Monthly Archives: June 2015

Sealand, the big Chinese copy, and WWIII

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Perhaps the smallest country in the world is the Republic of Sealand, a man-made island in the English Channel. Originally called Roughs Tower, Sealand is only 1/4 acre, 0.0004 mi2 in area, but expands to 1.5 square miles if you include the 0.7 mile sea-claim. The country was built, in international waters, by the British during WWII, and given semi-legitimate nation status through two diplomatic accidents over the next 20 years. This nation status would be a joke except that the precedent it establishes could start WW III.

Greetings from The King and Queen of the Republic of Sealand.

The Republic of Sealand. King Roy and Queen Joan wave their greetings. Note, gun, flag, and helipad.

The British constructed Fort Roughs to serve as a bulwark against German U-Boats that were sinking supply ships. The tower-fort is topped with a deck and a helipad platform. There is one gun still working, see photo, a remnant of WWII service. Hollow concrete tubes extend to the Rough Sands sand bar; these provide storage and housing for as many as 300 troops. After the war, Rough Tower went unused and was officially abandoned in 1956. It was occupied (salvaged, conquered) in December, 1966 by radio-pirates trying to break the BBC monopoly. One of the radio-pirates, a former British Major, Paddy Roy Bates, declared the fort-island a monarchy with Roy as King and his wife Joan as Queen. Sealand, declared itself an independent nation September 2, 1967. Aristocratic titles are for sale at a price.

The first of the diplomatic accidents underlying Sealand’s semi-legitimate claim to nation status is that, when the responsible British officials were asked whether they intended to remove the radio squatters, the official response was that England abandoned ownership and responsibility. If England abandoned ownership, so the argument goes, then anyone who took over would take possession “res derelicta and terra nullius”. From a legal point of view, it constituted extra-national territory and they could declare island-nation status plus (some) sea rights. Needless to say, the British navy didn’t see it that way, and as soon as independence was declared, they attacked the island-tower-nation. Bates returned warning shots and the navy brought a case against him in Crown court, Essex. The result: The Bates’s won effective recognition as the fort sat in international waters. This claim stood until 1978 when Sealand was successfully “invaded” by German pirates. The Bates family managed to “liberate” (take back) Sealand with the help of a Bond-movie helicopter stunt pilot, capturing a German pirate in the process. The king negotiated with the German government for the pirate’s release, and thus claim de-facto German recognition. Sealand participates in some international games (ultimate frisbee, mostly), and issues passports, stamps, and currency that is not accepted anywhere. Still, the British deliver mail as if it were a country, and no nation has formally contested Sealand’s statehood since. island-reclamation-sc-sea spotlight_81412

Man made Chinese Islands in the South Pacific

Man made Chinese Islands in the South Pacific

Sealand was something of a joke until 18 months ago when China began to create a string of much-larger copies in the South China Sea. Like Sealand they are in international waters, in this case among the uninhabited, Spratly and Parasel chains of coral reefs between Vietnam, the Philippines, Indonesia and Brunei. The Chinese built retainer walls around several of the reefs and have been filling the interior with sand and coral from the sea-bed. They’ve since added military housing, desalination plants, docks, and an airstrip.

 

If these islands are accepted as new nations, or (more likely) as extensions of China, and we accept China’s claim to 200 mile sea rights, this project would give China exclusive control over vast oil, mineral, and fishery wealth, as well as control over the South China sea shipping and air lanes, extending into existing sea rights of Vietnam, Indonesia, Brunei, and the Philippines — about 2,000,000 km2. The governments of Vietnam and The Philippines have complained, but China has ignored them and warned the US to stay out.

The new islands would seem to violate several international laws, but as the incursion doesn’t direct affect us, it seems we should avoid getting involved in a neighbor’s dispute. I’ve written previously on what makes a country, and have argued that it’s a combination of (1) having a defined land and population and (2) having enough of a government and military to maintain and defend itself as a nation. And (3) not doing anything so offensive to attract the complete disdain of other nations. So far there is no civilian population, but there is a military one, and as soon as the Chinese stop building, the islands will meet all of the above criteria, except perhaps #3.

Sealand is a recurring character in the Japanese manga, Hitalia -- dedicated to the more bizarre quirks of history, each country is represented by a character.

Sealand is a recurring character in the Japanese manga, Hitalia. Sealand is the smallest character, but has a dream of ruling the world one day.

