Minor amusement

I know I should use the time walking laps more productively, but I find it hard to compose in my head: I start a scene, but keep circling back to the beginning. Praying gets distracted too. So. Factoring numbers, anybody?

Everybody knows how to check if (in base 10) a number is divisible by 3: just add the digits, and if the sum is divisible by 3, so is the original. 9 is easy too: just add the digits, and if the sum is divisible by 9, so is the original. 2 is easy: is the right-most digit even? 5 is easy: is the right-most digit 0 or 5? 4 and 8 are easy to do sequentially, or you can look at the last two digits: if divisible by 4, the whole number is. The last 3: if divisible by 8, the whole number is.

Ah, but 7? Hmm. (Spoiler; there's a simple way to check, but I didn't know it then.)

If we've a number k whose digits are $N_n N_{n-1}...N_2 N_1 N_0$, where $N_0$ is the units digit, $N_1$ the 10's, and so on, we can write this as $\sum_i N_i 10^i$. That's trivial. Suppose we divide by 3, but divide each of the $10^i$ terms. For $i=0$ (i.e. 1), we have 0 R1. For $i=1$ we have 3R1, then 33R1, 333R1, etc. Now we have two parts: $\sum_i N_i 33..3$ (a nice integer) and a remainder of $\sum_i N_i (1) / 3$. The leftover part, the sum over the digits, determines whether the number is divisible by 3. OK, that's pretty simple, and proves that the old rule, which we knew already.

Dividing by 9 works the same way, except that the integer part after dividing by 9 is $\sum_i N_i 11..1$ with 1's instead of 3's. The remainders are also 1, just as before and the remainder term is also a sum of the digits, divided by 9.

How about 7?

i	$10^i$	integer	remainder
0	1	0	1
1	10	1	3
2	100	14	2
3	1000	142	6
4	10000	1428	4
5	100000	14285	5
6	1000000	142857	1
	etc

So, If you create the sum $1 N_0 + 3 N_1 + 2 N_2 + 6 N_3 ...$, if the sum is divisible by 7, so is the original number.

Granted, it's not as nice as the simple digit sum, but it works.

Before you ask, no, I only worked out the sketch of this on the track. I need pen and paper as much as the next person.

For those who have been snickering, yes, I looked this up and found the easy way too.

One way to think about the problem is to note that if you think of dividing the number into all the digits except the units digit, and the units digit, there'll only be 1 or 2 possibilities for the units digit for which the whole is divisible by 7. So maybe breaking the number up that way would be productive; maybe there's a simple relationship.

$k = 10 \times A + B$, where $B$ is a single digit. Now noodle around a bit: multiply by $5$. $5 \times k = 50 \times A + 5 \times B = 49 \times A + A + 5 \times B$. Part of that is obviously divisible by 7, so if $A + 5 \times B$ is divisible by 7, the original number is also. E.g. 4627 $4627 = 10{\times}462 + 7$, so $A=462$ and $B=7$. The formula says $462 + 5 \times 7 = 497$. Inspection says that's divisible by 7, so the original was too. Obviously you can use the formula $A - 2B$ as well. You'll find both easily on search engines.

Suppose we wanted to find a similar formula to tell us about 11. We need 2 digits for $B$, so we rewrite our number $k$ as $100 \times A + B$. Looking closer we see $100 \times A + B = 99 \times A + A + B$. Since 99 is already divisible by 11, we immediately see that if $A + B$ is divisible by 11, so is the original number. Check 7271: $72 + 71 = 143$, which is $11 \times 13$.

For 13, it isn't hard to see that $A + 3 \times B$ works: try it with 8593.

No doubt there are tables of these simple tricks somewhere

Yes, the church nursery posts a number in the sanctuary if a parent needs to come see to their child. And yes, I try to factor it.

Thinking about Rome

Roman values at ACOUP, hat tip to AstralCodex

The guardroom was one rod long and one rod wide

I have always found the temple measurements in Ezekiel 40-42 to be rather obscure. Why are these measurements supposed to be important enough to keep track of? They are clearly for a future or a possible temple, not one that existed then or since.

Revelation echoes this, with a twist: "Get up and measure the temple of God and the altar, and those who worship in it. Leave out the court which is outside the temple and do not measure it, for it has been given to the nations". That's suggestive: measurement relates to possession or ownership, perhaps? God owns it in the ultimate sense, but the temple is for the worshippers.

In Genesis there's a different kind of "measurement"; a measurement by foot, and one that puts Abraham in the place he/his is to possess. "Arise, walk about the land through its length and breadth; for I will give it to you."

I have no clue what the measurement numbers are supposed to signify in Ezekiel (if it's a physical future temple, why? in light of Hebrews 10), but I like the idea that measurement might signify "we are there." Measuring is something people do, even if is only "how many of us fit."

