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An Accomplishment


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For Science Teachers: A Safer Alternative to Liquid Mercury

Liquid mercury, in schools, poses three major problems:

  1. It is extremely toxic,
  2. It has a high vapor pressure, so you can be poisoned by invisible mercury vapor leaving any exposed surface of liquid mercury, and
  3. Playing with liquid mercury is a lot of fun.

These are compelling reasons to leave use of mercury to those at the college level, or beyond. In the opinion of this science teacher, use of liquid mercury in science classes, up through high school chemistry, inside or outside thermometers, is a bad idea. If the bulb at the bottom of a thermometer, as well as the colored stripe, looks silvery, as in the picture below (found on Wikipedia), then that silvery liquid is mercury, and that thermometer should not be used in labs for high school, let alone with younger children. Your local poison control center can help you find the proper thing to do with mercury in your area; it should definitely not just be thrown away, for we do not need this serious environmental toxin in landfills, where it will eventually reach, and poison, water. Red-stripe thermometers without any silvery line, on the other hand, are far safer, although broken glass can still cause injury.


I turned ten years old in 1978, and, by that time, I had already spent many hours playing (unsupervised) with liquid mercury, pouring it hand-to-hand, etc., so I know exactly how irresistible a “plaything” mercury can be, to children. Luck was on my side, and I suffered no ill effects, but I can state from experience that children should not be tempted with highly-toxic “mercury as a toy,” for it’s not a toy at all. Mercury spills require special “hazmat” training to clean up safely; anyone encountering such a spill who does not have such training should simply notify the proper authorities. In the USA, this means evacuating the area immediately, and then calling 911 — from far enough away to keep the caller from breathing invisible mercury vapor.

Fortunately, there is a safe alternative which can give students a chance to experiment with a room-temperature metal: an alloy of three parts gallium to one part indium, by mass. Gallium’s melting point is between normal human body temperature and room temperature, so it can literally melt in your hand (although a hot plate is faster). Indium, on the other hand, has a melting point of 156.6°C. For this reason, I will not buy a hot plate unless it can reach higher that that temperature. (Note: use appropriate caution and safety equipment, such as goggles and insulated gloves, with hot plates, and the things heated with them, to avoid burns.)

Once both elements are massed, in the proportions given above, they can then be melted in the same container. When they melt and mix together, they form an alloy which remains liquid at room temperature.

Some might wonder how mixing two elements can create an alloy with a melting point below the melting points of either of the two ingredients, and the key to that puzzle is related to atomic size. Solids have atoms which vibrate back and forth, but don’t move around each other. In liquids, the atoms are more disordered (and faster), and easily slip around each other. In solid, room-temperature gallium, all the atoms are of one size, helping the solid stay solid. Warm it a little, and it melts. With pure indium, this applies, also, but you have to heat it up a lot more to get it to melt. If the two metals are melted and thoroughly mixed, though, and then frozen (a normal freezer is cold enough), the fact that the atoms are of different sizes (indium atoms are larger than gallium atoms) means the atoms will be in a relatively disordered state, compared to single-element solids. In liquids, atoms are even more disordered (that is, they possess more entropy). Therefore, a frozen gallium/indium alloy, with two sizes of atoms, is already closer to a disordered, liquid state, in terms of entropy, than pure, solid gallium or indium at the same temperature. This is why the gallium-indium mixture has a melting point below either individual element — it requires a lower temperature to get the individual atoms to flow past each other, if they are already different atoms, with different sizes.

liquid metals

Those who have experience with actual liquid mercury will notice some important differences between it and this gallium-indium alloy, although both do appear to be silver-colored liquids. (This is why mercury is sometimes called “quicksilver.”) For one thing, their densities are different. A quarter, made of copper and nickel, will float on liquid mercury, for the quarter’s density is less than that of mercury. However, a quarter will sink in liquid 3:1 gallium-indium alloy. To float a metal on this alloy, one would need to use a less-dense metal, such as aluminum or magnesium, both of which sink in water, but float in liquid Ga/In alloy.

Other differences include surface tension; mercury’s is very high, causing small amounts of it on a floor to form little liquid balls which are difficult (and dangerous) to recapture. Gallium-indium alloy, by contrast, has much less surface tension. As a result, unlike mercury, this alloy does not “ball up,” and it will wet glass — and doing that turns the other side of the glass into a mirror. Actual mercury will not wet glass.

