Category: Press and Public Understanding of Science

Doritos™ Alchemy

I recently stumbled across this spec Doritos™ commercial David Ward made a six years ago. Really well done adaptations of the alchemist motif.

You gotta love the list of ingredients (also, not listed, Unicorn tears):

Staff of Anubis
Philosopher Stone
Rubber Hammer
Rubber Nails
Moon Rock Salt
Archimedes Screw
Harpsichord
Parachute
Blank
Bag of Holding
Cloud Mist
Elven joy
Lucky Penny
Love Song
Erlenmeyer Flask
Marcoscope
Sense of Wonder
Blankety Blanks
Temporal Glitch
Haiku
Nods
Sweeps
Beeps
Deeps
Sneeps
Reeps
Winks
Memories
Fireballs
Congratulations
Laughter
Lightening
Star Dust
Rings of a Tree
Mother’s Approval
Mountain Air
Cheesiness
Inspiring Footage
Smiles
Secret Ingredient
Smell of Morning
Love
Salt

Nice job guys—David was joined by Jack Dreesen, John Ramsey, and Byron Brown. I enjoy creative work like this.

Jon Pace & the Latest Prime Number

In case you missed it, the world has a new largest prime number called M77232917:

46733318335923109998833558556111552125132110281771449579858233859356792348052117720748431109974020884962136809003804931724836 … and on and on and on for another 23,249,300 digits.

That number is unimaginably large. It is so large that even analogies meant to help us wrap our minds around it are nearly unimaginable. Who can imagine a number that takes up 9,000 pages? Or imagine a number that stretches 73 miles?[1] Or imagine writing 5 digits per second for 54 days? Such are the ways mersenne.org tries to describe the number. (I might add, parenthetically, mersenne.org has the nicest website 1996 can buy).

The Great Internet Mersenne Prime Search page is Internet Retro at its finest.

The history of prime numbers in general is fascinating as is the history of Mersenne primes in particular. But I will save those for another post. Here I just want to draw attention to how the newly recognized prime status of this number has been noted in the press.[2] In particular, I’m intrigued by how different reports apportion credit for the “discovery” and how they describe Jon Pace, whose computer first identified the number as prime.

We might as well start with the post at mersenne.org that announces: GIMPS Project Discovers Largest Known Prime Number: 277,232,917–1. In case there was any doubt that the GIMPS project wanted to take credit for the discovery, the post continues:

The Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 277,232,917–1, having 23,249,425 digits. A computer volunteered by Jonathan Pace made the find on December 26, 2017. Jonathan is one of thousands of volunteers using free GIMPS software available at www.mersenne.org/download/ … GIMPS, founded in 1996, has discovered the last 16 Mersenne primes.

Make no mistake, GIMPS discovered this latest prime, along with the previous 16 Mersenne primes. And although Jon Pace installed and ran the software on his computer, the result had to be checked by four other people who also deserve credit. Oh, and credit goes to all the people who didn’t find a prime. Credit for the discovery, in this version, echoes the distributed nature of the labor but reserves pride of place for the GIMPS software and its developer:

GIMPS Prime95 client software was developed by founder George Woltman. Scott Kurowski wrote the PrimeNet system software that coordinates GIMPS’ computers. Aaron Blosser is now the system administrator, upgrading and maintaining PrimeNet as needed. …
Credit for this prime goes not only to Jonathan Pace for running the Prime95 software, Woltman for writing the software, Kurowski and Blosser for their work on the Primenet server, but also the thousands of GIMPS volunteers that sifted through millions of non-prime candidates. In recognition of all the above people, official credit for this discovery goes to “J. Pace, G. Woltman, S. Kurowski, A. Blosser, et al.”

Thanks for the CPU cycles and paying for the electricity to run your computer, Jon. But don’t feel slighted, GIMPS tends to celebrate its software over the people donating the computer time.

