Review: Newton’s Principia

Review: Newton’s Principia
The Principia

The Principia by Isaac Newton

My rating: 5 of 5 stars

It is shown in the Scholium of Prop. 22, Book II, that at the height of 200 miles above the earth the air is more rare than it is at the surface of the earth in the ratio of 30 to 0.0000000000003998, or as 75,000,000,000,000 to 1, nearly.


Marking this book as “read” is as much an act of surrender as an accomplishment. Newton’s reputation for difficulty is well-deserved; this is not a reader-friendly book. Even those with a strong background in science and mathematics will, I suspect, need some aid. The historian of mathematics Colin Pask relied on several secondary sources to work his way through the Principia in order to write his excellent popular guide. (Texts by S. Chandrasekhar, J. Bruce Brackenridge, and Dana Densmore are among the more notable vade mecums for Newton’s proofs.) Gary Rubenstein, a math teacher, takes over an hour to explain a single one of Newton’s proofs in a series of videos (and he had to rely on Brackenridge to do so).

It is not that Newton’s ideas are inherently obscure—though mastering them is not easy—but that Newton’s presentation of his work is terse, dense, incomplete (from omitting steps), and at times cryptic. Part of this was a consequence of his personality: he was a reclusive man and was anxious to avoid public controversies. He says so much himself: In the introduction to Book III, Newton mentions that he had composed a popular version, but discarded it in order to “prevent the disputes” that would arise from a wide readership. Unsurprisingly, when you take material that is intrinsically complex and then render it opaque to the public, the result is not a book that anyone can casually pick up and understand.

The good news is that you do not have to. Newton himself did not advise readers, even mathematically skilled readers, to work their way through every problem. This would be enormously time-consuming. Indeed, Newton recommended his readers to peruse only the first few sections of Book I before moving on directly to Book III, leaving most of the book completely untouched. And this is not bad advice. As Ted said in his review, the average reader could gain much from this book by simply skipping the proofs and calculations, and stopping to read anything that looked interesting. And guides to the Principia are certainly not wanting. Besides the three mentioned above, there is the guide written by Newton scholar I. Bernard Cohen, published as a part of his translation. I initially tried to rely on this guide; but I found that, despite its interest, it is mainly geared towards historians of science; so I switched to Colin Pask’s Magnificent Principia, which does an excellent job in revealing the importance of Newton’s work to modern science.

So much for the book’s difficulty; on to the book itself.

Isaac Newton’s Philosophiæ Naturalis Principia Matematica is one of the most influential scientific works in history, rivaled only by Darwin’s On the Origin of Species. Quite simply, it set the groundwork for physics as we know it. The publication of the Principia, in 1687, completed the revolution in science that begun with Copernicus’s publication of De revolutionibus orbium coelestium over one hundred years earlier. Copernicus deliberately modeled his work on Ptolemy’s Almagest, mirroring the structure and style of the Alexandrian Greek’s text. Yet it is Newton’s book that can most properly be compared to Ptolemy’s. For both the Englishman and the Greek used mathematical ingenuity to draw together the work of generations of illustrious predecessors into a single, grand, unified theory of the heavens.

The progression from Copernicus to Newton is a case study in the history of science. Copernicus realized that setting the earth in motion around the sun, rather than the reverse, would solve several puzzling features of the heavens—most conspicuously, why the orbits of the planets seem related to the sun’s movement. Yet Copernicus lacked the physics to explain how a movable earth was possible; in the Aristotelian physics that held sway, there was nothing to explain why people would not fly off of a rotating earth. Furthermore, Copernicus was held back by the mathematical prejudices of the day—namely, the belief in perfect circles.

Johannes Kepler made a great stride forward by replacing circles with ellipses; this led to the discovery of his three laws, whose strength finally made the Copernican system more efficient than its predecessor (which Copernicus’s own version was not). Yet Kepler was able to provide no account of the force that would lead to his elliptical orbits. He hypothesized a sort of magnetic force that would sweep the planets along from a rotating sun, but he could not show why such a force would cause such orbits. Galileo, meanwhile, set to work on the new physics. He showed that objects accelerate downward with a velocity proportional to the square of the distance; and he argued that different objects fall at different speeds due to air resistance, and that acceleration due to gravity would be the same for all objects in a vacuum. But Galileo had no thought of extending his new physics to the heavenly bodies.

By Newton’s day, the evidence against the old Ptolemaic system was overwhelming. Much of this was observational. Galileo observed craters and mountains on the moon; dark spots on the sun; the moons of Jupiter; and the phases of Venus. All of these data, in one way or another, contradicted the old Aristotelian cosmology and Ptolemaic astronomy. Tycho Brahe observed a new star in the sky (caused by a supernova) in 1572, which confuted the idea that the heavens were unchanging; and observations of Haley’s comet in 1682 confirmed that the comet was not somewhere in earth’s atmosphere, but in the supposedly unchanging heavens.

