Archive for 'Improbable investigators'

The Hercules Number: How a Dimensionless Physical Parameter Got Its Name

Tuesday, June 14th, 2016

I did not conceive or give birth to the Hercules Number. But I did name it. Here’s the story.

In science and mathematics, we often get to name things. To help with exposition, sometimes we essentially have to name them, because it can help us do a better job of explaining things. In fact, we also enjoy naming things. To borrow some words from the computer game Beyond Zork, we often want a scientific idea to “bask in the glow of a new-forged synonym.”

And we get to name all sorts of things—concepts, theorems, examples, equations, groups, graphs, manifolds, numbers, physical parameters, and more. Sometimes we name them after people—ideally after somebody other than ourselves, and occasionally even after the person who actually had the idea first—and other times we get to be more creative. Naturally, the same object can go by more than one name, especially when multiple scientific fields are involved. On occasion, we fail miserably in our naming adventures. In abstract algebra, for example, there are so-called extra special groups. (My abstract algebra professor at Caltech couldn’t tell us about them without giggling over the name, so that is how you should read the previous sentence.)

One of the peculiar traditions in continuum mechanics (and especially in fluid mechanics) is the incessant naming of dimensionless physical parameters: the Reynolds number, the Rayleigh number, the Prandtl number, the Péclet number, and myriad others. If one states all of these numbers quickly one after another, one would almost have a George Carlin routine, except with a lot less cussing.

Illustration of (a) why it is really hard to separate two interleaved books and (b) the dimensionless parameter now known as the Hercules number. This is figure 2, and the associated caption, in a quick study in Phys. Today 69, 6, 74 (2016).

Illustration of (a) why it is really hard to separate two interleaved books and (b) the dimensionless parameter now known as the Hercules number. [This illustration is Figure 2, and its associated caption, from a quick study in Phys. Today 69, 6, 74 (2016).]

 A recently-introduced dimensionless parameter that caught my eye was the Repunzel number from ponytail physics (the subject of the 2012 Ig Nobel Prize in physics). And the naming of this number was very much on my mind a few months ago when I wrote an entry in the Improbable Research blog about a very cool new paper in Physical Review Letters (PRL) on how hard it is to pull apart two interleaved phone books. The authors of the paper had introduced a dimensionless parameter, but it didn’t have a name. And it clearly required a Herculean effort to pull apart those phone books, so I knew what name I wanted to attach to that dimensionless parameter. So with inspiration that was part Herculean, part Oxonian (I have spent the last 9 years in Oxford surrounded by applied mathematicians who study continuum mechanics), and part Repunzelian, I wrote the following sentence:

Restagno and colleagues also fit the data to a curve of force versus a dimensionless amplification parameter—following the continuum-mechanics tradition of using cute names for dimensionless parameters, let’s call it the “Hercules number”—that depends on the number of pages, the page thickness, and the size of the overlap region between the books.

The authors of the PRL paper enjoyed the new monicker—one might even say that the Hercules number was basking in the glow of its new-forged synonym—and they mentioned it to me via Twitter. And now Kari Dalnoki-VeressThomas Salez, and Frédéric Restagno (three of the authors of the original PRL paper) have written a “quick study” in the June 2016 issue of Physics Today. As you’ll notice, they use the name Hercules number, and of course I am very pleased about that. I am always happy to contribute to mathematics and physics with my wit and snark.

Bonus: When it comes to naming a scientific idea after a person (and whether or not one has chosen the correct one), I would like to invoke the “Three Laws of Discovery” that are listed among the quotations on Ig Nobel laureate Michael Berry’s website:

  1. Discoveries are rarely attributed to the correct person. (Arnold’s Law, which is of course self-referential)
  2. Nothing is ever discovered for the first time. (Berry’s Law)
  3. Everything of importance has been said before by someone who did not discover it. (Whitehead’s Law, though I am not sure which Whitehead it is. I assume it is one of the mathematical ones.)

Another Bonus: The story of the penguin diagram in nuclear physics is absolutely lovely. (That name came about substantially through the efforts of Melissa Franklin, whom you may have heard on Improbable Research podcasts.)

