Of sangaku and wind farms

By Christopher Monckton of Brenchley

The Edo period in Japanese history ran from 1603-1867. For most of that period, 1639-1854, the nation kept itself deliberately aloof from all Western influence. Japan was closed to foreigners. Meanwhile, the aristocratic samurai class developed an intriguing and elegant method of demonstrating piety in their Shinto temples.

They would carve geometric problems, typically involving circles, on timber shingles, paint them colorfully, inscribe them in kanbun (Chinese characters with diacritical marks to distinguish the Japanese usage), and affix them to the temple walls as an inspiration to subsequent visitors.

The use of kanbun by the samurai was akin to the use of Greek by Roman orators or of Latin by the English aristocracy. The sangaku tablets, therefore, were near-exclusively of samurai origin and were comprehensible to their caste alone, and of course to the delighted deities.

Contemplating the monstrosity of the Navitus Bay wind farm proposal, I was struck by the irregularity of the suggested area for the wind farm (Fig. 1).


Figure 1. The proposed site for the Navitus wind array.

Looking at the shape of the proposed site, it is at once clear that the array is as close to the shore as the developers dare to make it, partly to reduce construction and maintenance costs and partly to minimize the formidable transmission losses in the undersea cable. But the edges of the array are defined more by sight-lines from the shore than by any other consideration.

How would a mathematician go about moving the array further out to sea and compensating for the transmission losses by minimizing the shadowing effect by which turbines take each other’s wind, regardless of the wind direction, as well as minimizing the visual impact?

The prevailing wind is south-westerly, but stretching a line of wind turbines north-west to south-east to capture it would represent an unacceptable hazard to coastal shipping.

One answer is to arrange the turbines in a circle, which provides minimal visual impact. But how to dispose the turbines within the circle to minimize wind shadowing still further?

Fig. 2 shows possible solution for 192 turbines, just two fewer than the Navitus array, and occupying approximately the same area of 68 square miles (the “8” was inadvertently omitted from my recent posting on the array – mea culpa).


Figure 2. An array of 192 wind turbines, each with a 505-ft span and separated from its neighbors by five spans, intended to minimize both visual impact and wind shadow.

Assuming that each turbine’s span is 505 feet, and that turbines must be five spans apart, the diameter of the array is approximately 9 miles 3 furlongs.

Before I reveal what all this has to do with sangaku tablets and their geometric problems based on properties of circles, this method of arranging the wind turbines can also be used to create an ingenious board – the mathematician’s version of the chessboard, if you like – where equal numbers of playing-spaces (let us call them “forts”) guard each straight row (let us call it a “street”), and an equal number of streets meet at each fort.

In the board shown in Fig. 3, there are 44 forts on 77 streets, with exactly four forts guarding each street and exactly seven streets meeting at each fort.


Figure 3. The mathematician’s chessboard

Some 30 years ago I successfully marketed a board game based on a layout similar to this one. The rules I came up with are below this posting. Gentle readers, your challenge – should you choose to accept it – is to devise as many sets of new rules as you can for this board. Then I shall relaunch the game with multiple sets of rules. One board, many games.

The criteria for your rules as follows. The game must be one of pure skill, with no element of chance. It must involve simple pieces placed on the board. The rules must be short, simple and quick to learn, yet the strategy should be complex enough to make the game both exciting for all and intellectually satisfying for good minds. Try out your rules before you send them in. If they’re any good, people will become hooked by the game. That’s how we’ll get the big sales, and you’ll get your royalties.

Now for the connection to the Japanese sangaku tablets. The extraordinary and surprising feature of the layout is that, although the forts are connected by straight streets, it is circles that determine the exact positioning of the nodes coincident with the forts. This is a startling and – as far as I know – hitherto-unsuspected property of circles. The samurai would have appreciated that.


Figure 4. The surprising relation between a network of straight lines and the intersections of a set of circles rotated at equal intervals about a common point on their circumferences.

Below, as promised, are my own rules for the game of Battle. I hope this harmless diversion involving “puzzling things in life” will have given pleasure.


