Of course, what with onion routers and all that, I can't really tell that pagerequests google believes to be originating in France actually mean the responsible client is actually located in France (traffic multipliers, aren't they funny?); since blogger stats don't include Internet Protocol addresses (not for me, anyway) I can't even be sure that it's really all one client fetching those pages. However. It just doesn't seem reasonable to suppose that ... thirty? ... frenchmen have been, continuously, for the last three days, looking at just the last four posts or so. Ockham, whatever may his issues have been, would rightly scoff at that notion.

Anyways, there we are! Bonne Journée et Bonne nuit, vous tous, et peut-être s'il y a entre vous deux ou trois vrais hommes, vous pouriez dire "salut", dans les commentaires?

## Wednesday, September 17, 2014

## 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,Venantius Fortunatus, Episcopus Pictaviensis

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.

## 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

$$ \mathbb{N} = \forall X, (X\to X) \to (X\to X) $$

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.

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.

*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.

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

## 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

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.

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

There's a nifty thing about primes — from Fermat's

*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

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

Also, slightly-older-me, don't be puffed-up, you might think

*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.
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