A Third Bonus: In mathematics, there is a problem called the Ten Martini Problem.

Quantifying the Smell of Urban Areas

Tuesday, June 7th, 2016

Data analysis has led to numerous insights into a diverse variety of complex systems. A new paper that gives a whiff of such insights is The Emotional and Chromatic Layers of Urban Smells by Daniele Quercia of Bell Labs, Luca Maria Aiello of Yahoo Labs, and Rossano Schifanella of University of Turin.

Quercia et al. write the following in their abstract:

People are able to detect up to 1 trillion odors. Yet, city planning is concerned only with a few bad odors, mainly because odors are currently captured only through complaints made by urban dwellers. To capture both good and bad odors, we resort to a methodology that has been recently proposed and relies on tagging information of geo-referenced pictures. In doing so for the cities of London and Barcelona, this work makes three new contributions. We study 1) how the urban smellscape changes in time and space; 2) which emotions people share at places with specific smells; and 3) what is the color of a smell, if it exists. Without social media data, insights about those three aspects have been dicult to produce in the past, further delaying the creation of urban restorative experiences.

As we can see from this work, no matter whether one is spending time in London or in Barcelona, a city by any other name would smell just as… uh, sweet. And perhaps be associated with just as much joy, trust, anticipation, or surprise?


A figure from the paper by Quercia et al. that examines the correlation between various types of emotions and various types of smells.

Clearly, this is research that we need to savor.

The senator whose method is: Make people LAUGH, NOT THINK

Tuesday, May 31st, 2016

U.S. Senator Jeff Flake has appropriated and dismembered our basic goal and method, which is to make people LAUGH, and then THINK. The senator lopped off the “think” part, to produce his own basic goal and method: to make people Laugh, and NOT think. You can see this on display in Senator Flake’s recent colorful press release and booklet, which ridicules scientific research.

We invented the phrase “make people LAUGH, then THINK”. It’s the essence of our magazine, the Annals of Improbable Research. It’s the essence of the Ig Nobel Prize Ceremony, which we administer, and which is now in its 26th year. Each year ten Ig Nobel Prizes are awarded for achievements that make people LAUGH, then THINK. Much of the research ridiculed in Senator Flake’s booklet has won Ig Nobel Prizes.

Senator Flake's booklet

Senator Flake’s booklet

Senator Flake’s Cartoon Book

Senator Flake’s press release says: “U.S. Sen. Jeff Flake (R-Ariz.) today released Twenty Questions: Government Studies That Will Leave you Scratching Your Head, an oversight report highlighting 20 hard-to-justify, taxpayer-funded studies that diverted more than $35 million that could have been better spent researching treatments for cancer, Alzheimer’s disease, and viral infections such as Zika and Ebola….”

Senator Flake’s booklet uses a cartoon style that’s usually meant to appeal to small children. You can download a copy of the the booklet by clicking on the image here.

Hard to Justify

The studies mentioned in Senator Flake’s booklet really are, as Senator Flake says, “hard-to-justify” — if, like Senator Flake, you insist on not justifying them.

Senator Flake and Einstein

Senator Flake’s booklet builds, it says, on the work of Einstein:

“The important thing is not to stop questioning,” urged Albert Einstein, one of the greatest minds of all time. That’s great advice for taxpayers.

Here’s what Senator Flake’s booklet does not mention: Einstein would ask lots of funny questions, and then Einstein would work to FIND THE ANSWERS to those questions.

Senator Flake’s funny booklet just asks a funny question, then laughs, then asks some other funny question, then laughs, then asks some other funny question, and so on, and so on.

Senator Flake’s booklet asks 20 questions. About one third of those questions concern research that was honored with Ig Nobel Prizes, or scientists who earned Ig Nobel Prizes for other research.


