I liked the spareness of the old one, but it didn’t look very good on mobile devices. Hence the update. About the only things I dislike about this one is that the formatting on quotations is a little large, and the navigation arrows at the bottom are reversed from the directions I’d prefer. I’ve put lush green grass in the header for now as an appeal for Spring to consider finally maybe arriving and sticking around.
I recently finished reading Thomas M. Disch’s novel Camp Concentration, which had more words in it that I didn’t know than any book I’ve read in years. Here are the new additions to my vocabulary.
- Orthoepy. n. The correct or accepted pronunciation of words.
- Lutulent. adj. The state or condition of being muddy or turbid.
- Resile. v. Abandon a position or course of action.
- Orgulous. adj. Haughty.
- Chrism. n. A mixture of oil and balsam, consecrated and used for anointing at baptism and in other rights of the Catholic, Orthodox, and Anglican churches.
- Hierodule. n. A slave or prostitute in service to a temple.
- Hypogeum. n. An underground chamber.
- Chiliad. n. 1. A group that contains 1,000 elements. 2. A millennium.
- Opsimath. n. A person who begins to learn or study only late in life.
- Jactitation. n. The restless tossing of the body in illness.
- Squitters. n. Diarrhea.
- Commination. n. The act of threatening divine vengeance.
- Electuary. n. A medical substance mixed with honey or another sweet substance.
- Meretricious. adj. Apparently attractive but having in reality no value or integrity.
- Rodomantade. n. Boastful speech or behavior.
- Concinnate. adj. Of speech or writing: put together with elegant style or propriety.
- Philoprogenitive. adj. Having many offspring.
- Emissile. adj. Capable of being protruded.
- Epalpibrate. adj. Lacking eyebrows.
- Viscid. adj. Glutinous, sticky.
- Atomy. n. A tiny fairy or sprite.
- Virescence. n. The state or condition of becoming green.
- Chyme. n. The pulpy acidic fluid that passes from the stomach to small intestine, consisting of gastric juices and partially digested food.
Jorge Luis Borges’ story “The Library of Babel” has long been an obsession of mine. The 1941 short story1 posits a library that contains every possible book-length2 combination of words. It’s probably my second-favorite short story3; I think about it all the time and teach it whenever I can. I once even wrote a program to output the digits of 251,312,000, the number of distinct books the Library of Babel contains, which produced a 2Mb text file of mostly zeros.4 So when my friend Tony Tulathimutte (about whom I’ve written before) asked me to consult on a “Library of Babel”-inspired essay he is writing on the algorithmic generation of literature, I doubt he had any idea what he was getting into. Tony asked:
Even if 251,312,000 is beyond astronomically large, I’m interested in getting as close as possible to a non-theoretical implementation of the Library. Can we work on a Fermi estimate of what it would take to assemble the library? Like, if we distributed the workload to every computer on Earth, or used the world’s fastest supercomputer (China’s Tianhe-2, 33.86 petaflops), or even assembled a Douglas-Adams-style Deep Thought Computational Matrix made of human brains (the human brain runs at an estimated 36.8 petaflops)? Or if Moore’s law holds, at what point would the processing power on Earth suffice to create the Library within the lifespan of the universe.
This is a completely reasonable question, but one that illustrates just how unnatural it is to think about numbers that are “beyond astronomically large.” The number of books in the Library of Babel is so big, no set of adjectives can meaningfully capture its hugeness. After all, things like petaflops, or the computational capacity of the human brain, are also too big to really conceptualize. So it makes sense that one might treat them all as members in equal standing of the Numbers Too Big To Think About club. But they aren’t. Here are three illustrations of the absurd magnitude of the Library of Babel.
First we’ll look at the initial question, how long would it take to generate the Library of Babel? Instead of addressing it the way Tony suggests, though, let’s approach the problem from the opposite direction: what is the fastest it’s possible to imagine generating the Library of Babel?
The Heisenberg uncertainty principle implies that there is a smallest possible size something can be, and a shortest possible time in which something can happen. These minimum quantities are built in to the basic workings of the universe, and are called the Planck units. The Planck time is equal to about 5.391 x 10-44 seconds. It isn’t physically possible for an event to occur in less time than that. Let’s imagine that we have computers capable of generating one Library of Babel Book (LoBB) per unit of Planck time. How many of these computers? Let’s be ambitious! Through some impossible alchemy, we will now turn every single atom in the observable universe into a computer capable of generating one LoBB per unit of Planck time.
