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?