Still, it’s in our interest to avoid WW III, and as the islands multiply, so does the chance of the sort of accident that started the Spanish-American War. All it would take is a ship taken or sunk near the islands, or a plane shot down under suspicious circumstances, and the war that started will not be a small or quick. I therefore have a modest suggestion based on Sealand: allow the islands conditional nation status, but as an aristocracy and require the sale of titles of nobility like Sealand does, or the sale of senate seats (like the Illinois Governor tried to do). With enough power in private hands a war could be averted. Peace is possible.

Robert E. Buxbaum, June 21, 2015. Sealand has actually tried selling the whole country in 2007. If you want to buy a title: lord, lady, baron, etc. Go to: sealandgov.org.

Gatling guns and the Spanish American War

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I rather like inventions and engineering history, and I regularly go to the SME, a fair of 18th to 19th century innovation. I am generally impressed with how these machines work, but what really brings things out is when talented people use the innovation to do something radical. Case in point, the Gatling gun; invented by Richard J. Gatling in 1861 for use in the Civil war, it was never used there, or in any major war until 1898 when Lieut. John H. Parker (Gatling Gun Parker) showed how to deploy them successfully, and helped take over Cuba. Until then, they were considered another species of short-range, grape-shot cannon, and ignored.

1876_Gatling_gun_NPS_Fort_Laramie_WY_by-Matthew_Trump_2004

A Gatling gun of the late 1800s. Similar, but not identical to the ones Parker brought along.

Parker had sent his thoughts on how to deploy a Gatling gun in a letter to West Point, but they were ignored, as most new thoughts are. For the Spanish-American War, Parker got 4 of the guns, trained his small detachment to use them, and registered as a quartermaster corp in order to sneak them aboard ship to Cuba. Here follows Theodore Roosevelt’s account of their use.

“On the morning of July 1st, the dismounted cavalry, including my regiment, stormed Kettle Hill, driving the Spaniards from their trenches. After taking the crest, I made the men under me turn and begin volley-firing at the San Juan Blockhouse and entrenchment’s against which Hawkins’ and Kent’s Infantry were advancing. While thus firing, there suddenly smote on our ears a peculiar drumming sound. One or two of the men cried out, “The Spanish machine guns!” but, after listening a moment, I leaped to my feet and called, “It’s the Gatlings, men! It’s our Gatlings!” Immediately the troopers began to cheer lustily, for the sound was most inspiring. Whenever the drumming stopped, it was only to open again a little nearer the front. Our artillery, using black powder, had not been able to stand within range of the Spanish rifles, but it was perfectly evident that the Gatlings were troubled by no such consideration, for they were advancing all the while.

Roosevelt and the charge up Kettle Hill, Frederick Remington

Roosevelt, his volunteers, and the Buffalo soldiers charge up Kettle Hill, Frederick Remington.

Soon the infantry took San Juan Hill, and, after one false start, we in turn rushed the next line of block-houses and intrenchments, and then swung to the left and took the chain of hills immediately fronting Santiago. Here I found myself on the extreme front, in command of the fragments of all six regiments of the cavalry division. I received orders to halt where I was, but to hold the hill at all hazards. The Spaniards were heavily reinforced and they opened a tremendous fire upon us from their batteries and trenches. We laid down just behind the gentle crest of the hill, firing as we got the chance, but, for the most part, taking the fire without responding. As the afternoon wore on, however, the Spaniards became bolder, and made an attack upon the position. They did not push it home, but they did advance, their firing being redoubled. We at once ran forward to the crest and opened on them, and, as we did so, the unmistakable drumming of the Gatlings opened abreast of us, to our right, and the men cheered again. As soon as the attack was definitely repulsed, I strolled over to find out about the Gatlings, and there I found Lieut. Parker with two of his guns right on our left, abreast of our men, who at that time were closer to the Spaniards than any others.

From thence on, Parker’s Gatlings were our inseparable companion throughout the siege. They were right up at the front. When we dug our trenches, he took off the wheels of his guns and put them in the trenches. His men and ours slept in the same bomb-proofs and shared with one another whenever either side got a supply of beans or coffee and sugar. At no hour of the day or night was Parker anywhere but where we wished him to be, in the event of an attack. If a troop of my regiment was sent off to guard some road or some break in the lines, we were almost certain to get Parker to send a Gatling along, and, whether the change was made by day or by night, the Gatling went. Sometimes we took the initiative and started to quell the fire of the Spanish trenches; sometimes they opened upon us; but, at whatever hour of the twenty-four the fighting began, the drumming of the Gatlings was soon heard through the cracking of our own carbines.

