“I heard there was, like, a car that runs on water … “
“Dude, no, there’ve been, like, six of them. But oil companies bought all the patents.”
A lot of the people who attend my poetry class in jail believe in freaky conspiracy theories. Somebody started telling me that the plots of various Berenstain Bears books are different from when he was a child, which is evidence that the universe bifurcated and that he’s now trapped in an alternate timeline from the path he was on before …
(New printings of some Berenstain Bears books really are different. Take Old Hat New Hat, a charming story about shopping and satisfaction: after the protagonist realizes that he prefers the old, beat-up hat he already owns to any of the newer, fancier models, a harried salesperson reacts with a mix of disgust and disbelieve. This scene has been excised from the board book version that you could buy today. Can’t have anything that tarnishes the joy of consumerism!)
I’ve written about conspiracy theories previously, but I think it’s worth re-iterating, in the interest of fairness, that the men in jail are correct when they assume that vast numbers of people are “breathing together” against them. Politicians, judges, police, corporate CEOs and more have cooperated to build a world in which men like my students are locked away. Not too long ago, it would have been fairly easy for them to carve out a meaningful existence, but advances in automation, the ease of international shipping, and changes to tax policy have dismantled the opportunities of the past.
Which means that I often find myself seriously debating misinterpretations of Hugh Everett’s “many worlds” theory (described midway through my essay, “Ashes”), or Biblical prophecies, or Jung-like burblings of the collective unconsciousness.
Or, last week, the existence of water cars.
In 2012, government officials from Pakistan announced that a local scientist had invented a process for using water as fuel. At the time, I was still running a webcomic – one week’s Evil Dave vs. Regular Dave focused on news of the invention.
When scientists argue that a water-powered car can’t exist, they typically reference the Second Law of Thermodynamics (also discussed in “Ashes”). The Second Law asserts that extremely unlikely events occur so rarely that you can safely assume their probability to be zero.
If something is disallowed by the Second Law, there’s nothing actually preventing it from happening. For an oversimplified example, imagine there are 10 molecules of a gas randomly whizzing about inside a box. The Second Law says that all 10 will never be traveling in the exact same direction at the same time. If they were, you’d get energy from nothing. They might all strike the north-facing wall at the same time, causing the box to move, instead of an equal number hitting the northern and southern facing walls.
But, just like flipping eight coins and seeing them all land heads, sometimes the above scenario will occur. It violates the Second Law, and it can happen. Perpetual motion machines can exist. They are just very, very rare. (Imagine a fraction where the denominator is a one followed by as many zeros as you could write before you die. That number will be bigger than the chance of a water-fueled car working for even several seconds.)
When chemists talk about fuel, they think about diagrams that look roughly like this:
The y axis on this graph is energy, and the x axis is mostly meaningless – here it’s labeled “reaction coordinate,” but you wouldn’t be so far off if you just think of it as time.
For a gasoline powered car, the term “reactants” refers to octane and oxygen. Combined, these have a higher amount of energy stored in their chemical bonds than an equivalent mass of the “products,” carbon dioxide and water, so you can release energy through combustion. The released energy moves your car forward.
And there’s a hill in the middle. This is generally called the “activation barrier” of the reaction. Basically, the universe thinks it’s a good idea to turn octane and oxygen into CO2 and H2O … but the universe is lazy. Left to its own devices, it can’t be bothered. Which is good – because this reaction has a high activation barrier, we rarely explode while refueling at the gas station.
Your car uses a battery to provide the energy needed to start this process, after which the energy of the first reaction can be used to activate the next. The net result is that you’re soon cruising the highway with nary a care, dribbling water from your tailpipe, pumping carbon into the air.
(Your car also uses a “catalyst” – this component doesn’t change how much energy you’ll extract per molecule of octane, but it lowers the height of the activation barrier, which makes it easier for the car to start. Maybe you’ve heard the term “cold fusion.” If we could harness a reaction combining hydrogen molecules to form helium, that would be a great source of power. Hydrogen fusion is what our sun uses. This reaction chucks out a lot of energy and has non-toxic byproducts.
But the “cold” part of “cold fusion” refers to the fact that, without a catalyst, this reaction has an extremely steep activation barrier. It works on the sun because hydrogen molecules are crammed together at high temperature and pressure. Something like millions of degrees. I personally get all sweaty and miserable at 80 degrees, and am liable to burn myself when futzing about near an oven at 500 degrees … I’d prefer not to drive a 1,000,000 degree hydrogen-fusion-powered automobile.)
With any fuel source, you can guess at its workings by comparing the energy of its inputs and outputs. Octane and oxygen have high chemical energies, carbon dioxide and water have lower energies, so that’s why your car goes forward. Our planet, too, can be viewed as a simple machine. High frequency (blue-ish) light streams toward us from the sun, then something happens here that increases the order of molecules on Earth, after which we release a bunch of low-frequency (red-ish) light.
(We release low-frequency “infrared” light as body heat – night vision goggles work by detecting this.)
Our planet is an order-creating machine fueled by changing the color of photons from the sun.
A water-fueled car is impractical because other molecules that contain hydrogen and oxygen have higher chemical energy than an equivalent mass of water. There’s no energy available for you to siphon away into movement.
I’m reasonably well-versed with small stuff. I’ve studied quantum mechanics, spent two years researching electronic structure, that sort of thing. I imagine that I’m about as comfortable as I’ll ever be with the incomprehensible probabilistic weirdness that underlies reality.
But although I helped teach introductory calculus-based physics, I’ve never learned about big things. I took no geometry in college, and most big physics, I assume, is about transferring equations into spaces that aren’t flat. The basic principle seems straightforward – you substitute variables, like if you’re trying to estimate prices in another country and keep plugging in the exchange rate – but I’ve never sat down and worked through the equations myself.
