Flatland- the annotated edition: experience hyperspace first-hand

Flatland: A Romance of Many Dimensions, is a pretty famous book, at least in certain circles. It is a book about space, in two and three dimensions, and was published in 1884 by Edwin A. Abbot. This is a great book to read to kids of nearly any age (depending on the details, maybe 4th graders, maybe 7th graders, maybe revisiting the book with 9th graders, or 14 year olds, who are studying geometry).

Flatland describes the world of A. Square and how his two-dimensional world is shaken up by a strange visitor who takes A. to the world of three dimensions, and beyond! The story touches on four dimensions, but also on one- and zero-dimensional matters. It is at once a fairy tale and a math lesson, with geometry being the focus, yet it is written in an accessible and amusing style (many parents will be able to follow it, at least most of the way- your kids might help!). You do have to be willing to handle the hyper-Victorian manner of speech adopted by the characters to enjoy the book.

A. Square's familiar two-dimensional world is similar to the world we see every day on flat sheets of paper, but its society is extremely rigid: class distinctions amongst men are made by the number of vertices their shapes posses: soldiers are triangles (with a vertex count of three) and gentlemen are squares (having a vertex count of four). The more vertices one has, the higher the social class. At one extreme are priests, who are circles: imagine a polygon increasing from square to pentagon to hexagon to ... an infinite number of vertices, and then you have a circle! Women, on the other hand, are all line segments in A. Square's world, though they are of different lengths. Before you get angry, please note that the author was an early proponent of educating women equally to men, so Flatland has to be read as the satire on Victorian society that is was, while simultaneously being a fairy tale and geometry lesson, and even science fiction. In fact, the extreme rigidity of rules for social behavior is pretty funny, but it can make the reader very glad not to live in such a world (I certainly hope you don't!).

It is a shocking but ultimately very pleasing experience for A. Square to learn about "spaceland", where three dimensions exist. We have the fun of accompanying him on the journey. One of the remarkable things about going from a two dimensional world to a three dimensional world is that many of the same techniques are used if one wishes to go from three to four dimensions, or from four to five to n dimensions. This progression is described up to four dimensions and a bit more, at least partly, in Flatland, and a number of modern "sequels" take us well beyond the fourth dimension. One such sequel is Flatterland by Ian Stewart. I had some trouble understanding Flatterland about a third of the way in, which made it difficult to read to the kids- I need to work at it some more.

The amazing thing about mathematics is the ability to treat multi-dimensional shapes with the same ease as their two- and three-dimensional counterparts. So, while it may be difficult to "see" what a 6-dimensional hypercube looks like, especially since we are mostly limited to two- and three-dimensional representations, it turns out to be pretty straightforward to calculate the surface area and volume of that 6-D hypercube (using the equations for surface area and volume of a 3-D cube as a starting point). If you can calculate all of the properties of a hyper-dimensional object, you do understand it quite well, even if this is hard to believe at first. We tend to have a sometimes crippling dependence on what we can see and hold, but math can free us to "see" far more.

Before you click off to another page, just consider that you already know a 4-D world in great detail: the 3-D world with time added as a fourth dimension. In fact, huge numbers of dimensions may be present in problems or hobbies you currently explore, but it may take a few moments with A. Square to realize it.

As I have recently come to learn, Edwin Abbott traveled in exciting intellectual circles, being friends with H. G. Wells, for example. This connection, and others to Victorian life and events, to a certain George Boole (of Boolean Algebra fame), the novel Frankenstein, and other cultural icons, are explained to us in the The Annotated Flatland: A Romance of Many Dimensions, with extensive notes and pictures provided by Ian Stewart. Mr. Stewart, who wrote the previously mentioned Flatterland, is a celebrated mathematics professor and author, with titles including Does God Play Dice? and Nature's Numbers to his credit. The additions by Stewart include marginal notes, a preface, an introduction, a chapter on the math of four dimensions, and an extensive bibliography, all of which help us to understand better both Abbott's primary tale and his subtext that satirized Victorian society.

The Annotated Flatland is highly recommended!

Note: E. A. Abbot passed away in 1926, in Hampstead (find notes and maps for Hampstead Heath by clicking on the link).