There are on the order of 1080 atoms in the observable universe. So let’s say we have that many computers… what’s that? Oh, you’re asking, “but what about dark matter?” It’s true. Scientists think there might be five times as much dark matter in the universe as there are atoms. So let’s be generous and bump it up ten times: we’ll say with have 1081 computers, each of which generates one LoBB per unit of Planck time. So, if we have 1081 computers generating about 1044 LoBBs per second, that means we generate 10125 LoBBs every year.
There are 251,312,000 possible LoBBs, which is on the order of 101,786,586. At a rate of 10125 LoBBs per year, it will take 101,786,461 years to finish making the whole Library, or on the order of 10106. Take a quick look at Wikipedia’s timeline of the far future. You’ll notice that the time when we finish making the Library at the fastest imaginable rate would be the sixth-to-last item on the list, coming well after the entire universe is a cold, dead cinder.
So the answer to Tony’s question is: never.
2. World Enough
But maybe you noticed that I cheated a little. I said I would consider the fastest it’s possible to imagine generating LoBBs, but calculated based on the fastest it would be physically possible to make them. We can imagine things faster than that, though. We can imagine just snapping our fingers and–poof!–a complete Library of Babel made in an instant! So, why not? Let’s consider that case. We now have the power to instantly assemble a Library of Babel.
Assemble it… out of what? I mean, what are we going to make the literal books out of? Not out of atoms; we already said that there are, generously, 1081 atoms worth of matter in the observable universe. Even if we could someone encode a LoBB in every atom, we wouldn’t come close to making 10106 of them. Not even if we could make a LoBB out of every subatomic particle.
The universe just doesn’t have enough stuff in it to make the Library of Babel.
3. Vaster Than Empires
So let’s add more stuff. We’ve already given ourselves the power to instantly reconfigure every atom in the universe. Why not give ourself the power to make new matter out of nothing while we’re at it? What happens then?
Turns out, even if we could conjure enough new matter to make the Library of Babel, the universe itself would be too small to hold it.
There’s a weird and fascinating result from black hole physics called the holographic principle. The holographic principle says that all the information needed to describe a volume of space, down to the minutest quantum detail, only ever takes as much space to encode as the surface area of the volume.5 That is, if you wanted to write down all the information necessary to perfectly describe every detail of what’s inside a room, you would always be able to fit all the information on just the walls. In this way, the entire universe can be thought of as a three dimensional projection of what is, on the level of information, a strictly two dimensional system. Sort of like a hologram, which is 2D but looks 3D. That’s where the principle gets its name.
In any normal region of the universe, the amount of information in a given volume will actually be much less than what you could encode on its surface area. For reasons having to do with thermodynamics that are too complicated to go into here, when you max out the amount of information a volume of space can contain, what you have is a black hole.6 Now, remember those Planck units from the beginning? Length was one of them; there’s a smallest possible size that the laws of nature will let something be. The most efficient possible encoding of information, per the holographic principle, is one bit per unit of Planck area, which is on the order of 10-70 square meters.
The observable universe has a radius of around 4.4 x 1026 meters. That gives it a surface area on the order of 1053 square meters, which means it can hold 10123 bits of information. That’s just the observable universe though; the whole universe is much, much bigger. We aren’t sure exactly how much bigger. It isn’t observable. But inflationary universe theory, which just got some strong confirming evidence, provides an estimate that the whole universe is 3 x 1023 times larger than the part of the universe we can see. Carry out the same calculations, and the estimated size of the whole universe means that it can contain 10170 bits of information.
Are you ready for how big the Library of Babel is?
If you assume that it takes a string of at least six bits to encode one of a set of 25 characters, then the whole Library of Babel would require about 1.3 x 102,369,708 bits. Even if we demiurgic librarians do violate the law of conservation of energy to bring the Library into being, the entire universe would collapse into a black hole long before we finished our project.
So: the Library of Babel is so large that the universe isn’t going to be around long enough to make it. And even if it was, there isn’t enough matter and energy to do it. And even if there was, before that point all of reality as we know it would be destroyed. That is how extreme things can get when you start dealing with “beyond astronomically large” numbers.