Who is this Jon Pace, well GIMPS say simply “Jonathan Pace is a 51-year old Electrical Engineer living in Germantown, Tennessee.” A nice, reasonable, scientific sounding person.

Science Daily just reposts the GIMPS report, changing the title slightly: “Largest known prime number discovered 50th known Mersenne prime ever found, on computer volunteered in collaborative project.”

Things begin to drift in the NPR story, “A Tenn. Man Recently Discovered The Largest Prime Number Known To Humankind.” Perhaps we shouldn’t be surprised that NPR with its preference for the human-interest story would highlight Jon Pace:

This past week, a FedEx employee from Germantown, Tenn., made a massive discovery — and it wasn’t in any packages. John Pace found the largest prime number known to humankind. …
Pace found his prime as part of an online collective called the Great Internet Mersenne Prime Search, or GIMPS. Pace and thousands of volunteers ran software on their personal computers crunching numbers day-in and day-out.

In this version, Pace discovered the prime and, moreover, its “his prime” (later the article refers to it as “Pace’s prime”). Not only is Pace the only one to get credit for the discovery, he is no longer an electrical engineer. Instead, he’s a FedEx employee. The two are by no means mutually exclusive. I am not suggesting they are. I am, rather, drawing attention to the fact that in the NPR version Pace’s primary marker of identity is his status as a FedEx employee whereas in the GIMPS post his primary identity is as an electrical engineer.

Popular Science adds a bit more to the story, “How a FedEx employee discovered the world’s largest prime number.” In this version Pace gets credit for the discovery, that he used the GIMPS software is just part of the process.

What does change in this version is Pace’s identity. Now he’s not only a FedEx employee—“a flight operations finance manager with the Memphis-based delivery behemoth”— but also a deacon at his church, the Germantown Church of Christ where he does, among other things, IT support. He installed the GIMPS software on one of the computers at the church.

Yes, Jon Pace is a Deacon at the Germantown Church of Christ, for whatever that’s worth.

The NY Times shifts the emphasis again: “How a Church Deacon Found the Biggest Prime Number Yet (It Wasn’t as Hard as You Think).” By this point, Pace is given sole credit for having discovered the prime number. Equally interesting, his identity has shifted to emphasize his role as a deacon at the Germantown Church of Christ:

A prime number discovery in December was made in the unlikeliest of places: on a church computer in a Memphis suburb.…
But for this behemoth to come to light, someone had to have installed free software used to search for Mersenne prime numbers, and that someone is Jon Pace, a deacon, FedEx finance manager and math aficionado who had spent 14 years hunting for such a number.

According to the article, Pace is prouder of “the 20 years [he has] served as deacon at Germantown” than of discovering the new prime number.

Discovery appears to be a rather slippery concept. What does it mean to discover a prime number? In what sense do numbers exist or not exist before we write them down? Surely nobody is suggesting the number 277,232,917–1 was discovered. But its primeness was discovered, or perhaps realized. In this case, discovery seems to be rather traditional, like discovering gold or the New World. Something pre-existed in some way before a human stumbled into it, but the identity, characteristics, and value of that something had to be recognized before we could talk about it and apportion credit. Here we see GIMPS asserting credit for the “discovery” whereas NPR or the NY Times are perfectly happy to give Pace the credit. Credit for the discovery is ambiguously related to labor—GIMPS thinks the intellectual labor that created the software more important than the volunteer labor (and donated electricity and other operating expenses); the NY Times thinks the human who owns the donated computer and pays to operate them more important.

And what about that human, in this case Jon Pace? GIMPS emphasizes Pace’s identity as an electrical engineer, though electrical engineering is only one part of his identity—along with his undergraduate degree in electrical engineering he has an M.B.A., is a flight operations finance manager,[3] and is a deacon at his church. And according to the NY Times, he is most proud of being a deacon. How is Pace’s reported identity related to the values different organizations hold? How does Pace’s identity as an electrical engineer reinforce the image that GIMPS wants to project? Why does Popular Science and the NY Times draw attention to Pace’s identity as a deacon in a church? I don’t believe that GIMPS didn’t know Pace was a deacon, though they chose not to acknowledge that aspect of his identity. The NY Times, by contrast and somewhat surprisingly to me, chose to draw attention to Pace’s work as a deacon at his church.