Map of the Attack on Kettle Hill and San Juan Hill in the Spanish American War.

Map of the Attack on Kettle Hill and San Juan Hill in the Spanish-American War, July 1, 1898 The Spanish had 760 troops n the in fortified positions defending the crests of the two hills, and 10,000 more defending Santiago. As Americans were being killed in “hells pocket” near the foot of San Juan Hill, from crossfire, Roosevelt, on the right, charged his men, the “Rough Riders” [1st volunteers] and the “Buffalo Soldiers [10th cavalry], up Kettle Hill in hopes of ending the crossfire and of helping to protect troops that would charge further up San Juan Hill. Parker’s Gatlings were about 600 yards from the Spanish and fired some 700 rounds per minute into the Spanish lines. Theyy were then repositioned on the hill to beat back the counter attack. Without the Parker’s Gatling guns, the chances of success would have been small.

I have had too little experience to make my judgment final; but certainly, if I were to command either a regiment or a brigade, whether of cavalry or infantry, I would try to get a Gatling battery–under a good man–with me. I feel sure that the greatest possible assistance would be rendered, under almost all circumstances, by such a Gatling battery, if well handled; for I believe that it could be pushed fairly to the front of the firing-line. At any rate, this is the way that Lieut. Parker used his battery when he went into action at San Juan, and when he kept it in the trenches beside the Rough Riders before Santiago.”

Here is how the Gatling gun works; it’s rather like 5 or more rotating zip guns; a pall pulls and releases the firing pins. Gravity feeds the bullets at the top and drops the shells out the bottom. Lt’ Parker’s deployment innovation was to have them hand-carried to protected positions, near-enough to the front that they could be aimed. The swivel and rapid fire of the guns allowed the shooter to aim them to correct for the drop in the bullets over fairly great distances. This provided rapid-fire accurate protection from positions that could not be readily hit. Shortly after the victory on San Juan HIll, July 1 1898, the Spanish Caribbean fleet was destroyed July 3, Santiago surrendered July 17, and all of Cuba surrendered 4 days later, July 21 (my birthday) — a remarkably short war. While TR may not have figured out how to use the Gatling guns effectively, he at least recognized that Lt. John Parker had.

A new type of machine gun, a colt browning repeating rifle, a gift from Con'l Roosevelt to John Parker's Gatling gun detachment.

Roosevelt gave two of these, more modern, Colt-Browning repeating rifles to Parker’s detachment the day after the battle. They were not particularly effective. By WWI, “Gatling Gun” Parker would be a general; by 1901 Roosevelt would be president.

The day after the battle, Col. Roosevelt gifted Parker’s group with two Colt-Browning machine guns that he and his family had bought, but had not used. According to Roosevelt, but these rifles, proved to be “more delicate than the Gatlings, and very readily got out-of-order.” The Brownings are the predecessor of the modern machine gun used in the Boxer Rebellion and for wholesale deaths in WWI and WWII.

Dr. Robert E. Buxbaum, June 9, 2015. The Spanish-American War was a war of misunderstanding and colonialism, but its effects, by and large, were good. The cause, the sinking of the USS Maine, February 15, 1898, was likely a mistake. Spain, a decaying colonial power, was a conservative monarchy under Alfonso XIII; the loss of Cuba seems to have lead to liberalization. The US, a republic, became a colonial power. There is an inherent friction, I think between conservatism and liberal republicanism, Generally, republics have out-gunned and out-produced other countries, perhaps because they reward individual initiative.

An approach to teaching statistics to 8th graders

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There are two main obstacles students have to overcome to learn statistics: one mathematical one philosophical. The math is somewhat difficult, and will be new to a high schooler. What’s more, philosophically, it is rarely obvious what it means to discover a true pattern, or underlying cause. Nor is it obvious how to separate the general pattern from the random accident, the pattern from the variation. This philosophical confusion (cause and effect, essence and accident) is exists in the back of even in the greatest minds. Accepting and dealing with it is at the heart of the best research: seeing what is and is not captured in the formulas of the day. But it is a lot to ask of the young (or the old) who are trying to understand the statistical technique while at the same time trying to understand the subject of the statistical analysis, For young students, especially the good ones, the issue of general and specific will compound the difficulty of the experiment and of the math. Thus, I’ll try to teach statistics with a problem or two where the distinction between essential cause and random variation is uncommonly clear.