The most important differences, of course, is that indium and gallium are far less toxic than mercury, and that this alloy of those two elements has a much lower vapor pressure than that of mercury. Gallium and indium are not completely non-toxic, though. Neither indium nor gallium should be consumed, of course, and standard laboratory safety equipment, such as goggles and gloves, should be worn when doing laboratory experiments with these two elements.

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A Polyhedral Journey, Beginning With an Expansion of the Rhombic Triacontahedron

The blue figure below is the rhombic triacontahedron. It has thirty identical faces, and is one of the Catalan solids, also known as Archimedean duals. This particular Catalan solid’s dual is the icosidodecahedron.

Rhombic Triaconta

I use a program called Stella 4d (available here) to transform polyhedra, and the next step here was to augment each face of this polyhedron with a prism, keeping all edge lengths the same.

Rhombic Triaconta augmented

After that, I created the convex hull of this prism-augmented rhombic triacontahedron, which is the smallest convex figure which can enclose a given polyhedron.

Convex hull

Another ability of Stella is the “try to make faces regular” function. Throwing this function at this four-color polyhedron above produced the altered version below, in which edge lengths are brought as close together as possible. It isn’t possible to do this perfectly, though, and that is most easily seen in the yellow faces. While close to being squares, they are actually trapedoids.

ch after ttmfr

For the next transformation, I looked at the dual of this polyhedron. If I had to name it, I would call it the trikaipentakis icosidodecahedron. It has two face types: sixty of the larger kites, and sixty of the smaller ones, also.

ch after ttmfr dual

Next, I used prisms, again, to augment each face. The height used for these prisms is the length of the edges where orange kites meet purple kites.

aug ch after ttmfr dual

Lastly, I made the convex hull of the polyhedron above. This convex hull appears below.

Convex hull again


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Explaining China, Part III: Basic International Etiquette Involving the Chinese, as well as their Korean and Japanese “Neighbors,” and Americans


Multiple East Asian nations are discussed in this post, the third of a series which began here, and is usually focused only on China, and the Han Chinese. Those nations are The People’s Republic of China (the PRC); Taiwan, officially known as the Republic of China (ROC); North Korea; South Korea; and Japan. Many Americans, when they see a person whom they think is from East Asia (based on appearance), will simply guess — and sometimes they go even further, and guess out loud. This is usually not intentional rudeness, but it is a socially-dangerous breach of etiquette, made all the more serious if a spoken guess is an incorrect one. The reasons for this are complex, involving such things as tense relationships between ethnic groups and historical atrocities. The etiquette-based solution to avoid walking into a metaphorical minefield, once understood, is a simple set of principles. If you simply want to look for the principles, and skip the explanation of how I learned these things, and why they make sense, simply look for the red, centered text.

1. Listen carefully, before and after talking.

2. Silence is seldom considered rude.


3. Every interaction (as might happen playing the game above) is an opportunity to learn.

The board and stones above will be recognized, as the game of go, by many people around the world. Go is the national game of Japan. Although I would never say this if I were in Japan, this game originated in China. The Chinese call it weiqi (pronounced “way-chee”), and the Japanese call it igo (this word sounds like the English word “ego”). Japan introduced this game to the Western world, which is why its English name is similar to the Japanese, rather than the Chinese, name. However, I did not learn this game from a Chinese nor a Japanese person, so, when in the presence of this teacher (who taught me taekwondo as well), I had to remember to call the game baduk, its name in Korean.

4. If you must guess about ethnicity, keep your guesses to yourself.

At the time I learned both go and taekwondo, I was a young teenager. The angriest I ever saw this teacher was an occasion where an American adult assumed, out loud, that he was Japanese. Being young, I didn’t put cause and effect together by myself, but it was later explained to me: during World War II, which had ended less than forty years ago at that time, atrocities had been committed by Japanese during World War II in South Korea. My teacher immigrated to the United States from South Korea a generation later, in 1977, and the angriest I ever saw him was in reaction to this blunder by the American who called him Japanese, because of what had happened to his nation during WWII.

There have been many other conflicts between East Asian nations, as well, including the China, which was also invaded by Japan. Following WWII (which ended with the USA dropping two atomic bombs on Japanese cities), the Korean War started, which brought China into conflict with both Koreans and the USA. All these conflicts are within living memory, meaning that there are people still alive who remember these things happening. These international conflicts (and earlier ones, of course) are a major reason for inter-ethnic conflict, and few people want to be confused with their historical enemies.

