‌Two

‌‌Things that Matter

An Improbable Innovation

‘Circular Transportation Facilitation Device’

a/k/a ‘the wheel’ by John Keogh (Australian Innovation Patent no. 2001100012, granted and honoured, jointly with the patent office, with the 2001 Ig Nobel Prize in technology)

Some of what’s in this chapter: Breaching, by means of a shoe • Making horrid, chilling sounds • Skipping and hopping • Plumbing the masticatory mechanism, aurally • Glug-glugging • OmmmmmmmmOMmmmmmOMmm • Self-encrustation with bees and music • Foreseeing football on Mars • Basic black, in the desert • Walking with washing machines • A strapless dress, forcefully

The Great Untied-Shoelace Experiment

Details about the late Norbert Elias’s international untied-shoelace experiments were difficult to track down. But Ingo Mörth found them.

Mörth, a professor at the Johannes Kepler Universität in Linz, Austria, broke the news in an article called ‘The Shoe-lace Breaching Experiment’, published in the June 2007 issue of Figurations: Newsletter of the Norbert Elias Foundation: ‘Norbert Elias started a series of breaching experiments, beginning ad hoc, and ending in various situations in Spain, France, England, Germany, and Switzerland. He strolled around in all these contexts with intentionally untied and trailing shoe-laces.’

Elias had an eminent career as a sociologist, beginning in Germany in the 1930s. After retiring as a reader at University of Leicester in 1964, he went a-wandering, doing sociological research as a byproduct of his tourism.

In the Spanish fishing village of Toremolinos in 1965, giggling girls spurred him to realize that his left shoelaces ‘were untied and trailing’. Mörth describes the magic that resulted: ‘By retying the loose shoe-lace, Elias had the feeling of being included in the village community – at least for a moment, and based on the community aspect of the everyday reality in the village, people took notice and nodded approval of his rectifying something that had a disturbing appearance.’

Elias thereupon began his experiments, strolling across Europe with deliberately untied shoelaces. In England ‘mostly elderly gentlemen reacted by communicating with me on the danger of stumbling and falling’. In Germany ‘older men only looked at me somewhat contemptuously, whereas women reacted directly and tried to ‘clean up’ the obvious disorder, on the tram as well as elsewhere’.

The professor and his laces thusly pioneered – though the academic world mostly failed to celebrate him and them for it – what are now known as ‘breaching experiments’. American sociologist Harold Garfinkel coined the term and rose to fame by conducting a series of such activities. As Mörth explains, these experiments ‘breached the taken-for-granted assumptions underlying everyday situations, thereby generating consternation and embarrassment among other people present’.

Elias’s many fans in the Norbert Elias Foundation and elsewhere were aware that he had done something with shoelaces, but because Elias did not publish a formal academic study, most did not know that they could read a firsthand account of what, where, and when he did it. Thanks to Mörth, scholars can now learn that Elias’s historic report was published in the German weekly magazine Die Zeit in 1967, in the travel section, under the headline ‘Die Geschichte mit den Schuhbändern’ (‘The Story of the Shoe-Laces’).

In publicizing the existence of Elias’s original account, Mörth flung open a door through which researchers had, for forty years, thought themselves restricted to only a squinting glance.

Mörth, Ingo (2007). ‘The Shoe-lace Breaching Experiment.’ Figurations: Newsletter of the Norbert Elias Foundation 2 (27): 4–6.

Elias, Norbert (1967). ‘Die Geschichte mit den Schuhbändern.’ Die Zeit, 17 November.

An Improbable Innovation

‘Garment Device Convertible to One or More Facemasks’

a/k/a a brassiere that, in an emergency, can be quickly converted into a pair of protective masks, by Elena N. Bodnar, Raphael C. Lee, and Sandra Marijan (US Patent no. 7,255,627, granted 2007 and honoured with the 2009 Ig Nobel Prize in public health)

From ‘Garment Device Convertible to One or More Facemasks’

Chilling Sounds

Fingernails on a blackboard. Why does the very phrase send chills down one’s back? The question has annoyed scientists for at least 2300 years. Aristotle mentioned the existence of what he called ‘hard sounds’, but didn’t try very hard to explain them.

