Explaining China, Part I: The Scope of This Series, Which Includes the PRC, the ROC, the Han, and Greater China

China and environs

I’m bringing a new topic to my blog. I’m going to attempt to explain things about China, the largest nation in which the Han (that’s the way to write, in English, the Chinese name for the Chinese people, as an ethnic group) form the majority, as well as the largest nation on Earth, by population. The map above comes from this website. If you’re wondering why, in the map above, Taiwan is the same color as the People’s Republic of China, this series of blog-posts is definitely for you. In a future post, I will deal with the historical reasons for the China/Taiwan puzzle, and the current state of that interesting situation. (“May you live in interesting times” is not a nice thing to say directly to any of the Han, by the way, no matter where they live. It is considered by many people to be part of an ancient Chinese curse, although the veracity of this claim is disputed — a topic for another post, later in this series.)

If you find China, Taiwan, puzzles in general, mysteries which are not fictional, history, current events, and/or the Han to be interesting topics, then this irregularly-published series of blog-posts is for you. If you aren’t interested in any of those topics, my assumption is that you wouldn’t have read this far, anyway. To those who miss the other topics about which I blog, don’t worry: posts in this series will not be the only topic I blog about, by any means, for the fact that I am interested in many things, and blog on many topics, is not going to change.

The People’s Republic of China is also known as mainland China, Red China, the PRC, Communist China, or simply “China.” The government of the PRC is often referred to simply as “Beijing,” the city which is the capital of the PRC. Taiwan, by contrast, is officially known as the Republic of China, or the ROC, or even, by some people, “Taiwan, China” (a term I tend not to use). The ROC’s government can be referred to as “Taipei,” the ROC’s capital, to distinguish it from the government in Beijing. My preferred way to refer to the nation-state which is actually under the control of the Beijing government is to call it the PRC, and I use ROC, often, to refer to the nation-state actually under the control of the Taipei government, which most people call Taiwan, a term I also use. When I only write “China,” I mean the PRC. I also use the term “Greater China,” which is explained below.

The Han are in the majority in both the PRC and the ROC, and these two regions are collectively known as “Greater China,” which sounds like, and in some ways actually is, one nation with two governments, since both governments claim to be the only legitimate government of the nation which is all of Greater China (and, yes, that is confusing, along with “China Proper” on the map above). All of these topics: the nations, governments, regions, and people, are mysteries for most people on Earth — and topics for future posts in this series.

I am not of the Han. I do not speak, read, nor write any variety of the Chinese language. Also, I have yet to visit any part of Greater China. By contrast, I am known as a teacher of both science and mathematics, as someone who does “math problems for fun” (as my blog’s heading-cartoon, which I did not write, puts it), as well as a blogger on many topics that have previously had little to do with China, until this post, from yesterday, which analyzed current events worldwide, starting with recent developments in China. I do not want anyone to think I just started studying China yesterday, for that would not be correct. I do feel that I owe anyone who has read this far an explanation for exactly one thing: why should anyone care what I have to say on these subjects? I will explain that in Part II of this ongoing series . . . and tackling the PRC/ROC puzzle will be coming later, as will other topics.

Elementary School Mathematics Education Mysteries

mystery

Since these two problems are really the exact same problem, in two different forms, why not just use “x” to teach it, from the beginning, in elementary school, instead of using the little box? The two symbols have the exact same meaning!

To the possible answer, “We use an ‘x’ for multiplication, instead, so doing this would be confusing,” I have a response: why? Using “x” for multiplication is a bad idea, because then students have to unlearn it later. In algebra, it’s better to write (7)(5) = 35, instead of 7×5 = 35, for obvious reasons — we use “x” as a variable, instead, almost constantly. This wouldn’t be as much trouble for students taking algebra if they had never been taught, in the first place, that “x” means “multiply.” It’s already a letter of the alphabet and a variable, plus it marks spots. It doesn’t need to also mean “multiply.”

Why are we doing things in a way that causes more confusion than is necessary? Should we, as teachers, not try to minimize confusion? We certainly shouldn’t create it, without a good reason for doing so, and these current practices do create it.

These things may not be mysteries to others, but they certainly are to me.

[Note: for those who do not already know, I am a teacher of mathematics. However, I do not have any experience teaching anything at the elementary level. For this particular post, that’s certainly relevant information.]

The First High-Resolution Images from Pluto Have Arrived, and They Bring a Major Mystery: Where Are the Impact Craters?

pluto-observations-through-the-years

As new pics from the Pluto/Charon system become available, you can’t beat the image gallery at the New Horizons portion of NASA’s website to keep up with them, which is where I found this .gif file showing images of Pluto itself throughout the years. It culminates in the latest, and most detailed, image of any part of Pluto — a small portion of its surface. To see more of the latest pics, as they are released, I refer you to that web-page. NASA plans to keep it updated with the latest from the Pluto/Charon system, for months to come, as new images are transmitted, received, and processed.

The big surprise today is not the “heart of Pluto” that’s gotten so much press this week, but something newly discovered (and completely unexpected) with the latest small batch of new pics: on both Pluto and Charon, they can’t find a single impact crater. Not one. And that is just flat-out weird. Here, see for yourself (same image source): unexpected ice mountains, check; unexpectedly-smooth plains, check; craters — hey, the craters are missing!

nh-plutosurface

According to everything we know, impact craters should be there. The ice mountains and numerous plains are mysteries, also, but it is the lack of craters which really has scientists puzzled this morning. Everyone expected to see lots of impact craters, myself included. Small worlds, so far from the sun, should have frozen internally long ago, based on present models, making them geologically dead, and therefore unable to “erase” impact craters (seen on dozens of other planets, dwarf planets, satellites, and asteroids) with surface-altering geological activity. This mass-erasure-of-craters happens on a only a few other solid bodies in the solar system, such as Earth, and Jupiter’s moon Io — both larger, and much warmer, than anything in the Pluto/Charon system. Some scientists are already going public with conjectures for the energy source needed to keep Pluto and Charon crater-free. However, I have yet to read any such conjecture which I find convincing, which is why I am not including them in this post. (Such guesswork is easy to find, though, here, among other places.)

On the other hand, the scientific community has had very little time, yet, to explain this new puzzle; there might be a convincing explanation out there by this time next week — or this could persist, as one of many mysteries in astronomy, for decades. At this point, it is too early to even venture a guess regarding when, if ever, this mystery will be solved.

A Half-Solved Mystery: Rotating a Sine Wave

Image

A Half-Solved Mystery

A few minutes ago, I wondered how to write a function whose graph would be a sine curve, but one that undulated above and below the diagonal line y=x, rather than the x-axis, as is usually the case. How to accomplish such a 45 degree counterclockwise rotation?

Well, first, I abandoned degrees, set Geometer’s Sketchpad to radians, and then simply constructed plots for both y = x and y = sin(x). Next, I added them together. The result is the green curve (and equation) you see above.

This only half-solves the problem. Does it undulate above and below y=x? Yes, it does. However, if you rotate this whole thing, clockwise, one-eighth of a complete turn, so that you are looking at the green curve going along the x-axis, you’ll notice that it is not a true sine curve, but a distorted one. Why? Because it was generated by adding y-values along the original x-axis, not by a true rotation.

I’m not certain how to correct for this distortion, or otherwise solve the problem. If anyone has a suggestion, please leave it in a comment. [Note: an astute follower of this blog has now done exactly that, so I refer the reader to the comments for the rest of the story here.]