Category Archives: Science Communication

Communicating the Continuum Hypothesis

I have a friend who is shall we say, pessimistic, about science communication. He thinks it’s too much risk for too little gain, too many misunderstandings while the most important stuff is so abstract the public will never understand it anyway. When I asked him for an example, he started telling me about a professor who works on the continuum hypothesis.

The continuum hypothesis is about different types of infinity. You might have thought there was only one type of infinity, but in the nineteenth century the mathematician Georg Cantor showed there were more, the most familiar of which are countable and uncountable. If you have a countably infinite number of things, then you can “count” them, “one, two, three…”, assigning a number to each one (even if, since they’re still infinite, you never actually finish). To imagine something uncountably infinite, think of a continuum, like distance on a meter stick, where you can always look at smaller and smaller distances. Cantor proved, using various ingenious arguments, that these two types of infinity are different: the continuum is “bigger” than a mere countable infinity.

Cantor wondered if there could be something in between, a type of infinity bigger than countable and smaller than uncountable. His hypothesis (now called the continuum hypothesis) was that there wasn’t: he thought there was no type of infinite between countable and uncountable.

(If you think you have an easy counterexample, you’re wrong. In particular, fractions are countable.)

Kurt Gödel didn’t prove the continuum hypothesis, but in 1940 he showed that at least it couldn’t be disproved, which you’d think would be good enough. In 1964, though, another mathematician named Paul Cohen showed that the continuum hypothesis also can’t be proved, at least with mathematicians’ usual axioms.

In science, if something can’t be proved or disproved, then we shrug our shoulders and say we don’t know. Math is different. In math, we choose the axioms. All we have to do is make sure they’re consistent.

What Cohen and Gödel really showed is that mathematics is consistent either way: if the continuum hypothesis is true or false, the rest of mathematics still works just as well. You can add it as an extra axiom, and add-on that gives you different types of infinity but doesn’t change everyday arithmetic.

You might think that this, finally, would be the end of the story. Instead, it was the beginning of a lively debate that continues to this day. It’s a debate that touches on what mathematics is for, whether infinity is merely a concept or something out there in the world, whether some axioms are right or wrong and what happens when you change them. It involves attempts to codify intuition, arguments about which rules “make sense” that blur the boundary between philosophy and mathematics. It also involves the professor my friend mentioned, W. H. Woodin.

Now, can I explain Woodin’s research to you?

No. I don’t understand it myself, it’s far more abstract and weird than any mathematics I’ve ever touched.

Despite that, I can tell you something about it. I can tell you about the quest he’s on, its history and its relevance, what is and is not at stake. I can get you excited, for the same reasons that I’m excited, I can show you it’s important for the same reasons I think it’s important. I can give you the “flavor” of the topic, and broaden your view of the world you live in, one containing a hundred-year conversation about the nature of infinity.

My friend is right that the public will never understand everything. I’ll never understand everything either. But what we can do, what I strive to do, is to appreciate this wide weird world in all its glory. That, more than anything, is why I communicate science.

Reader Background Poll Reflections

A few weeks back I posted a poll, asking you guys what sort of physics background you have. The idea was to follow up on a poll I did back in 2015, to see how this blog’s audience has changed.

One thing that immediately leaped out of the data was how many of you are physicists. As of writing this, 66% of readers say they either have a PhD in physics or a related field, or are currently in grad school. This includes 7% specifically from my sub-field, “amplitudeology” (though this number may be higher than usual since we just had our yearly conference, and more amplitudeologists were reminded my blog exists).

I didn’t use the same categories in 2015, so the numbers can’t be easily compared. In 2015 only 2.5% of readers described themselves as amplitudeologists. Adding these up with the physics PhDs and grad students gives 59%, which goes up to 64.5% if I include the mathematicians (who this year might have put either “PhD in a related field” or “Other Academic”). So overall the percentages are pretty similar, though now it looks like more of my readers are grad students.