Still, some excellent pop-science books on gravity have been published recently. My favorite of these was On Gravity by A. Zee – it’s quite short, and has everything I assume you’d want from a book like this: bad humor, lucid prose, excellent pacing. Zee has clearly had a lot of practice teaching this material to beginners, and his expertise shines through.
Near the end of the book, Zee introduces black holes – gravity at its weirdest. Gravity becomes stronger as the distance between objects decreases – it follows an “inverse square law.”
If our moon was closer to Earth, the tides would be more extreme. To give yourself a sense of the behavior of inverse square laws, you can play with some magnets. When two magnets are far apart, it seems as though neither cares about the existence of the other, but slide them together and suddenly the force gets so strong that they’ll leap through the air to clank together.
But because each magnet takes up space, there’s a limit to how close they can get. Once you hear them clank, the attractive magnetic force is being opposed by a repulsive electrostatic force – this same repulsion gives us the illusion that our world is composed of solid objects and keeps you from falling through your chair.
Gravity is much weaker than magnetism, though. A bar magnet can have a strong magnetic field but will have an imperceptible amount of gravity. It’s too small.
A big object like our sun is different. Gravity pulls everything together toward the center. At the same time, a constant flurry of nuclear explosions pushes everything apart. These forces are balanced, so our sun has a constant size, pouring life-enabling radiation into the great void of space (of which our planet intercepts a teensy tiny bit).
But if a big object had much more mass than our sun, it might tug itself together so ardently that not even nuclear explosions could counterbalance its collapse. It would become … well, nobody knows. The ultra-dense soup of mass at the center of a black hole might be stranger than we’ve guessed. All we know for certain is that there is a boundary line inside of which the force of gravity becomes so strong that not even light could possibly escape.
Satellites work because they fall toward Earth with the same curvature as the ground below – if they were going faster, they’d spiral outward and away, and if they were going slower, they’d spiral inward and crash. The “event horizon” of a black hole is where gravity becomes so strong that even light will be tugged so hard that it’ll spiral inward. So there’s almost certainly nothing there, right at the “edge” of the black hole as we perceive it. Just the point of no return.
If your friends encounter a black hole, they’re gone. Not even Morse-code messages could escape.
(Sure, sure, there’s “Hawking radiation,” quantum weirdness that causes a black hole to shrink, but this is caused by new blips in the fabric of reality and so can’t carry information away.)
The plot of Saga, by Brian K. Vaughan and Fiona Staples, revolves around a Romeo & Juliet-esque romance in the middle of intergalactic war, but most of the comic is about parenting. K read the entire series in two days, bawling several times, and then ran from the bedroom frantic to demand the next volume (unfortunately for her, Vaughan & Staples haven’t yet finished the series).
Saga is masterfully well-done, and there are many lovely metaphors for a child’s development.
For instance, the loss of a child’s beloved caretaker – babysitters, daycare workers, and teachers do great quantities of oft under-appreciated work. In Saga, the child and her first babysitter are linked through the spirit, and when the caretaker moves on, the child feels physical pain from the separation.
A hairless beast named “Lying Cat” can understand human language and denounces every untruth spoken in its present – allowing for a lovely corrective to a child’s perception that she is to blame for the traumas inflicted upon her.
Perhaps my favorite metaphor in Saga depicts the risk of falling into a black hole. Like all intergalactic travelers, they have to be careful – in Saga, a black hole is called a “timesuck” and it’s depicted as a developing baby.
My favorite scene in the film Interstellar depicts the nightmarish weirdness of relativistic time. A massive planet seems perfectly habitable, but its huge gravitational field meant that the years’ worth of “Everything’s okay!” signals had all been sent within minutes of a scout’s arrival. The planet was actually so dangerous that the scout couldn’t survive a full day, but decades would have passed on Earth before anyone understood the risk.
Gravity eats time.
So do babies. A child is born and the new parents might disappear from the world. They used to volunteer, socialize, have interests and hobbies … then, nothing.
I recently attended a singer-songwriter’s performance with my buddy Max. I have difficulty sitting still, so I’d brought paper and some markers to draw horrible cartoons while we listened.
After the show, Max and I caught up. We briefly mentioned our work (he is building things; I am alternating between typing, reading children’s books, and spraying down my popsicle-sticky kids with a hose) and started hashing philosophy. Max digs the old stuff – he’s currently reading Lucretius’s On the Nature of Things, which speculates on both the existence of atoms and reasons why we are conscious.
I told him once that K won’t let me talk about free will at parties, so Max often goads me into it. He’s always loved the image of K hovering with a flyswatter, waiting for me to broach her ire by describing the experiment that would disprove the existence of free will. “We can’t do it yet, but if a non-destructive brain scan at sufficient molecular accuracy … “ SWAT!
I described Hugh Everett’s many-worlds interpretation of quantum wave-function collapse – the idea that with every coin-flip, the universe splits into two and time keeps marching on with the coin having landed both heads and tails. A lot of physicists like dispensing with probability and randomness. Not me – I think the world needs a little chaos. Even if our choices were totally unpredictable, we might not have free will, but if the universe was predictable, sensible and orderly, then we definitely wouldn’t be free.
If you feel like you have free will, that’s almost the same as having it – but how free would you feel if researchers could strap you into a scanner and predict your fate more impeccably than any fortuneteller?
If every coin flip created a new world, and inside one your consciousness would be extinguished before you learned the result of the flip, then you could only consciously perceive yourself as experiencing the other outcome. Someone could flip a coin hundreds of times and you’d always see it landing heads, if the you inside every tails world was instantly ablated.
I was scribbling out diagrams, jotting numbers, and drawing an experimental apparatus with a research subject exploding into flames. Max leaned back, folded his arms over his chest, and mused, “But what I want to know is where love comes into it.”
I added a few more jagged flames, then set down my pen.