A good case to get around the philosophical issue is gambling with crooked dice. I show the class a pair of normal-looking dice and a caliper and demonstrate that the dice are not square; virtually every store-bought die is not square, so finding an uneven pair is easy. After checking my caliper, students will readily accept that these dice are crooked, and so someone who knows how it is crooked will have an unfair advantage. After enough throws, someone who knows the degree of crookedness will win more often than those who do not. Students will also accept that there is a degree of randomness in the throw, so that any pair of dice will look pretty fair if you don’t gable with them too long. I can then use statistics to see which faces show up most, and justify the whole study of statistics to deal with a world where the dice are loaded by God, and you don’t have a caliper, or any more-direct way of checking them. The underlying uneven-ness of the dice is the underlying pattern, the random part in this case is in the throw, and you want to use statistics to grasp them both.

Two important numbers to understand when trying to use statistics are the average and the standard deviation. For an honest pair of dice, you’d expect an average of 1/6 = 0.1667 for every number on the face. But throw a die a thousand times and you’ll find that hardly any of the faces show up at the average rate of 1/6. The average of all the averages will still be 1/6. We will call that grand average, 1/6 = x°-bar, and we will call the specific face average of the face Xi-bar. where i is one, two three, four, five, or six.

There is also a standard deviation — SD. This relates to how often do you expect one fact to turn up more than the next. SD = √SD2, and SD2 is defined by the following formula

SD2 = 1/n ∑(xi – x°-bar)2

Let’s pick some face of the dice, 3 say. I’ll give a value of 1 if we throw that number and 0 if we do not. For an honest pair of dice, x°-bar = 1/6, that is to say, 1 out of 6 throws will be land on the number 3, going us a value of 1, and the others won’t. In this situation, SD2 = 1/n ∑(xi – x°-bar)2 will equal 1/6 ( (1/6)2 + 5 (5/6)2 )= 1/6 (126/36) = 3.5/6 = .58333. Taking the square root, SD = 0.734. We now calculate the standard error. For honest dice, you expect that for every face, on average

SE = Xi-bar minus x°-bar = ± SD √(1/n).

By the time you’ve thrown 10,000 throws, √(1/n) = 1/100 and you expect an error on the order of 0.0073. This is to say that you expect to see each face show up between about 0.1740 and 0.1594. In point of fact, you will likely find that at least one face of your dice shows up a lot more often than this, or a lot less often. To the extent you see that, this is the extent that your dice is crooked. If you throw someone’s dice enough, you can find out how crooked they are, and you can then use this information to beat the house. That, more or less is the purpose of science, by the way: you want to beat the house — you want to live a life where you do better than you would by random chance.

As a less-mathematical way to look at the same thing — understanding statistics — I suggest we consider a crooked coin throw with only two outcomes, heads and tails. Not that I have a crooked coin, but your job as before is to figure out if the coin is crooked, and if so how crooked. This problem also appears in political polling before a major election: how do you figure out who will win between Mr Head and Ms Tail from a sampling of only a few voters. For an honest coin or an even election, on each throw, there is a 50-50 chance of head, or of Mr Head. If you do it twice, there is a 25% chance of two heads, a 25% chance of throwing two tails and a 50% chance of one of each. That’s because there are four possibilities and two ways of getting a Head and a Tail.

pascal's triangle

Pascal’s triangle

You can systematize this with a Pascal’s triangle, shown at left. Pascal’s triangle shows the various outcomes for a coin toss, and shows the ways they can be arrived at. Thus, for example, we see that, by the time you’ve thrown the coin 6 times, or polled 6 people, you’ve introduced 26 = 64 distinct outcomes, of which 20 (about 1/3) are the expected, even result: 3 heads and 3 tails. There is only 1 way to get all heads and one way to get all tails. While an honest coin is unlikely to come up all heads or tails after six throws, more often than not an honest coin will not come up with half heads. In the case above, 44 out of 64 possible outcomes describe situations with more heads than tales, or more tales than heads — with an honest coin.