Rules of engagement

The objective is to drive all opposing forces from the battlefield.

The battlefield has 44 forts guarding 77 streets. Four forts guard each street. Seven streets meet at each fort. At the outset, the city is empty of all forces.

Alliances: Blue with Green, Red with Yellow may fight as pairs of allies, or armies may fight singly.

The attack: Each army attacks in turn: Blue, Red, Green, Yellow, etc. Each army’s sortie is in two phases: first, expulsion (wherever possible), then occupation.

Suppose that it is Blue, allied with Green, whose turn is to attack.

1. Expulsion

On every street, street by street, every soldier Blue outnumbers is expelled (at the beginning of the battle, of course, there are no soldiers to expel) –

Ø 2 or 3 Blues on a single street expel 1 Red, Green or Yellow soldier on that street.

Ø 1 Blue stands off against 1 Red, Green or Yellow soldier on the same street.

Ø 2 Blues stands off against 2 Red, Green or Yellow soldiers on the same street. But …

Ø 2 Blues expel 2 soldiers of different colours (e.g. Red & Green) on the same street.

Ø If expulsion exposes soldiers of other colours on cross streets, Blue expels them too.

Ø Blue must expel even outnumbered Green allies on any street (this is friendly fire)

Ø Blue returns all expelled soldiers to their commanders for later re-use.

Some examples:


2. Occupation

When Blue has expelled all possible soldiers, a Blue soldier is stationed at any empty fort, ending the attack. Occupying a fort marks the end of Blue’s sortie.

Victory: An army whose last soldier is expelled retires defeated, though its ally, if there is one, may fight on. The army or alliance that drives all enemy soldiers out of the city wins.

Some hints on basic strategy

Strategy: You will learn the rules of engagement in five minutes. But the strategy, especially with two armies in each of two alliances, is surprisingly complex.

Know the terrain: The battlefield gives equal weight to each fort and each street.

Force deployment is critical. At the beginning, there are no soldiers to expel. Deploy soldiers so as to maximize their power to attack opposing armies, to minimize the risk that they themselves will be attacked, to avoid friendly fire against allied armies, and to command as much of the field as possible.

Attack is the best form of defense. The Rules of Engagement favor aggressive tactics and penalize defensiveness.

Superior force wins. On any street, outnumbered soldiers are expelled.

Choice of position is key. Look for – and eventually learn to create – chances to attack on two or more streets by the deployment of a single well-placed soldier.

Alliances can be made or broken. Armies can fight either as standalone units or as allied forces. With three armies in play, for instance, two armies can form a temporary alliance to target the third. This game can be particularly challenging, as the two trailing forces form temporary alliances to try to fight back against the dominant army.

Unity is strength: On any street, two soldiers of the attacking army defeat and expel two soldiers from different armies, but stand off against two soldiers of one army. This rule reflects the fact that a single, united force is often stronger than divided forces. It also makes the classic game between two Generals each commanding two allied armies a particularly fascinating challenge.

Friendly fire must be avoided if possible. Under the Rules of Engagement, the attacking army must always expel all soldiers from armies that it outnumbers on any street, even if those expelled are from an allied army.

Rout: In Battle, the disastrous knock-on effects of losing one or two vital units in the field are simulated. During an army’s sortie, if it expels a soldier from one street, opposing soldiers on other streets intersecting with the fort previously occupied by the expelled soldier may become outnumbered too. If so, they, too, are expelled before the attacking army stations its soldier at any vacant fort. Beware! A defeat can quickly become a rout.

Attrition: The army or alliance in the lead can pressure its opponents to concede victory at any time.

Blitzkrieg: The game can be played against the clock, with a time limit on each move. Or the whole game can be ended at a fixed time, when the army or alliance with the most soldiers in the field is declared victorious.

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April 30, 2014 6:39 pm

Figure 4 reminds me of the childhood Spirograph

April 30, 2014 6:45 pm

In warfare isn’t there always an element of change? The stronger force doesn’t always win. Thus even when hopelessly outnumbered, there is still an incentive to do battle to the very end.
Why not consider introducing an element of chance?