Despite the small difference, I am a bit worried: it looks like I’m losing non-physicist readers. I could flatter myself and think that I inspired those non-physicists to go to grad school, but more realistically I should admit that fewer of my posts have been interesting to a non-physics audience. In 2015 I worked at the Perimeter Institute, and helped out with their public lectures. Now I’m at the Niels Bohr Institute, and I get fewer opportunities to hear questions from non-physicists. I get fewer ideas for interesting questions to answer.

I want to keep this blog’s language accessible and its audience general. I appreciate that physicists like this blog and view it as a resource, but I don’t want it to turn into a blog for physicists only. I’d like to encourage the non-physicists in the audience: ask questions! Don’t worry if it sounds naive, or if the question seems easy: if you’re confused, likely others are too.

Why I Wasn’t Bothered by the “Science” in Avengers: Endgame

Avengers: Endgame has been out for a while, so I don’t have to worry about spoilers right? Right?

Right?

Anyway, time travel. The spoiler is time travel. They bring back everyone who was eliminated in the previous movie, using time travel.

They also attempt to justify the time travel, using Ant Man-flavored quantum mechanics. This works about as plausibly as you’d expect for a superhero whose shrinking powers not only let him talk to ants, but also go to a “place” called “The Quantum Realm”. Along the way, they manage to throw in splintered references to a half-dozen almost-relevant scientific concepts. It’s the kind of thing that makes some physicists squirm.

And I enjoyed it.

Movies tend to treat time travel in one of two ways. The most reckless, and most common, let their characters rewrite history as they go, like Marty McFly almost erasing himself from existence in Back to the Future. This never makes much sense, and the characters in Avengers: Endgame make fun of it, listing a series of movies that do time travel this way (inexplicably including Wrinkle In Time, which has no time travel at all).

In the other common model, time travel has to happen in self-consistent loops: you can’t change the past, but you can go back and be part of it. This is the model used, for example, in Harry Potter, where Potter is saved by a mysterious spell only to travel back in time and cast it himself. This at least makes logical sense, whether it’s possible physically is an open question.

Avengers: Endgame uses the model of self-consistent loops, but with a twist: if you don’t manage to make your loop self-consistent you instead spawn a parallel universe, doomed to suffer the consequences of your mistakes. This is a rarer setup, but not a unique one, though the only other example I can think of at the moment is Homestuck.

Is there any physics justification for the Avengers: Endgame model? Maybe not. But you can at least guess what they were thinking.

The key clue is a quote from Tony Stark, rattling off a stream of movie-grade scientific gibberish:

“ Quantum fluctuation messes with the Planck scale, which then triggers the Deutsch Proposition. Can we agree on that? ”

From this quote, one can guess not only what scientific results inspired the writers of Avengers: Endgame, but possibly also which Wikipedia entry. David Deutsch is a physicist, and an advocate for the many-worlds interpretation of quantum mechanics. In 1991 he wrote a paper discussing what happens to quantum mechanics in the environment of a wormhole. In it he pointed out that you can make a self-consistent time travel loop, not just in classical physics, but out of a quantum superposition. This offers a weird solution to the classic grandfather paradox of time travel: instead of causing a paradox, you can form a superposition. As Scott Aaronson explains here, “you’re born with probability 1/2, therefore you kill your grandfather with probability 1/2, therefore you’re born with probability 1/2, and so on—everything is consistent.” If you believe in the many-worlds interpretation of quantum mechanics, a time traveler in this picture is traveling between two different branches of the wave-function of the universe: you start out in the branch where you were born, kill your grandfather, and end up in the branch where you weren’t born. This isn’t exactly how Avengers: Endgame handles time travel, but it’s close enough that it seems like a likely explanation.

David Deutsch’s argument uses a wormhole, but how do the Avengers make a wormhole in the first place? There we have less information, just vague references to quantum fluctuations at the Planck scale, the scale at which quantum gravity becomes important. There are a few things they could have had in mind, but one of them might have been physicists Leonard Susskind and Juan Maldacena’s conjecture that quantum entanglement is related to wormholes, a conjecture known as ER=EPR.