Similarly, in a poll of an even election, the result will not likely come up even. This is something that confuses many political savants. The lack of an even result after relatively few throws (or phone calls) should not be used to convince us that the die is crooked, or the election has a clear winner. On the other hand there is only a 1/32 chance of getting all heads or all tails (2/64). If you call 6 people, and all claim to be for Mr Head, it is likely that Mr Head is the true favorite to a confidence of 3% = 1/32. In sports, it’s not uncommon for one side to win 6 out of 6 times. If that happens, it is a good possibility that there is a real underlying cause, e.g. that one team is really better than the other.

And now we get to how significant is significant. If you threw 4 heads and 2 tails out of 6 throws we can accept that this is not significant because there are 15 ways to get this outcome (or 30 if you also include 2 heads and 4 tail) and only 20 to get the even outcome of 3-3. But what about if you threw 5 heads and one tail? In that case the ratio is 6/20 and the odds of this being significant is better, similarly, if you called potential voters and found 5 Head supporters and 1 for Tail. What do you do? I would like to suggest you take the ratio as 12/20 — the ratio of both ways to get to this outcome to that of the greatest probability. Since 12/20 = 60%, you could say there is a 60% chance that this result is random, and a 40% chance of significance. What statisticians call this is “suggestive” at slightly over 1 standard deviation. A standard deviation, also known as σ (sigma) is a minimal standard of significance, it’s if the one tailed value is 1/2 of the most likely value. In this case, where 6 tosses come in as 5 and 1, we find the ratio to be 6/20. Since 6/20 is less than 1/2, we meet this, very minimal standard for “suggestive.” A more normative standard is when the value is 5%. Clearly 6/20 does not meet that standard, but 1/20 does; for you to conclude that the dice is likely fixed after only 6 throws, all 6 have to come up heads or tails.

From skdz. It's typical in science to say that <5% chances, p <.050 are significant. If things don't quite come out that way, you redo.

From xkcd. It’s typical in science to say that <5% chances, p< .05. If things don’t quite come out that way, you redo.

If you graph the possibilities from a large Poisson Triangle they will resemble a bell curve; in many real cases (not all) your experiential data variation will also resemble this bell curve. From a larger Poisson’s triange, or a large bell curve, you  will find that the 5% value occurs at about σ =2, that is at about twice the distance from the average as to where σ  = 1. Generally speaking, the number of observations you need is proportional to the square of the difference you are looking for. Thus, if you think there is a one-headed coin in use, it will only take 6 or seven observations; if you think the die is loaded by 10% it will take some 600 throws of that side to show it.

In many (most) experiments, you can not easily use the poisson triangle to get sigma, σ. Thus, for example, if you want to see if 8th graders are taller than 7th graders, you might measure the height of people in both classes and take an average of all the heights  but you might wonder what sigma is so you can tell if the difference is significant, or just random variation. The classic mathematical approach is to calculate sigma as the square root of the average of the square of the difference of the data from the average. Thus if the average is <h> = ∑h/N where h is the height of a student and N is the number of students, we can say that σ = √ (∑ (<h> – h)2/N). This formula is found in most books. Significance is either specified as 2 sigma, or some close variation. As convenient as this is, my preference is for this graphical version. It also show if the data is normal — an important consideration.

If you find the data is not normal, you may decide to break the data into sub-groups. E.g. if you look at heights of 7th and 8th graders and you find a lack of normal distribution, you may find you’re better off looking at the heights of the girls and boys separately. You can then compare those two subgroups to see if, perhaps, only the boys are still growing, or only the girls. One should not pick a hypothesis and then test it but collect the data first and let the data determine the analysis. This was the method of Sherlock Homes — a very worthwhile read.

Another good trick for statistics is to use a linear regression, If you are trying to show that music helps to improve concentration, try to see if more music improves it more, You want to find a linear relationship, or at lest a plausible curve relationship. Generally there is a relationship if (y – <y>)/(x-<x>) is 0.9 or so. A discredited study where the author did not use regressions, but should have, and did not report sub-groups, but should have, involved cancer and genetically modified foods. The author found cancer increased with one sub-group, and publicized that finding, but didn’t mention that cancer didn’t increase in nearby sub-groups of different doses, and decreased in a nearby sub-group. By not including the subgroups, and not doing a regression, the author mislead people for 2 years– perhaps out of a misguided attempt to help. Don’t do that.

Dr. Robert E. Buxbaum, June 5-7, 2015. Lack of trust in statistics, or of understanding of statistical formulas should not be taken as a sign of stupidity, or a symptom of ADHD. A fine book on the misuse of statistics and its pitfalls is called “How to Lie with Statistics.” Most of the examples come from advertising.