Monday, August 18, 2014

Timing! (?)

So, a couple years ago I registered my amusement on the timing of the feast in Visitationis; recently it also occurred to me that the Church really likes the completions of things, consummations and perfections; this is why MOST of the feasts are "birthdays" in coelis, what look to The World like deathdays... anwyays, "the week after John's (ordinary) birthday" turns out, on reflection, to be an excellent day for a feast, being as it is the Octave Day and hence the day Zachary took tablet and style to say "his name is John" and then sing the Benedictus. A fine occasion to mark as the completion of what Mary traveled to visit her cousin for to accomplish!

So there, slightly-younger-me, take that!

Also, slightly-older-me, don't be puffed-up, you might think this note rather funny, some day.

Tuesday, August 12, 2014

Rebuke from Heaven

Today, it would seem, St. Louis Marie Grignon-de-Montfort accused me of "intellectual pride", and counted me among
numerous puffed-up scholars, conceited with critical spirits who have plenty to say against the best established and most solid practises of piety,
and then he suffered our poor benighted congregation the condecension "not to give them needless occasion of criticism".

Oh! The sting! But I'm going to try, ad experimentum as it were, to be shaped by the sting and see what comes of it.

Oremus pro invicem

Sunday, July 20, 2014

Symbols

Aren't symbols amazing things? One can make an abstracted thing (a gesture, or a sound, or a mark) and indicate to a watching, listening, or reading soul at some remove what is going on in one's own soul! That other soul can perhaps then act on what they learn by these symbols! Another interesting feature of symbols is their sensitivity to context. When The Lord through Moses ordered the Passover meal in preparation for the Exodus, He had them write on their doors
the first letter of the word
חי
which signifies “living”, from which was Eve's name; but to their neighbors the slaves of the gods of Egypt, this “life” was written in the blood of lambs, and looked like death. A “sign which shall be contradicted”, if you will.

So (I am told) some bloodthirsty folk in another end of the crescent have taken to abbreviating “Nazarene” on houses they suspect of holding devotees of ... you know. And sorrows follow, gloriosa in conspectu Domini...

We could outdo them in symbols, of course.

Sunday, July 13, 2014

Irrationally contented in this vale of tears

I enjoyed one of my not-too-significant, probably-unimportant, nonetheless-delightful little mathy revelations a couple days ago, which followed on “remembering”, as Plato/Socrates would call it, that natural constructions tend to be functorial; and the result was
\[ \Sigma \varphi = \Sigma \vartheta \vee \vartheta\star\Omega\Sigma\vartheta \]... and now I must apologize, for mathematician is usually working at the top of a large wobbly stack of definitions and usually can't even see the one two or three layers down...
  • A Cateogory, as the mathematician intends it, has a collection of objects, and possibly a collection of relations between pairs of objects, and an operation of composing adjacent relations between three objects, and... stuff. For instance, you might have the family of human languages for objects, with translating dictionaries as relations between them. If you have a french-english dictionary and an english-italian dictionary, you might attempt to compose them into an experimental french-italian dictionary, and this might have suprising consequences!
  • Functors are the natural relations between categories that give you a “category of categories”; A functor connects objects of one category to objects of the other, as well as connecting relations between objects to relations between respective connected objects --- but because of the echoing clearly heard in “category of categories”, there are furthermore relations between functors with the same origin and same landing ...
  • A construction “being functorial” is an informal way of saying: we first thought of it in terms of the objects of some category, and then realized it related to the relations between the objects as well; more echoing... we like echoes.
And that's what happened through Friday; a construction I usually think of only in terms of objects (homotopical figures), I recognized anew was also realized on relations between them (continuous maps).

Anyways, these weird socratic-recollections congealed into something mathematically-writable after I joined an impromptu schola for to sing a Requiem Mass for Fr. Kenneth Walker — it seems he once attended school with some of my neighbors, before I or they moved in to town. It was a beautiful sorrow, and a beautiful evening, and a remarkably uncongested ride home with the choirmaster's wife as the full moon was rising.