April 30, 2014 6:47 pm

typo: element of chance

April 30, 2014 6:48 pm

haven’t begun to read Monckton’s thread yet, but this is in Scientific American. Huffpo/Media Matters/Salon all have beat-ups on this non-story already:
1 May: Business Insider: Lauren F. Friedman: Fox Denies Telling Scientific American Editor Not To Discuss Climate Change
Michael Moyer, an editor at Scientific American, was invited to “Fox & Friends” this morning to discuss “futuristic trends.”…
Things didn’t go quite as planned…
MOYER TWEET: Fox & Friends producer wanted to talk about future trends. I said #1 will be impacts of climate change. I was told to pick something else…
When we reached out to Fox News, they denied that climate change was the issue.
“We invited Michael on for a segment on technological and scientific trends we can expect in the future. We worked closely with him and his team and there was never an issue on the topic of climate change,” Suzanne Scott, SVP of programming at Fox News, said in a statement. “To say he was told specifically not to discuss it, would be false.”…
You can read Moyer’s whole story over at Scientific American …LINK
VIDEO: Here’s the full segment, as it aired.
Disclosure: The author has written for Scientific American

george e. smith
April 30, 2014 6:55 pm

Wow !
I’m going to have to cut and paste your exposition, so I can print it out for study.
But It caught my attention, because of an idle pastime of my own; that being observing, and counting the number of spokes on the wheels of an automobile, and then passing a personal judgment on the “attractiveness” of each observed pattern; driven primarily, by the number of spokes.
Even numbers, I conclude, look rather bland, and numbers like three or five are also unattractive. This doesn’t seem to be correctable by merely designing the spoke shape differently.
My conclusion is that the most pleasant looking wheels have seven spokes, and that prime numbers look best, and it doesn’t matter much what the spoke design is (aesthetically).
So the second choice in my arbitrary list of preference order, is just the eleven spokes of your game board’s intersecting circles.
The circular pattern is quite stunning; and it makes me wonder if there is a different seven spoke board, that might explain why seven seems to me to be the magic number for attractive wheel spokes.
I’ve never seen an unattractive seven spoke wheel, and the smaller number of eleven spoke wheels, have also been very easy on the eyes.
I have seen several 13 spoke wheels, but it seems to get much trickier to design spokes for larger numbers. 19 spokes is so far the largest prime wheel, I have observed.
Anyway; thanks for your puzzle, even without trying the game; just the game board, seems like an artwork, worth obtaining.

April 30, 2014 7:09 pm

Hungry Hungry Hippo started this way.

April 30, 2014 7:14 pm

Blue red yellow green Did I miss the part of where the hell these come from ? It looks good but needs work as to how you put these different colored piece’s on the board ” In play” when you never told me where or how I get them . Or powerup from red to blue I’m lost on that but strategy game it is . :>)

Chad Wozniak
April 30, 2014 7:16 pm

I once invented but did not successfully market a game in which I attempted to eliminate the mass memorization of every possible line of play that is required to play grandmaster chess. It combined the rules of chess and checkers, had four players and many. many more pieces with more different moves than in chess, with the general idea of forcing the players to think and make it up as they went, rather than using a bank of memorized lines of play.
While this may be strictly speaking off topic, one could draw parallels between the boilerplate, rote responses of global warming alarmists concerning climate change (grandmaster chess), on the one hand, and the innovative thinking and research being done by skeptics who don’t think every question has been or can be answered (my game).

April 30, 2014 7:21 pm

*** this says “with 1 more episode to air”. this was supposed to be 8-10 episodes! one can only hope “one” is the right figure.
29 April: National Review Online: Greg Pollowitz: Showtime’s Years of Living Dangerously Still Struggling to Attract Viewers
James Cameron’s celebrity-filled global-warming propaganda series is bombing in the ratings. Here are the Nielsen numbers from Sunday April 27:
At Showtime, NURSE JACKIE and CALIFORNICATION stayed at 0.2 (although the latter needed rounding up to get to that number), and YEARS OF LIVING DANGEROUSLY remained at a tiny 0.04 with 1 more episode to air***…
James Cameron: “This isn’t just about landmark television but about growing a global movement.”…
Pollowitz: A landmark failure more like it.