Discovery, it turns out, is pretty difficult to pin down.


  1. I suspect most people can identify cities that are roughly 73 miles apart but have no concept of what that distance actually is (FYI, it’s about 73 miles from Haverford College to the New Jersey shore, e.g., Ocean City). Now remove the bookending cities and challenge people to think about 73 miles of highway stretching through undulating grasslands or through the desert—suddenly the distance becomes meaningless. And how are we supposed to relate to 73 miles? A person walking will have a very different relationship to that distance than a person who thinks of driving it.  ↩

  2. And yes, that tortured expression, “newly recognized prime status” was intentional, an effort to avoid words like “discovered” and “found,” and an effort to draw attention to what strikes me as interestingly new here, i.e., our recognition that this number has a set of features that we call prime.  ↩

  3. I confess, I have no idea what a flight operations finance manager is. Flight operations manager I can imagine. Finance manager again makes sense. The two together, however, confuse me.  ↩

The Use and Abuse of Isaac Newton

Bitcoin’s recent rise has prompted an ever growing number of people to misstate and otherwise abuse Newton’s laws of motions. Predictions of a Bitcoin crash typically invoke “Newton’s Law of Universal Gravity [which] states that what goes up must come down” or some version of that “law”. The whole Newton’s law of “what goes up must come down” is a trope in reporting on any price surge, e.g., individual stocks, gold prices, S&P500, etc. Should we be concerned that Newton’s laws of motion don’t, in fact, say “what goes up must come down?”

Bitcoin is just the latest in posts and articles appealing to Newton’s laws. Seems every author wants to “understand” some complex economic, political, or social situation by applying Newton’s laws.

Newton’s third law is a favorite spot of abuse. Andrew Mitrovica writing about political resistance says:

In the cacophonous age of Donald Trump , Americans would do well to recall Isaac Newton’s Third Law: For every action, there is an equal and opposite reaction.
Americans would be wise not only to remember this axiom of physics and, indeed, politics, but they must be prepared to exercise it finally and emphatically, en masse, in defiance of a dystopian regime’s toxic actions at home and abroad.

Really? Newton’s third law is an “axiom of … politics?”

This use and abuse of Newton is not new, e.g., see “Newton’s Third Law states that every action produces an equal and opposite reaction. He was talking about physics. But it’s equally applicable to less scientific stuff as well” from 2009. Stanley Bing then goes on to use Newton’s third law to describe (predict?) human behavior. While Bing got the law right, he like so many others misapplied. Newton’s laws describe the motions of macroscopic objects moving at relatively slow speeds, not the behavior of humans (or stock markets or currency exchanges or …).

Newton’s first law doesn’t escape flogging. Apparently Tom Lee of Fundstrat Global Advisors thinks Newton’s first law applies to stock prices (the original post is behind a paywall, so I rely on quotations from it):

Newton’s ‘law of motion’ applies to stocks in mid-September — 90% of time, if stocks up between 5% to 20%year-to-date (YTD), gains continue to year-end (YE).

Newton’s first law does not apply to stock prices (or gold prices or Bitcoin prices or the price of kale at your local organic grocery store).

Just to be clear: Newton’s laws of motion do not apply to any market. They apply to physical systems of everyday objects moving in everyday ways.

Will you please stop abusing Isaac Newton?

Astrolabes and S•Town

On Thursday, February 16, at 5:36 PM I was standing in a faculty meeting when my phone vibrated. I fished it out of my pocket and looked at the screen. I had just received a voicemail and a text from the same number, a number I didn’t recognize. The text asked, simply: “Is this the phone of Darin Hayton?”