In short, the old system was becoming unsustainable; and yet, nobody could explain the mechanism of the new Copernican picture. The notion that the planets’ orbits were caused by an inverse-square law was suspected by many, including Edmond Haley, Christopher Wren, and Robert Hooke. But it took a mathematician of Newton’s caliber to prove it.

But before Newton published his Principia, another towering intellect put forward a new system of the world: René Descartes. Some thirty years before Newton’s masterpiece saw the light of day, Descartes published his Principia Philosophiæ. Here, Descartes summarized and systemized his skeptical philosophy. He also put forward a new mechanistic system of physics, in which the planets are borne along by cosmic vortexes that swirl around each other. Importantly, however, Descartes’s system was entirely qualitative; he provided no equations of motion.

Though Descartes’s hypothesis has no validity, it had a profound effect on Newton, as it provided him with a rival. The very title of Newton’s book seems to allude to Descartes’s: while the French philosopher provides principles, Newton provides mathematical principles—a crucial difference. Almost all of Newton’s Book II (on air resistance) can be seen as a detailed refutation of Descartes’s work; and Newton begins his famous General Scholium with the sentence: “The hypothesis of vortices is pressed with many difficulties.”

In order to secure his everlasting reputation, Newton had to do several things: First, to show that elliptical orbits, obeying Kepler’s law of equal areas in equal times, result from an inverse-square force. Next, to show that this force is proportional to the mass. Finally, to show that it is this very same force that causes terrestrial objects to fall to earth, obeying Galileo’s theorems. The result is Universal Gravity, a force that pervades the universe, causing the planets to rotate and apples to drop with the same mathematical certainty. This universal causation effectively completes the puzzle left by Copernicus: how the earth could rotate around the sun without everything flying off into space.

The Principia is in a league of its own because Newton does not simply do that, but so much more. The book is stuffed with brilliance; and it is exhausting even to list Newton’s accomplishments. Most obviously, there are Newton’s laws of motion, which are still taught to students all over the world. Newton provides the conceptual basis for the calculus; and though he does not explicitly use calculus in the book, a mathematically sophisticated reader could have surmised that Newton was using a new technique. Crucially, Newton derives Kepler’s three laws from his inverse-square law; and he proves that Kepler’s equation has no algebraic solution, and provides computational tools.

Considering the mass of the sun in comparison with the planets, Newton could have left his system as a series of two-body problems, with the sun determining the orbital motions of all the planets, and the planets determining the motions of their moons. This would have been reasonably accurate. But Newton realized that, if gravity is truly universal, all the planets must exert a force on one another; and this leads him to the invention of perturbation theory, which allows him, for example, to calculate the disturbance in Saturn’s orbit caused by proximity to Jupiter. While he is at it, Newton calculates the relative sizes and densities of the planets, as well as calculates where the center of gravity between the gas giants and the sun must lie. Newton also realized that gravitational effects of the sun and moon are what cause terrestrial tides, and calculated their relative effects (though, as Pask notes, Newton fudges some numbers).

Leaving little to posterity, Newton realized that the spinning of the earth would cause a distortion in its sphericity, making the planet marginally wider than it is tall. Newton then realized that this slight distortion would cause tidal locking in the case of the moon, which is why the same side of the moon always faces the earth. The slight deformity of the earth is also what causes the procession of the equinoxes (the very slow shift in the location of the equinoctial sunrises in relation to the zodiac). This shift was known at least since Ptolemy, who gave an estimate (too slow) of the rate of change, but was unable to provide any explanation for this phenomenon.

The evidence mustered against Descartes’s theory is formidable. Newton describes experiments in which he dropped pendulums in troughs of water, to test the effects of drag. He also performed experiments by dropping objects from the top of St. Paul’s Cathedral. What is more, Newton used mathematical arguments to show that objects rotating in a vortex obey a periodicity law that is proportional to the square of the distance, and not, as in Kepler’s Third Law, to the 3/2 power. Most convincing of all, Newton analyzes the motion of comets, showing that they would have to travel straight through several different vortices, in the direction contrary to the spinning fluid, in order to describe the orbits that we observe—a manifest absurdity. While he is on the subject of comets, Newton hypothesizes (correctly) that the tail of comets is caused by gas released in proximity to the sun; and he also hypothesizes (intriguingly) that this gas is what brings water to earth.