All you out there, keep well; I hope to be back again next Sunday, too.

All honour to Mother Mary, and all Glory and Praise to God the Holy Trinity be; animae omnium fidelium defunctorum, misericordiae Domini, requiescant in pace.

Saturday, July 5, 2014

Adventures II

For the Desk of J. Herriot, VD.

This one is all-narrative. Almost entirely unrelated, so far as I know, except for me.

On the way out from the grocery, I met (as you do) a little dog tied to one of those movable polished steel advert holders they keep near the door so that you're primed for the "deals" inside... a very loud but nonetheless friendly little dog. I said "hello" and smiled, and off I went.

I had almost got to my bike to tie up the prizes of the night and travois them home, when: CRASH! And after looking back to the door I'd just left, after some seconds incomprehension, it dawned upon us waiting for whatever that said little excitable dog had pulled over that advert frame, the automatic door had obligingly opened and let him out, and the little dog was either barking at or trying to run away from that scary loud heavy shiny thing that seemed to be holding him.

One of us tried to untie the leash and right the frame, while I apparently crouched down and tried to soothe the dog. Great job I did, he wriggled himself out of his harness and went on yapping! He wasn't in any mood to run far, though; wandering confused for a bit, he suffered himself to be picked up, and I was happy to return him to whoever claimed responsibility for the fellow. Said master was at least as glad to see him, and proceeded to tie him to a more-secure post of modest description (fixed to the pavement), quite outside the boxbuilding.

And we (presumably) all went safely home. But it occurs to me now I may have forgotten to return my shopping cart. Still, a happy ending!

one of the smaller creatures

Monday, June 30, 2014

Adventures

So my big brother drove up last week's weekend and then we went driving around, did some camping, visited long-lost-relatives; it was a good time.

Me playing some Bach for Detroit; in good tune, that piano!

Elder on my right (frame left) in Smalltown Somewhere

On the Sunday which was either Corpus Christi or within the octave of Corpus Christi,

Mass was here.
we were greeted on leaving Mass by two strange figures who, it turns out, are members of a network of local protestant communes that call themselves "the Twelve Tribes". Their openning question was "what did you hear, today?" and the easy answer was "the Gospel, of course". These two were part of a crew that go sailing about the world in a ship called "Peacemaker", which is a delight to behold. Bless the lot of them, whether they like it or not. I wish I had thought to tell them that Mother Church is a ship, too, indeed an Ark, the Barque of Peter.

It just makes me a bit sad that they seem to be holding themselves outside both the Sacraments and the living memory of the Church. They claim that they take their "rule" (though they don't call it that) from Acts 2:44-45, and so I want to tell them the story of St. Francis of Assisi and how he tried to compose his rule of Gospel verses when he sought papal recognition for his order; I want to tell them of the Bégin communities in France and such, so they can study why they don't seem to have prospered; I want them to have a good shepherd under the Good Shepherd. I hope they may be good, all of them.

Now I must dive back under the conjectures and puzzles. Like, suppose
\[ \mathbb{S^1}\overset{2}\to\mathbb{S}^1\to P^2 \] is a cofiber sequence, so that \[ \Sigma P^2 \overset{2}\to \Sigma P^2 \to P^2 \wedge P^2 \to \Sigma^2 P^2 \] is also a cofiber sequence (this also shows that the second "$2$" is not trivial!); there ISN'T a map $\Sigma^2 P^2 \to P^2\wedge P^2$ that factors the identity, but there might be one that factors the next "$2$". If there is, is it useful?

So, see you perhaps next Sunday again!

Sunday, June 15, 2014

Identity, reference, address; praise, worship, life

So, there is from events last Sunday, a flurry of debate going about whether a certain close family of doxopraxical cultures is doing something reasonably similar, in a similar direction, to what the Catholic Church does. In particular, there is a resurgence of argument among bloggy Catholics, whether the Divinity is in partwise known to members of the cultures of this close family, and whether they render Him worship, or whether they perhaps worship another.