I stepped outside and listened to the voicemail. The person identified himself as a researcher for This American Life, asked if he had reached Darin Hayton, and wanted to ask about astrolabes. His message sounded urgent. I was intrigued. Why would anybody feel a pressing need to learn about astrolabes, at 5:30 on a Thursday evening? And why would that person not just turn to Wikipedia or some other on-line resource?[1] So I decided to respond.

As I was still, at least physically, in a meeting, I texted rather than phoned and offered to call later that evening or the next morning. He asked that I call him as soon as I was free.

Texting with the guy who turned out to be a researcher for This American Life.
When I phoned he immediately started asking about astrolabes. He had clearly done some research on them but wanted to confirm what he had learned—e.g., Hipparchus had developed the mathematics but not an instrument; early instruments dated from the late 9th century; you could use it to tell time. He was particularly interested in developments introduced by 10th-century Islamic scholars. He asked about different innovations we might attribute to them and wanted to know how they improved the astrolabe. Most of the innovations he mentioned cannot easily or definitively be traced back to early Islamic instrument makers. We chatted for 10–15 minutes. As our conversation wound down, I tried to find out why he was so interested in astrolabes. He offered few details, saying only that he was doing research for an up-coming This American Life show on a man from Alabama who had studied astrolabes and had even built his own. He wouldn’t tell me the man’s name, but did mention that he had recently died.[2]

After we hung up I tweeted about my brush with fame. I am clearly a nerd since I think having This American Life phone me constitutes fame.

I tweeted about my brush with fame—clearly I’m a nerd because I think talking to This American Life constitutes fame.
Fifteen minutes or so later as I stood in my bathroom brushing my teeth, my phone rang again. Same guy confirming a couple points and asking if his formulation was correct. Something to the effect: the Greek astronomer Hipparchus developed the mathematics behind the astrolabe and 10th-century Islamic scholars refined it to time their daily prayers. Yes, I said, that’s fine.

Because I am always late to the party, I didn’t hear about S•Town until late April, a month or so after it was released and became an instant hit.[3] Finally, when a friend suggested I listen to it because they “talk about astrolabes,” I downloaded it and listened while I repaired my washing machine. Sure enough, about 15 minutes in John B. McLemore (the main character) mentions astrolabes:

Because kids are talking about getting girls, or deer hunting, or football. Whereas I was interested in the astrolabe, sundials, projective geometry, new age music, climate change, and how to solve Rubik’s cube.


But he doesn’t say much more. Then, 30 minutes later, the astrolabe suddenly returns in the context of telling time.[4] Brian Reed, the host, reflects on various methods for tracking time, then describes the astrolabe:

BRIAN REED: The astrolabe looks kind of like a clock crossed with a compass. It’s a flat dial with a map of the night sky laid over it, and a pointer, or I guess a sight, attached on top of that. You pick a star in the sky, and aim the sight at it, twist the sky map until it aligns with the sight in a certain way. And then the dial shows you your direction, as well as the month, day, and time.

It’s a beautiful, complex device. And as a kid, John longed to figure it out, to put himself inside the brains of the people who puzzled through the earliest versions—the Greek astronomer Hipparchus, who devised the mathematics behind it, or the 10th century Islamic scholars, who refined the invention to help them time their daily prayers.

John wanted to go through what they had to go through to create an astrolabe. Which is why he made his own, designed specifically for the coordinates of this house. It hangs on the wall of his mother’s bedroom. That’s what he’s showing me, his astrolabe, when Skyler Goodson happens to walk in the front door.

When I heard this, I immediately recalled the man who had phoned six weeks earlier asking about astrolabes. There, in Brian Reed’s brief description, was the final version of what the man on the phone had crafted. It turns out that the man on the phone had been doing research for S•Town.

Thanks to S•Town and John B. McLemore, astrolabes are enjoying their 15 minutes of fame. Reddit pages on S•Town have astrolabe discussions. Websites promise to show you “How to Build an Astrolabe Like John B. McLemore From ‘S- Town’.” S•Town fans are turning up in museums asking to see astrolabes.