Look, I’m a clever dude. I’ve always been good at math, despite having taken very few math classes. I’m well read, hard working, and adept at solving puzzles. But I was never the best with emotions. Before I had kids, nobody would’ve mistaken me for any sort of love expert.
Max shook his head. We both knew that wasn’t really love.
But I’m a cold, rational scientist. Max trusts his intuition that something mystical is happening in the world. What kind of explanation might satisfy us both?
So we tried again. The world is real. There is, as best we can tell, a single, objective reality surrounding us. But our consciousness has no access to that world.
In reality, the computer I’m typing this essay on is composed of mostly empty space. Electrons flit blurrily around atomic nuclei – when I reach toward the keys, electrons in my fingertips are repelled, giving me the illusion that the computer is solid. One by one receptors in the cone cells of my eyes interact with incident photons, letting me believe that I am constantly seeing a room full of smooth, hard surfaces. My consciousness gobbles sensory data and creates a representation of the world.
And it’s within those representations that we live. Some philosophers question why humans are conscious. Others speculate that iPhones have consciousness as well. Just like us, a modern telephone integrates a wide variety of external perceptions into its conception of the world.
In any case, because we live within our perception of the world, as opposed to the world per se, love really does change the universe. By opening ourselves up to the world, we suddenly find ourselves to be inside a different world. A physicist might not notice the difference after you let yourself love – but that physicist isn’t inside your head. A physicist’s truth is not always the truth that matters.
From the beginning, artists understood that time travel either denies humans free will or else creates absurd paradoxes.
This conundrum arises whenever an object or information is allowed to travel backward through time. Traveling forward is perfectly logical – after all, it’s little different from a big sleep, or being shunted into an isolation cell. The world moves on but you do not… except for the steady depredations of age and the neurological damage that solitary confinement inevitably causes.
A lurch forward is no big deal.
Consider one of the earlier time travel stories, the myth of Oedipus. King Laius receives a prophecy foretelling doom. He strives to create a paradox – using information from the future to prevent that future, in this case by offing his son – but fails. This story falls into the “time travel denies humans free will” category. Try as they might, the characters cannot help but create their tragic future.
James Gleick puts this succinctly in his recent New York Review essay discussing Denis Villeneuve’s Arrival and Ted Chiang’s “Story of Your Life.” Gleick posits the existence of a “Book of Ages,” a tome describing every moment of the past, present, and future. Could a reader flip to a page describing the current moment and choose to evade the dictates of the book? In Gleick’s words,
Can you do that? Logically, no. If you accept the premise, the story is unchanging. Knowledge of the future trumps free will.
(I’m typing this essay on January 18th, and can’t help but note how crappy it is that the final verb in that sentence looks wrong with a lowercase “t.” Sorry, ‘merica. I hope you get better soon.)
Gleick is the author of Time Travel: A History, in which he presents a broad survey of the various tales (primarily literature and film) that feature time travel. In each tale Gleick discusses, time travel either saps free will (a la Oedipus) or else introduces inexplicable paradox (Marty slowly fading in Back to the Future as his parents’ relationship becomes less likely; scraps of the Terminator being used to invent the Terminator; a time-traveling escapee melting into a haggard cripple as his younger self is tortured in Looper.)
It’s not just artists who have fun worrying over these puzzles; over the years, more and more physicists and philosophers have gotten into the act. Sadly, their ideas are often less well-reasoned than the filmmakers’. Time Travel includes a long quotation from philosopher John Hospers (“We’re still in a textbook about analytical philosphy, but you can almost hear the author shouting,” Gleick interjects), in which Hospers argues that you can’t travel back in time to build the pyramids because you already know that they were built by someone else, followed by with the brief summary:
Admit it: you didn’t help build the pyramids. That’s a fact, but is it a logical fact? Not every logician finds these syllogisms self-evident. Some things cannot be proved or disproved by logic.
Gleick uses this moment to introduce Godel’s Incompleteness Theorem (the idea that, in any formal system, we must include unprovable assumptions), whose author, Kurt Godel, also speculated about time travel (from Gleick: If the attention paid to CTCs [closed timelike curve] is disproportionate to their importance or plausibility, Stephen Hawkins knows why: “Scientists working in this field have to disguise their real interest by using technical terms like ‘closed timelike curves’ that are code for time travel.” And time travel is sexy. Even for a pathologically shy, borderline paranoid Austrian logician).
Alternatively, Hospers’ strange pyramid argument could’ve been followed by a discussion of Timecrimes [http://www.imdb.com/title/tt0480669/], the one paradox-less film in which a character travels backward through time but still has free will (at least, as much free will as you or I have).
But James Gleick’s Time Travel: A History doesn’t mention Timecrimes. Obviously there are so many stories incorporating time travel that it’d be impossible to discuss them all, but leaving out Timecrimes is a tragedy! This is the best time travel movie (of the past and present. I can’t figure out how to make any torrent clients download the time travel movies of the future).
Timecrimes is great. It provides the best analysis of free will inside a sci-fi world of time travel. But it’s not just for sci-fi nerds – the same ideas help us understand strange-seeming human activities like temporally-incongruous prayer (e.g., praying for the safety of a friend after you’ve already seen on TV that several unidentified people died when her apartment building caught fire. By the time you kneel, she should either be dead or not. And yet, we pray).
Timecrimes progresses through three distinct movements. In the first, the protagonist believes himself to be in a world of time travel as paradox: a physicist has convinced him that with any deviation from the known timeline he might cause himself to cease to exist. And so he mimics as best he can events that he remembers. A masked man chased him with a knife, and so he chases his past self.
In the second movement, the protagonist realizes that the physicist was wrong. There are no paradoxes, but he seems powerless to change anything. He watched his wife fall to her death at the end of his first jaunt through time, so he is striving to alter the future… but his every effort fails. Perhaps he has no free will, no real agency. After all, he already remembers her death. His memory exists in the form of a specific pattern of neural connections in his brain, and those neurons will not spontaneously rearrange. His memory is real. The future seems set.