John West
April 30, 2014 7:37 pm

War in the Round
2 player turn based (rounds) game
Game pieces consist of stackable chips like poker chips except sized to fit the forts.
Each player gets 11 stacks of 5 chips placed on the very inner circle for one player and the very outer circle for the other.
Each player gets 3 moves per round. A move consists of moving any number of chips from any fort to any fort connected to it with a straight line. The players take turns making moves within the rounds, the player that moves first in the alternating pattern being determined at the beginning of the game either by mutual agreement or coin flip.
At the end of each round a chip is added to each fort occupied by at least one chip.
Battles are determined by the number of chips, chips annihilating each other at a 1:1 ratio. For example if player1 moves four chips from a fort he occupies to a fort occupied by player2 with three chips the move would result in player1 occupying the fort with one chips.
The game is won by completely annihilating the other player or for a quick game the player that holds 25 forts for 3 rounds.

April 30, 2014 7:55 pm

Well, Al Gore invented the internet, and it looks like you invented Chinese Checkers…(sarc) Hey I like your game – simple, yet complicated. A better arrangement of the windmills – can have one power line from the center of the arrangement. I hope they don’t take your advice though – would still be a “white elephant”. Too expensive for what you get out of it – $ vs power…

Janice Moore
April 30, 2014 7:55 pm

And some battles end … like… this……..
“… Ben-Hadad king of Aram mobilized his entire army and marched up and laid siege to Samaria. there was a great famine in the city; the siege lasted so long that a donkey’s head sold for eighty shekels of silver, and {1/4 lb. or 100g} of seed pods for five shekels. ***
Elisha replied, ‘Hear the word of the Lord. … “About this time tomorrow, {12 lbs. or 5.5kg} of the finest flour will sell for a shekel and {20 lbs. or 9kg} of barley will sell for a shekel at the gate of Samaria.”‘ … The officer on whose arm the kind was leaning said to the man of God, ‘Look, even if the Lord should open the floodgates of the heavens, could this happen?’ ***
Now there were four men with leprosy at the entrance of the city gate. … At dusk they got up and went to the camp of the Arameans. When the reached the edge of the camp, no one was there, for the Lord had caused the Arameans to hear the sound of chariots and horses and a great army, so that they said to one another, ‘Look, the king of Israel has hired the Hittite and Egyptian kings to attack us!’ So they got up and fled… . they left the camp as it was and ran for their lives. ***
… messengers … reported to the king. then the people went out and plundered the camp of the Arameans. So a seah of the finest flour sold for a shekel, and two seahs of barley sold for a shekel, as the Lord had said.”
II. Kings 6:24 – 7:20.
Markets can collapse overnight.
October 19, 1987

Windmills and the like could be abandoned tomorrow.
Take heart!
God, not the Enviroprofiteers, is, even now, in control.
And many of us are praying.
{Note to all atheists: No religion is being taught here. That I below assert my own belief backed up by a story from an ancient Hebrew historical account and also report to you that some people pray is not telling you to believe nor to do as I do. If the mere quoting of the Bible and mentioning of prayer is offensive, the cause l1es within you, not this post.}

Janice Moore
April 30, 2014 7:57 pm

“That I above {moved my paragraph — oops!} assert… .”

April 30, 2014 8:25 pm

The Edo period was as much if not more about preventing polluting influences from the west for sure, mainly China.
That attitude remains to this day.

HGW xx/7
April 30, 2014 8:33 pm

Our faithful, roving reporter Pat says (or rather, Mr. Moyer tweeted):
“MOYER TWEET: Fox & Friends producer wanted to talk about future trends. I said #1 will be impacts of climate change. I was told to pick something else…”
Okay, if you have the gall to ignore any scrap of evidence to the contrary, to ignore poll after poll after poll of average American attitudes, and are so wrapped up in your ‘belief’ that you truly believe that the effects of climate change are going to dominate trends in the future, you, my ‘friend’, are nothing but a rabid, close-minded, left-wing, blind-as-a-bat, propogandist. Fox knocking down your idea may have ended up saving you a lot of flac. (For the record, I don’t watch any 24-news, right or left.)
ScAm has fallen so far, it’s mind-boggling. I can see why they were fawning over Mann-iac, probably getting their matching mock-turtlenecks autographed.