5. An understanding of history can explain much basic etiquette.

Later still, I encountered other ways people can make social blunders of related types. For example, anyone born in the USA is an American citizen, and can be legitimately called an American — and that’s a term to which most American citizens do not object. If the person’s parents came from, say, Taiwan, and they are ethnically of the Han, this creates a situation few Americans understand, for the whole China/Taiwan thing is certainly complex. Under such circumstances, it’s perfectly understandable that one might prefer to be called “American,” rather than having to try to explain exactly which China one’s parents immigrated from. Many Americans, after all, do not even know that two Chinese governments (the PRC’s in Beijing, and the ROC’s in Taipei, both claiming for decades to be the government of all of Greater China) exist. 

However, there is an even better way to refer to individual people — any people, anywhere.

6. When possible, use people’s names and/or titles, expressed politely, and pronounced correctly.

With my taekwondo and baduk teacher, for example, it was seldom necessary to call him anything other than “Mr. Lee,” or simply, “sir.” I knew he was Korean, and from South Korea, but that was seldom discussed. I learned much by simply paying attention to him, and he taught me a lot. Later, I learned things about Japan, mostly from exposure to, and conversation with, Japanese people. Still later, I began learning about China (both the PRC and the ROC) and the Han, and found that my best sources of information were — no surprise — people of the Han, themselves.

7. For more detailed advice on etiquette, seek insider sources.

This means that, if you’re preparing to visit mainland China (the PRC), and want advice to avoid social blunders there, you’ll get your best information from those who have lived in the PRC. Similar principles apply to other places, such as my learning elements of Korean etiquette from a Korean. With people who are currently located in the PRC, though, one must carefully stay on topic, and there is one topic which must be avoided.

8. To avoid putting them in danger from their own government, do not discuss political issues with anyone located in the People’s Republic of China.

This would also apply to North Korea (formally: the Democratic People’s Republic of Korea, or DPRK), but that is far less likely to come up, simply because the PRC now encourages foreign tourism there, while the DPRK remains a closed society, as the PRC was during the reign of Chairman Mao. Both of these governments are totalitarian, are perfectly willing to kill their own citizens, and will not tolerate any propaganda (discussing, say, democracy, or human rights, would count as propaganda), except for their own.

Principle #9, below, is essential to understanding anything about these East Asian nations. When I studied East Asian history in graduate school, this was my starting point.

9. China ≠ Japan ≠ Korea.

10. Remember that these are basic principles only, and use #7 to learn more.

It would be a mistake for anyone to take this as a complete list, for it is not.

[Image credit: I found the image of a weiqi/baduk/igo/go set on eBay, right here. It is for sale for the next few weeks.]

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Calvin and Hobbes, and Election 2016

The current American election cycle was predicted, with amazing accuracy, in the late 20th Century, by Bill Watterson, the creator of Calvin and Hobbes. Evidence will follow. We’ll start with ignorance and apathy, both of which are certainly involved in American elections.



Not wanting to vote and not being allowed to vote are, of course, two different things to Calvin.


While he’s being ignorant and apathetic, Calvin is, at least, honest. Honesty is something which we definitely need, and currently do not have, in American politics, from the left or the right.


If only this fictional duo qualified under the Constitution, we’d be facing this choice, which certainly seems better than the choice we actually have:

Watterson understood, well, the corrupting role of money in politics.


The big issue politicians do not talk about enough is the environment. Why do they not devote more energy to that? Money, of course. The love of money drives people to do harmful and irrational things, and this includes things with obviously-negative environmental impact.

calvin and dryer

He also created numerous cartoons about pollsters and lobbyists, taking them every bit as seriously as these people deserve to be taken.





America has a lot of single-issue voters. They are not safe from Watterson’s satire. This cartoon is as on-target today as it was when it first appeared.


For what purposes was Calvin willing to do research? Could his spray-painting ambitions include negative campaign ads?


I certainly think so. 

The next cartoon applies equally well, in my opinion, to the words and actions of both Donald Trump and Hillary Clinton.


If the next cartoon doesn’t remind you of the Trump-or-Clinton choice we face, and what an amazing waste of time and energy it is to have to make such an absurd “choice,” please read it again. 


Finally, here’s Calvin’s invention of the perfect bipartisan slogan for this campaign season, and its nausea-inducing choice between bad (Clinton) and worse (Trump).


“So what?” Indeed.

[To obtain all these cartoons, and many more, I recommend purchasing this boxed set: the complete collection of Calvin and Hobbes.]


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