## 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