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The mathematics of balloon animals

Feedback is delighted to be pointed towards an old but still vital piece of research that presents “a general mathematical and algorithmic theory for balloon-twisting structures”
Josie Ford

Feedback is our weekly column of bizarre stories, implausible advertising claims, confusing instructions and more

Bloons and doubloons

This edition of Feedback is an exercise in time travel – in that every item is something from absolutely ages ago that we somehow missed. We would feel guilty, but it is the summer holidays (in the northern hemisphere, anyway) and many readers will have half an eye on their errant children, so we thought we could get away with it.

So, cast your minds back to 2008. This, obviously, was the year of the 20th Canadian Conference on Computational Geometry, . A large amount of research was at this conference, but reporter Matthew Sparkes recently stumbled across a by Erik Demaine, Martin Demaine and Vi Hart. It presents “a general mathematical and algorithmic theory for balloon-twisting structures”.

If you didn’t grasp that, allow us to clarify: it’s about the geometry of balloon animals. The authors develop a mathematical framework that allows them to calculate how many balloons you need to generate a particular shape, whether it is a dog (one) or some complicated polyhedron like a dodecahedron (10). These, naturally, are referred to as “Platonic balloons”.

Throughout the paper, the authors use the term “bloon” to refer to a mathematical entity equivalent to a balloon. Feedback wasn’t clear why this neologism was necessary, until we realised that they were therefore able to refer to a balloon of twice the usual length as a “doubloon”.

Curious to know what the authors had been up to since, Feedback went a-searching. Hart became a science populariser on YouTube, then a senior manager at Microsoft. Meanwhile, Martin and Erik are father-and-son researchers and artists, both fascinated by the mathematics of folding.

Erik, a professor at the Massachusetts Institute of Technology, has been in New Scientist a lot. Recent papers include “” and ““. More from Erik, please.

Testing times

Continuing on the topic of being very late to things, reader Derek Long flagged a paper from 2018, “ and major trauma when jumping from aircraft: randomized controlled trial”. It reports on a study called “PArticipation in RAndomized trials Compromised by widely Held beliefs aboUt lack of Treatment Equipoise (PARACHUTE)”.

(Side note: that is a truly excellent scientific acronym. We haven’t had any of those in a while.)

The problem posed is one of evidence. “Parachutes are routinely used to prevent death or major traumatic injury among individuals jumping from aircraft. However, evidence supporting the efficacy of parachutes is weak and guideline recommendations for their use are principally based on biological plausibility and expert opinion.” If readers haven’t yet twigged: the paper is satirical, poking fun at the idea that even the most common-sense interventions should be tested in a full randomised controlled trial.

As the authors write: “In seminal work published in the BMJ in 2003, a systematic search by Smith and Pell for randomized clinical trials evaluating the efficacy of parachutes during gravitational challenge yielded no published studies.”

Feedback actually ran across that back in 2004. The authors noted they were “unable to identify any randomised controlled trials of parachute intervention” and suggested that “everyone might benefit if the most radical protagonists of evidence based medicine organised and participated in a double blind, randomised, placebo controlled, crossover trial of the parachute”. Oof.

Fifteen years later, they did do a trial. This showed that “parachute use did not significantly reduce death or major injury”, with the slight caveat that “the trial was only able to enroll participants on small stationary aircraft on the ground”. This was helpfully illustrated by a photo of one of the participants jumping, parachute-less, out of a grounded plane. As the authors say: “Our findings should give momentary pause to experts who advocate for routine use of parachutes for jumps from aircraft in recreational or military settings.”

Witty Zwicky

Some concepts can’t be traced back to their origins. One such is the spherical cow joke, which illustrates the difficulties of working with highly simplified and abstract models of complicated, real-world situations. It involves a physicist who figures out how to improve productivity on a dairy farm, but their solution only works for spherical cows in a vacuum. Nobody seems to know who came up with this: the oldest references place it , but the origin stories are all vague and one reference the cows with chickens.

However, another sphere-based physicist joke seems to be older. Feedback has just learned, many decades after the fact, about an insult deployed by Fritz Zwicky, who, in the 1930s, produced some of the first evidence for dark matter. A noted curmudgeon, Zwicky was fond of referring to people he disliked as “spherical bastards”. Such a person is a bastard no matter which way you look at them.

Feedback will be using that from now on. But we also want to know the etymology (if that is quite the term) of spherical bastards, chickens and cows. Any insights welcome.

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