But then there is a third movement: this is the reason Timecrimes surpasses all other time travel tales. The protagonist regains a sense of free will within the constraints imposed by physics.
Yes, he saw his wife die. How can he make his memory wrong?
Similarly, you’ve already learned that the Egyptians built the pyramids. I’m pretty confident that none of the history books you’ve perused included a smiling picture of you with the caption “… but they couldn’t have done it without her.” And yet, if you were to travel back to Egypt, would it really be impossible to help in such a way that no history books (which will be written in the future, but which your past self has already seen) ever report your contributions.
Indeed, an analogous puzzle is set before us every time we act. Our brains are nothing more than gooey messes of molecules, constrained by the same laws of physics as everything else, so we shouldn’t have free will. And yet: can we still act as though we do?
We must. It’s either that or sit around waiting to die.
Because the universe sprung senselessly into existence, birthed by chance fluctuations during the long march of eternity… and then we appeared, billions of years later, through the valueless vagaries of evolution… our actions shouldn’t matter. But: can we pretend they do?
Instead of standing in front of a discount mall Santa and pretending to smile while somebody snaps our photo, my family records an album to send as our holiday card. Usually thirty minutes or so of original music played by family and friends.
Eight to ten songs a year, over the course of a decade, eats up a lot of ideas. Some evenings my brother and I would dither after everyone else went to bed. For 2013‘s Curse of the Ratist, our dithering included bowing a bass guitar hung on a wall mount. We aimed a microphone at a picture frame hung from that same wall some seven feet away.
You can bow a wide variety of objects and get interesting sounds. Violins, sure, but also any saw from the hardware store (which can give very human-like vocal tones), cymbals (these are lovely because they sound like sci-fi UFO landings… but be sure to ask first, because drummers will get upset if your rosin makes their cymbals sticky), the bell of some horns. Friction from the bow starts the object vibrating, and a vibrating object will push and pull at the nearby air, creating a traveling sound wave.
Or friction from a bow might start strings vibrating, which shakes the body of a bass, which shakes the wall it’s hanging from, which shakes a picture frame, which pushes and pulls the air, ready to be amplified by a microphone’s diaphragm. But the basic idea — an object wobbles back and forth to make sound — is the same.
Vibrations underly the workings of many aspects of the world. During college, I worked on a research project for a theoretical physicist who was curious whether residual vibrational energy contributed to DNA strand breaks. I scoff whenever I hear talk about a cure for cancer — “cancer” is an umbrella term to describe the inevitable imperfections that accumulate when you copy something over and over — but it is feasible to reduce the rate at which humans develop cancer. DNA strand breaks are one of the causes.
The research I was doing wasn’t going to save anyone, though. I was modeling a scenario in which electricity flows through the stacked bases as though a strand of DNA were a wire. The excess charge would cause each base it touched to change shape… then, when the charge jumped off, the base would return to its original shape. It would start vibrating. Can that vibrational energy transfer to the phosphate backbone and cause a strand to break?
Um, no. Probably not. After I’d worked on the project for about a year, I finally did a bunch of background reading and realized that our hypothesis was misguided. I was doing fancy calculations to model a process that almost certainly didn’t happen. Oops!
I did learn that it’s better to do research first, then work. Now I spend some two thirds of my work time reading, one third typing. I’d rather not waste another year.
Still, it was reasonable for my professor to think that vibrations would be involved. All matter has a wave-like nature. Vibrations rule the world.
In The Jazz of Physics, Stephon Alexander likens all vibrations to music. For instance, the nucleation of stars and galaxies from the homogeneous superheated cloud that burst into being in the Big Bang. My preferred analogy for this process is the concept of “snowballing” in game design — a small early advantage gives a player a boost throughout the game, making that player a clear favorite to win.
If you start with a large enough cloud of homogeneous gas — a universe-sized cloud — quantum fluctuations will cause some regions to be slightly more dense than others. These dense regions will then suck in neighboring molecules because they have a little bit of extra gravity. Over time, the inequality will grow: the rich get richer. But, in this case, that’s a good thing. It means galaxies can form.
Alexander’s preferred analogy is to music. He likens the early universe, with its pressure density waves, to an instrument.
And what does the CMB [cosmic background radiation] actually sound like? Some cosmologists have turned the frequencies of the CMB into sound, and though it is not very musical, it is not pure noise either. What is fascinating is there was an original quantum sound, which caused the first primordial vibrations in the plasma [that homogeneous cloud of gas that filled the early universe], and though this sound is categorized as white noise, its beauty is in the eyes of the beholder.
I find this analogy to be a stretch. But some of the others Alexander presents are lovely. For instance, his description of the interaction energy between neighboring spins in a magnetic material:
On the other hand, when neighboring spins disagree … there is more interaction energy caused by the tension between the disagreeing spins. One can imagine two people in a discussion. If they agree, there will be less to discuss, less interaction. If they disagree, they will interact more, trying to shift the other’s viewpoint.
I’ll definitely use his analogy the next time I teach this! Alexander found a clever similarity between two concepts, and that similarity will help others understand the idea from physics.
Whereas the analogy between cosmology and music, though clever, doesn’t seem like it’ll help many people learn physics. I know a fair bit about both music theory and physics, and I still struggled at times to follow Alexander’s logic.
I was also sad to see a bit of the physics presented incorrectly. For instance, his explanation of the photoelectric effect, for which Einstein won the Nobel Prize. Alexander writes that, until the early 1900s,
physicists thought a beam of light was like water coming out of a hose. If the volume of water is increased, the water will have more momentum. The same behavior was expected of light waves. But something different was seen in the photoelectric effect: no matter how intense the light, the same number of electrons came flying out. However, increasing the frequency of the light — essentially, making it bluer — caused the light to hit more electron homeruns. Two conclusions were drawn from this experiment:
1. Depending on the situation, light can behave like either a wave or a particle.
2. The kinetic energy that a beam of light imparts to electrons is related to the frequency of the light and not the intensity.