© James K. Bashkin, 2007

Technorati Tags:victorian, flatland. mathematics, geometry, flatterland, does god play dice?, nature's numbers, edwin abbott, ian stewart, n-dimensional, 4th dimension, fairy tale, the annotated flatland, hampstead, hampstead heath
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Murder in China and Tibet, and London; Peter Rozovsky!

OK, so I read Qiu Xiaolong's books a while ago and gave an impressionistic synopsis of the first one, Death of a Red Heroine that was probably influenced by the second (A Loyal Character Dancer). If you want to read a more more detailed series of analysis, complete with references to major newspaper articles, and insight, go to Detectives Beyond Borders, which the author Peter Rozovsky kindly referred me to, and search for Qiu Xiaolong. Sorry, I can't get the link to work to take you to exactly the right place yet. But, so much for my "no objective standards" comment- now I feel pressure! Added later: here is the link to Qiu Xiaolong I was missing.

So, on to The Skull Mantra (TSM) by Eliot Pattison and The Murder Room (TMR) by P.D. James. I read both of these in August, with rather different results. I won't repeat my comments about the Pattison book already made to Peter Rozovky's blog, so here is where to search for them (my answer to the question in the Sept 1, 2007 post). Again, sorry about my poor HTML skills- I have to sort out why the links I had were not working.

I did struggle a little at the beginning of TSM, and had started it before but not gotten far. This time I had the good sense to read on. Contrast this with TMR, which starts with a beloved T. S. Eliot quote (from Burnt Norton)* and moves quickly to that area outside of London much loved by fictional characters, being approximately three miles north from 221B Baker Street, and by real people, including authors: Hampstead Heath. The Heath is crisscrossed by roads but is really quite large, with open grassy areas, wooded regions and walking or running paths to tempt lovers, criminals and healthy English people of a certain age. The reader is immediately put in the care of a perfect host, the urbane Commander Adam Dalgliesh, a published poet* whose day job happens to be at New Scotland Yard. TMR was easy to start, like candy or a bottle of single malt.

*see Qiu Xiaolong's inspector Chen!

Now, before I go on, I should dispense with some psychological baggage. Until this August, I had boycotted P. D. James for about 30 years. Why? Because the books were bad? No, rather the opposite. I found the writing to be so good, the characters to be so engaging and the story to be so gripping that when I finally learned who the villain was the last time I read James, I was too depressed to want to go through that experience again- the fellow was too likable (ignoring the crime, anyway). Oddly enough, looking over the back catalog online today, I haven't been able to figure out which book caused this reaction- I'll have to go to the library and read the last chapters of all of them, because I remember that chapter vividly (given the way my 49-year old memory works, I might well find out I was boycotting the wrong author, but I will get to the bottom of it).

So where are we? TSM has us spending time inside a prison work-camp and building roads by hand, high on a Tibetan mountain. While doing so, we start to learn about Tibetan prayers and religion through the eyes of a true outcast, a hated Chinese prisoner embedded within the Tibetan prisoners. However, in a spirit that may be relatively unique to Tibet, some of the imprisoned monks welcome their Chinese "comrade", if over time, so that he is much more at home with the prisoners than with the abusive Chinese guards, Warden, or any other ethnic Chinese he is likely to meet in Tibet.

Everything, and I mean eventually EVERYTHING, is turned upside down by the discovery of a headless body by the prison work crew, right where they are supposed to build the rode. The only experienced detective in the region is the mysterious Chinese prisoner whose file contains no information because he committed no crime, except to attempt to expose corruption by a Party official too powerful to fight. It is a bit like the world of the Chateaux d'If from Alexandre' Dumas' The Count of Monte Cristo or The Man in the Iron Mask, where a note from royalty could imprison a man for life without due process. Oh, it sounds a bit like imprisonment at Guantanamo Bay, too, though I hope that will come to an end before long. So is the mystery going to be placed in the hands of the lowest of the low, a former inspector reviled and made to disappear by his fellow Chinese and reviled by many of the Tibetans he will meet? (Tibet has been colonized violently by China in an ongoing process that started on October 1, 1949)

As I read deeper into TSM, the memories of his institutionalized mistreatment and cherished, but deeply hidden, memories of time with his father show us a man who has learned to survive by fighting his instincts, keeping his head buried, and now, against his will, that head is plucked out of the sand, its eyes are forced open, and he is given the choice of solving the crime or watching the massacre of his fellow prisoners. Why such drama? Because the Tibetan respect for the dead and fear of evil spirits means that the road building will not restart unless and until the murder can be cleared up in a way that mitigates all superstition. So, solve this crime for me and make sure I like the answer, is essentially what the local military commander orders the prisoner, who is given some freedom of movement, a driver and a translator.

