Terracotta Army

On Thursday, I went to see the Terracotta Army exhibit at the British Museum. It was stunning. Breathtaking. Incredible.


The exhibit is situated in the reading room, a circular sanctuary in the middle of the museum roofed by an airy dome descending effortlessly into shelves of beautiful old books and haunted by the whispers of the famous literary figures (both real and fictional) who frequented the library. With the exhibit in place, the books are hidden from view, but you can still gaze up into the dome above.

The exhibit is constructed well; it's educational and beautiful but not overwhelming. You wind through the history, learning how the First Emperor conquered the various "warring states", uniting a vast area under the rule of his Qin (pronounced Chin, and from which we get the name "China") dynasty. He learned tricks of trade and warfare from the various people he conquered, using his new-found knowledge to further expand his empire and to effectively rule it once established. He standardized everything: the size and construction of crossbows, to easily replace arrows and triggers; the spacing of wheels on chariots, to match the ruts in the extensive system of roads he had built across the country; weights and measures; "small seal script", doing away with regional differences in the written language; laws and punishments; and coins, declaring his circular coin with a square hole in the middle the only valid currency, doing away with older and often larger coins, some of which were in the shape of knives and arrowheads (quite logically, as knives and arrowheads were objects of value). He organized a huge labor force to extend and connect the various walls built by previous rulers into the initial incarnation of the Great Wall.

And he feared death. He wanted to live and rule forever. With a typical Chinese mix of superstition and practicality, he sought out means of extending his life while simultaneously preparing for his death. The preparations for his death were massive. The construction of over 8,000 of these terracotta warriors, horses, court officials and entertainers required an incredible organization of labor. They were mass produced, but modified by hand so that each was unique. They're so beautiful. If the prospect of spending his afterlife guarded by these exquisite works of art could not soothe his reservations about death, then nothing could.

There's so much more to say, so much more to this incredible story. The layout of the pits (protected by mountains and water, with the army facing the only direction unprotected by natural barriers) and the Emporer's own mausoleum (which remains untouched). The fact that this massive clay army was forgotten by the world for so long, until chance unearthed a warrior in a farmer's well. Every piece inscribed with the names of the laborers and overseers who worked on them, for quality control purposes. The elegant and life-like bronze sculptures of birds (herons and swans) in the musicians' pit. The musicians. The acrobats. The bronze replicas of chariots and drivers. The stone replicas of interlocking leather armor. The mystery and beauty of the whole thing, and of every tiny little detail.

Geeks and Hackers

In Chinese class the other night, the word 电脑 (diǎn nǎo = electric brain = computer) came up in a reading again. One of the students in our class is a professor in the computer science department, and he asked our teacher how to say "geek" in Chinese (strenuously denying that this term might be applied to him). She didn't understand at first, so we had to describe the concept of geek to her. When she realized what we meant, she said there was a word for it. In Chinese, as in English, they have the phrase "book worm" (书虫 = shū chóng), so a geek is a 网虫 (wǎng chóng), or "internet worm"—or maybe "web worm" is a better way to say it. Then she gave us the term 黑客, pronounced hēi kè, which is simply a phonetic approximation of "hacker"; it literally means "black guest".

Cornered

I'm trying to compute the first homology group of upper half space H_3 modulo the action of Γ_0(N) with coefficients in a particular Γ_0(N)-module M. (Here, N is an ideal in the ring of integers of an imaginary quadratic field.) I've been studying Cremona's method, which uses a topological argument and is applied with trivial coefficients. To see the topological argument, he first compactifies the upper half space H_3 by adding points at all the cusps and a point at infinity. This doesn't change the homology, but allows a straightforward tessellation of upper half space, making it easy to see how to compute the homology group.

In my situation, with non-trivial coefficients, I have to compute "homology with local coefficients". There's a nice topological description of this, using a system of local groups, or bundle of groups, which is like a vector bundle, but with groups instead of vector spaces. But with non-trivial coefficients, I can't just attach points at the cusps and compactify that way. It's not good enough. The problem is that we need to be able to identify this covering space (bundle of groups) with H_3* x M modulo the diagonal action of Γ_0(N). But if we take H_3* to be the usual compactification, then (if I understand this correctly) the stabilizers in Γ_0(N) of the cusps may be non-trivial, which means that our resulting covering space will not be identifiable with H_3* x M modulo the diagonal action of Γ_0(N). So instead of adding points at the cusps and infinity, I have to add corners, and these corners will probably each consist of an entire half plane! What will that do to my tessellation?

En route to my local Royal Mail depot