Tuesday, August 26, 2014

Guest Post from Beyond The Grave!

In what might just be a scoop over DuckDuckGo, I would like to share with you a letter which P. G. Wodehouse reports having received... he does not say when, but the return was Obuasie, which is very likely Obuasi in Ghana

Dear Sir,

I have heard your name and address highly have been recommended to me by a certain friend of mine that you are the best merchant in your city London. So I want you to send me one of your best catalogue and I am ready to deal with you until I shall go into the grave.

Soon as possible send me early.

I remain,
Yours very good truly.

And if anything in that sounds familiar, remark then to yourself that there is very little of novelty under the illumination of our fusion furnace in the sky.

Friday, August 22, 2014

Hm... 32, eh? That's $2\times 2 \times 2 \times 2\times 2$. Just for amusement, $3 \times 3 \times 3 \times 3 \times 3$ is 243, whereas Abraham himself only lived to 170. Two is a very odd prime, you know, the way its powers pack so closely together that way and other things...

There's a nifty thing about primes — from Fermat's little theorem $$n^p \equiv n \pmod{p} \tag{Fermat}$$ we have a factorization $$x^p - x \equiv x (x+1) (x+2) \cdots (x+p-1) \pmod{p}$$ which in particular gives $$(p-1)! \equiv -1 \pmod{p} ;$$ on the other hand, if $q$ is a composite number, then $q = p N$ for some minimal prime $p$ and some $N$ which is not smaller than $p$. That is, either $p = 2$ and $N =2$, or $2 \lt N$ ; in the first case, $p N = 2 \times 2 = 4$ and $3 ! = 6 \equiv 2 \pmod{4}$; in all other cases, we have one of $p \lt N$ or $2 \lt p = N \lt 2 p \lt 3 p \leq q$, both of which lead to $q = p N | ( q - 1 ) !$, so that the full repertoire of $( q-1) ! \pmod{q}$ is : $-1$, if $q$ is prime ; $2$, if $q = 4$; $0$ otherwise. The odd case out, $q=4$, highlights in a number-theory way just how odd the thickness of powers of $2$ really is. It also arises as a thing in my research, the natural operations in homotopy... but never mind that for now! It's my Birthday, and I think I'll have a sleep.

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

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