Black Mountain, NC

What's interesting to see/do around there? The Biltmore doesn't sound like my cup of tea. I gather there are a number of scenic areas nearby. My wife has a conference at Ridgecrest.

Advice

A reader has asked whether she should return to college after dropping out several years ago. She’s still young, not yet thirty. Advice is dangerous stuff. If taken and the outcome is unhappy, the advice-giver has set himself up for resentment and blame. Rather, I urged my reader to examine her motives and expectations. She’s smart and better-read than most of her contemporaries, so a typical college curriculum could crush her.

Titan testimony

The BBC is reporting on Lochridge's testimony about the Titan's implosion. The pictures are hair-raising--but lack explanation. Delamination as dramatic as that in the picture on the left would almost certainly have been spotted when the submersible was checked after a dive--and why would it delaminate so deep in the structure? What was the test they used that created that split?

The places of greatest stress, and greatest likelihood of water infiltration, would be where the composite met the endcap (or a penetration, but you get extra longitudinal compression from the endcap). I'd expect microscopic water infiltration at an edge flaw to cause the outer layer to delaminate (maybe with a little crackling noise?). That makes the composite structure just a tiny bit thinner there, and exposes the next layer to the water. Maybe there's a flaw handy; maybe not. But I (and apparently quite a few others) would expect material fatigue after a while, and the next layer's boundary with the endcap to slowly fribble.

The picture on the right screams for context. Is that supposed to be a typical layer? Do they pull regular test samples? (If not, why not?)

FWIW, when the leak broke through, the water speed would have been about 270m/sec--end to end in 24msec. A blink is about 100msec. Leaks are bad things

Signs of the times

We'd been having the local paper delivered for over 30 years, and went to online-only a couple of months ago. Delivery was just too expensive to justify. I'd looked at the publishing company's financials a few years ago, and we're not the only ones--what's keeping revenues up for them is printing fliers and whatnot for a wider and wider range.

Two obvious signs of problems are the size of the paper itself (getting slimmer and slimmer) and the ratio of ads to copy (larger and larger)

One I hadn't thought of is the comics. They'd been going with a half-page, of which two were popular re-runs (Peanuts and For Better or Worse). The online edition had an additional page, with a mix of popular and less so--including (would Madison subscribe to a newspaper without it?) Doonesbury.

I hadn't bothered to ask how much these subscriptions cost the newspaper, but I assume that the more popular strips cost more, the reruns a bit less, and the less popular and the drama serials still less.

They just redid their amusements pages, and pretty much everything is new. I get the sense that the comics are a bundle, and not the top-tier bundle either. If my gut reaction that the mix isn't tailored to the community isn't enough evidence: they got rid of Doonesbury. Zippy may aim for a similar demographic, but I'm not familiar enough to say, nor do I care to do the research.

It's no skin off my nose, but that's another metric to watch.

I suppose I should start examining the sports section a bit more carefully. Local sports news is something that they can't acquire just by piggybacking on the national wire services. I figure that'll be the last thing to be cut, and when I see cuts or shortcuts there, the paper will be almost dead. Maybe counting bylines?

Tis the Gift to be Simple

"Unless you change and become like little children, you will never enter the kingdom of heaven."

I'll not try to unpack all of that, but one thing little children are good at is "being in the moment." Not for long; steadfastness is not one of the frontline virtues in a child. But there's something admirable in the pure enjoyment of the taste of icecream. The flip side is the pure horror and rejection of the abomination of cottage cheese. Oh wait, that's me as an adult.

A rainbow to me as an adult isn't a "pure thing": it recalls the other rainbows I've seen and made, and who I was with, and other memories fun and sad. A bath is a simple sensual pleasure, and maybe it recalls other baths and other oceans. But it isn't perfected by having the radio play Carmen while I'm eating a fudge sundae. Adding too many other related pleasures can detract from fully enjoying any of them.

Our pocket shrines help keep us out of the moment, of course, but so (at least for me) does the "narrator", the "drunken monkey stung by a scorpion". And neither is good for steadfast concentration and enjoyment.

I need to work more on "doing one thing at a time."

Benghazi

I remember wondering what was going on in Benghazi--what was Stevens doing in this out of the way post? Somebody pointed out that some connected Saudis were in the area, getting out of Dodge as fast as they could, and that there was a rumor about weapons going to Syrian rebels. And what had just been opened up? Gaddaffi's arms stash--he had weapons to provide for one of the largest armies in the world at the time. (I didn't say one of the strongest, notice.) (I assume some of those arms wound up spread among Islamist groups in Africa.)