This is only the roughest of lists. Omitted, for example, are some of the mathematical advances Newton makes in the course of his argument. Even so, I think that the reader can appreciate the scope and depth of Newton’s accomplishment. As Pask notes, between the covers of a single book Newton presents work that, nowadays, would be spread out over hundreds of papers by thousands of authors. The result is a triumph of science. Newton not only solves the longstanding puzzle of the orbits of the planets, but shows how his theory unexpectedly accounts for a range of hitherto separate and inexplicable phenomena: the tides, the procession of the equinoxes, the orbit of the moon, the behavior of pendulums, the appearance of comets. In this Newton demonstrated what was to become the hallmark of modern science: to unify as many different phenomena as possible under a single explanatory scheme.

Besides setting the groundwork for dynamics, which would be developed and refined by Euler, d’Alembert, Lagrange, Laplace, and Hamilton in the coming generations, Newton also provides a model of science that remains inspiring to practitioners in any field. Newton himself attempts to enunciate his principles, in his famous Rules of Reasoning. Yet his emphasis on inductivism—generalizing from the data—does not do justice to the extraordinary amount of imagination required to frame suitable hypotheses. In any case, it is clear that Newton’s success was owed to the application of sophisticated mathematical models, carefully tested against collections of physical measurements, in order to unify the greatest possible number of phenomena. And this was to become a model for other intellectual disciples to aspire to, for good and for ill.

A striking consequence of this model is that its ultimate causal mechanism is a mathematical rule rather than a philosophical principle. The planets orbit the sun because of gravity, whose equations accurately predict their motions; but what gravity is, why it exists, and how it can affect distant objects, is left completely mysterious. This is the origin of Newton’s famous “I frame no hypothesis” comment, in which he explicitly restricts himself to the prediction of observable events rather than speculation on hidden causes (though he was not averse to speculation when the mood struck him). Depending on your point of view, this shift in emphasis either made science more rational or more superficial; but there is little doubt that it made science more effective.

Though this book is too often impenetrable, I still recommend that you give it a try. Few books are so exalting and so humbling. Here is on display the furthest reaches of the power of the human intellect to probe the universe we live in, and to find hidden regularities in the apparent chaos of experience.



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Review: Howards End

Review: Howards End
Howards End

Howards End by E.M. Forster

My rating: 5 of 5 stars

It is the little things one bungles at. The big, real ones are nothing when they come.


The last time I reviewed a novel by E.M. Forster, I wound up blubbering with praise; and now I find myself in similar circumstances. As with A Passage to India, I find Howards End exemplary in every respect: the themes, characterization, the prose, the pacing, the plot. I ought also to mention Forster’s versatility. Though rarely funny, Forster is capable of romantic lyricism, gritty realism, and flighty philosophy. Most convincing of all is his control. Nothing is overdone or heavy-handed—which requires a mixture of technique and taste. While exploring social problems, one never feels that the novel is being unduly interrupted; while constructing a character into an archetype, one never feels that the individual is lost; and the story, though carefully plotted, rarely feels predictable or contrived.

Yet Forster is not a great novelist for his skill alone. He is great because of his insight. More than any novelist I know, Forster is able to connect the inner with the outer life (which is the theme of this novel, and the source of its most famous quote: “Only connect”). Forster is able to show, in other words, how social and economic circumstances breed characters; and how even intelligent and well-meaning characters fail to escape the bounds of their class and nation. He shows, for example, how the money inherited by Margaret and Helen allows for their mental freedom; how Mr. Wilcox’s life of business molds him into a well-meaning shell; and how, despite his best efforts, Leonard Bast cannot help but be shaped by his poverty.

However, if the novel has a message, it is this: even if the inner life is powerless to change material circumstances, it is ultimately the more important aspect of life. This is because, when a tragedy strikes, and mere business acumen or worldly knowledge will not suffice, it is emotional fortitude that is required. Mr. Wilcox has a sort of false strength—a fragile ego he hides behind, a sort of masculine bluff which is easily shattered. Margaret, by contrast, is able to endure tragedies because of her self-knowledge. She is not afraid of the darker aspects of her mind; thus she can look with equanimity upon herself and others, accepting their flaws while seeing their potential. This is what Forster means by “connect”: connecting “the beast” with “the monk”—that is, admitting one’s desires instead of hiding behind a false screen of decency. Only so can we achieve self-knowledge.



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Don Bigote: Chapter 6

Don Bigote: Chapter 6

The story until now:

  1. Don and Dan Build a Shelter
  2. Don and Dan Take a Flight
  3. Don and Dan Go to Spain
  4. Don and Dan Do Drugs
  5. Don and Dan Find God

Don and Dan Find Themselves

“Tell me what you saw,” Dr. Krajakat says, in a low soothing voice, to Don Bigote.

