Thursday, October 2, 2014

H - S - H

Dear All,

It's been grand, even if I have not. Yesterday Dad was kind enough to drive me back to Hometown Suburb from Metropolitan, for perhaps two months, perhaps more, with the object of doing "nothing but research" (which I can never seem to make feasible over there, and still less so since TA appointments dried up over the Summer). And So.

Write to qnoodles at google's free mail service if you like, and keep thee well.

The Bat

Sunday, September 14, 2014

Happy Feast Day

O crux viride lignum quia super te pependit redemptor rex Israel; O quam dulce lignum, quam dulces clavos, quam dulcia ferens pondera; O quam pretiosum lignum, quam pretiosa gemma quae Christum meruit sustinere.

and also

Vexilla regis prodeunt,
fulget crucis mysterium,
quo carne carnis conditor
suspensus est patibulo.

Confixa clavis viscera
tendens manus, vestigia
redemptionis gratia
hic inmolata est hostia.

Quo vulneratus insuper
mucrone diro lanceae,
ut nos lavaret crimine,
manavit unda et sanguine.

Inpleta sunt quae concinit
David fideli carmine,
dicendo nationibus:
regnavit a ligno deus.

Arbor decora et fulgida,
ornata regis purpura,
electa, digno stipite
tam sancta membra tangere!

Beata cuius brachiis
pretium pependit saeculi!
statera facta est corporis
praedam tulitque Tartari.

Fundis aroma cortice,
vincis sapore nectare,
iucunda fructu fertili
plaudis triumpho nobili.

Salve ara, salve victima
de passionis gloria,
qua vita mortem pertulit
et morte vitam reddidit.
Venantius Fortunatus, Episcopus Pictaviensis

Monday, September 8, 2014

What a Thousand Looks Like

Usually, multiplication is about generalizations of the relation between areas and lengths; but it can also be accomplished by nesting or iteration, which is sort-of how multiplication gets implemented in Alonzo Church's Lambda calculus and also in polymorphic type theory as the natural transformations
$$ \mathbb{N} = \forall X, (X\to X) \to (X\to X) $$
and so on...

Anyways, Paul collected some hyssop seeds
and expressed some interest in how many plants that makes.

So, just for fun and perhaps for reference, here are $ 1600 = 10 \times 10 \times 4 \times 4 $ black squares arranged in a square of squares; something between one and two thousand. Note that you can probably see the spaces between the squares. Note that you can't see the spaces between most of Paul's seeds.

This kind of visual counting can add interest to films and historical photographs involving well-organized collections of people and all sorts of other things.

There are easily two thousand people watching, from the further stands, looking at us

Another way to think about it: your fancy camera today probably boasts some megapixels per photo; which means you could capture a thousand people, dedicating a few thousand pixels per figure, with a camera you then hide in your pocket. If they'll sit still long enough.

Thursday, September 4, 2014

Truth in art

Pay attention in the first twenty seconds!

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

The traditional annual note

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.