As described by Borges: 25 symbols, 40 symbols per line, 80 lines per page, 410 pages. ↩
Second only to “Bloodchild” by Octavia Butler. ↩
This is because, physically speaking, information is the same thing as entropy. If my Thermo Thursday posts go on long enough, I may eventually explain this. I’ll try to remember to update this footnote if I do. ↩
Big congratulations to Karen Joy Fowler, author of my favorite novel from last year, for winning the PEN/Faulkner award! A well-deserved recognition for an outstanding book. Here’s the Washington Post’s article on the award, which contains plot spoilers. But eventually this spoiler is going to reach you anyway. If you want to preserve your reading experience and haven’t gotten a copy yet, go! Now! Read it! It’s out in paperback! What are you waiting for?
As previously mentioned, graduate school was hell on my reading. To get back in the groove I resolved that this year I would read at least one book a week. Twelve weeks in, I’m ahead of schedule. Here are the first twenty books I’ve read this year. (Collage above made with this online tool.)
- The No. 1 Ladies’ Detective Agency by Alexander McCall Smith. This one failed to impress me, and I doubt I will read any other books in the series.
- Solaris: The Definitive Edition by Stanislaw Lem (audiobook). This is the new translation direct from Polish released in 2008. I’d tried to read the previous translation once, which was actually a retranslation from French, and found it unimpressive. I loved the direct translation, though, and can see why it’s held in such esteem among Lem’s works.
- Tuf Voyaging by George R. R. Martin. This is a reread, inspired by the book’s presence on Kevin Brockmeier’s list of his 50 favorite SFF books. I thought it delightful fun the first time, and I still feel that way about it. It’s a collection of linked short stories, but both times I’ve read it in a single sitting.
- The Book Thief by Markus Zusak. This is really a gorgeous, ambitious book. Carmen Machado loves it, and had been recommending it for a few years. The novel’s formal conceit is that it is narrated by Death, and while this is achieved with great sensitivity and beautiful language, my own lack of affection for Cartesian dualism means I found it less affecting than I otherwise might. I suspect that’s why I merely really liked it rather than loving it.
- Superman/Shazam: First Thunder by Judd Winick and Joshua Middleton. I was inspired to read this by Justin Pierce, who posted to Facebook a page from it in which Superman is furious when he learns that Captain Marvel is a transformed child. That scene was probably the best thing in the book, but it was fun.
- The Genocides by Thomas Disch. This is another one from Kevin’s list. It’s one of the bleakest books I’ve ever fully enjoyed. Humanity is uncomplicatedly eliminated as unseen aliens turn the planet into a monoculture for a genetically engineered crop. As unremitting an apocalypse as I’ve ever read.
- Arcadia by Tom Stoppard. This, as is obvious if you’ve clicked the very first link in the first paragraph, is a reread. I bought a bunch of copies of the play and threw a table reading party. We all drank mulled wine and hammed it up.
- Options by Robert Sheckley. After Van Choojitarom challenged people to come up with a novel odder than Voyage to Arcturus (which I still need to read), I offered this as a possibility. When I was 16 it seemed to me merely a memorably enthusiastic work of metafiction. Reading it now, though, it strikes me as an absurdist take on the difficulties of the creative process. Reading it makes me feel like I do when I’m struggling at the keyboard, and yet it’s entertaining. It’s also short enough that despite the overt metafictional elements, it doesn’t wear out its welcome. Might be my favorite Sheckley now. (Note if you’re planning to give it a shot, I’m pretty sure the opening few chapters intentionally read as terribly-written. Which is to say, I think they are well written, but in intentionally bad prose.)
- Childhood’s End by Arthur C. Clarke. Yet another from Kevin’s list. I read it as a kid and didn’t find it terribly impressive then, by Kevin’ and Jo Walton’s appreciation for the book convinced me to give it another chance. They were right. It’s really an excellent book, for all the reasons Jo outlines. Also, I realize I must have been under ten years old the last time I read it, because I remember thinking that if the events in the book were to happen, I would have been among the posthuman cohort.
- Where Late the Sweet Birds Sang by Kate Wilhelm. I’d never read one of her novels, and this one won the Hugo award in 1977, so seemed a good place to start. I didn’t enjoy it as much as I wanted to. I liked the opening section well enough, and the writing is good throughout, but I found culture of the clone generations unconvincing.
- Sarah Canary by Karen Joy Fowler. I love everything by Fowler I’ve ever read, which is several short stories and now three novels. This one is now my second favorite, behind We Are All Completely Beside Ourselves, my favorite novel I read last year. Sarah Canary is lyrical and brilliant. Also, this is yet another one from Kevin’s list, which has yet to lead me astray.