“It is somewhat obscured in the misty recesses of my memory, but I clearly remember the exalted feeling of having made an important discovery.”

“Yes?” the doctor says coaxingly.

“Perhaps discovery is not the right word… It was more like a vision, a sort of sense of being in a world where every wrong is right, a kind of utopia of freedom and righteousness—blessedly free from the dastardly conspiracy that so plagues the world today…”

“And did you see…  her?”

“Her?”

“Yes, her.”

“You mean, the mother?”

“Yes, her! Mother Ayahuasca!”

“I did!” Bigote says, with a tone of eureka. “I remember it all now… She came to me from above, like an angel, with her flowing green hair and her flaming red eyes… and she picked me up and held me in her arms, and whispered something in my ear…”

“What was it?” the doctor hisses.

“That… everything, everything is opposite.”

“Yes!” the doctor says, throwing up his hands in triumph.

“I think he’s ready,” Pierre says quietly.

“Yes, I agree,” the doctor says. “I quite agree.”

§

“Listen,” I say, “you can’t trust these people. They’re all loonies here.”

We are sitting, alone, in our bunk beds in the campsite.

“I believe at least most of them are not Canadian, Chopin,” Bigote tells me. “In any case, I do not see why you are so alarmed. If these people were working for the conspiracy then they surely would have pounced already. What would be the point in waiting?”

“But, dude,” I say, “just think about it. We’re out here in the middle of nowhere, everyone is a hippie on drugs, and this doctor wants to send you into some cave. I mean, how can they know it’s safe? There could be bears, snakes, wolves, or… whatever there is in Portugal. Or you can get lost, or fall into a pit, or the walls can collapse and you can be trapped like those miners in that country on the news.”

“Oh ye of little faith,” Bigote says. “I have no fear for my personal safety. Besides, the chance of attaining knowledge which, very possibly, will be vital in our battle against the conspiracy, is worth whatever the concomitant risks of this procedure. And if something happens to me, you will be left behind to carry on the mission.”

“So you’re seriously going into the cave?”

“I am.”

“You’re gonna trust these people you just met with your life?”

“Most heartily.”

“Well then,” I say, “I’m going with you.”

“Now, now, dear Chopin,” Bigote says, laughing, “I am flattered by this display of squirish loyalty, but do not be rash. I am a man of experience and training, and, moreover, owing to my comparatively advanced age, it could hardly be argued that an accidental death would be greatly tragic. But in your case there is an obvious and manifest difference; you are young, and (the conspiracy permitting) you have many years ahead of you, some of which may indeed be happy.”

“If you’re going, I’m going,” I say, crossing my arms.

“Pray reconsider.”

“I’m not leaving you alone to be killed by these crazies.”

“Oh, such words are harsh.”

“This is the way it’s gonna be,” I say, imitating my mom.

Now, I am hoping that by insisting on going with him I might get him to wise up to the loco-ness of this plan. It’s a gamble, I know. But what else am I going to do? I am in way too deep with Bigote now to back out. We’ve broken who knows how many laws; we’ve seen people killed, and then stolen their stuff. I mean, it’s all the way or bust, the way I see it.

“If this is how you feel,” Bigote says, “then so be it.”

Oh shit.

§

“This is the entrance to Sub World,” Dr. Crackerjack (or whatever his name is) says, pointing to a small sliver of an opening in a hillside. “This is where Mother Ayahuasca dwells. The cave was discovered about a decade ago by a married couple on a picnic. The two of them stumbled in, and now the both of them are high shamans in the rainforests of Brazil. We pilgrims have been visiting the magic cave ever since. It works wonders.”

“I am thoroughly intrigued,” Bigote says. “Let us waste no more time!”

“Wait!” Pierre shouts, as Bigote starts marching towards the cave. “We have got to tie you up first.”

“Tie us up?” I say, already so nervous my bowels are misbehaving.

“So you don’t get lost,” he explains, and then pulls out two long nylon chords from his backpack. Quickly and expertly, he wraps one around my waist, ties it securely, and does the same with Bigote.

“They are prepared,” Pierre says to the doctor.

“Okay, now the both of you, listen to me carefully,” the doctor says. “Walk into the cave slowly. Be careful, since it is completely dark inside, so take care not to hit your head or to fall. However, this stage of the journey only lasts a few minutes. Eventually you will see a light in the distance. Follow it. The rest will be clear.”

“I thank you for your counsel,” Bigote says. “And now, no more words. For it is a time of action.”

Pierre and the doctor nod gravely. Bigote turns to the cave and begins to march. I follow him, trying my best to walk normally despite the knot of anxiety in my abdomen.