In the mid-1980s, three scientists assaulted the problem directly, subjecting volunteers to a battery of electronically synthesized nails-on-blackboard screeching. D. Lynn Halpern, Randolph Blake, and James Hillenbrand at Northwestern University in Evanston, Illinois, published details in the journal Perception and Psychophysics. They called their study ‘Psychoacoustics of a Chilling Sound’.

First, they ran some tests to establish exactly where nails-on-a-blackboard ranks in the hierarchy of annoying sounds.

They recruited a panel of volunteers – a different group from the one that would later undergo the intensive, dedicated exposure to the Sound of Sounds. The panel listened to recordings of sixteen different, hypothetically ‘annoying’ sounds. They rated just how annoying each was. This ranged from not very (for chimes, rotating bicycle tyres, and running water) to excruciating. Jingling keys mildly annoyed some people. Then, increasingly less pleasant, came the sounds of a pencil sharpener; a blender motor; a dragged stool; a metal drawer being opened; scraping wood; scraping metal; and rubbing two pieces of Styrofoam together. But the annoyance of fingernails-on-a-blackboard topped them all.

Halpern, Blake, and Hillenbrand, having established this simple fact, then converted the tape recording to a digital signal, so that they could manipulate and experiment with constituent high and low pitches. The formal report notes the researchers’ belief that the signal was of good quality. ‘To the authors and several other reluctant volunteer listeners’, they write, ‘the digitized, filtered signal sounded very similar to, and just as unpleasant as the original.’

The original recorded, pre-digitized sound was not actually of scraping fingernails, but of something known, from previous experiments, to be very like it. In a footnote, Halpern, Blake, and Hillenbrand confide that ‘the instruction set used in this study included a description of [a] three-pronged garden tool being dragged across a slate surface. Virtually all subjects shuddered upon reading this portion of the instructions.’

The shuddering volunteers listened to several different, digitally doctored versions of the sound, and rated the unpleasantness of each.

The study’s conclusion, when all was scraped and done, is perhaps worth quoting: ‘Our results demonstrate that the unpleasant quality associated with the sound of a solid object scraped across a chalkboard is signaled by acoustic energy in the middle range of frequencies audible to humans. High frequencies, contrary to intuition, are neither necessary nor sufficient to elicit this unpleasant association. Still unanswered, however, is the question of why this and related sounds are so grating to the ear.’

The story didn’t end there, of course. In 2004, Josh McDermott and Marc Hauser of Harvard University conducted a series of acoustic and psychological experiments. In the process, they discovered a major difference between Harvard students and cotton-top tamarin monkeys. Harvard students actively avoid fingernail-on-blackboard sounds when given the opportunity, but tamarins generally don’t. McDermott and Hauser hazard some guesses about why this is so – they suggest it may be in some way related to our ability to appreciate or deplore music.

The 2006 Ig Nobel Prize in the field of acoustics was awarded to Halpern, Blake, and Hillenbrand for their chilling research. Still, the mystery endures, giving cold discomfort to almost everyone who hears about it.

Halpern, D. Lynn, Randolph Blake, and James Hillenbrand (1986). ‘Psychoacoustics of a Chilling Sound.’ Perception and Psychophysics 39: 77–80.

McDermott, Josh, and Marc Hauser (2004). ‘Are Consonant Intervals Music to Their Ears? Spontaneous Acoustic Preferences in a Nonhuman Primate.’ Cognition 94: B11–B21.

Hop, Skip, and Reach Conclusions

When do young adults skip and hop, and why? These are the questions raised by Allen W. Burton, Luis Garcia, and Clersida Garcia. Their answers appear in the research report ‘Skipping and Hopping of Undergraduates: Recollections of When and Why’. Burton, at the University of Minnesota, and Garcia and Garcia, at Northern Illinois University, write that ‘the purpose of this study was to compare the reasons why young adults skip and hop and when they last skipped and hopped’.

The researchers collected data from 253 female and 411 male university students. Each of those young adults was asked two skipping and two hopping questions:

1. Approximately how long ago did you last spontaneously skip?
2. Why did you skip? In other words, what elicited your skipping behaviour?
3. Approximately how long ago did you last spontaneously hop?
4. Why did you hop? In other words, what elicited your hopping behaviour?