Long-time readers of the blog might remember I got annoyed a while back, when Caltech promoted ER=EPR using a different Disney franchise. The key difference here is that Avengers: Endgame isn’t pretending to be educational. Unlike Caltech’s ER=EPR piece, or even the movie Interstellar, Avengers: Endgame isn’t really about physics. It’s a superhero story, one that pairs the occasional scientific term with a character goofily bouncing around from childhood to old age while another character exclaims “you’re supposed to send him through time, not time through him!” The audience isn’t there to learn science, so they won’t come away with any incorrect assumptions.

The a movie like Avengers: Endgame doesn’t teach science, or even advertise it. It does celebrate it though.

That’s why, despite the silly half-correct science, I enjoyed Avengers: Endgame. It’s also why I don’t think it’s inappropriate, as some people do, to classify movies like Star Wars as science fiction. Star Wars and Avengers aren’t really about exploring the consequences of science or technology, they aren’t science fiction in that sense. But they do build off science’s role in the wider culture. They take our world and look at the advances on the horizon, robots and space travel and quantum speculations, and they let their optimism inform their storytelling. That’s not going to be scientifically accurate, and it doesn’t need to be, any more than the comic Abstruse Goose really believes Witten is from Mars. It’s about noticing we live in a scientific world, and having fun with it.

This Week, at Scientific American

I’ve written an article for Scientific American! It went up online this week, the print versions go out on the 25th. The online version is titled “Loopy Particle Math”, the print one is “The Particle Code”, but they’re the same article.

For those who don’t subscribe to Scientific American, sorry about the paywall!

“The Particle Code” covers what will be familiar material to regulars on this blog. I introduce Feynman diagrams, and talk about the “amplitudeologists” who try to find ways around them. I focus on my corner of the amplitudes field, how the work of Goncharov, Spradlin, Vergu, and Volovich introduced us to “symbology”, a set of tricks for taking apart more complicated integrals (or “periods”) into simple logarithmic building blocks. I talk about how my collaborators and I use symbology, using these building blocks to compute amplitudes that would have been impossible with other techniques. Finally, I talk about the frontier of the field, the still-mysterious “elliptic polylogarithms” that are becoming increasingly well-understood.

(I don’t talk about the even more mysterious “Calabi-Yau polylogarithms“…another time for those!)

Working with Scientific American was a fun experience. I got to see how the professionals do things. They got me to clarify and explain, pointing out terms I needed to define and places I should pause to summarize. They took my rough gel-pen drawings and turned them into polished graphics. While I’m still a little miffed about them removing all the contractions, overall I learned a lot, and I think they did a great job of bringing the article to the printed page.

Book Review: We Have No Idea

I have no idea how I’m going to review this book.

Ok fine, I have some idea.

Jorge Cham writes Piled Higher and Deeper, a webcomic with possibly the most accurate depiction of grad school available. Daniel Whiteson is a professor at the University of California, Irvine, and a member of the ATLAS collaboration (one of the two big groups that make measurements at the Large Hadron Collider). Together, they’ve written a popular science book covering everything we don’t know about fundamental physics.

Writing a book about what we don’t know is an unusual choice, and there was a real risk it would end up as just a superficial gimmick. The pie chart on the cover presents the most famous “things physicists don’t know”, dark matter and dark energy. If they had just stuck to those this would have been a pretty ordinary popular physics book.

Refreshingly, they don’t do that. After blazing through dark matter and dark energy in the first three chapters, the rest of the book focuses on a variety of other scientific mysteries.