We reach the cave’s mouth. Like he’s an astronaut in a movie or something, Bigote turns to me, nods, and then steps into the cave. I mutter a kind of fake prayer (you know, the kind of weird under-the-breath wishing that even non-religious people do), try to walk inside, but then I panic and hesitate for a second. A part of me says, fuck this, let’s go back. Then I worry that I’ll lose track of Bigote in the darkness, so I gulp down my nerves and walk inside.

I hit my head on the rocks immediately.

“God fucking shit…”

“Peace, Chopin,” Bigote’s voice says, ahead of me. “This is no time for obscenities.”

“Sorry, sir, it’s just these rocks are so hard.”

“Indeed, they are quite durable, as I have myself noticed through observation. Unless I am mistaken, the cave is primarily granite.”

I walk forward, hands out in front, until I bump right into him.

“Careful, my faithful companion,” Bigote says.

“Oh, sir, I don’t like this,” I say, grabbing onto his arm so as not to lose him. “Can we just sit down here for a few hours, and tell them it was great when we come out?”

“What an idea!” Bigote laughs.

We are edging forward, him in front, me behind, clinging to his boney arm. Normally I’d feel weird in this situation but, you know, when you’re in a cave different rules apply. This is what I’d always say to my buddies when we were in the man cave.

We move on in total silence and total darkness, the only sound the soft padding of our feet on the rocky ground as we slowly shuffle forward. It feels like how I imagine it is to be in one of those sensory-deprivation chambers that I saw on a video that one of my friends—well, she’s not really my friend, but I follow her since she’s sort of cute—posted on LickFace™ a few months ago. It’s like these things where you go into a pod that’s full of warm water, and when the door closes you can’t feel or see or hear or smell anything, and you’re supposed to be like super zen or something like that (though I gotta say so far this cave is not at all zen). I don’t know, it’s something people in Norway to do, I guess because they’re bored from the snow.

For about five minutes nothing much happens. Well, it could have been an hour for all I know. Time is hard to estimate when your in a cave like that. But just then, somewhere in the blank space in front of us, we hear:

Thump.

“Oh my god of my god oh my god,” I say, and hug Bigote’s waist. “We’re gonna die.”

“Calm yourself, Chopin,” Bigote says. He tries to keep moving ahead but I hold him there.

“Let go of me, you fool.”

“Shhhh,” I say, squeezing him as tightly as I can.

We listen for a few moments. I’m breathing hard from panic, and Bigote is huffing from trying to breathe with my arms clenched around his chest. I’m sweating like I’m trying to work off a hangover at the gym, and I feel like my legs are made of jello shots.

And then:

Thump.

It sounds closer this time. I lose it completely.

“Oh please oh please, let’s go!” I start crying and babbling hysterically. “Oh, sir please let’s get out of here. Oh! Owowowow!”

“Will you quit that nonsense!” Bigote says, and tries peeling my arms from around his waist.

“Look you, whatever you are!” he then shouts into the darkness. “Unlike my assistant here, I am unafraid of things that go bump in the night! So, beware, for that makes me dangerous!”

“Oh god, please somebody help us!” I scream. My eyes are streaming tears, my nose is dripping mucus, and I’m farting uncontrollably. My arms and legs are frozen in place—Bigote’s stuck in my embrace—we’re completely defenseless. This is the end, I know it.

And, just then, we hear another noise. It sounds like:

Psssssfffffftt.

In other words, it sounds like a hissing and slightly wet fart. A sharp shart, if you will.

I don’t know whether this is a good or a very bad sign… but the sound keeps repeating. I listen in wild fear, mentally trying to make sense of what it could be… a bear? a snake? a rabid beaver? But the more I listen, the more the sound begins to take shape. Yes, it is most definitely flatulent, but it also has a certain… articulation. Wait, it’s somebody speaking!

“Pssslease pffdon’t fffffffpanic,” the fart voice says. “You have arrived.”

§

The cave is gone. Either that, or we’re gone. I’m not a philosopher or anything, so I don’t know. Point is, we’re not in the cave anymore.

Instead, we’re in a room where all the surfaces are made of little pieces of glass, like a fun-house or something. It’s super trippy. Everywhere I turn, up, down, right, left, I see myself in a thousand little pieces. And since everything is reflecting everything else, the room is multiplied infinitely in every direction. Like I said, it’s super trippy, and it gives me a stomach ache—as if I wasn’t feeling weirded-out enough already. Worse than the mirrors is the smell. It’s nasty, like something rotten, or like that one time I did an experiment in chem class using sulfur. But the worst part of all is that there is someone in this room with Bigote and me…

It’s a man, I think… He’s completely naked, so it should be easy to tell. But he’s standing on his arms, with his legs up flapping in the air, and his ass pointed right towards us. A pretty hairy ass, too, which is why I think it’s a dude.

