My parents remodeled their master bathroom, and my mother decided to install a sleek, Japanese robo-toilet. It sits there in its little room, compact, inert, until it senses someone approaching. Then it opens up a big, glowing, angler fish mouth and hisses. If I were exploring a crashed alien spacecraft and encountered an object with this sort of gaping solicitousness, I’d expect my flesh to be feeding its babies by now.
Category: Blog
Because I’m fickle. I’m sure I’ll settle on something I like eventually. Until then, the nearly nobody who looks regularly at this website may enjoy a stimulating variety of layout and appearance.
Eagle-eyed Kevin Brockmeier alerted me that my name was printed in the Daily Iowan, as part of the list of the class of 2014’s favorite professors. As you can see, we’re an exclusive group.
I’ve started using IFTT to aggregate my favorite tweets to Evernote. Here are the things I favstarred this week.
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The gift of divine foresight will be shewn by these holy signs:
- A new season of Arrested Development happens
- and it features Michael Bluth having to pull GOB on his broken-down Segway like a rickshaw driver
- to escape from the swamp home of a family of alien crab monsters with whom Michael gets involved after mistaking their crab monster daughter, Courtney Cox, for the famous human woman of the same name.
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.
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 story; 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. 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 was happy to help. 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.
1. Time
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 1043 LoBBs per second, that means we generate 10124 LoBBs every second, 10131 LoBBs per year.
There are 251,312,000 possible LoBBs, which is on the order of 101,834,097. At a rate of 10131 LoBBs per year, it will take 101,833,966 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 one of the last items on the list, coming well after the entire universe is a cold, dead, iron 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 somehow 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, which 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.3 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, a metaphor from which 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.4 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, and we can use that length to define a new unit, the Planck area. 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. As for the Library, 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 a number of bits on the order, once again, of 10106. 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.
There is a version of the story online, but I much prefer the translation by Andrew Hurley in Collected Fictions. ↩
As described by Borges: 25 symbols, 40 symbols per line, 80 lines per page, 410 pages. ↩
I’ve previously posted a video to an excellent introduction to the holographic principle. You can find that here. ↩
This is because, physically speaking, information is the same thing as entropy. ↩
When Thermo Thursday returns it will be all about adiabatic and isothermal compression, but this was the last week of classes and I got busy. And then I did a podcast this afternoon rather than physics. I’ll try to link to that podcast soon. I also might do a makeup Thermo post this weekend. But for now I’m tired, so no derivations tonight.
Photo by Alice Gribbin
Here’s me, sitting in the Frank Conroy Reading Room in my NPR Planet Money t-shirt. I started listening to the Planet Money podcast, an economics podcast started by some of the producers of This American Life, right when it started in 2008. For years they’ve wanted to produce a t-shirt and track how it moves through the global economy, from cotton to yarn to cloth to clothes to consumers. Now, people who backed their Kickstarter are starting to get their shirts, and everyone can learn the details about how these objects came to be on a page where they’ve aggregated their reporting. It’s been a fascinating story to follow, with everything from large-scale investigations of the history of international trade to personal stories about individual factory workers.
My single strongest brand loyalty is to Tom Bihn bags. They’re brilliantly designed, attractive, near-indestructible, and made in the USA. I describe them as the Apple of bags. My first was an Empire Builder briefcase that I got when I went to Trinity, in an attempt to save my spine from my high school habit of carrying every textbook and binder around on my back in a bag that weighed half as much as I did. I carried it all through college, but it turned out to be so spacious that it didn’t really solve the problem; I still carried around more weight than my shoulders could really support. But as Tom Bihn bags have a modular design, I was able to take out the Brain Cell insert, attach a strap to it, and use it as a minimal MacBook case. Once the 11″ MacBook Air came out I went fully minimal and bought a Ristretto (original style, it’s since been updated) and for the last three years have never carried more than it could hold. 90% of the time that’s all I need, but very occasionally I’ve wanted something more capacious. Then, a Hanukkah miracle: I now own a Synapse 19.
It’s a small, six pocket backpack with shaped shoulder straps and removable sternum and waist straps that, once adjusted, hugs the body better than any pack I’ve ever owned. Mine is the navy blue nylon with Iberian red Dyneema interior, as pictured in the front panel shots here.1 (Though there are many other options. You can even get the whole thing in Dyneema, which is thinner than the nylon but reduces the empty weight by 7%.) The back panel is padded with a breathable mesh overlay to keep your back from sweating, and all of the zippers are rubberized for water resistance. The main compartment is an open space with a 2/3-height elastic pocket along the front. There are o-ring anchor points for attaching keychain lanyards or modular organizers, and it has two pairs of webbing loops to which you can attach the cache with rails to turn it into a checkpoint friendly laptop bag. Traveling to and from Texas for Thanksgiving, I found it very convenient to not have to take out my computer when going through airport security. Instead you just slide the cache out the top of the bag and let the whole thing go through the X-ray machine.
Directly in front of the main compartment is a tall, narrow water bottle pocket, centered on the bag so that it doesn’t throw off the balance when it’s on your back. I don’t carry a water bottle, but this pocket is also perfectly sized for a small book, e-reader, or tablet. I’ve been using it to hold my iPad Mini. The two side pockets are curved and positioned such that they can be easily access while the pack is being worn by dropping one shoulder strap and pulling it around under your arm. One side has sewn-in pen sleeves and the other has a soft, sueded pocket for holding something you don’t want scratched. The website suggest a cell phone, but I’ve been keeping my backup hard drive in mine. Both side pockets have o-ring anchors, as does the small front top pocket behind the logo. The bottom pocket is full width and deeper than it looks. I’ve been keeping gloves, a wool cap, and my unused straps in there.
So far I’ve used it as my only bag on an overnight to Madison, and as my under-seat carryon for my trip back to Texas, and its been perfect for both. Even when I was packing clothes and toiletries along with my computer for the overnight trip, I didn’t quite max out its capacity. That said, it’s still small enough that I’m not at risk for hurting my back again. It easily sits near my feet in a full car, and can hook across the back of a restaurant chair without tipping it over when I stand up. The weather hasn’t been conducive yet to wearing it while riding my bike, but it has been perfect for every other task I’ve thrown at it. It’s the best backpack I’ve ever used. (If this design is attractive but the small size isn’t a plus for you, there’s also the Synapse 25, which is 30% larger but has the same layout.)
Photos from Tom Bihn’s site. ↩