Hmm. Buying up loose gear and having Saudi's deniably ship it to Syrian rebels? It seemed plausible--the first part of it laudable.

Close but no cigar. Apparently they were trying to buy back weapons they'd given to Libyan rebels. Alarming stupidity at every turn...

Amusement for a little while

I'd never heard of BunaB before. The instruction sheet for the BunaB #7 is reproduced at SamuelJohnson's site, together with links for images for the board and instructions for the Zudirk game (BunaB#2). ("ZUDIRK is a modern adaptation of a game believed to have originated on the Scilly Islands, off the coast of Cornwall, England, centuries before the arrival of the Romans. A favorite sport of High Priests of the Druidic cult, it was originally played outdoors, the implements--burning tinder, heart-shaped boulders, stone adzes and condemned criminals.")

Well, over a million Pet Rocks sold--and apparently they're still selling. Why not BunaB?

Over the years I've bought a number of things that never were used--some substantially more expensive than these novelties.

over-wise

Grim cites the Havamal on one of AVI's posts:

54

It is best for man to be middle-wise,
Not over cunning and clever:
The learned man whose lore is deep
Is seldom happy at heart.

The usual way I've heard this described is that it's no joy to know the terrible things that you can't dodge, and also that knowing too many options causes paralysis by analysis, which is often worse than merely being wrong.

It reminds me of Ecclesiastes: "Do not be excessively righteous and do not be overly wise. Why should you ruin yourself?"

The first half of that verse is widely argued, of course. The second half in turn reminds me of Luke 12:47-48. "From everyone who has been given much, much will be required."

and also: "Let not many of you become teachers, my brethren, knowing that as such we will incur a stricter judgment."

I'm already not wonderful at doing what I know I ought. What would it be like if instead of fuzzy generalities and "close enough" I knew with exquisite precision what I should be doing, and still didn't obey?

In any event, I suspect I'd be found innocent if charged with excessive wisdom.

Unfamiliar symbols

"Great is Artemis of the Ephesians!" I wonder if any of those silver images of the temple are still around. There are statues of Artemis still around; she seems to have canes in her hands (canes are also seen in a crude lead figure, so if it was a stability artifact it was in the original--it looks top heavy). No idea what that was taken to mean. The Artemis has a garment with lions and cows and antelopes and whatnot, and women on the sides--small breasted, possibly to avoid competition with the vast array of breasts the goddess sported. I assume the multitude of breasts has to do with fertility and providing for the world. The effect is remarkably ugly.

I haven't turned up any silver images of the temple. Probably all were melted long ago.

One of the images of Artemis' head has her eyes rolled up in an expression that seems almost Hindu--which wouldn't be terribly surprising. The city clerk spoke of an image fallen from heaven. Was that a special inner shrine with a meteorite, or had stories been told that this top-heavy thing had really fallen from the sky?

I’ve suggested before that polytheism is the compromise you get when different tribes with different gods met. I think it can work a bit the other way too. If you have a pile of gods you have to keep up with the appropriate seasonal rituals with each, but perhaps one takes your fancy--say Krishna. I suspect that the more people are devoted to a single god in the pantheon, the more that one will take on aspects that others are nominally the managers of. A fertility goddess could easily pick up aspects of wrath, and even of battle--if people cared about her enough. (Priests might have a little competition going here too--one stop shopping, get all your prayers done here...)

Be that as it may, I look at the statue and find it opaque. And this is the relic of a literate people, from whom we have many documents--there's some connection between us still. And then I look at the pictures at Göbekli Tepe. Wild guesses, all.

Great was Artemis of the Ephesians Wright's site has a picture of what's left: a mismatched column with a stork's nest on top. The ruins of the temple were scavenged to build a basillica, and eventually the ruins of that for a mosque, and the mosque isn't in great shape now either.

There's always somebody..

Via a comment at Sippican Cottage, behold The Christian Topography by Cosmas Indicopleustes ('India-voyager').

There can be few books which have attracted more derision, mixed with wonder, than the Christian Topography of Cosmas Indicopleustes. It advances the idea that the world is flat, and that the heavens form the shape of a box with a curved lid. The author cites passages of scripture which he distorts wildly in order to support his thesis, and attempts to argue down the idea of a spherical earth by stigmatizing it as 'pagan.' The approach to scripture is discreditable, and the conclusion made simply wrong.

The book is often cited as evidence that Christianity introduced the idea of the flat-earth into the world, and brought in the age of ignorance. This is hardly fair, since Cosmas does not represent a mainstream of any kind, personally or spiritually. The latter pages of his work are devoted to rebutting the criticism of his fellow-monks, that what he was saying was wrong.

It almost makes current political discourse look sensible. I almost made it through Book 1.