“Welcome,” he says. But the voice doesn’t come from his mouth… He literally farts the words out of his upturned ass. I gag a little.

“How dare you act so obscenely, you curr!” Bigote shouts.

“Please be calm,” the ass retorts. “I assure you that I mean no disrespect.”

An uncomfortable silence follows, as Bigote and I try to figure out what’s going on. Finally Bigote says:

“Are you Mother Ayahuasca?”

At this, the ass explodes into staccato, rapid-fire farts: pft-pft-pft-pft-pft-pft. I think it’s laughing. I gotta admit I’m very impressed. One of my buddies back home can fart on command, but he has nothing like this level of control. This guy could be on a TV show. When he settles down, he says (or farts, not sure):

“I apologize for laughing, but everyone who comes down here asks me that, even though I implore them, when they return to the surface, to dispel this myth. And frankly, I do not see what a hallucinogenic concoction from the Amazon rainforest has to do with us, down here.”

“Who are you then?” Bigote says.

“My name is Harry,” the ass responds, folding his upturned legs with dignity. “And I am a member of the Subterraneans.”

“I beg your pardon?”

“The Subterraneans. You see, thousands of years ago, when people began to settle down and start farming, a small group of dissenters decided that the agricultural life wasn’t for them. The rigid schedule, the bland and steady diet, the sedentary lifestyle—they found it to be an unbelievable bore. So they struck out to find another way. Eventually, during a bad storm, some of them got lost in this cave and never found their way out. Over the millennia we have adapted to our new domain. Indeed, I think you will find that we are much happier than you surface dwellers.”

“So why are we here?” Bigote asks.

“Well, you see your surface bodies would be completely unable to cope with the conditions inside our city, so we have constructed this chamber to allow for communication between our two worlds. The mirrors, you see, are to magnify the meager source of light we have available. And the atmosphere is equal parts oxygen and methane (you likely have noticed the smell), so that we both can breathe. We, of course, have no need of light or mirrors in Sub City (as our capital is called), since our world is pitch black, and our eyes have long since atrophied from disuse.”

“I see,” Bigote says. “But why are we here in the first place?”

“Ah, well it’s part of a new government outreach program. We decided that diplomatic isolation was no longer a defensible policy in a globalizing world, and so built this chamber to make contact with the surface world. The fact that ayahuasca rituals take place here was a lucky coincidence.”

“So,” Bigote says, hesitating, “you are here to explain your world to us, is that right?”

“Correct.”

“My attention is yours.”

“I believe the best procedure is for you to ask me what you wish to know. I will answer as best I can.”

“How are you speaking out of your ass?” I blurt out, dying to find out.

“Chopin, how rude!” Bigote says.

“No, it’s quite alright,” the ass says. “Everyone asks me that. In short, the lack of oxygen deep underground caused a change in our biology. We switched from breathing oxygen to breathing methane, and our anuses thus became the primary mode of communication. The ability to delicately manipulate objects or to run quickly are also of little use where we live. Thus, we switched from feet-walking to hand-walking, freeing our muscular feet for the heavy lifting needed in carving out our existence underground.”

“That’s crazy, dude.”

“No, it is evolution.”

“Well,” Bigote says, “I suppose I should start with the most obvious question: Is your society, too, under threat by the Muslim-Mexican conspiracy?”

“What is that?”

“Why, it is the most dastardly plot in all of history! It is a scheme formed by the alliance of the religion of Islam and the nation of Mexico, along with various other groups such as feminists and vegans, in order to destroy western society as we know it!”

“It is a conspiracy formed between a religion and a nation?”

“Yes, that is exactly it.”

“Oh no, that is not a problem here,” Harry says. “You see, we have found that religions are more trouble than they’re worth. Centuries ago, we had a lot of problems with this institution. Everyone was getting all worked up over which god to worship, what god said what, who was the true prophet of god, what kind of hat god wants you to wear, what kind of food god wants you to eat, and on and on. So eventually we just decided to abolish all religion.”

“Even Christianity?”

“If that is a religion, then yes.”

“That’s monstrous!”

“Whatever you may think, it has worked out quite well. We haven’t had any violence due to conflicting supernatural beliefs in hundreds of years. We did the same thing with nations, too, since we found that people would get similarly worked up over which nation was the best—with the best customs, the best food, the best culture, and all the rest—so we decided that nations are formally illegal.”

“My God!” Bigote says. “But some nations are the source of brilliant and vital traditions!”

“We have found through experience that any group that does not include everyone, and which requires its members to eat, act, and think a certain way, causes social issues that are best avoided through unity. That is why we also outlaw special diets (except for medical reasons) and political parties.”