One argument proposed in favour of identity-of-referent between God the Holy Trinity and whomever it is our estranged-in-faith neighbors worship is the commonality between our respective first credal formulae: Credo in unum Deum and There is one god ... (I beg your pardon, I do not read or write or understand the language of the source text, and rely on others' translations). The argument proceeds: since we both assert there is only One, they must be the same one. It echoes (or perhaps is echoed in) something from Zen and the Art of Motorcycle Maintenance, (and now I must kick my mirror for that I can't find the book and don't trust myself to quote from memory — if you've read it, you'll know what I mean); whether or not the argument works... I am suspicious, of course. My mathematical training has taught me to be suspicious of claims of identity. Certainly, if the category spanned by Holy Trinity and the subject of our strange neighbors' worship indeed contains exactly One, then that One is both our God and their one-and-only-god, but this is begging the question. Heck, there's exactly One of me, and no-one would ever suggest that I and He are the same One!

Even more suspicious am I of claims that a list of properties is useful for naming something. That might sound strange, but my stockroom bad example is
\[ \lim_{x\to\infty} \sin x \]
The $\lim$ part of the expression means we are trying to pin down a number by its properties. If there is such a thing, then (by defining properties of $\lim$ in the relevant context) there is exactly one; but that doesn't tell us that there actually is such a thing. It so happens, indeed, that there isn't. And the absence of such a thing is even deeper than the strange-looking expression $\sqrt{-1}$! But I digress.

However, I particularly want not to say that these neighbours of ours are entirely lacking in reverence for the One, True, Creator God. There are one or two long prayers these our neighbours say in a particular context which we as Christians could most fittingly recite with sincerity and devotion, given a suitable understanding of all the words (which I learned from Robert Reilly who also writes about music). I think I want to move the question away from one of whether we and they worship the same God, but whether we both worship the same God.

Consider,

3 Time passed, and Cain brought the Lord an offering out of the crops the land had given him; 4 Abel, too, brought an offering, and his offering was out of the first-born of his flock, with their fat. On Abel, and on his offering, the Lord looked with favour, 5 but not upon Cain, or his offering; so that Cain was much enraged, and his looks were lowering.
Can it be doubted that Cain and Abel both sought favour of the One God, by means of sacrifice? Or can it be doubted that in one was found acceptable worship, and in the other was not? And so a more interesting question is: what sacrifice do our neighbours offer? And can it be pleasing to God?

From the other end of our revelation,
21 Believe me, woman, Jesus said to her, the time is coming when you will not go to this mountain, nor yet to Jerusalem, to worship the Father. 22 You worship you cannot tell what, we worship knowing what it is we worship; salvation, after all, is to come from the Jews; 23 but the time is coming, nay, has already come, when true worshippers will worship the Father in spirit and in truth; such men as these the Father claims for his worshippers.
Note! it is implicit in the language here that worship means sacrifice; for one can pray and sing hymns to God anywhere, but for sacrifice one must have an altar, and the Jews had one altar, in the Temple in Jerusalem, within hearing of the Ark (originally) wherein dwelt the presence of God! But our Lord turns aside the issue of place, letting it give place to truth, which is the matter for contemplation and the object of study. But of the Samaritan he says: "You worship you cannot tell what". One needn't read it as saying "what you worship is not God", but it does cut between the worship and the truth of it. Whether or not the god of our neighbours is our God indeed, they most of them would deny that one can or should try to know God himself. If they nonetheless, without the Church and Her Sacraments, without knowledge or understanding, give worship to the Father in Spirit and Truth, it seems to me it is by God's own grace, and not the doxis or praxis of their culture. I can't believe that it is always so, but I cannot say that it is never so.

A blessed Trinity Sunday to all of you,
cantis amator