Ed, 'Mr' Jones
April 30, 2014 9:10 pm

“mock-turtlenecks” ? When I was a boy, they were called “Dickies” or, prhaps “Dickeys”.
Appropriate name now, if you know what I mean.

F. Ross
April 30, 2014 9:18 pm

Re: fig 2. By publishing your improved wind farm design you may inadvertantly be helping the promoters of the project you wish to stop.
Fig. 4 bears a pleasing resemblance to the chrysanthemum, which, I believe, is the national flower of Japan.

F. Ross
April 30, 2014 9:31 pm

inadvertantly</strike for inadvertently. Spelinge sucks.

F. Ross
April 30, 2014 9:33 pm

Oh hell, fingers just not working right tonight. Fuggedaboudit.

April 30, 2014 9:55 pm

Waaay too much time on your hands. Sorry, I’m in a pissy mood. Better to hang it up and try again tomorrow.

george e. smith
April 30, 2014 10:09 pm

“””””…..{Note to all atheists: No religion is being taught here. That I below assert my own belief backed up by a story from an ancient Hebrew historical account and also report to you that some people pray is not telling you to believe nor to do as I do. …..”””””
All that matters Janice, is that it matters to you. That it matters not, to (some) others, should NOT matter to you.

April 30, 2014 10:26 pm

I had an idea at one time that if you placed hollow, metal rectangular containers in the right pattern, it would work as a rectenna… for tornadoes. That might work even better than a trailer park.

Janice Moore
April 30, 2014 11:24 pm

Dear F. Ross Happens to the best of the commenters, here. We got it! You were just fine. Nice insight.
@ Hoser — LOL — You’re a good sport. What refreshing candor.
Dear George Smith,
Thank you.
Hope your sister is okay.
(and son in college, too)
Gratefully yours,

April 30, 2014 11:50 pm

i think a game like this is being played in ukraine right now.
if numbers always beats high tech then our defence strategy is flawed relying as it does on tech rather than size? take afghanistan -did anyone actually calculate how many troops in forts it would take to control a country? the uk had a fort strategy [backed up by artillery and air power cover] and lost when they became encircled by mines making them prisoners in their forts.

JJM Gommers
May 1, 2014 12:13 am

A small correction of the entry by the Lord, the Dutch only had contacts with Japan and had a site on the island of Desima, opposit of Nagasaki and did all kind of trade with Japan including visits

John R Walker
May 1, 2014 12:20 am

For wind turbines I have a circular design I like better – it’s called ZERO!

May 1, 2014 12:26 am

Currently its probably not a war game as war involves trickery and chance and who controls the streets is as important as who controls the forts. So both streets and forts need to be occupiable so people can get blocked into forts by those who controls the streets . Also pieces should be converted to the colour of the team that captures them [like in Ukraine- people swap sides]. Every war also has chance [weather, accidents,traitors,spies, deception etc] so in a war game chance is a valid part of the equation [without the heavy rain and Napoleon being ill and not making the crucial decisions Waterloo probably would have been lost. The mud played a crucial role at agincourt.]
different units move at different speeds.
but if you want no chance then chess [what the west plays] is a game of attrition and GO [what the chinese play] is a game of capture ground. If you study the chinese economic strategy they are playing GO. Also such games are games of perfect intelligence ie you can see where the other persons ‘troops’ are all the time which is not the case in real life.
ok if we assume the above picture is just a map then if it were me if i wanted to make a war game out of that map then you go to the master of war rules Sun Tzu and his book Art of War and make the rules out of that and modify the board if needed. Sun Tzu is what they teach in military academies so anything based on him will appeal to the military mind. Actually you could have 2 versions one a war game and one dressed up as a treasure hunt or something with pretty colours for those not into war but who would still find the challenge appealing [like candy crush]

May 1, 2014 12:31 am

Where will the diesel generators that really produce the power be sited? Will it be on the Isle of Wight, out of sight, out of mind?

