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30 December 2009 / April


Since approximately my first week at Williams, I have not read a word for my own pleasure while at college, at least not one that wasn’t depicted on a screen of one sort or another.  This concerned me a little.  I worried that in addition to my diminishing enjoyment of fiction, I was no longer able to enjoy reading at all.  I worried that the internet had decreased my attention span beyond rescue, that school had rendered me incapable of reading for fun, that I would no longer be privy to the great privilege of losing myself in a good book.

All that changed when I started reading Anathem by Neal Stephenson.

Mostly because I had other things to worry about, like what the hell all these totally invented words meant.  XKCD has already made its typical astute commentary on the sheer number of made-up words in Anathem, but the full import of that didn’t sink in until I read the epigraph of the book, which isn’t really a normal epigraph at all but the (fictional) dictionary entry of “Anathem”– which you’d think would be helpful.  But you know how you sometimes laugh about dictionary definitions that use more complicated words than the ones they’re defining?

Anathem: (1) In Proto-Orth, a poetic or musical invocation of Our Mother Hylaea, which since the time of Adrakhones has been the climax of the daily liturgy […]  (2) In New Orth, an aut by which an incorrigible fraa or suur is ejected from the math and his or her work sequestered […]


There’s a glossary in the back if you want to cheat, but even that doesn’t make much sense until you’re a couple dozen (or in some cases, a couple hundred) pages into the book.  But if you want to appreciate the full glory of Anathem, I implore you not to cheat.  It’s like a puzzle.  A really awesome puzzle.  Tolerate the confusion and frustration knowing that the feeling you get when you figure it out will be worth the trouble.

If the thought of reading a thousand-page book that is like one big frustrating puzzle chills you to the bone, steer well clear of Anathem.  Because if you don’t like puzzles, you’re probably not particularly mathematically or philosophically minded, you’re probably not particularly inclined to read appendices about configuration spaces, and you therefore probably will not particularly enjoy immersing yourself in an alternate universe where science, math, logic, and philosophy take the place of religion.

The world of Anathem, roughly speaking, is like Earth, but with the proverbial ivory tower manifested.

It’s a strange world for sure, but inevitably there are myriad similarities with our own, and therefore myriad opportunities for satire.  Particularly regarding the relations between ivory tower folk and everyone else.  “There might as well be [an infinite amount of money],” says one character, “but most of it gets spent on pornography, sugar water, and bombs.  There is only so much that can be scraped together for particle accelerators.”

By the way, this is probably the first real hardcore science fiction book I’ve read, so it’s quite possible that much of what I’ve said and will say is unnecessary for anyone who’s read sci-fi.  For instance, I get the feeling that more than any other genre of fiction, sci-fi is all about ideas.  There are some intense action scenes in Anathem, there’s page-turning edge-of-chair-gripping keep-you-up-at-night suspense, and there’s a kind of awkward little romantic subplot that you wish would go away but you honestly would miss if it weren’t there at all.

But there are also pages and pages of people walking through a garden or eating dinner while talking about truly fascinating ideas that are a godsend to a nonfiction junkie like myself.  The book, like all other stories in existence (or so I’m convinced), is chock-full of clichés, but they’re easy to ignore when the ideas are so innovative.

In fact, my least favorite parts of the book were when the protagonist was making his way around the world and not really discussing any ideas at all.  I could actually describe the various sections of the book in this way: the very beginning when I was suffocated by confusion; most of the first half when I was starting to understand the language and the world, the characters were starting to understand the events at hand, and everything was getting very very interesting; the part I just mentioned where there’s a lot of action and not a lot of ideas; and the last third which is basically a pedal-to-the-metal sprint to the end, packed with both action and ideas.

From this it’s might be clear that the second section is my favorite.  The second section made me think this was the best book I’d read all year.  Which might still be true, but to be honest I don’t really remember what books I’ve read this year.

And to be honest, there are plenty of other things besides the excess of vocabulary and the dull action scenes (…not an oxymoron, I promise) that make Anathem less than perfect.  First of all, there are typos in the glossary.  I mean, come on, what the hell?  Then there are some rather subtle flaws of logic, which are probably inevitable in such an otherwise well-constructed universe; I’ll avoid pointing them out because there are spoilers.

Finally, the very ending is atrocious.  I’m talking like the last paragraph, the last few words.  I won’t pretend to know of a better way to conclude such an extensive and epic work, but I certainly would not have ended it the way Stephenson did.

But even that seems just a minor quibble in light of what I found truly amazing about Anathem.  It described a world with a large group of people who have devoted their lives to intellectual pursuits, with absolutely no intention or obligation of ever making something useful out of them, and to whom it need not be explained why that can still be fulfilling.  To me, that’s pretty cool.

The last book of great length I remember reading in a short intense span of time around Christmas was Gödel Escher Bach, a book I found equally absorbing– and, somewhat surprisingly, for some of the same reasons. Books like these make me read up on proofs of the Pythagorean Theorem, write out mathematical statements in symbols of logic, and ponder concepts first broached to me in computer science classes (explained after the jump).

Books like these make me think.  To me, that’s pretty cool too.


Now onto random musings on directed acyclic graphs…  The lines that got me thinking about DAGs were these:

Here “directed” just means “arrows are unidirectional.”  The modifier “acyclic” means that the arrows can’t go around in a circle, i.e., if we have an arrow from A to B, we can’t also have an arrow from B to A.

First of all, this explanation is a little misleading– or maybe it only is in my eyes.  Assuming that the arrows are edges and A and B vertices, what he really means is that if there is a path from A to B, there is not a path from B to A, where a path is just what it sounds like: a sequence of arrows/edges leading from the start vertex to the destination vertex.

In CS this past semester, we saw both directed and undirected graphs, and we implemented undirected edges just as two directed edges pointing in opposite directions.  It’s like thinking of a two-lane road as two one-way roads that happen to share the same start and destination (albeit switched).  This is pretty silly when it comes to roads, but useful when thinking about graphs.

Once you think about undirected graphs this way, you find that the phrase “directed acyclic graph” is redundant.  An acyclic graph has to be directed, because an undirected graph would have a path– in fact, an arrow– from B to A every time there was an arrow from A to B. So an acyclic graph is kind of like a generalization of a directed graph: not only does it have none of the simple, two-vertex cycles that undirected graphs have, but it also lacks more complicated multi-vertex cycles.

All this would be easier to explain and understand with pictures, but I’m much too lazy to make them.

The specificity and clarity of the term “directed acyclic graph” is useful and I have no objection to it.  But I’m a fan of finding generalizations wherever they may be hiding.

(Disclaimer: I am such a noob when it comes to discussing any of this technical stuff.  So please don’t eat me alive.  You should kill me first.  Thanks.)


One Comment

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  1. Rafael Lizarralde / Dec 30 2009 12:09 pm

    About directed acyclic graphs, the term stems from the way that graphs are classified: they typically divide into directed and undirected, as the first and usually highest order of classification.

    And as for sci-fi books… The ones with the intriguing ideas are the best! Here are some recommendations:
    Brave New World
    Ender’s Game
    Snow Crash

    You’ve probably already gotten to some of those, but if not, get thee on thy way!

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