“But if all this stuff is against the law,” I say, “then half of your people must be in jail.”

“Why, you surface-dwellers are always shocked when I say this, but we have no jails in Sub World.”

“Let me guess,” Bigote says, “mass execution?”

“The thought of such barbarism!” Harry said, fart-chuckling. “No, no, nothing of the sort. We have a very efficient process for dealing with people who break the law. First, they must publicly apologize in front of a large crowd. This is to engender a sense of shame and responsibility. Then they must complete a certain number of community service hours, which normally consists of some menial task, such as garbage collection. Meanwhile, they attend therapy and rehabilitation sessions, in which they are given the psychological and social support to properly readapt to society. This is followed by a probationary period, in which they are provisionally allowed to return to normal life, with periodic monitoring to ensure their proper readjustment.”

“I highly doubt the efficacy of this procedure,” Bigote says.

“Oh, I assure you it’s quite successful. My father once had to undergo this process because he got a speeding ticket in his mole-mobile. And now he obeys the speed limit ‘religiously,’ you might say.”

“That is all fine and dandy,” Bigote says, “but what about the unrepentant criminals? Surely there must be a certain number who refuse to participate, or who are too violent to be amenable to such gentle correction.”

“There have been cases in the past when rehabilitation was impossible, and the criminal was sent into exile into the deeper recesses of the caves. But such a thing has not happened in generations. You see, our criminal system is not simply recuperative, but preventative. Yearly psychological examinations, administered in schools (and all of our teachers undergo psychological training), allow us to catch troublesome cases early, when therapy is most effective.”

“Excuse me the luxury of disbelief,” Bigote says, waving his hand. “But I doubt that all the therapy in the world can eliminate our violent tendencies. Surely, there must be assaults and murders in your society.”

“Yes, occasionally.”

“And you are saying that you do not administer a harsher punishment to those who take a human life?”

“In the case of murder, the perpetrator is forced to attend a meeting of reconciliation with the family of the victim, in order for the criminal to realize the full extent of emotional pain he has caused, and in order for the victims to avoid harboring self-destructive hateful or vengeful feelings. The ceremony ends with everyone rubbing their anuses together, which is the traditional gesture of goodwill in our society.”

“This is absurd! Such a procedure hardly satisfies the dictates of justice! The perpetrator of such a heinous act must suffer. To force the family of the victim to forgive him is cruel! They have a right to be angry.”

“I assure you, for generations we tried to use a system of castigation—corporal punishment, isolation, imprisonment, even death—to deal with crimes, but the end result never fully satisfied. Harsh punishments had the double drawback of making criminals unavailable or unfit for useful social roles in the future, while failing to act as a serious deterrent to other would-be criminals. So we had lots of crime and lots of prisoners. Furthermore, though there was a sense of emotional satisfaction in punishing wrongdoers, we found that indulging in such sentiments led, in turn, to anti-social behavior on the victims’ part, thus perpetuating a cycle of violence.”

“Such dry logic may have its certain appeal,” Bigote spits, “but we are creatures of sentiment, and our emotional natures cannot be denied.”

“We have come to the opposite conclusion,” Harry replies. “Long experience has taught us that many emotions, positive or negative, can have unintended negative social consequences. Love is an excellent example of this phenomenon.”

“Oh, I would like to hear this.”

“Our original hypothesis was that individuals would naturally be best able to choose a partner for themselves. But this had puzzling consequences. Separation was common, and many couples who remained together reported high levels of unhappiness and dissatisfaction, especially when children were involved. After some investigation we were forced to conclude that individuals are inept at choosing partners. In well over three-fourths of the cases we looked into, the choice was unambiguously sub-optimal. Curiously, it is not that individuals are, on the whole, bad judges of character: they do well in choosing friends. Rather, we found that the intense feelings of passionate love commonly involved in courtship severely clouded people’s ability to make wise decisions about a partner.”

“So then how, in your infinite wisdom, do you manage marriage?”

“It is a simple system. First, love-matches are heavily discouraged. We have anti-love campaigns in school, and anti-love poems, songs, and stories are very common in the media, illustrating the danger of this temptation. And we have found that, in the absence of media promoting the idea of romantic love, it very rarely develops spontaneously. Our studies have shown that most love is merely the imitation of fictional tropes—and, of course, imitating fiction is not sustainable. In the rare cases that a couple does spontaneously fall in love, then they are assigned community service in different communities, to ensure the destruction of the relationship.”

“You are monsters!”

“I admit that it seems rather hard when we have to separate an enamored couple. This happened to one of my cousins, a few years back, a terribly excitable girl. But the social stability achieved through this process speaks for itself.”

“Social stability?” Bigote says. “How can loveless marriages be stable?”