It’s true that, with low energy light, increasing the intensity won’t change the number of electrons flying out. With low-intensity, low-energy light, zero electrons will be ejected, and with high-intensity, low-energy light, you’ll still get zero. But as long as you’re using the right color of light (i.e., short wavelength), the number of electrons ejected is proportional to intensity. That’s how photomultiplier tubes work.
The kinetic energy that one photon imparts to one electron is a function of the frequency of light. The kinetic energy that a beam of photons imparts to electrons is a function of both the frequency and the intensity of light.
And a few of the supposed parallels between music and physics threw me. Alexander quotes the jazz saxophonist Mark Turner as saying, “When I’m in the middle of a solo, whenever I am most certain of the next note I have to play, the more possibilities open up for the notes that follow.” This is something many people can relate to. Too many options can be daunting. When a few constraints are imposed — guidelines for a project, or musical traditions that identify one note as “making sense” to play next whereas others would not — most people find they can be more creative. When I give the dudes in my writing class a prompt that’s too open-ended, a lot of them stare at their blank sheets of paper without writing anything.
But I have trouble relating the freedom & creativity that a little bit of structure engenders (maybe I should’ve turned this into an analogy about parenting instead) to the uncertainty principle.
Still, it was a fun little book. If you’re somebody who loves both music and physics, you might want to check it out.
When you aim a telescope at the night sky, you can see a lot of stars. You have to look harder than if Edison hadn’t been such a persistent tinkerer, but they’re all still out there.
From the colors of light emitted by each star, you can estimate its size. And there are big whorls of gas, too. These clouds also interact with light in a predictable way. By looking up at the sky through a telescope, you can make a guess as to the total amount of stuff is out there.
But your guess would be wrong.
There’s another way you could guess: our solar system is spinning around the center of the Milky Way galaxy, held within its orbit by gravity. Since we know how fast we’re moving, we know how much gravity there must be. If there were more, we’d spiral inward to our doom, if there were less, we’d careen into space.
We’re held in place by more gravity than you’d expect if the only matter in our galaxy were stuff you could see. Unseen stuff must be tugging us, too! “Dark matter” refers to whatever is creating all the excess gravity we feel that can’t be accounted for by what we see.
“Dark matter” was discovered using logic very similar to Gabriel Zucman’s in The Hidden Wealth of Nations. Dark matter is invisible when we look through a telescope, but we can identify where it must be when we look at clusters of stars that could only have their current shape if held together by a lot of extra gravity. Similarly, money in illegal tax havens is invisible when we look at each nation’s tax records, but we can identify when it must exist when we look at all nations collectively and see strange absences of money. In Zucman’s words (translated by Teresa Lavender Fagan):
The following example shows it in a simple way: let’s imagine a British person who holds in her Swiss bank account a portfolio of American securities — for example, stock in Google. What information is recorded in each country’s balance sheet? In the United States, a liability: American statisticians see that foreigners hold US equities. In Switzerland, nothing at all, and for a reason: the Swiss statisticians see some Google stock deposited in a Swiss bank, but they see that the stock belongs to a UK resident — and so they are neither assets nor liabilities for Switzerland. In the United Kingdom, nothing is registered, either, but wrongly this time: the Office for National Statistics should record an asset for the United Kingdom, but it can’t, because it has no way of knowing that the British person has Google stock in her Geneva account.
As we can see, an anomaly arises — more liabilities than assets will tend to be recorded on a global level. And, in fact, for as far back as statistics go, there is a “hole”: if we look at the world balance sheet, more financial securities are recorded as liabilities than as assets, as if planet Earth were in part held by Mars. It is this imbalance that serves as the point of departure for my estimate of the amount of wealth held in tax havens globally.
Of course, in the case of tax havens, we know what the invisible stuff is. Money is money. I mean, sure, it’s more likely to be stocks or stakes in hedge funds or the like than big bundles of dollar bills, but you get the idea.
Whereas, dark matter? No one knows for certain what it is.
In Lisa Randall’s Dark Matter and the Dinosaurs, she describes several of the prevailing theories for what this unseen stuff might be.
Before I say more, I should include a disclaimer: I’ve studied a lot of physics, but only for objects atom-sized or larger, planet-sized or smaller. Which might sound like a wide range, but it isn’t wide enough. Randall’s book builds toward a hypothesis involving extremely small particles agglomerated into clouds more massive than stars.
Randall says that her primary motivation in writing the book was not to advocate for a link between the arrangement of dark matter in our galaxy and the asteroid collision that killed the dinosaurs. She described her aims in a letter to the New York Review of Books, but it’s a strange letter — it puzzles me that she’d be so ardent about a distinction between the words “invisible” and “transparent” when several proposals for dark matter described in her book would indeed be astronomically invisible but not transparent, and when she herself uses the words interchangeably in chapter titles and the text through the latter half of her book.
But that dino tie-in was why I wanted to read the book. I assume it’s why you’re reading this review.
So I think it’s worth describing why I thought it was so bizarre that she wrote a book about this hypothesis, even though I did learn some interesting facts from the first half.
One of the favored explanations for the nature of dark matter is that it’s made of “weakly-interacting massive particles,” or “WIMPs.” Giant detectors are being built to test this. Big vats of xenon buried deep underground. WIMPs are postulated to interact through a short-range nuclear force, but not through electromagnetism.
It doesn’t feel good to type a sentence like the one above and know that it’s both essential to an explanation and likely to sound like gobbledygook.
