm). Jerome's translation, which is not quite the ancient text of the Missal (just think of that!) has
1 Qui habitat in abscondito Excelsi in umbraculo Domini commorabitur
2 dicens Domino spes mea et fortitudo mea Deus meus confidam in eum
3 quia ipse liberabit te de laqueo venantium de morte insidiarum
4 in scapulis suis obumbrabit tibi et sub alis eius sperabis
5 scutum et protectio veritas eius non timebis a timore nocturno
6 a sagitta volante per diem a peste in tenebris ambulante a morsu insanientis meridie
7 cadent a latere tuo mille et decem milia a dextris tuis ad te autem non adpropinquabit
8 [verumtamen oculis tuis videbis et ultionem impiorum cernes
9 tu enim es Domine spes mea Excelsum posuisti habitaculum tuum
10 non accedet ad te malum et lepra non adpropinquabit tabernaculo tuo]

11 quia angelis suis mandabit de te ut custodiant te in omnibus viis tuis
12 in manibus portabunt te ne forte offendat ad lapidem pes tuus

13 super aspidem et basiliscum calcabis conculcabis leonem et draconem
14 quoniam mihi adhesit et liberabo eum exaltabo eum quoniam cognovit nomen meum
15 invocabit me et exaudiam eum cum ipso ero in tribulatione eruam eum et glorificabo
16 longitudine dierum implebo illum et ostendam ei salutare meum
From the Vulgate
For comparison,
Qui hábitat in adjutório Altíssimi, in protectióne Dei cæli commorábitur.
℣. Dicet Dómino: Suscéptor meus es tu et refúgium meum: Deus meus, sperábo in eum.
℣. Quóniam ipse liberávit me de láqueo venántium, et a verbo áspero.
℣. Scápulis suit obumbrábit tibi, et sub pennis ejus sperábis.
℣. Scuto circúmdabit te véritas ejus: non timébis a timóre noctúrno.
℣. A sagítta volánte per diem, a negótio perambulánte in ténebris, a ruína et dæmónio meridiáno.
℣. Cadent a látere tuo mille, et decem míllia a dextris tuis: tibi autem non appropinquábit.
℣. Quóniam Angelis suis mandávit de te, ut custódiant te in ómnibus viis tuis.
℣. In mánibus portábunt te, ne umquam offéndas ad lápidem pedem tuum.

℣. Super áspidem et basilíscum ambulábis, et conculcábis leónem et dracónem.
℣. Quóniam in me sperávit, liberábo eum: prótegam eum, quóniam cognóvit nomen meum.
℣. Invocábit me, et ego exáudiam eum: cum ipso sum in tribulatióne.
℣. Erípiam eum et glorificábo eum: longitúdine diérum adimplébo eum, et osténdam illi salutáre meum.
Mass Propers, extracted from the Una Voce of Orange County pdf
I'm sure that Holy Mother Church has something quite urgent in mind in giving us these consoling words to contemplate so frequently on this day when She remembers a great slander and calumny against them, and The Word's triumph over these slanders. Rather than suggest what specifically that might be, I will simply echo the thought that you should contemplate them, too.

I do have one little textual theme to clamor on—not greatly important, but it caught my mind, so you see that rehersing the chant the day before has great advantages—and that is in the sixth versicle, "A sagitta volante..."; Jerome's translation from the Septuagint (... I think?) speaks of "peste in tenebris", while the Missal has "negotio ambulante in tenebris". This "negotio" is remembered in the English word "negotiate", which describes a process between two or more persons suggesting various things to eachother, as long as the other says "no, no, no", or in Latin, "nego, nego". The "negotio" itself is translated by the Douay-Rheims/Challoner as "business", but whatever may be so pestilential about shady business that it fits in this Psalm... on the other hand, a temptation by the Devil who would have God deny God to worship his darkness, that sounds like a negotio indeed. An offer that must be refused; but forget not that to refuse evil is properly to affirm The Good.

*... which may well be yesterday...

Sunday, February 10, 2013

the Merry Quarantine to Come

What ought to make us sorrowful, of course (and which really does, though for specks and planks we often cannot see it) the state of sin. Beatitude is met through the narrow path that connects these leading lights: the knowledge (a good thing) of sorrow's nature (also, from Creation, good) as the warning about sin. Follow that narrow path to safe harbour! "Rend your hearts, not your garments", and if I do, then the divine surgeon can make a new heart in me. Goodness knows, I need it. If doing these things also makes us happy, then rejoice! (For, of course, you already are!) I write this becase:

That Dame Who Would Be Saturday warns us against Brian Brother Blessed.

Actually, no, the Public Service Announcement warns us that Ash Wednesday is Coming. Like, this week. Or, as the web-log-writer known only as sibi (self-publishing under the tautological "me", and who would appear to appear (don't forget yours truly) cat-like) put it, Happy Quinquagesima!

OK, most everyone in the world will read this not before the feria primum thereof (it already is, here), but all the same […]. Or, perhaps, even more so! In any case, such is the furthest extent of announcements in the public service legible in Miss Hebdomada's note, after which she proceeds to luxuriate in heresies the good scriptrix has previously written against. Obviously, it is all in good fun. As is all of this!