“You see, love is allowed to develop within the marriage, but not to precede it. When a person is ready to marry, they follow this procedure: they apply to the Department of Partnership. Then psychologists evaluate members of the opposite sex (or whatever the case may be, depending on the individual’s preference) among the individual’s  friends—the theory being that freely-chosen friendship leads to more stable marital bonds than passionate emotional choice. When a suitable match is found (using various psychological criteria), the marriage is proposed, and continues with the consent of both parties. And I am happy to say that this procedure has almost entirely eliminated divorce. You see, when love is not involved, people enter a relationship with moderate and realistic expectations, and so are seldom disappointed enough to wish to leave.”

“This is a travesty!” Bigote snorts. “This is like solving the problem of heart attacks by putting everyone into an artificial coma. You have robbed life of all its poetry!”

“Poetry is a matter of taste,” Harry replies. “And in my opinion our anti-love poets produce some truly beautiful lines. For my part, I have been in a happy marriage for thirty years, and have not grown tired of my wonderful wife even once.”

“But this whole business of letting committees decide things, it’s preposterous,” Bigote says, waving his arms. “You can never achieve greatness in any realm of life through mere procedures and logic and calculation. Passion is the spark that sets fire to our life, and makes them worth living.”

“For a long time, there were many in Sub World who agreed with you. And of course we have exhaustively tested out this hypothesis. But ultimately we have had to reject the idea that passionate desire is socially useful. In many realms of life, it is quite the opposite—socially destructive. Take politics as an example.”

“Go on, then. Tell us how wrong we are.”

“Well, for a long time it was assumed that the people who were the most motivated to be politicians should be the ones in charge. Thus we experimented with a democratic system, in which these individuals would compete for votes, the theory being that the person who receives the most votes would be the one who is the most skillful leader, the most motivated worker, and the most ideologically representative of the population. But we were mistaken in this. Time and time again, the people who won were merely charismatic. While some proved to be capable leaders, the large majority were exalted mediocrities, whose only true interest was power and prestige, and who were willing to say anything to get it.”

“I admit that this has been our sad experience on the surface world as well.”

“Another problem we ran into is that our leaders, once established, bred an incestuous community. By this I mean they would mainly associate with one another, becoming an isolated class. Rather than working on behalf of the community, they merely worked to further entrench themselves in their positions. Sure they would appear to oppose one another ideologically. But this was mainly a show to convince their voters of their own legitimacy.”

“Again, I have seen it happen all too often,” Bigote says. “So what did you do about it?”

“The solution was easily found, once we abandoned the idea that people should follow their passion to become leaders. Rather, we realized that the reverse is the case: people with no interest in leading should lead, since they are the least likely to be corrupted by access to power. Thus we have replaced elections with a lottery. A person randomly chosen is more likely to represent the views of their community, rather than the interests of the elite. But of course even a normal person may have their judgment warped through access to executive control: so this is why we strictly limit the amount of time that any person can spend in the government. For most positions the term limit is one year. After this year is up, the next leader is chosen through another lottery process. It is called the Yearly Shuffle, and it’s a great festive occasion. My grandfather and my sixteen-year-old daughter were both chosen so far.”

“My word!” Bigote says. “A lottery!? Very well, I admit that such a silly procedure may help to eliminate corruption. But this comes at the cost of great leadership. Where would the world be if Charlemagne, Napoleon, Alexander the Great, Julius Caesar, or Ronald Reagan were passed over by some random process, or were only allowed to rule for one year! Yes, there are plenty of corrupt politicians in the world—of this I am much too certain—but great talent naturally rises to the top, and compensates for this human waste!”

Just then I feel a strong pressure on my abdomen—and it isn’t what it usually is.

“Ah, it appears it is time for you to go,” Harry says. “Give my regards to that doctor up there, and do let him know about Mother Ayahuasca.”

Suddenly I am tugged from behind with so much power that I fall backwards, lose my breath, and black out.

§

A confused mass of voices reaches my ears:

“Are they alright? Wow, they smell awful. How’s their breathing? Normal? Get the smelling salts. Keep them on their sides, that’s it.”

Slowly the world stops spinning, and I begin to recollect myself. Asleep? Was it all a dream?

Someone sticks something under my nose, and I am overwhelmed by a powerful rancid smell.

“Jesus fucking hell,” I say, sitting bolt upright and thrashing around with my hands. “Get that shit away from me.”

“It appears that he is fine,” Pierre says. “We pulled them out before the methane got to their heads.”

“Tell me, young one,” Dr. Krajakat says to me, smiling, as he bends down towards me. “Did you see it?”

“See what?”

“The… the place where everything is opposite?”

“Opposite? I’ll say! Down there, everything is ass backwards!”