# Poll: How Do You Get Here?

I’ve been digging through the WordPress “stats” page for this blog. One thing WordPress tells me is what links people follow to get here. It tells me how many times people come from Google or Facebook or Twitter, and how many come from seeing a link on another blog. One thing that surprised me is that some of the blogs people come here from haven’t updated in years.

The way I see it there are two possible explanations. It could be that new people keep checking the old blogs, see a link on their blogroll, and come on over here to check it out. But it could also be the same people over and over, who find it more convenient to start on an old blog and click on links from there.

WordPress doesn’t tell me the difference. But I realized, I can just ask. So in this post, I’m asking all my readers to tell me how you get here. I’m not asking how you found this blog to begin with, but rather how, on a typical day, you navigate to the site. Do you subscribe by email? Do you google the blog’s name every time? RSS reader? Let me know below! And if you don’t see an option that fits you, let me know in the comments!

# Valentine’s Day Physics Poem 2021

It’s Valentine’s Day this weekend, so time for another physics poem. If you’d like to read the poems from past years, they’re archived with the tag Valentine’s Day Physics Poem, accessible here.

Passion Project

Passion is passion.

If you find yourself writing letter after letter,
be they “love”,
or “Physical Review”

Or if you are the quiet sort
and notice only in your mind
those questions, time after time
whenever silence reigns:
“how do I make things right?”

uncertain,
futures,
each so different
still have one
thing
in common.

If you could share that desert island, that jail cell,
and count yourself free.

You’ve found your star. Now it’s straight on till morning.

# Newtonmas in Uncertain Times

Three hundred and eighty-two years ago today (depending on which calendars you use), Isaac Newton was born. For a scientist, that’s a pretty good reason to celebrate.

Last month, our local nest of science historians at the Niels Bohr Archive hosted a Zoom talk by Jed Z. Buchwald, a Newton scholar at Caltech. Buchwald had a story to tell about experimental uncertainty, one where Newton had an important role.

If you’ve ever had a lab course in school, you know experiments never quite go like they’re supposed to. Set a room of twenty students to find Newton’s constant, and you’ll get forty different answers. Whether you’re reading a ruler or clicking a stopwatch, you can never measure anything with perfect accuracy. Each time you measure, you introduce a little random error.

Textbooks worth of statistical know-how has cropped up over the centuries to compensate for this error and get closer to the truth. The simplest trick though, is just to average over multiple experiments. It’s so obvious a choice, taking a thousand little errors and smoothing them out, that you might think people have been averaging in this way through history.

They haven’t though. As far as Buchwald had found, the first person to average experiments in this way was Isaac Newton.

What did people do before Newton?

Well, what might you do, if you didn’t have a concept of random error? You can still see that each time you measure you get a different result. But you would blame yourself: if you were more careful with the ruler, quicker with the stopwatch, you’d get it right. So you practice, you do the experiment many times, just as you would if you were averaging. But instead of averaging, you just take one result, the one you feel you did carefully enough to count.

Before Newton, this was almost always what scientists did. If you were an astronomer mapping the stars, the positions you published would be the last of a long line of measurements, not an average of the rest. Some other tricks existed. Tycho Brahe for example folded numbers together pair by pair, averaging the first two and then averaging that average with the next one, getting a final result weighted to the later measurements. But, according to Buchwald, Newton was the first to just add everything together.

Even Newton didn’t yet know why this worked. It would take later research, theorems of statistics, to establish the full justification. It seems Newton and his later contemporaries had a vague physics analogy in mind, finding a sort of “center of mass” of different experiments. This doesn’t make much sense – but it worked, well enough for physics as we know it to begin.

So this Newtonmas, let’s thank the scientists of the past. Working piece by piece, concept by concept, they gave use the tools to navigate our uncertain times.

# Halloween Post: Superstimuli for Physicists

For Halloween, this blog has a tradition of covering “the spooky side” of physics. This year, I’m bringing in a concept from biology to ask a spooky physics “what if?”

In the 1950’s, biologists discovered that birds were susceptible to a worryingly effective trick. By giving them artificial eggs larger and brighter than their actual babies, they found that the birds focused on the new eggs to the exclusion of their own. They couldn’t help trying to hatch the fake eggs, even if they were so large that they would fall off when they tried to sit on them. The effect, since observed in other species, became known as a supernormal stimulus, or superstimulus.

Can this happen to humans? Some think so. They worry about junk food we crave more than actual nutrients, or social media that eclipses our real relationships. Naturally, this idea inspires horror writers, who write about haunting music you can’t stop listening to, or holes in a wall that “fit” so well you’re compelled to climb in.

(And yes, it shows up in porn as well.)

But this is a physics blog, not a biology blog. What kind of superstimulus would work on physicists?