Based on the results of that survey, Burton, Garcia, and Garcia conclude that hopping and skipping are not the same thing. Not to undergraduate students. At least, not as far as when and why are concerned. At least, not completely. Their report explains in detail.

That’s the story on the when and why of hopping and skipping. Now, how about the how?

Claire Farley, Reinhard Blickhan, Jacqueline Saito, and Richard Taylor at Harvard University published a massive six-page report on their experiments with ‘hopping frequency in humans’. Two young women and two young men did the hopping, individually, on a treadmill. The treadmill ran, so to speak, at various speeds. Each individual turned out to have a preferred hopping frequency, at which she or he most strongly resembled (in certain respects) a rock glued atop a spring.

That’s true of hopping on two feet. Hopping on one foot is an entirely different question. Or at least it has the potential to be an entirely different question. That potential was explored in research done by G. P. Austin, G. E. Garrett, and D. Tiberio at Sacred Heart University, in Fairfield, Connecticut. In June 2002 they leaped into public view with a report entitled ‘Effect of Added Mass on Human Unipedal Hopping’. Six months later they popped up again, with ‘Effect of Frequency on Human Unipedal Hopping’. The next year they jumped into sight yet again, with ‘Effect of Added Mass on Human Unipedal Hopping at Three Frequencies’.

Have they gained a leg up on their professional competitors? How high will their ambitious research programme take them? We shall see.

Burton, Allen W., Luis Garcia, and Clersida Garcia (1999). ‘Skipping and Hopping of Undergraduates: Recollections of When and Why.’ Perceptual and Motor Skills 88: 401–6.

Farley, Claire T., Reinhard Blickhan, Jacqueline Saito, and C. Richard Taylor (1991). ‘Hopping Frequency in Humans: A Test of How Springs Set Stride Frequency in Bouncing Gaits.’ Journal of Applied Physiology 71 (6): 2127–32.

Austin, G. P., G. E. Garrett, and D. Tiberio (2002). ‘Effect of Added Mass on Human Unipedal Hopping.’ Perceptual and Motor Skills 94 (3): 834–40.

Austin, G. P., D. Tiberio, and G. E. Garrett (2002). ‘Effect of Frequency on Human Unipedal Hopping.’ Perceptual and Motor Skills 95 (3): 733–40.

Austin, G. P., D. Tiberio, and G. E. Garrett (2003). ‘Effect of Added Mass on Human Unipedal Hopping at Three Frequencies.’ Perceptual and Motor Skills 97 (2): 605–12.

Sounds Delicious

Can a machine identify what you’re chewing, merely from the sound? Yes, if you are at a laboratory in Zurich, Switzerland, or Hall-in-Tirol, Austria, and if you are chewing potato crisps, apples, mixed lettuce, cooked pasta, or boiled rice.

Oliver Amft, Mathias Stäger, and Gerhard Tröster of the Swiss Federal Institute of Technology, and Paul Lukowicz of Austria’s University for the Health Sciences, Medical Informatics and Technology (UMIT), describe their work succinctly: ‘using wearable microphones to detect and classify chewing sounds (called mastication sounds) from the user’s mouth’. But, they explain, this is just stage 1 of their dream. It’s an unusual dream: to build a computer-based machine ‘that precisely and 100% reliably determines the type and amount of all and any food that the user has consumed’.

Nothing about stage 1 is easy. The scientists list three different approaches that a machine might take in trying to sense someone’s food intake automatically:

1. detecting and analysing chewing sounds,
2. using electrodes mounted on the base of the neck (e.g., in a collar) to detect and analyse bolus swallowing,
3. using motion sensors on hands to detect food intake-related motions.

Amft, Stäger, Tröster, and Lukowicz chose option (a). It, alone, seemed within the range of the technology available to them today.

Their report is written for specialists, but contains delights for everyone. My favourite is the graph titled ‘Chewing sound and speech recording in a room with background music’, which depicts the sound intensity during a minute-long span. The graph’s four segments are labelled ‘eating lettuce’, ‘user speaking’, ‘eating pasta’, and ‘music playing’.