The book contains a mix of problems that get serious research attention (matter-antimatter asymmetry, high-energy cosmic rays) and more blue-sky “what if” questions (does matter have to be made out of particles?). As a theorist, I’m not sure that all of these questions are actually mysterious (we do have some explanation of the weird “1/3” charges of quarks, and I’d like to think we understand why mass includes binding energy), but even in these cases what we really know is that they follow from “sensible assumptions”, and one could just as easily ask “what if” about those assumptions instead. Overall, these “what if” questions make the book unique, and it would be a much weaker book without them.

“We Have No Idea” is strongest when the authors actually have some idea, i.e. when Whiteson is discussing experimental particle physics. It gets weaker on other topics, where the authors seem to rely more on others’ popular treatments (their discussion of “pixels of space-time” motivated me to write this post). Still, they at least seem to have asked the right people, and their accounts are on the more accurate end of typical pop science. (Closer to Quanta than IFLScience.)

The book’s humor really ties it together, often in surprisingly subtle ways. Each chapter has its own running joke, initially a throwaway line that grows into metaphors for everything the chapter discusses. It’s a great way to help the audience visualize without introducing too many new concepts at once. If there’s one thing cartoonists can teach science communicators, it’s the value of repetition.

I liked “We Have No Idea”. It could have been more daring, or more thorough, but it was still charming and honest and fun. If you’re looking for a Christmas present to explain physics to your relatives, you won’t go wrong with this book.

Underdetermination of Theory by Metaphor

Sometimes I explain science in unconventional ways. I’ll talk about quantum mechanics without ever using the word “measurement”, or write the action of the Standard Model in legos.

Whenever I do this, someone asks me why. Why use a weird, unfamiliar explanation? Why not just stick to the tried and true, metaphors that have been tested and honed in generations of popular science books?

It’s not that I have a problem with the popular explanations, most of the time. It’s that, even when the popular explanation does a fine job, there can be good reason to invent a new metaphor. To demonstrate my point, here’s a new metaphor to explain why:

In science, we sometimes talk about underdetermination of a theory by the data. We want to find a theory whose math matches the experimental results, but sometimes the experiments just don’t tell us enough. If multiple theories match the data, we say that the theory is underdetermined, and we go looking for more data to resolve the problem.

What if you’re not a scientist, though? Often, that means you hear about theories secondhand, from some science popularizer. You’re not hearing the full math of the theory, you’re not seeing the data. You’re hearing metaphors and putting together your own picture of the theory. Metaphors are your data, in some sense. And just as scientists can find their theories underdetermined by the experimental data, you can find them underdetermined by the metaphors.

This can happen if a metaphor is consistent with two very different interpretations. If you hear that time runs faster in lower gravity, maybe you picture space and time as curved…or maybe you think low gravity makes you skip ahead, so you end up in the “wrong timeline”. Even if the popularizer you heard it from was perfectly careful, you base your understanding of the theory on the metaphor, and you can end up with the wrong understanding.

In science, the only way out of underdetermination of a theory is new, independent data. In science popularization, it’s new, independent metaphors. New metaphors shake you out of your comfort zone. If you misunderstood the old metaphor, now you’ll try to fit that misunderstanding with the new metaphor too. Often, that won’t work: different metaphors lead to different misunderstandings. With enough different metaphors, your picture of the theory won’t be underdetermined anymore: there will be only one picture, one understanding, that’s consistent with every metaphor.

That’s why I experiment with metaphors, why I try new, weird explanations. I want to wake you up, to make sure you aren’t sticking to the wrong understanding. I want to give you more data to determine your theory.

Journalists Need to Adapt to Preprints, Not Ignore Them

Nature has an article making the rounds this week, decrying the dangers of preprints.

On the surface, this is a bit like an article by foxes decrying the dangers of henhouses. There’s a pretty big conflict of interest when a journal like Nature, that makes huge amounts of money out of research scientists would be happy to publish for free, gets snippy about scientists sharing their work elsewhere. I was expecting an article about how “important” the peer review process is, how we can’t just “let anyone” publish, and the like.

Instead, I was pleasantly surprised. The article is about a real challenge, the weakening of journalistic embargoes. While this is still a problem I think journalists can think their way around, it’s a bit subtler than the usual argument.