Well for one, this sounds a lot like some criticisms of string theory. Instead of a theory that just unifies some forces, why not unify all the forces? Instead of just learning some advanced mathematics, why not learn more, and more? And if you can’t be falsified by any experiment, well, all that would do is spoil the fun, right?

But it’s not just string theory you could apply this logic to. Astrophysicists study not just one world but many. Cosmologists study the birth and death of the entire universe. Particle physicists study the fundamental pieces that make up the fundamental pieces. We all partake in the euphoria of problem-solving, a perpetual rush where each solution leads to yet another question.

Do I actually think that string theory is a superstimulus, that astrophysics or particle physics is a superstimulus? In a word, no. Much as it might look that way from the news coverage, most physicists don’t work on these big, flashy questions. Far from being lured in by irresistible super-scale problems, most physicists work with tabletop experiments and useful materials. For those of us who do look up at the sky or down at the roots of the world, we do it not just because it’s compelling but because it has a good track record: physics wouldn’t exist if Newton hadn’t cared about the orbits of the planets. We study extremes because they advance our understanding of everything else, because they give us steam engines and transistors and change everyone’s lives for the better.

Then again, if I had fallen victim to a superstimulus, I’d say that anyway, right?

*cue spooky music*

# Congratulations to Roger Penrose, Reinhard Genzel, and Andrea Ghez!

The 2020 Physics Nobel Prize was announced last week, awarded to Roger Penrose for his theorems about black holes and Reinhard Genzel and Andrea Ghez for discovering the black hole at the center of our galaxy.

Of the three, I’m most familiar with Penrose’s work. People had studied black holes before Penrose, but only the simplest of situations, like an imaginary perfectly spherical star. Some wondered whether black holes in nature were limited in this way, if they could only exist under perfectly balanced conditions. Penrose showed that wasn’t true: he proved mathematically that black holes not only can form, they must form, in very general situations. He’s also worked on a wide variety of other things. He came up with “twistor space”, an idea intended for a new theory of quantum gravity that ended up as a useful tool for “amplitudeologists” like me to study particle physics. He discovered a set of four types of tiles such that if you tiled a floor with them the pattern would never repeat. And he has some controversial hypotheses about quantum gravity and consciousness.

I’m less familiar with Genzel and Ghez, but by now everyone should be familiar with what they found. Genzel and Ghez led two teams that peered into the center of our galaxy. By carefully measuring the way stars moved deep in the core, they figured out something we now teach children: that our beloved Milky Way has a dark and chewy center, an enormous black hole around which everything else revolves. These appear to be a common feature of galaxies, and many others have been shown to orbit black holes as well.

Like last year, I find it a bit odd that the Nobel committee decided to lump these two prizes together. Both discoveries concern black holes, so they’re more related than last year’s laureates, but the contexts are quite different: it’s not as if Penrose predicted the black hole in the center of our galaxy. Usually the Nobel committee avoids mathematical work like Penrose’s, except when it’s tied to a particular experimental discovery. It doesn’t look like anyone has gotten a Nobel prize for discovering that black holes exist, so maybe that’s the intent of this one…but Genzel and Ghez were not the first people to find evidence of a black hole. So overall I’m confused. I’d say that Penrose deserved a Nobel Prize, and that Genzel and Ghez did as well, but I’m not sure why they needed to split one with each other.

# Pseudonymity Matters. I Stand With Slate Star Codex.

Slate Star Codex is one of the best blogs on the net. Written under the pseudonym Scott Alexander, the blog covers a wide variety of topics with a level of curiosity and humility that the rest of us bloggers can only aspire to.

Recently, this has all been jeopardized. A reporter at the New York Times, writing an otherwise positive article, told Scott he was going to reveal his real name publicly. In a last-ditch effort to stop this, Scott deleted his blog.

I trust Scott. When he says that revealing his identity would endanger his psychiatric practice, not to mention the safety of friends and loved ones, I believe him. What’s more, I think working under a pseudonym makes him a better blogger: some of his best insights have come from talking to people who don’t think of him as “the Slate Star Codex guy”.

I don’t know why the Times thinks revealing Scott’s name is a good idea. I do know that there are people out there who view anyone under a pseudonym with suspicion. Compared to Scott, my pseudonym is paper-thin: it’s very easy to find who I am. Still, I have met people who are irked just by that, by the bare fact that I don’t print my real name on this blog.

I think this might be a generational thing. My generation grew up alongside the internet. We’re used to the idea that very little is truly private, that anything made public somewhere risks becoming public everywhere. In that world, writing under a pseudonym is like putting curtains on a house. It doesn’t make us unaccountable: if you break the law behind your curtains the police can get a warrant, similarly Scott’s pseudonym wouldn’t stop a lawyer from tracking him down. All it is, is a filter: a way to have a life of our own, shielded just a little from the whirlwind of the web.

