Thursday, August 30, 2012

An Unfounded Conjecture

Dear Philosophia,

Recall the curious event of Genesis 11:1-9.

1 And the earth was of one tongue, and of the same speech.
2 And when they removed from the east, they found a plain in the land of Sennaar, and dwelt in it.
3 And each one said to his neighbour: Come, let us make brick, and bake them of stones, and slime instead of mortar.
4 And they said: Come, let us make a city and a tower, the top whereof may reach to heaven: and let us make our name famous before we be scattered abroad into all lands.
5 And the Lord came down to see the city and the tower, which the children of Adam were building.
6 And he said: Behold, it is one people, and all have one tongue: and they have begun to do this, neither will they leave off from their designs, till they accomplish them in deed.
7 Come ye, therefore, let us go down, and there may not understand one another's speech.
8 And so the Lord scattered them from that place into all lands, and they ceased to build the city.
9 And therefore the name thereof was called Babel, because there the language of the whole earth was confounded: and from thence the Lord scattered them abroad upon the face of all countries.

Because it is fun to conjecture, I have concocted me a conjecture upon the manner in which God did thwart the city planners of Sennaar:

Wednesday, August 29, 2012

To Seek Out Prudent Truths

Dear Amavero,

Without pretending to really know what is best, I would at least offer hope that some good thing may be found, "by dint of trying", as St. Jean Vianney put it (in a translation read me by Utrecht).

Sunday, August 26, 2012

A story of excellence for your Sunday or Monday

Dear amici, dear amicae,

Let's start near the end.

Thursday, August 23, 2012

Say, when was the last time... ?

Oh, hello, there!

I'm not actually here (that is, even less than usual), having written this about two weeks ago; but, well, anyways, today the atmospheric tropical cycle count clicks over the third primorial, a curious number: $2 \times 3 \times 5$. If you were counting on digits you'd need two ordinary humans including one pair of feet. Some of my family seem to be making much of this number; I'm still slightly less than half my mother's age, if only for a couple more weeks. Hobbit-wise, I'm still just in my tweens. Well.

Have a pleasant day, if by any means you can; I know I will!

PS. You know, people make much of how $2$ is the "only even prime"; well, that's not saying much --- it's the first positive even number; it is the standard by which all evens are measured. One might as well say that $3$ is the "only trial prime" and $5$ the "only quicuncial"... but enough!

Monday, August 13, 2012

About talking at cross-purposes

Dear Passerby,

One of the weird things about being a Humptydumpty Mathematician is that you very quickly get used to the idea (so quickly that you usually don't think about it) that the meaning of a word --- the signification of a symbol --- is essentially inseparable from its use.

Once we have this hammer in our grasp, we may go hunting for nails; let me pry some up and we'll see if it's in any way handy.

Sunday, August 12, 2012

Out of Mrs. C's Enchiridion

Let us recall


Here dies another day
During which I have had eyes, ears, hands
And the great world round me;
And with tomorrow begins another.
Why am I allowed two?
--Uncle Gilbert

And so I am reminded that it's much too long since I did one of these.

$$ \begin{array}{rl}
\mathrm{XXVI} &\mbox{All this crazy internet}\\
\mathrm{XXVII} &\mbox{Friends with excellent Common Sense}\\
\mathrm{XXVIII} & \mbox{Small towns just a train-ride away}\\
\mathrm{XXIX} & \mbox{The stars over cornfields}\\
\mathrm{XXX} &\mbox{Birthdays in the family}

Saturday, August 11, 2012

A House has an inside and an outside and a neighborhood

For the purpose of being well-understood, I was raised (though no-one ever mentioned it) not under the declaration that all men inherit the right to "life, liberty and pursuit of happiness", but rather in a realm which proclaimed "peace, order, and good government". Whether either of us now enjoys any of these goods is a question best left to future historians, perhaps, but never mind.

It would seem there is room for disagreement on the prudence of civil law recognizing the unique and preeminently worthy character of the free and total union of Man and Woman made concrete in the free and total union of one man and one woman coenduring with their common Earthly survival.

I recently highlighted differing opinions on this matter from two good and thoughtful Catholic fathers with whom I respectfully disagree.1 The one asserts that "the state [has to] define marriage and know who is married in order to answer two questions: who owns what and whose kids are whose;" the other affirms his belief "that [one] should not be prohibited from pursuing a legal union with whomever [he?] like, according to the beliefs of another religion or in the eyes of government."

Thursday, August 9, 2012

In prelude to some later-to-develope thoughts

Dear Moose,

Compare and contrast, two Catholic men who by their writing and thoughtfulness have much impressed me.

In the North corner, Darwin
In the South, John C.

Er... the cardinal directions cited here bear no relation to anything in the world of real; they're just meant to be different.

b.g. gruff II

Wednesday, August 1, 2012

Apocrypha Topologica II

Dear Mathematicelli,

If I may proceed,

The Cretan king Minos seems to have hit upon the psychological trick of bewildering his prisoners into imagining a topological obstruction where in fact the obstacle was only metric: that of the Labyrinth (with intimidating monster to keep you distracted). The solution that let Theseus escape the Labyrinth has found renewed popularity of late, and so is worth elaborating. Ariadne's reasoning might conceivably have run thus:

• If one enters the labyrinth and comes to its center, then one has got (and can get) from there to here

• Walking the same way backwards, one can get there from here

• What is wanted is some means to remember the path one took in getting here, and then to reverse it

• Since I don't know how long a path one might need to follow, the keeper of the memory had better be long!

In other words, we keep more information than just the fact that two points are connected by a path: we remember the whole path between them. Some recenter mathematicians more inclined to vandalism have suggested painting the walls of the labyrinth to remind yourself of where you have been --- which is sufficient data to escape, if you paratroop into the maze under cover of darkness; but the solution proposed by Ariadne and adopted by Theseus makes it easier to tidy-up afterwards: unroll a string as you walk along, and then follow it in reverse, winding the string again!

A point worth noting, which may have escaped Ariadne and Theseus in their flight, is that the re-winding and the follow-backwards phases of the solution can be performed in either order if only the string itself is slippery enough --- this could have been remarkably handy if the labyrinth had been under water, and had they wanted to get fish out of it without the fish seeing them and becoming suspicious. It also points out something special in the total path followed by Theseus through the Labyrinth: it is contractible!

Dungeons we may pass over, as well as the castle and siege warfare. Chain mail is about as old. But Somewhen between the Visigoths and Polyphony was discovered knitting. These, like most mechanical inventions, rely on metric phenomena to make their topology useful, but it is unquestionably their underlying topology that is used. (As a side-note, there's a lovely film-reference back to Ariadne in The Name of the Rose, where Adso returns his knit sweater to a trivial topology in order to escape a non-planar labyrinth! I'm curious how the Vandal painters would fare here!) If you'll forgive a jump-forward, the topologist Poincaré seems to have observed a woman knitting, and independently invented purling on the spot. I don't know what the full topological significance of that is, but the ubiquity of What Is certainly makes itself plain to those who can see it; for which give thanks to God, I think. About such other oddities as the Borromean rings we have remarked elsewhere.

I have no idea what's coming next; but this isn't a bad lot. We've more-or-less covered ±1800. Prof. Cauchemar