So, electromagnetism? This underlies the physics of our world. “Electromagnetism” means, roughly, interacting with electricity and light. It’s why we tend not to fall through floors or walk through walls. Electrons repel each other, similar to the way two negative-ended magnets will squirm when you try to push them close to one another. All the atoms of your body, and all the atoms of the floor, are slathered in electrons. And so with every step you take, the electrons in the floor push against the electrons in your feet, keeping you afloat in a sea of mostly empty space.
But if dark matter doesn’t interact with electromagnetic forces, it could pass right through you.
Which might sound goofy or ghostly, but this much seemed reasonable to me. After all, seemingly solid matter has been shown to be permeable repeatedly in the past. I don’t just mean the loppered sea, the unnavigably thick waste thought to surround the known world during the Middle Ages. Do you know about the gold foil experiment?
The gold foil experiment was designed to test: are solids solid? Particles were blasted at a sheet of gold foil. If the sheet was solid, the particles should bounce off or get stuck. Maybe rip holes in the foil. But if the foil is mostly empty space, most particles should zip right through.
Helium nuclei were launched at the foil. Most passed right through. Only a rare few struck something solid and ricocheted. The sheet of metal — which would seem solid if you touched it with your finger, because electron density in your skin gets pushed away by electrons in the metal foil — was permeable to “naked” nuclei, tiny balls of protons & neutrons not slathered in electron density.
Randall explains this with the analogy of parallel social networks. Alternatively, you could think about the behavior of animals. If a foreign squirrel comes into my yard, the squirrel who lives in our big tree will chase it away. But rabbits can hop through without being harassed by that squirrel.
Because rabbits and squirrels don’t compete for food or mates, they can pass right through each others’ territories.
(I hadn’t realized until recently that rabbits are also very territorial. It took a lot of yelling before I was able to convince our pet rabbit Kichirou, who fancies himself something of a warrior, that he didn’t need to urinate on the bed & belongings of a dear friend when she came to visit. He thought she was usurping our home. She wasn’t! She just wanted to nap, eat ice cream, & work on her art! Silly rabbit.)
A squirrel, running toward another squirrel’s territory, might appear to ricochet. The resident squirrel will launch into action, intercept & chase away the intruder. But a rabbit can travel in a straight-ish leaf-nibbling line.
In the gold foil experiment, alpha particles (another name for those naked helium nuclei) pass right through electrons’ territory. But they ricochet off other nuclei’s territory. Dark matter could pass even closer. It might share zero interactions with ordinary matter other than gravity, in which case it could travel anywhere unmolested, or it might have only the “weak nuclear force” in common with ordinary matter, in which case it would still have to pass very close to another nucleus before it bounced or swerved.
Electromagnetic forces kick in earlier than the weak nuclear force. You can compare this to human senses. If you’re out for a stroll at the same time I’m jogging with our pitbull Uncle Max, you can see us from farther away than you can smell us. Even though Uncle Max still smells very pungently bad from the several times he’s been skunked this year. Dude needs to learn that skunks don’t want to play.
I think that’s enough background to give you a sense of Randall’s hypothesis, which begins with the following:
Maybe our planet has been periodically bombarded with asteroids — as in, most of the time few asteroids hit, and every so often there are a bunch of collisions.
Maybe the time interval between these collisions is approximately 30 million years long.
Maybe our solar system wobbles up and down across the central plane of the Milky Way as we orbit.
Maybe the time interval for these wobbles is the same 30 million years.
Maybe traversing the central plane of the Milky Way is what increases the chance of stray asteroids hitting us (if the likelihood does periodically increase).
Maybe not all dark matter is made of the same stuff.
Maybe some of the dark matter (not that we know what any of it is), in addition to interacting through gravity, has a self-attractive force that it uses to cluster together.
Maybe dark matter, if the right fraction of it had this property, would form a big disc across the central plane of our galaxy.
Maybe the up & down wobble of our solar system (if it occurs) causes it to cross that disc (if it exists) every 30 million years or so, which is why asteroid bombardment increases at those times (if it does).
This long string of conjectures is the main reason I thought a book-length treatment of this hypothesis was premature. To my mind, it is a disservice to the general public to cloak hypothetical storytelling in the trappings of academic science. I think this passage Randall wrote about Occam’s Razor really demonstrates why I have qualms:
Both casual observers of science and scientists themselves frequently employ Occam’s Razor for guidance when evaluating scientific proposals. This oft-cited principle says that the simplest theory that explains a phenomenon is most likely to be the best one.
Yet two factors undermine the authority of Occam’s Razor, or at least suggest caution when using it as a crutch. … Theories that conform to the dictates of Occam’s Razor sometimes similarly address one outstanding problem while creating issues elsewhere — usually in some other aspect of the theory that embraces it.
My second concern about Occam’s Razor is just a matter of fact. The world is more complicated than any of us would have been likely to conceive. Some particles and properties don’t seem necessary to any physical processes that matter — at least according to what we’ve deduced so far.
I disagree with this sentiment… especially in a book targeted toward a popular audience. It’s true that the world is sometimes very complex. But we need Occam’s Razor because elaborate explanations can always fit data better than simple explanations. This is why conspiracy theorists are able to account for every single detail — look at that man shaking an umbrella! It’s a signal! — whereas a simpler explanation — it was a lone crazy with a gun — leaves much unaccounted for.
In science, the problem is called “overfitting data.” If you have ten dots on a chart, you might be able to draw a straight line that passes kinda close to all of them… but a squiggly line could be drawn right through every single point!
Occam’s Razor suggests: stick with the line. Unless there’s a compelling reason to believe a more complicated explanation is correct, you shouldn’t try to account for every single detail.
Similarly, if Randall thought there was compelling astronomical data that showed our solar system wobbling up and down at the same times that asteroid strikes increase in frequency, she ought to propose that these phenomena are linked. But, given that these data are already nebulous, why complicate the proposal by saying that a dark matter disc underlies the link? Why say that a particular fraction of dark matter needs to have a certain type of force in order to form a disc of that shape?