I know there are journalists who follow this blog. If you have contacts in the Times tech section, or know someone who does, please reach out. I want to hope that someone there is misunderstanding the situation, that when things are fully explained they will back down. We have to try.

# The Wolfram Physics Project Makes Me Queasy

Stephen Wolfram is…Stephen Wolfram.

Once a wunderkind student of Feynman, Wolfram is now best known for his software, Mathematica, a tool used by everyone from scientists to lazy college students. Almost all of my work is coded in Mathematica, and while it has some flaws (can someone please speed up the linear solver? Maple’s is so much better!) it still tends to be the best tool for the job.

Wolfram is also known for being a very strange person. There’s his tendency to name, or rename, things after himself. (There’s a type of Mathematica file that used to be called “.m”. Now by default they’re “.wl”, “Wolfram Language” files.) There’s his live-streamed meetings. And then there’s his physics.

In 2002, Wolfram wrote a book, “A New Kind of Science”, arguing that computational systems called cellular automata were going to revolutionize science. A few days ago, he released an update: a sprawling website for “The Wolfram Physics Project”. In it, he claims to have found a potential “theory of everything”, unifying general relativity and quantum physics in a cellular automata-like form.

If that gets your crackpot klaxons blaring, yeah, me too. But Wolfram was once a very promising physicist. And he has collaborators this time, who are currently promising physicists. So I should probably give him a fair reading.

On the other hand, his introduction for a technical audience is 448 pages long. I may have more time now due to COVID-19, but I still have a job, and it isn’t reading that.

So I compromised. I didn’t read his 448-page technical introduction. I read his 90-ish page blog post. The post is written for a non-technical audience, so I know it isn’t 100% accurate. But by seeing how someone chooses to promote their work, I can at least get an idea of what they value.

I started out optimistic, or at least trying to be. Wolfram starts with simple mathematical rules, and sees what kinds of structures they create. That’s not an unheard of strategy in theoretical physics, including in my own field. And the specific structures he’s looking at look weirdly familiar, a bit like a generalization of cluster algebras.

Reading along, though, I got more and more uneasy. That unease peaked when I saw him describe how his structures give rise to mass.

Wolfram had already argued that his structures obey special relativity. (For a critique of this claim, see this twitter thread.) He found a way to define energy and momentum in his system, as “fluxes of causal edges”. He picks out a particular “flux of causal edges”, one that corresponds to “just going forward in time”, and defines it as mass. Then he “derives” $E=mc^2$, saying,

Sometimes in the standard formalism of physics, this relation by now seems more like a definition than something to derive. But in our model, it’s not just a definition, and in fact we can successfully derive it.

In “the standard formalism of physics”, $E=mc^2$ means “mass is the energy of an object at rest”. It means “mass is the energy of an object just going forward in time”. If the “standard formalism of physics” “just defines” $E=mc^2$, so does Wolfram.

I haven’t read his technical summary. Maybe this isn’t really how his “derivation” works, maybe it’s just how he decided to summarize it. But it’s a pretty misleading summary, one that gives the reader entirely the wrong idea about some rather basic physics. It worries me, because both as a physicist and a blogger, he really should know better. I’m left wondering whether he meant to mislead, or whether instead he’s misleading himself.

That feeling kept recurring as I kept reading. There was nothing else as extreme as that passage, but a lot of pieces that felt like they were making a big deal about the wrong things, and ignoring what a physicist would find the most important questions.

I was tempted to get snarkier in this post, to throw in a reference to Lewis’s trilemma or some variant of the old quip that “what is new is not good; and what is good is not new”. For now, I’ll just say that I probably shouldn’t have read a 90 page pop physics treatise before lunch, and end the post with that.

# This Is What an Exponential Feels Like

Most people, when they picture exponential growth, think of speed. They think of something going faster and faster, more and more out of control. But in the beginning, exponential growth feels slow. A little bit leads to a little bit more, leads to a little bit more. It sneaks up on you.

When the first cases of COVID-19 were observed in China in December, I didn’t hear about it. If it was in the news, it wasn’t news I read.

I’d definitely heard about it by the end of January. A friend of mine had just gotten back from a trip to Singapore. At the time, Singapore had a few cases from China, but no local transmission. She decided to work from home for two weeks anyway, just to be safe. The rest of us chatted around tea at work, shocked at the measures China was taking to keep the virus under control.

Italy reached our awareness in February. My Italian friends griped and joked about the situation. Denmark’s first case was confirmed on February 27, a traveler returning from Italy. He was promptly quarantined.

I was scheduled to travel on March 8, to a conference in Hamburg. On March 2, six days before, they decided to postpone. I was surprised: Hamburg is on the opposite side of Germany from Italy.