For the record, peer review is usually presented as much more important than it actually is. When a scientific article gets submitted to a journal, it gets sent to two or three experts in the field for comment. In the best cases, these experts read the paper carefully and send criticism back. They don’t replicate the experiments, they don’t even (except for a few heroic souls) reproduce the calculations. That kind of careful reading is important, but it’s hardly unique: it’s something scientists do on their own when they want to build off of someone else’s paper, and it’s what good journalists get when they send a paper to experts for comments before writing an article. If peer review in a journal is important, it’s to ensure that this careful reading happens at least once, a sort of minimal evidence that the paper is good enough to appear on a scientist’s CV.

The Nature article points out that peer review serves another purpose, specifically one of delay. While a journal is preparing to publish an article they can send it out to journalists, after making them sign an agreement (an embargo) that they won’t tell the public until the journal publishes. This gives the journalists a bit of lead time, so the more responsible ones can research and fact-check before publishing.

Open-access preprints cut out the lead time. If the paper just appears online with no warning and no embargoes, journalists can write about it immediately. The unethical journalists can skip fact-checking and publish first, and the ethical ones have to follow soon after, or risk publishing “old news”. Nobody gets the time to properly vet, or understand, a new paper.

There’s a simple solution I’ve seen from a few folks on Twitter: “Don’t be an unethical journalist!” That doesn’t actually solve the problem though. The question is, if you’re an ethical journalist, but other people are unethical journalists, what do you do?

Apparently, what some ethical journalists do is to carry on as if preprints didn’t exist. The Nature article describes journalists who, after a preprint has been covered extensively by others, wait until a journal publishes it and then cover it as if nothing had happened. The article frames this as virtuous, but doomed: journalists sticking to their ethics even if it means publishing “old news”.

To be 100% clear here, this is not virtuous. If you present a paper’s publication in a journal as news, when it was already released as a preprint, you are actively misleading the public. I can’t count the number of times I’ve gotten messages from readers, confused because they saw a scientific result covered again months later and thought it was new. It leads to a sort of mental “double-counting”, where the public assumes that the scientific result was found twice, and therefore that it’s more solid. Unless the publication itself is unexpected (something that wasn’t expected to pass peer review, or something controversial like Mochizuki’s proof of the ABC conjecture) mere publication in a journal of an already-public result is not news.

What science journalists need to do here is to step back, and think about how their colleagues cover stories. Current events these days don’t have embargoes, they aren’t fed through carefully managed press releases. There’s a flurry of initial coverage, and it gets things wrong and misses details and misleads people, because science isn’t the only field that’s complicated, real life is complicated. Journalists have adapted to this schedule, mostly, by specializing. Some journalists and news outlets cover breaking news as it happens, others cover it later with more in-depth analysis. Crucially, the latter journalists don’t present the topic as new. They write explicitly in the light of previous news, as a response to existing discussion. That way, the public isn’t misled, and their existing misunderstandings can be corrected.

The Nature article brings up public health, and other topics where misunderstandings can do lasting damage, as areas where embargoes are useful. While I agree, I would hope many of these areas would figure out embargoes on their own. My field certainly does: the big results of scientific collaborations aren’t just put online as preprints, they’re released only after the collaboration sets up its own journalistic embargoes, and prepares its own press releases. In a world of preprints, this sort of practice needs to happen for important controversial public health and environmental results as well. Unethical scientists might still release too fast, to keep journalists from fact-checking, but they could do that anyway, without preprints. You don’t need a preprint to call a journalist on the phone and claim you cured cancer.

As open-access preprints become the norm, journalists will have to adapt. I’m confident they will be able to, but only if they stop treating science journalism as unique, and start treating it as news. Science journalism isn’t teaching, you’re not just passing down facts someone else has vetted. You’re asking the same questions as any other journalist: who did what? And what really happened? If you can do that, preprints shouldn’t be scary.