Yes, storytelling is important. These wild explanations have a vital role in science — they inspire experiments to test the ideas. If some of the experiments yield positive results, then it’s worth telling the story to the public. But the initial speculation? That part isn’t science. It seems unhelpful for a Harvard professor to promote it as such.
I was also thrown off by some of the pop culture references that pepper the text. Most seemed unnecessary but innocuous, like “WIMPs [weakly-interacting massive particles], unlike Obi-Wan Kenobi, are not our only hope, though as far as these detection methods are concerned, they are in many ways our best one. Direct detection works only when there is some interaction between Standard Model and dark matter particles, and WIMP models guarantee that possibility.” Mentioning Star Wars didn’t seem to accomplish anything other than an are you paying attention? nudge in the ribs, but the allusion didn’t impede my understanding.
Worse was a metaphor that misrepresents the history of economic injustice in the United States without elucidating the physics Randall is describing:
Another proposed explanation for the paucity of observed satellite galaxies and sparser-than-expected inner galaxy cores is that supernova explosions expel material out of the inner portions of their host galaxies, leaving behind a far less dense inner core. The resulting dark matter distribution might be compared to that of an urban population in its densest inner city regions, where — in the aftermath of unrest — explosions of violence have stemmed the growth to leave a depleted core. The inner galaxy that has seen too much supernova outflow doesn’t grow in density toward the center any more than would a sparsely occupied inner city.
Analogies often are the best way to explain science to a general audience. Take something unfamiliar, show how it’s similar to something people know. And no analogy is perfect, obviously. There will always be differences between the unfamiliar scientific concept and the everyday experience you’re relating it to.
But it can hurt understanding when an analogy is used incorrectly. Perhaps there are climates where rabbits and squirrels do compete for food, in which case my earlier analogy for the behavior of non-interacting particles might confuse someone. If such a climate exists, a person living there might think, What’s he talking about? I watch squirrels chase rabbits all the time!
Regarding galaxies that have low density near the center, I think the comparison to urban unrest doesn’t work. In cities, violence usually follows a drop in population; violence doesn’t cause the drop. Here’s Matthew Desmond’s description from Evicted:
Milwaukee used to be flush with good jobs. But throughout the second half of the twentieth century, bosses in search of cheap labor moved plants overseas or to Sunbelt communities, where unions were weaker or didn’t exist. Between 1979 and 1983, Milwaukee’s manufacturing sector lost more jobs than during the Great Depression — about 56,000 of them. The city where virtually everyone had a job in the postwar years saw its unemployment rate climb into the double digits. Those who found new work in the emerging service sector took a pay cut. As one historian observed, “Machinists in the old Allis-Chalmers plant earned at least $11.60 an hour; clears in the shopping center that replaced much of that plant in 1987 earned $5.23.
These economic transformations — which were happening in cities across America — devastated Milwaukee’s black workers, half of whom held manufacturing jobs. When plants closed, they tended to close in the inner city, where black Milwaukeeans lived. The black poverty rate rose to 28 percent in 1980. By 1990, it had climbed to 42 percent.
After poverty came squalor. After squalor, violence.
To me, it sounds disquietingly like blaming the victims to claim that violence drove people away, when in reality the violence only began after the middle class & most of the decent jobs had left.
Not that I know of a better analogy for the low-density interiors of galaxies. The best I can think of are the ring-like structures of bacterial colonies — they end up that way because early generations deplete all the nutrients from the center and fill it with toxic waste — but that isn’t a good analogy because many people are equally unfamiliar with bacterial growth patterns.
Nobody’s gonna suddenly understand if you compare an unfamiliar concept to something else that’s equally unfamiliar.
All told — and despite the fact that I learned a fair bit from the first half of the book — I can’t think of anyone whom I’d recommend Dark Matter and the Dinosaurs to. The idea is interesting, sure. If you’re an astronomer, maybe you should think about experiments to test it. But working astronomers wouldn’t need all the background information presented in the book — they would want to read Randall & Reece’s article in Physical Review Letters instead. You get the hypothesis and some supporting data in just five pages, as opposed to 300+ pages for the hypothesis alone.
That leaves general audiences. But, this isn’t science yet! This is storytelling. Toward the end of the book, Randall even mentions that there’s enough speculation underlying the hypothesis for the whole thing to be illusory:
What astrophysicists were really saying was that there was no need for a dark disk. Given the uncertainties in densities in all the known gas and star components, the measured potential could be accounted for by known matter alone.
I think it’s situations like this that really demonstrate the value of Occam’s Razor. Our knowledge of the world is imperfect. One way to acknowledge our ignorance is to prefer simple explanations: instead of accounting for every single detail, we accept that some details about what we think we know might be incorrect. The man was shaking an umbrella because of an inside joke? You mean, he had no idea the president would die? That’s an awfully big coincidence, don’t you think?
Why write an entire book — with such an attention-grabbing title! — when all the data you’re accounting for might be measurement uncertainties?
In economics, proofs often begin with the words If we consider a ball of radius R centered at the point X in R n … I wrote those words so many times. Reading them now, they sound quite strange to me.
A math course called “real analysis” was a prerequisite for economics. Presumably real analysis would’ve taught me to write proofs, perhaps well enough that I’d understand why I wrote the words I did. But my university had recently implemented an online registration system, and its glitchiness meant I could skip pre-reqs, and that I was able to enroll in both economics and inorganic chemistry during the 10 am to 11:30 time slot. I attended economics except when there was a chemistry exam. And still don’t know for certain what “real analysis” entails.
But I know that the word “ball,” in the world of mathematics, is a generic term for round things. You have two dots in one dimension, a circle in two, a sphere in three, then a “ball” in four or more.