Much tension in the book comes from mixed allegiances amongst Chinese military, political and policing institutions and amongst Tibetan factions, tribes or monasteries, some of whom may be dealing illegally with drugs, antiquities or both. Some witnesses and other participants in the events belong to these various factions. However, the slow re-emergence of the inspector's pride, which seemed to have been beaten and starved out of existence, provides a forward motion to the story, as the inspector struggles less and less with himself and more with the mystery at hand. The inspector is not the only person who finds his pride re-awakened by the circumstances: his assigned army chauffeur/guard/watch-dog is forced to face the humanity of the Tibetan people he is oppressing, and forced to recognize that his "work" is a sad, shameful and unsuitable end to a proud military career.

One of the best parts of the book is the development of our relationship with the military commander (not the same person as the prison camp warden). This man is not shown as a caricature, and ultimately he needs the truth as badly as the inspector, creating a situation that could prove fatal for all.

The nearby presence of a Western mining operation and the first bus-load of tourists for the season place spatial and temporal bounds on the investigation, yet long journeys across high desert and through dangerous mountain passes must be negotiated in attempts to track down a witness before he can be killed by the as-yet unidentified murderer(s).

Further complicating things is the discovery of a cave, in between the prisoner's work camp and the Western-leased mine, filled with skulls dating back to the beginning of Tibet's recorded time. This introduces a possible motive for murder, in that some group, Chinese or Western, is looting the artifacts, a highly illegal act.

Ultimately, an unwavering attention to detail in the face of the many feints and misdirections carried out by the murder(s) allows the inspector to track certain key artifacts that may or may not be missing, and to tease out the web of people connected with them so that the crimes begin to unravel. However, even with many of the basics of the case seemingly within our grasp, a series of absolutely shocking, yet immediately credible, revelations awaits us.

The end of TSM is a typical race against time in some ways, but there is nothing typical about the setting or the motivations of its key people, let alone the brilliant manipulations that have been carried out to insulate the puppet master(s) from the actions that caused so much destruction of life. After the slow start lasting maybe 12 pages, I read the book pretty much straight through, trying not to rush or miss anything, trying to keep separate and distinct the different temples and tribes and their roles, but increasingly anxious about the fates of all concerned.

So wither The Murder Room? TMR has plenty of its own misdirection, with contemporary murders in a museum apparently copying a set of murders from long ago, memorialized in that very museum (which is dedicated to the period between WWI and WWII). There are sympathetic characters, there are unpleasant characters, there are characters about whom one is ambivalent. After the first crime, there is more murder and attempted murder, and more lives may seemingly yet be lost at any point. So we have urgency. We also have the parallel story of Dalgleish's love interest, who is inconveniently located at Cambridge, and some internal police politics that are trumped by "larger" concerns, a catch-phrase for so much now, as it probably always has been (sorry Caesar, the seating plan for today's committee meeting is "need to know, only").

The problem is that the larger forces at play (i.e. National Security) really aren't at play. Instead we have a bunch of government ministers, judicial appointees, and wealthy people trying to protect each other, regardless of whether the case is solved or not (and with blatant disregard for potential additional victims). This may have resonated strongly in the U.K. after the revelations about how false confessions were obtained by torturing suspected IRA members, but in today's world, in the USA, this seems like an old story, a story that is probably being acted out now in real life, but one that has no more hook than last year's headlines. It is expected behavior, and why should we care how some other member of the privileged classes justifies his or her self-serving behavior? Fine, throw them in jail (or pardon them if you are President Bush), but don't expect me to be shocked that somebody in authority lied, or even compromised National Security for personal or political gain. I've been living with a Vice President who outed a covert CIA operative during wartime. Didn't we formerly execute people for treason? Now they go on the lecture circuit. So, for me, this book started out like gangbusters and ended up a bust. It is an OK read- the language is good (which is not so common these days), the minor characters are well drawn, and the workings of Dalgleish's mind are a pleasure, but the final third of the book is a major disappointment that left me feeling completely disconnected from the fate of the criminal(s).

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