May 1, 2014 1:17 am

I asked this question on the first wind turbine thread but didn’t see it answered.
This part of the south coast is one of the premier yachting venues in the world. Will the turbines ‘steal’ the wind from the yachts and will the yachts be excluded from large areas of the ocean around the turbines. If so, how will that be enforced?

Crispin in Waterloo but really in Singapore
May 1, 2014 1:47 am

The reality of armies and soldiers is that moving a large group is much more difficult than a small one (think SEALS teams) and the effectiveness of an armed group reduces as the size goes up, measured on a per-soldier basis.
Thus the equality of forces is OK, mathematically and practically, during a stand-off, but when they are unequal a simple rule of ‘double’ should apply.
The idea of guerilla warfare is that small forces can defeat a lumbering one (think Afghanistan again) if they are persistent.
Two rules come to mind. If a small force can ‘see’ a large one, the general can choose to ‘nibble’ away at it by removing his one man and one from the larger opposing force. Thus 5 in one fort exposed to 5 individuals with line-of-sight means removing all, if the singleton general wants, but not if the general with 5 in one place wants. This reflects the reality of having to occupy a territory.
Another possibility is that the number of soldiers needed to defeat a group requires double the number of defenders. In real life, to guarantee a win, it is taken that the attacking force must be 3 times the resisting force. Double would be easy to calculate. Seven can’t rout 4 and this would change the ‘routing’ opportunities which I view as a weakness in the original rules. Currently the rout is more a result of rules, not the result of what is being simulated. The ‘street rules’ can exist for one-on-one or outnumbering but only for singletons. Forts or groups can be captured with an ‘overwhelming force’ of double that number.

View from the Solent
May 1, 2014 1:54 am

Hmmm. I see more than a hint of graph theory here. I’ll have to dig out my relevant texts and study them again to meet the Noble Lord’s challenge.

May 1, 2014 2:04 am

Assuming that each turbine’s span is 505 feet, and that turbines must be five spans apart, the diameter of the array is approximately 9 miles 3 furlongs.

For those of us who don’t think in the idiotic Imperial Units (which apart from horseracing in the UK which is still in miles and furlongs, is pretty much everybody) here is that sentence again in units we can understand:

Assuming that each turbine’s span is 154 metres, and that turbines must be five spans apart, the diameter of the array is approximately 15 kilometres.

May 1, 2014 2:04 am

Far too complicated for the Great Unwashed. If the great Scarne could not get the public to warm to his game of genius “Teeko”……..

Richard Barraclough
May 1, 2014 3:32 am

John A says:
May 1, 2014 at 2:04 am
Assuming that each turbine’s span is 505 feet, and that turbines must be five spans apart, the diameter of the array is approximately 9 miles 3 furlongs
This also caught my eye? I wondered whether it had been rounded to the nearest chain, or (rod, pole or perch). And whether the area covered by the wind farm could be converted to roods? Or perhaps Christopher Monkton is an avid horse racer?

May 1, 2014 4:53 am

Lordy lordy…your game board design reflects elements of the ‘Flower of Life’ (http://en.wikipedia.org/wiki/Flower_of_Life). Sacred Geometry – and why not?

May 1, 2014 5:00 am

Without doing the math, my first thought would be to investigate a layout based on the Fibonacci series spirals. Works for sunflowers and pineapples.

May 1, 2014 5:30 am

Richard Barraclough
I just found myself thinking that these units mean nothing to me. Since practically all of science is conducted in SI units, perhaps Viscount Brenchley could forgive the French just this once and get with the programme.