Here are some of the things the scientists say they learned in having their machine analyse a total of 650 ‘chewing sequences’ produced by four healthy chewers:

• Good quality chewing sound signal can be obtained by placing a microphone in the ear canal.
• Chewing sounds can be discriminated from a signal containing a mixture of speech, silence and chewing.
• Listening to a sequence of chewing sounds, it is possible to identify the beginnings of the individual single chews.
• Chewing-sound-based discrimination between very different kinds of food – the kinds mentioned above – is possible with greater than eighty percent accuracy.

This all builds on decades of work that began with Swedish Institute for Food Preservation Research scientist B. K. Drake’s 1963 study ‘Food Crushing Sounds: An Introductory Study’.

The study of chewing sounds is a very specialized field. (For an extreme example, see ‘Crisp Sounds’ on page 138.) The field apparently acquired a name in 1966, when British dentist D. M. Watt published a paper called ‘Gnathosonics: A Study of Sounds Produced by the Masticatory Mechanism’.

Amft, Stäger, Tröster, and Lukowicz are proud of their chew-sound-analysis achievement. But mindful of technology’s limits, they aim to keep their aims simple. In their words: ‘The system does not need be fully automated to be useful ... it is perfectly sufficient if at the end of the day the system can remind the user that for example “at lunch you had something wet and crisp (could have been salad) and some soft texture stuff (spaghetti or potatoes)” and asks him to fill in the details.’

Amft, Oliver, Mathias Stäger, Paul Lukowicz, and Gerhard Tröster (2005). ‘Analysis of Chewing Sounds for Dietary Monitoring.’ UbiComp 2005: Proceedings of the 7th International Conference on Ubiquitous Computing, Tokyo, Japan, 11–14 September: 56–72.

Drake, B. K. (1963). ‘Food Crushing Sounds: An Introductory Study.’ Journal of Food Science 28 (2): 233–41.

Watt, D. M. (1966). ‘Gnathosonics: A Study of Sounds Produced by the Masticatory Mechanism.’ Journal of Prosthetic Dentistry 16 (1): 73–82.

Pour Laws

When physics professors take to the bottle, they can be tenacious about it. Take Christophe Clanet and Geoffrey Searby, who wrote a highly condensed, fourteen-page report called ‘On the Glug-Glug of Ideal Bottles’, which was published in the Journal of Fluid Mechanics. Like so much of the literature emerging from Europe during the past two centuries, this study celebrates what happens when liquid is poured from a container.

The pair of de-bottling experts is based at the Institut de Recherche sur les Phénomènes Hors Equilibre in Marseille, France. Both men are fascinated by bubbles and motion. Searby heads a French–German committee doing research on rocket engine combustion, while Clanet has become tops in the physics subspecialty of skipping stones across ponds.

‘Glug-glug’ is now a technical term, thanks mostly to Clanet and Searby. They tried it out at a physics conference in 1997, presenting a talk called, plainly, ‘On the Glug-Glug of the Bottle’. Their opening words were circumspect: ‘We study experimentally the emptying of a vertical cylinder of diameter D and length L.’ The audience response was such that Clanet and Searby continued their exploration of glug-glugs. They delved into the theoretical aspects, as well as the empirical.

Their follow-up paper begins with a dramatic sentence: ‘An image of life is a return to the thermodynamic equilibrium of death via the oscillations of our heartbeats.’ Then, with a quick literary pirouette, they describe the ‘onomatopoeic glug-glug’ of an emptying bottle. ‘This oscillatory behaviour’, they remind us, ‘starts at the opening and continues until the bottle is empty.’

The apparent weight of the bottle lurches way up and slightly less down, up, down, up, down, until the liquid is gone. Clanet and Searby produced a graph of this behaviour, a visual form of glug-glug that some scientists find as delightful as the sound.

The experiment involved Newtonian liquid, a tank, two valves, a pump, a pressure sensor, a camera, and a laser beam. It built upon the pioneering bubble-behaviour work done in the late 1940s by Geoffrey Taylor at the University of Cambridge. Taylor’s bubbles inspired a ragged, international line of experimentation on bottle-emptying that culminated with the Clanet/Searby glug-glug work.

The fruits of the experiment are sweet. Through painstaking work, Clanet and Searby elucidated the basic law of glug-glug: the time needed to empty a bottle depends on the diameter of the bottle, and also on the diameter of the hole.