- The Steps of the Sun by Walter Tevis. This is the last of Tevis’s science fiction novels that I hadn’t read, after reading The Man Who Fell to Earth and Mockingbird last year. I have yet to read anything by Tevis I don’t find engrossing, but this is a weird one. The opening I loved so much it seemed on pace to become a favorite, but toward the end the book takes a turn that I’m still trying to figure out my feelings toward. I still liked it, but I think less than the previous two.
- Bad Behavior by Mary Gaitskill. I’d read a few of these stories before, such as “Secretary” (the basis for the movie) and “A Romantic Weekend”(a favorite of mine), but never the whole collection. It’s good. Completely unsentimental psychological realism, full of obsessions and kinks. I’ve got another Gaitskill collection on deck for later.
- The Lifecycle of Software Objects by Ted Chiang. This was a reread that I assigned my science fiction writing class, in advance of Ted doing a Skype visit. I think this book is perfect.
- Hawkeye vol. 1 by Matt Fraction and David Aja. This was a gift from Matt when I visited Portland. It’s great fun, deserving of all the superlatives on the cover. Each issue is a tiny, clever action movie, the cleverest one from the point of view of a dog.
- The League of Extraordinary Gentlemen: Century: 2009 by Alan Moore and Kevin O’Neill. After Portland I find myself on a bit of a comics kick. This is the third of the Century volumes, and I didn’t enjoy it that much. Harry Potter as the antichrist was fun enough, but at this point LoEG seems more about enacting its conceit than about telling a story. Still, there were some nice tender scenes between Orlando and Mina.
- Weapons of the Metabarons by Alejandro Jodorowsky, Travis Charest, and Zoran Janjetov. A fairly forgettable addendum to an unforgettable series. I bought an omnibus collection of the original Metabarons series in Portland and will probably reread it soon.
- The Brief History of the Dead by Kevin Brockmeier. Kevin’s writing is beautiful. This book is about a city populated by everyone who is dead but still remembered by someone alive, and what happens to that city when everyone on Earth starts to die.
- Fourth Mansions by R. A. Lafferty. I bought this book on the strength of its chapter titles, which are things like “Now I will dismember the world with my hands” and “But I eat them up, Frederico, I eat them up.” This book was…strange. Not bad, but not good either. I’m not convinced that it is about anything except itself. It’s an internally consistent system of symbolism that doesn’t necessarily have any relevance to the real world. The language was very entertaining, but it’s verbal fireworks bursting above an insubstantial landscape.
- Nemo: Heart of Ice by Alan Moore and Kevin O’Neill. I liked this more than Century: 2009, because it’s more strongly narrative and because I enjoyed the H. P. Lovecraft and John Campbell references. Still a minor work, though.
Thermo Thursday returns. But on a Tuesday! WHO COULD HAVE SUSPECTED?
This section introduces isothermal and adiabatic compression. Isothermal compression is compression that occurs so slowly that no heat is added to the gas. For isothermal compression of an ideal gas, the temperature remains constant, so you can use the ideal gas law, , and the integral equation for work done during compression, , to derive that . Since work is being done but the temperature is not changing, heat must be flowing out of the gas, in an amount equal to the work being done. On a PV graph, an isothermal compression takes the shape of a concave-up hyperbola.
Adiabatic compression, in contrast, happens so fast that no heat escapes from the gas during the process. Thus, for adiabatic compression, . The PV curve for this starts on a lower temperature isotherm and ends on a higher temperature isotherm. To find an equation for the shape of that curve, we look at the equipartition of energy theorem, , where f is the number of degrees of freedom per molecule. The infinitesimal change in energy along the curve is then given by . If we assume the compression is quasistatic, then from the equation for work we know that . (We can say this because we previously established that in adiabatic compression the entire change in energy comes from work.) This gives . Now you can plug in the ideal gas law for P and do some canceling to get . This ends up simplifying down to for some constant C. If you are looking for pressure instead of temperature, you can use the ideal gas law to rewrite this for some constant D, where and is called the adiabatic constant.
Problem 1.35: Derive from .
I’m going to use a subscript on the constant term to show when that side of the equations changes. Let’s start with . I want to get this equation in terms of pressure, so we use the ideal gas law to say that . This gives us
Raising both sides of the equation to the power 2/f and moving the constant terms to the right side gives
I can then combine the volume terms,
Problem 1.36: In the course of pumping up a bicycle tire, a liter of air at atmospheric pressure is compressed adiabatically to a pressure of 7 atm. (Air is mostly diatomic nitrogen and oxygen.)