Richard Barraclough
May 1, 2014 5:47 am

John A
The UK is a complete mish-mash of imperial and metric units. Road distances in miles, petrol in litres, temperatures (mostly) in celsius, body-weights in stones, wind-speeds in knots or miles per hour, pressure in pascals (or hectopascals), Jeremy Clarkson on Top Gear getting excited about horse-power, and plenty of other inconsistencies.
However, my biggest surprise came when I grew grain in South Africa. In order to follow price trends at the world’s biggest grain market in Chicago, I had to convert from cents per bushel into Rands per tonne. Can you believe that a bushel of maize (corn to Americans) weighs 56 pounds, while a bushel of wheat weighs 60 pounds – and this in possibly the world’s most technologically advanced country.

Monckton of Brenchley
May 1, 2014 7:17 am

Mr Savage should not underestimate those whom he calls the “great unwashed”. They bought the original Battle game in large numbers. Besides, the rules are in fact simple: the manufacturer rightly insisted on that.

May 1, 2014 8:00 am

Thanks but your game looks too complicated for me. I will stick with nine men’s morris. Easier on the neurons.

Mike McMillan
May 1, 2014 8:41 am

ferdberple says: April 30, 2014 at 6:39 pm
Figure 4 reminds me of the childhood Spirograph

Reminds me more of a chart we had here long ago of the interconnectedness of climate paper references and authors.

May 1, 2014 10:35 am

Isn’t that a lotus flower?

Sun Spot
May 1, 2014 11:07 am

I don’t understand why Mosher hasn’t done a drive by yet ?

May 1, 2014 11:16 am

Following Spain’s absorption of Portugal in 1580, the Tokugawa shogunate became ever more anti-Catholic, leading to the exclusion of foreigners from Japan in 1639 by Tokugawa Iemitsu. However, Protestant Dutch ships were allowed to deal with Chinese merchants on an island off Nagasaki, since the Netherlands was at war with Spain. Under some restraints, Chinese ships were welcomed, which could also bring in European goods, but purchase & ownership of such goods were also regulated.
The shogunate had previously encouraged Jesuit missionaries in order to counter the power of Buddhist institutions.

May 1, 2014 11:58 am

Janice Moore says:
April 30, 2014 at 7:55 pm
{Note to all atheists: No religion is being taught here. That I below assert my own belief backed up by a story from an ancient Hebrew historical account and also report to you that some people pray is not telling you to believe nor to do as I do. If the mere quoting of the Bible and mentioning of prayer is offensive, the cause l1es within you, not this post.}
I don’t blame you for enunciating it.
Are you done now ?
It is really boring.

May 1, 2014 12:15 pm

In relation to the board layout in this post the user Schofe mentioned the Flower of Life. This is relevant because while the post says:

This is a startling and – as far as I know – hitherto-unsuspected property of circles. The samurai would have appreciated that.

This property may be startling, but it is not unsuspected. Plenty of people have observed it before. I made a similar graph in school during some project or another. I think there was actually a fairly simple proof for it. Maybe someone with a better affinity for geometry could shed some light on it.

May 1, 2014 12:33 pm

Richard Barraclough says:
May 1, 2014 at 5:47 am
It all depends upon what you are used to using. I have trouble thinking in terms of price per tonne as opposed to dollars or pounds per bushel. A remarkable number of crops weigh in at 60 ppb, BTW. There are slight differences as to type & grade of wheat.
Granted, the metric system is easier to use.

Mike McMillan
May 1, 2014 3:21 pm

F. Ross says: April 30, 2014 at 9:18 pm
… Fig. 4 bears a pleasing resemblance to the chrysanthemum, which, I believe, is the national flower of Japan.

Think cherry blossom instead. Chrysanthemum is the Emperor’s flower.
One reason for using bushels instead of weight for corn is that the weight varies with the grain moisture content. 15½ % moisture is the storage standard for corn,

george e. smith
May 1, 2014 9:08 pm

“”””””…..Janice Moore says:
April 30, 2014 at 11:24 pm …..””””””
Janice, I think sis is doing ok, but haven’t had any contact for a couple of weeks. I sent her a laptop security cable, to chain her computer to the bed. It took fed-ex about a month, to finally deliver it from the depot across the street from her apartment, to her next door neighbor, who was the third person, I tried to get it delivered to. They found the “hospital”, but couldn’t find the patient; nor could the hospital, where she’s at. Maybe the laptop got stolen already.
son is still working on a degree, instead of supporting me.