Visitors to Harvard’s museum are S•Town fans and want to see astrolabes.
Hey This American Life, perhaps you would like to do a whole show on astrolabes. While not as eccentric as John B. McLemore, I have built my own astrolabe, I know its history better than most, and I’m available. Your researcher/fact checker has my number. Have him give me a call.


  1. In talking to him, it seems he started with on-line resources, including my An Introduction to the Astrolabe.  ↩
  2. He probably used a euphemism, but somehow I think John B. McLemore would have preferred “died,” and I prefer it.  ↩
  3. And because I can’t just be late to the party, I find out late that I am late to the party, I learned about S•Town while listening to an old podcast of Wait Wait…Don’t Tell Me featuring Sarah Koenig[3a] that I had downloaded and then didn’t listen to for nearly a month. And even then I was in no hurry to listen to S•Town.  ↩

    3a. I should probably point out that the name Sarah Koenig meant nothing to me because I am one of perhaps only a handful of people, including John B. McLemore, who has never listened to Serial and only vaguely knows what it is.  ↩

  4. To be exact, Brian Reed’s description of the astrolabe comes at 44:05 into chapter 1. Astrolabes are mentioned in two other places: the first time is about 16 minutes into chapter 1; the last time is 2:35 into chapter 7. I don’t think I would say, as my friend did, that they “talk about astrolabes” in S•Town, but any popular culture reference is better than none.  ↩

Yet Another Flat Earther

In a footnote to a previous post I worried that in a post on Columbus and the flat earth myth Valerie Strauss had preferred the opinions of a mathematician over the expertise of a historian. And in fact, Strauss did prefer the dilettante to the expert. She rejected the historian’s conclusions, which were based in training, evidence, and experience, and relied instead on the opinions of a non-expert, which ignored both evidence and experts.

Perhaps because she is awed by mathematics or assumes scientists are smarter than everybody else, Strauss aped the mathematician Robert Osserman’s fantasy about people in the early middle ages believing in a flat earth. Osserman was an accomplished mathematician at Stanford. He was also celebrated for bringing “math to a broad audience.” Turns out, he also happens to have been a flat earther.

Rober Osserman’s Poetry of the Universe

For reasons that make little sense, Osserman repeats a particular version of the flat earth myth in his Poetry of the Universe. Chapter 2, “Encompassing the Earth,” opens with a rejection of the idea that Columbus proved the earth was round. Osserman even calls out this myth, saying

One of the enduring myths of the Western world is that in order to gain support for his expeditions, Christopher Columbus had to first overcome a pervasive belief that the earth was flat rather than round …

So far, so good. But then Osserman succumbs to the fantasy,

The myth undoubtedly stems in part from a compression of the historical past, conflating the early Middle Ages, when a belief in a flat earth was indeed widespread in Europe, with the late Middle Ages…

Osserman too traffics in the flat earth myth.

No, the myth doesn’t stem from a “compression of the historical past” but rather a willful rejection of the historical past, a willful rejection of historical fact, a willful rejection of evidence, and a profound intellectual laziness validated by arrogance and hubris. I am confident that Osserman had multiple colleagues at Stanford who could have explained to him how his beliefs were wrong, were myths. All he had to do was dial an extension or walk across campus and ask them. But he chose not to. He chose, instead, to traffic in a myth, to spread misinformation, and to do so with the authority of being a “mathematician.”

That authority was persuasive. It dazzled Strauss and convinced her to reject the expertise of the historian in favor of the unfounded beliefs of the mathematician. Her preference for the mathematician has, in turn, disseminated the myth yet further, now robed in the authority of a Washington Post column that claims to be grounded in research and to be a resource for teachers and parents. Unfortunately, Strauss has mislead the teachers, parents “(and everyone else)” who reads her column.