(a) What is the final volume of this air after compression?
I will treat the air as a diatomic ideal gas for these calculations, which means the air molecules have five degrees of freedom. This gives me . For adiabatic compression, , so
which for an initial pressure of 1 atmosphere and volume of 1 liter, and final pressure of 7 atmospheres, gives a final volume of 0.25 atmospheres.
(b) How much work is done in compressing the air?
The total change in energy is the heat added or lost plus the work done, . Since this is adiabatic compression, there is no heat lost to the environment, so the entire change in energy is due to work. From the equipartition of energy theorem and the ideal gas law I can write , which for this system gives
Plugging in =0.25 L, =7 atm, =1.0 L, =1 atm, converting to SI units, and calculating gives an energy added due to work of 189.5 J.
(c) If the temperature of the air is initially 300 K, what is the temperature after compression?
I can use the equation to say that
Plugging in the values and calculating this out gives a final temperature of 522 K.
Problem 1.37: In a Diesel engine, atmospheric air is quickly compressed to about 1/20 of its original volume. Estimate the temperature of the air after compression, and explain why a Diesel engine does not require spark plugs.
Since the air is compressed “quickly,” I will assume adiabatic compression, and since it’s air that’s being compressed it has the same degrees of freedom as the previous problem. So I can use the last equation from part (c) above, plug in , and simplify to get
So if the initial temperature of the air is 300 K, then after compression the temperature will rise to around 990 K. Since the ignition temperature of Diesel fuel is 483 K, the air after compression is hot enough to ignite it without a spark.
Problem 1.38: Two identical bubbles of gas form at the bottom of a lake, then rise to the surface. Because the pressure is much lower at the surface than at the bottom, both bubbles expand as they rise. However, bubble A rises very quickly so not heat is exchanged between it and the water. Meanwhile, bubble B rises slowly (impeded by a tangle of seaweed), so that it always remains in thermal equilibrium with the water (which has the same temperature everywhere). Which of the two bubbles is larger by the time they reach the surface? Explain your reasoning fully.
Bubble A undergoes adiabatic compression (in this case, expansion), while bubble B undergoes isothermal compression. Initially, the bubbles are identical, so their pressures and volumes are equal. For isothermal compression, where C is a constant, and for adiabatic compression . The constants C must be the same, because the bubbles are initially identical. Since , . Thus, the bubble that undergoes isothermal compression, bubble B, is larger when it reaches the surface. This can be seen by visual inspection of a graph depicting an isotherm and an adiabat. Notice that for the same initial conditions, the volume of the isotherm rises faster than that of the adiabat.
My friends are talented and prolific! Look at their things!
- “Luxury Shopping, From The Other Side of the Register” – In December Carmen Machado wrote for the New Yorker about what it’s like to be working retail during the busiest shopping days of the year.
- “Bummed Out and Ugly” – Alice Sola Kim with a beautiful and personal remembrance of Philip K. Dick.
- “Crossroads and Coins: A Review of Naomi Mitchison’s Travel Light” – Amal El-Mohtar writing for NPR, another quite personal piece. Having recently read the book myself, I can confirm that it is as delightful as Amal claims.
- “Scattered Leaves” – Ben Mauk writing for the New Yorker about the current practice of dismembering ancient manuscripts and selling individual pieces of them on eBay, as well as the long history of “book breaking.”
- “To Flip a Flop” – Also in the New Yorker, Elizabeth Weiss writes about the economics of the broadway show, using the example of the largely unsuccessful Spiderman: Turn Off the Dark.
The last time I saw a gameplay video that made me this excited, it was the first teaser video for Portal. A Carnegie Mellon team calling themselves Pillow Castle Games are developing a first person puzzler built around a mechanic that uses projection phenomena for object manipulation. I bought Portal when it came out even though I didn’t have a machine to play it on, and I’d likely go to similar lengths to mess around with this.
Michael J. Pollard, who was nominated for an Academy Award for his role as C. W. Moss in Bonnie and Clyde, had a guest star turn on the 1988 television show Superboy. Superboy was notable for recasting the parts of both Clark Kent and Lex Luthor between seasons 1 and 2, and also for being the only entry in the Superman mythos set entirely in Florida. But judging from his Wikipedia page, which currently contains no mention of it, Michael J. Pollard’s involvement has been largely forgotten. That’s a historical oversight which needed correcting, so for posterity I’ve put together a seven minute cut of this treasure. Enjoy.
EDIT: Well that was fun while it lasted.