May 1, 2014 9:11 pm

Mike McMillan says:
May 1, 2014 at 3:21 pm

F. Ross
May 1, 2014 9:48 pm

McMillan says:
May 1, 2014 at 3:21 pm
Re; Japanese flowers… you may be right. Google search, though, shows quite a diversity of opinion between cherry blossoms and chrysanthemums

May 2, 2014 3:29 am

OK let’s have some fun, and keeping in tone with WUWT preoccupations. Here my rules
Intersection aren’t fort, they are shale gas reservoirs.
The objective is to “exploit” as many gas as possible. This is done by creating “derricks”, figurated by a stack of 2 or more pawns, and moving them around leaving behind pawns that figure “gas wells”.
At the begining each player gets his colour (up to 4 for practical reason), and a first “derrick” of 2 pawns of that colour, that he places where he wants.
Players play in turn, one after the other. During a turn the player
1) gets a a single new pawn, that he places atop a derrick (nowhere else) ; the player choose the colour of the pawn and may use someone else colour.
2) may, if he wants, move a part of a derrick toward an new place ; the rules are
2a) the top pawn of the chosen derrick must be of the same colour that the chosen new pawn (it, of course, can be the very same pawn, just put on the chosen derrick in step 1 ; but please note that you can put a pawn on a derrick and move some other derrick)
2b) the moving part of the derrick is the top part, and must be no less than 2 pawns, so that it remains a derrick ; the staying part is the bottom part of the previous derrick, can be any size, and it becomes either a new “gas well” if it is a sigle pawn, or a new derrick if it is 2 pawns or more. special rule : if the new gas well or derrick is not of the same colour that the moving derrick, then the player that moved the derrick must give a “lawyer point” to the owner of the colour.
2c) the new place must be a single move afar (no more) and unexploited (not even by the same player) .
The game end when no derrick can move. The player with the most gas well wins (derricks do NOT count) ; in case of a tie the player with the most lawyer points wins.
Obviouly you must secure the largest territory to exploit by leaving a trail of gas well behing your derricks ; this would be boring on a chessboard, but on this special board it will be more tricky. And you also may try to have enemies “painted in a corner” by moving their derricks, but this comes at a cost (lawyer points).

Monckton of Brenchley
May 2, 2014 9:33 am

If paqyfelye will be kind enough to try out his game and report back, I’ll be happy to consider adding his set of rules to the box.

May 2, 2014 10:18 am

As a oh-by-the-way, 4 passengers in a private plane were just killed when their low-flying airplane crashed into the swinging blades of a wind farm …

May 2, 2014 1:54 pm

More information about these four innocents killed by the “green” revolution of spinning wind turbine blades in the clouds …
4 die in plane crash at South Dakota wind power farm
April 30, 2014
By Dorothy Davis Ballard

The wreckage of Piper Lance aircraft returning from Hereford, Texas, was discovered Monday after crashing into a wind turbine in South Dakota, reports The Associated Press. The lives of the pilot and all three passengers were claimed in the accident, which is currently under investigation.
The single-engine plane registered to a Donald J. Fischer crashed into one of 27 wind turbines at the South Dakota Wind Energy Center during a return trip from a Texas cattle sale. There is speculation that strong winds and reduced visibility due to fog may have played a role in the crash, but an official cause has not been given.
Wednesday the AP reported fragments from the wreckage would be transported to Colorado for further examination, with a primary question for investigators being to why the pilot was flying so low. A representative from the National Transportation Safety Board told the AP the pilot was not in communication with air traffic controllers when the plane crashed. It is also unclear if the pilot had filed a flight plan.
The 40.5 megawatt South Dakota Wind Energy Center is owned by NextEra Energy and began operations in 2003. Located in Hyde County, South Dakota the wind farm is comprised of 27 GE 1.5 MW turbines each approximately 213 feet tall.”

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