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!