The number of dimensions is what the “n” stands for in “R n.” In the world of economics proofs, you might have any number. Of course, in our day to day lives, most of us are familiar with only two or three (yes, yes, physicists claim that we should understand four, because we move along three spatial axes and time. But I can move forward and back, left and right, up and down. I’ll continue to think of my world as three-dimensional until I learn to move with equal faculty into the future and the past). But economists need more because they like to give each variable its own dimension. Instead of “up and down,” a dimension in an economics proof might be the weather, the number of factories, the number of workers in a population.
Sliding along an axis can seem incredibly grim if you momentarily forget that a proof is supposed to be abstract. It’s just an imaginary line projecting endlessly through space, but what does it mean?
For workers, sliding back toward zero means lives destroyed, people unemployed, hustling to pay rent, to keep the lights on, to feed their kids. Or worse. Alongside Primo Levi in the Buna concentration camp, the number of workers could be varied at will. There seemed to be endless numbers of condemned to add, and each decrease meant another murdered man.
Luckily, in class we worked quickly enough that there was no time to think of that. The professor would scrawl his solution upon the board, I’d copy it into my notes, struggling to keep up.
Or perhaps I lost you earlier. Maybe you hadn’t realized that there even were proofs in economics. I hadn’t, before I enrolled. I expected only to draw crisscrossing lines, mark where they intersected, claim that should be your greeble’s price. A “greeble” being, for some reason or other, the default name for an imaginary product for which the supply and demand can be used to determine a price.
I learned about these mythical “greebles” in high school, in an economics class that moved many-fold more slowly than the university class. In high school there was more time to sit and wonder what a greeble was. I drew pictures in my spiral notebook. Most of these pictures made the greeble look like either a strange pet or a military weapon. There were many vicious-looking weapons drawn in my high school notebooks. I hated being there. I wrote stories about blowing up the school. Not that I was a violent kid. I was already vegetarian because I hated hurting things. But I certainly drew a lot of death and destruction. Then, of course, the Columbine shootings happened and I had to stop drawing those pictures. Writing those stories. Murderous ideation was no longer safe. Even once I’d stopped, they started sending me to the principle’s office about once a month. That did not make me like school more.
From then on, at my school, even suicidal ideation was something you had to keep to yourself. Luckily, I was a pretty happy kid. I rarely thought about that sort of thing more than once a day. Still don’t.
But, yes, in economics there are proofs. One famous proof we reproduced was “Arrow’s impossibility theorem,” which states mathematically that if a population is trying to vote, they’re doomed. There is no fair voting system that picks the most-preferred candidate out of a set of three or more. Your options are a dictatorship or else electing some schmuck whom nobody really wants.
Maybe that sounds like an argument in favor of a two-party system. But it isn’t, not really. If you’re worried that from a set of options the best one won’t be picked, the best solution isn’t to offer only two of the crummier options from that set. People still won’t get what they want. All you’ve accomplished is to blast even their illusion of a fair choice. In a two-party system people are still doomed, but they’re so clearly doomed that you don’t even need Kenneth Arrow’s fancy proof for them to know it.
As it happens, it’s election season again. It so often is, because “election season” seems to run approximately two years out of each four-year presidential term, and sometimes a year or more for even two-year congressional terms, and huge numbers of people devote eighty, ninety, hundred hour work weeks toward their efforts to get this dude or that dude or (finally!) this lady elected.
Whenever I feel bad about how long I’ve spent working on a project, I remember the number of person hours that are guaranteed to be wasted each election cycle. Because huge numbers of people work full-time to get their preferred candidate elected, and all but one won’t win. Maybe they console themselves by thinking at least by running, we helped change the tenor of the national debate! But, let’s be real. Even when fewer than a third of the populace votes for a dude, he’ll refer only to the (bizarre!) electoral college numbers and claim to have received a clear mandate for action.
Nobody cares about the platform the losers were running on. And most everybody is guaranteed to be a loser. Even (especially?) the voters.
My personal political inclinations include taxation to assess the fair price of business externalities, free trade, open borders, lax enforcement against possession of tools for self-harm (drugs), strict enforcement against possession of tools for other-harm (guns, automobiles), progressive income taxes such that people pay (or are reimbursed) relative to what they’d likely lose or gain if we had anarchy instead of our current government.
If I were trying to be cheeky, I’d draw a parallel between my ideas about progressive income tax and the conceptual framework behind electric potential, the idea that the energy at each point is equal to the work that would’ve been done to drag a test charge there from infinitely far away. Instead of a field-less void somewhere far off in the distance, I imagine people being launched into their current wealth or poverty from an undifferentiated state of Hobbesian anarchy.
But maybe the physics metaphor would seem too twee. So (a la Trump, I’m not going to say they’re weak. But they’re weak), I won’t subject you to it.
I’m pro-genetically modified foods, anti-pesticide. Pro-vaccination, pro-childhood nutrition, against our current quantity of medical spending. Most doctors think there needs to be a conversation about how much the government should pay for each quality-of-life-adjusted year. I think even that is not enough. We need a concurrent conversation about how long humans should live. About what we as a people consider to be the meaning of life and the best way for our spending to reflect that. Because any threshold for how much we’ll spend on each quality-of-life-adjusted year will result in untenable costs if medical advances keep allowing people to live longer.
All of which means that, yup, as ever, no politician will (or should, honestly) care about what I stand for. I’ll vote for the old hippie commie guy in the primary (if I get to vote. I probably won’t get to, though. My state’s primary is scheduled relatively late), and then throw away my vote in the general election (what with our electoral college, most people’s votes are submerged at that stage. I think there’ll be something like eight states where the vote will be close enough that all people waiting in line for their turn in the booth can delude themselves into thinking that their votes matter).
Which, again, does sound awful. Like, isn’t there a better way?
Well, yes. There is a better way. There are many better ways than the strange system our country has contrived. But at least I had the experience of jotting out the full proof to know that there is no perfect way.
(Somehow I’d deluded myself into thinking that typing this essay would make me happy. I see now that I was wrong.)