That week, my friend who went to Singapore worked from home again. This time, she wasn’t worried she brought the virus from Singapore: she was worried she might pick it up in Denmark. I was surprised: with so few cases (23 by March 6) in a country with a track record of thorough quarantines, I didn’t think we had anything to worry about. She disagreed. She remembered what happened in Singapore.

That was Saturday, March 7. Monday evening, she messaged me again. The number of cases had risen to 90. Copenhagen University asked everyone who traveled to a “high-risk” region to stay home for fourteen days.

On Wednesday, the university announced new measures. They shut down social events, large meetings, and work-related travel. Classes continued, but students were asked to sit as far as possible from each other. The Niels Bohr Institute was more strict: employees were asked to work from home, and classes were asked to switch online. The canteen would stay open, but would only sell packaged food.

The new measures lasted a day. On Thursday, the government of Denmark announced a lockdown, starting Friday. Schools were closed for two weeks, and public sector employees were sent to work from home. On Saturday, they closed the borders. There were 836 confirmed cases.

Exponential growth is the essence of life…but not of daily life. It’s been eerie, seeing the world around me change little by little and then lots by lots. I’m not worried for my own health. I’m staying home regardless. I know now what an exponential feels like.

P.S.: This blog has a no-politics policy. Please don’t comment on what different countries or politicians should be doing, or who you think should be blamed. Viruses have enough effect on the world right now, let’s keep viral arguments out of the comment section.

# Valentine’s Day Physics Poem 2020

It’s Valentine’s Day, time for my traditional physics poem. I’m trying a new format this year, let me know what you think!

Cherish the Effective

Self-styled wise men waste away, pining for the Ultimate Theory.
I tell you now: spurn their fate.
Scorn the Ultimate.
Cherish the Effective.

When you dream of an Ultimate Theory, what do you see?
Every worry,
Every weakness,
Resolved?
A thing of beauty?
A thing of
of beauty?

Nature, she has her own worries.
You won’t get it.
And you’ll hurt, and be hurt, in the trying.

You need a theory that isn’t an ending.
A theory you
only
start
understanding
But can always discover.
No rigid, final truth,
But gentle corrections.
And as you push
The scale
The energy
Your theory always has room for something new.

A theory like that, we call Effective.
A theory you can live
your
life
with.
It’s worth more than you think.

# Math Is the Art of Stating Things Clearly

Why do we use math?

In physics we describe everything, from the smallest of particles to the largest of galaxies, with the language of mathematics. Why should that one field be able to describe so much? And why don’t we use something else?

The truth is, this is a trick question. Mathematics isn’t a language like English or French, where we can choose whichever translation we want. We use mathematics because it is, almost by definition, the best choice. That is because mathematics is the art of stating things clearly.

An infinite number of mathematicians walk into a bar. The first orders a beer. The second orders half a beer. The third orders a quarter. The bartender stops them, pours two beers, and says “You guys should know your limits.”

That was an (old) joke about infinite series of numbers. You probably learned in high school that if you add up one plus a half plus a quarter…you eventually get two. To be a bit more precise:

$\sum_{i=0}^\infty \frac{1}{2^i} = 1+\frac{1}{2}+\frac{1}{4}+\ldots=2$

We say that this infinite sum limits to two.

But what does it actually mean for an infinite sum to limit to a number? What does it mean to sum infinitely many numbers, let alone infinitely many beers ordered by infinitely many mathematicians?

You’re asking these questions because I haven’t yet stated the problem clearly. Those of you who’ve learned a bit more mathematics (maybe in high school, maybe in college) will know another way of stating it.

You know how to sum a finite set of beers. You start with one beer, then one and a half, then one and three-quarters. Sum $N$ beers, and you get

$\sum_{i=0}^N \frac{1}{2^i}$

What does it mean for the sum to limit to two?

Let’s say you just wanted to get close to two. You want to get $\epsilon$ close, where epsilon is the Greek letter we use for really small numbers.

For every $\epsilon>0$ you choose, no matter how small, I can pick a (finite!) $N$ and get at least that close. That means that, with higher and higher $N$, I can get as close to two as a I want.

As it turns out, that’s what it means for a sum to limit to two. It’s saying the same thing, but more clearly, without sneaking in confusing claims about infinity.

These sort of proofs, with $\epsilon$ (and usually another variable, $\delta$) form what mathematicians view as the foundations of calculus. They’re immortalized in story and song.

And they’re not even the clearest way of stating things! Go down that road, and you find more mathematics: definitions of numbers, foundations of logic, rabbit holes upon rabbit holes, all from the effort to state things clearly.

That’s why I’m not surprised that physicists use mathematics. We have to. We need clarity, if we want to understand the world. And mathematicians, they’re the people who spend their lives trying to state things clearly.