But, really, who ever said that Lent should make one gloomy? (Come to that, who needs Lent before they are gloomy?) That sounds like entertaining sloth, which obviously is willing to wrong, which is itself wrong. So! Remember:
$$ \frac{\vdash \mathrm{Prosecco}}{\vdash \diamond (\mbox{God loves us and wants us to be happy})} $$
with, of course, Uncle Gil's caveat that the prosecco is for when you're already happy.

Since the Season of Lent is a gift of God through the Church, it is clearly a means to our happiness, and any suspicion of duplicity in the shape of anticipated happiness before any good act is done is a diabolical distraction from which you should now distract yourself, say, with some Shrove Tuesday festivity.

Strange Isoperimetry

Here we see a triangle constructed with all three sides tangent to an external circle. Because the solid and dotted blue segments have a common point and are bounded by tangencies to a common circle, they are the same length; similarly, the solid and dotted red lines have the same length; therefore the perimeter of the triangle is equal to the sum of the segments between the apex (of cyan and magenta) and the external tangencies --- which two segments are also equal; in particular, the perimeter is determined by the apex angle and the circle radius.

By way of a converse, the envelope of triangles within fixed rays (as the cyan and the magenta, continued away from the apex) and having a fixed perimeter is a circle arc tangent to those fixed rays at a distance of half the fixed perimeter from their intersection.

Friday, February 8, 2013

From beginning to end, but never mind the middle

Dear Ludwig...

Something that seems to have made an impression on me (it was some years ago now), I stepped into the family van to ride from Grandma's to Our House, and via radio caught the finale of what was, for me, a frustrating symphony to listen to, though I'd never heard it before. It sounded like a young, energetic composer whose only knowledge of orchestral music was late Beethoven symphonies. There were simply too many ideas, and they all sounded too familiar --- this motif, that's definitely the 5th, and there goes 3rd of Chorale, and now back to Pastorale we go...

Dramatic finish, just like the end of... oh, now I can't remember which. The kindly announcer lets us know.

It was Beethoven, of course. No, not a patchwork, but original Beethoven; the First symphony. Young, energetic, and easily too many ideas. But, it seems, he went on to work out a great many of them properly!

... the Audience

Monday, January 14, 2013

An imagined dialogue.

Isc (silently): That... that sounds like Jacob.

Θ: It is Jacob.

Isc: Why is Jacob pretending to be Esau?

Θ: Rebekah's got him all worried up about how our blessing Esau would turn out for him.

Isc: Good Lord, I smell Esau's shirt.

Θ: Yes, and that's not all!

Isc: ... goatskin? Does he really think I can't tell the difference between my son's hands and my goats? I thank You that it isn't raining.

Θ: Indeed, he really thinks to have drawn the wool over your eyes, as it were.

Isc: So, what do I do now?

Θ: You will have to recite the blessing from the other side. It is too bad that neither of them will understand until... well, I still have my plans for them.

Thursday, January 10, 2013

Sounds like a bit much?

Dr. Thursday, that flower of a papist and programmer, writes

I have just written the LARGEST piece of source code I have ever done in my entire life. The source code measures about a quarter of a gigabyte, and yes, that does include comments. In fact, one routine probably exceeds all the source code I have ever written, in my BS, my MS, my PhD, and over 30 years of industrial software development.

And even nicer, it is provably correct... the acedemics would drool at that.
So I did a silly little test: for twenty-seven seconds I typed out as quickly as I could an easy-to-think-of sequence, "one two three four..." and it came to 110 bytes, including some errors. At such a rate, without sleeping eating or other dull interruptions, it would take about two years, I had my machine tell me, to produce a quarter of a gigabyte. I actually don't think I could tolerate more than a couple hours of just typing on just one thing in any given day, so that forty years is a more reasonable estimate.

I can only imagine that something of the project involved an automation of the code-writing process; that would not only make the typing go swifter, it would also make the proof-checking simpler for, if you are careful, you can be sure that your helper-program only outputs correct code! Now, the Doctor assures us that his programs are doing something... something for him, though I'm quite ignorant as to what, except that one of them I'm pretty sure is writing the last of them.

Now, I don't really know why Dr. Thursday insists on having such a huge program to do I-don't-know-what, because there's a much shorter program that will do everything. Yes, everything. Well, given infinite space to work in, it will eventually do everything that can be done by an ordinary computer in finite time. It's called algorithmic search and takes about $n^2 \log(n)$ steps to run the first $n$ programs about $n$ steps each, unless they stop first. Now, admittedly, this is something of a blunt-force weapon, much like proving Wiles' Theorem That Settled Fermat's Last Puzzle by listing all the proofs possible. Now that we know it has a proof, we know you'll get to a proof eventually, but whether that happens before the next big crunch I don't know.

But, there it is.

Sunday, January 6, 2013

Oh, Hello!

Hello, blog!

Hello, post editor;

Hello, comment form;

Hello, archive;

Hello, saved drafts (not today, though, not today...);

King John was not a good man
He had his little ways...
... blockquote;

Hello, included maths, as
$$ \mathrm{Hom}(\mathrm{Ind}_H^G R, S) \simeq \mathrm{Hom}(R,\mathrm{Res}^G_H S) \tag{Frobenius} $$
for instance;

Hello, names of regular readers, and the odd passers-by;

Hello, actual readers (because it's personal!);

Hello, New Year and Epiphany!

Who knows what'll happen? God alone. Bless you, all.