Senator Flake’s booklet uses a technique that makes things appear horribly expensive. The table of contents lists a BIG RED DOLLAR AMOUNT next to each research item. You might mistakenly think that that this BIG RED DOLLAR AMOUNT is what the research item cost. You would be wrong. The booklet diligently explains — on a different page, in small, dense text — that the BIG RED DOLLAR AMOUNT is just a BIG RED DOLLAR AMOUNT:

METHODOLOGY. Specific dollar amounts expended to support each study were not available for the projects profiled in this report. Most were conducted as parts of more extensive research funded with government grants or financial support. The costs provided, therefore, represent the total amount of the grant or grants from which the study was supported and not the precise amount spent on the individual studies. This is not intended to imply or suggest other research supported by these grants was wasteful, unnecessary or without merit.

Here are some of the first items in Senator Flake’s booklet. (Each of these was awarded an Ig Nobel Prize, by the way!):




If you apply this same BIG RED DOLLAR AMOUNT technique to Senator Flake’s own booklet, here’s what you get:


What’s It All About?

Three of the items in Senator Flake’s booklet are research performed by Professor David Hu of Georgia Tech:




The logo of Improbable Research and of the Ig Nobel Prizes

The logo of Improbable Research and of the Ig Nobel Prizes

Professor Hu and his team were awarded an Ig Nobel Prize for that pee research. Professor Hu wrote an essay about this, for Scientific American. What he wrote will probably make you laugh, then think. We suggest you read it:

Confessions of a Wasteful Scientist

Three of my projects appeared last week on a senator’s list of questionable research. Allow me to explain

But, if you like to ridicule things because those things are unfamiliar, don’t read Professor Hu’s writing. And don’t look at the actual work of the other Ig Nobel Prize winners or any of the other people on Senator Flake’s list.

If you want to laugh, but not think, pay attention to Senator Flake.

Pedestrian Potential-Collision Standoffs, and Symmetry Breaking

Saturday, May 28th, 2016

We’ve all experienced this phenomenon: you and someone else are walking towards each other in opposite directions, and you don’t want to collide. Do you shift to the left or to the right? And how should you shift to avoid a standoff? In a new paper on the arXiv, physicists Nickolas Morton and Shaun Hendy of the Department of Physics at University of Auckland have examined this problem through the lens of statistical mechanics. Here is an excerpt from their abstract:

If both make the same choice then passing can be completed with ease, while if they make opposite choices an embarrassing stand- off or collision can occur. Pedestrians who encounter each other frequently can establish “social norms” that bias this decision. In this study we investigate the effect of binary decision-making by pedestrians when passing on the dynamics of pedestrian flows in order to study the emergence of a social norm in crowds with a mixture of individual biases. (…) We construct a phase diagram that shows that a social norm can still emerge provided pedestrians are sufficiently attentive to the choices of others in the crowd. We show that this collective behaviour has the potential to greatly influence the dynamics of pedestrians, including the breaking of symmetry by the formation of lanes.




Happy words from painful insect stings [podcast 64]

Wednesday, May 18th, 2016

Justin Schmidt, an emotional fellow, took notes when he was notably stung by a different species of ant, bee, or wasp. Schmidt then turned those notes and emotions into little almost-poems, each just 15 or 20 words long. Those sting-pain notes and emotions, read aloud by QI elves, overflow this week’s Improbable Research podcast.

SUBSCRIBE on, iTunes, or Spotify to get a new episode every week, free.

This week, Marc Abrahams  — with dramatic readings by James Harkin, Dan Schreiber, Anne Miller, Steve Colgan, and Alex Bell (elves from QI, the Museum of Curiosity, No Such Thing As a Fish, and No Such Thing As the News) — tells about:

  • Justin Schmidt‘s book, which includes the Schmidt Sting Pain Index with the poetical descriptions — The Sting of the Wild, by Justin O. Schmidt, Johns Hopkins Press, 2016. ISBN: 9781421419282.sting-wild-420pix
  • A short video, by his university, about Justin Schmidt:
  • A fan video, by the San Diego Natural History Museum, about Justin Schmidt and the Schmidt Sting Pain Index:

The mysterious John Schedler or the shadowy Bruce Petschek perhaps did the sound engineering this week.

The Improbable Research podcast is all about research that makes people LAUGH, then THINK — real research, about anything and everything, from everywhere —research that may be good or bad, important or trivial, valuable or worthless. CBS distributes it, on the CBS web site, and on iTunes and Spotify).