Of course, this is the law for an idealized bottle shape – a can rather than the beloved Coca-Cola bottle or other quirky form. Even for a Coke can, though, there remains the open question of the tab-shaped opening. Clanet and Searby used a cylinder with a circular hole. Whether and how much a different hole shape affects the glug-glug is, almost needless to say, a matter for further research.

Clanet, Christophe, and Geoffrey Searby (2004). ‘On the Glug-Glug of Ideal Bottles.’ Journal of Fluid Mechanics 510: 145–68.

Clanet, C., G. Searby, and E. Villermaux (1997). ‘On the Glug-Glug of the Bottle.’

American Physical Society, Division of Fluid Dynamics Meeting, 23–25 November, abstract #Df.10.

Davies, R. M., and Geoffrey Taylor (1950). ‘The Mechanics of Large Bubbles Rising Through Liquids and Through Liquids in Tubes.’ Proceedings of the Royal Society of London, Series A 200 (22 Feb): 375–90.

The Repetitive Physics of Om

Two Indian scientists are wielding sophisticated mathematics to dissect and analyse the traditional meditation chanting sound ‘Om’. The Om team has published six monographs in academic journals. These plumb certain acoustic subtleties of Om, which the researchers say is ‘the divine sound’.

Om has many variations. In a study published in the International Journal of Computer Science and Network Security, the researchers explain: ‘It may be very fast, several cycles per second. Or it may be slower, several seconds for each cycling of [the] Om Mantra. Or it might become extremely slow; with the mmmmmm ... sound continuing in the mind for much longer periods, but still pulsing at that slow rate. It is somewhat like one of these vibrations:

OMmmOMmmOMmm ...

OMmmmmOMmmmmOMmmmm ...

OMmmmmmmmOMmmmmmmmOMmm

The important technical fact is that no matter what form of Om one chants at whatever speed, there is always a basic Omness to it.

Ajay Anil Gurjar and Siddharth A. Ladhake published their first Om paper, titled ‘Time-Frequency Analysis of Chanting Sanskrit Divine Sound “OM”’, in 2008. Ladhake is the principal at Sipna’s College of Engineering and Technology in Amravati, India. Gurjar is an assistant professor in that institution’s department of electronics and telecommunication. Both specialize in electronic signal processing. They now subspecialize in analysing the one very special signal.

In their introductory paper, Gurjar and Ladhake explain (in case there is someone unaware of the basics) that: ‘Om is a spiritual mantra, outstanding to fetch peace and calm. The entire psychological pressure and worldly thoughts are taken away by the chanting of Om mantra.’

No one has explained the biophysical processes that underlie this fetching of calm and taking away of thoughts. Gurjar and Ladhake’s time-frequency analysis is a tiny step along that hitherto little-taken branch of the path of enlightenment.

They apply a mathematical tool called wavelet transforms to a digital recording of a person chanting ‘Om’. Even people with no mathematical background can appreciate, on some level, one of the blue-on-white graphs included in the monograph. This graph, the authors say, ‘depicts the chanting of “Om” by normal person after some days of chanting’. The image looks like a pile of nearly identical, slightly lopsided pancakes held together with a skewer, the whole stack lying sideways on a table. To behold it is to see, if nothing else, repetition.

At the end, Gurjar and Ladhake write: ‘Our attentiveness and our concentration are pilfered from us by the proceedings take place around us in the world in recent times ... By this analysis we could conclude steadiness in the mind is achieved by chanting OM, hence proves the mind is calm and peace to the human subject.’

Much as people chant the sound ‘Om’ over and over again, Gurjar and Ladhake repeat much of the same analysis in their other five studies, managing each time to chip away at some slightly different mathematico-acoustical fine point.

Gurjar, Ajay Anil, and Siddharth A. Ladhake (2008). ‘Time-Frequency Analysis of Chanting Sanskrit Divine Sound “OM”.’ International Journal of Computer Science and Network Security 8 (8): 170–75.

–– (2009). ‘Spectral Analysis of Sanskrit Divine Sound OM.’ Information Technology Journal 8: 781–85.

–– (2009). ‘Optimal Wavelet Selection For Analyzing Sanskrit Divine Sound “OM”.’ International Journal of Mathematical Sciences and Engineering Applications 3 (2): 225–33.

–– (2009). ‘Analysis of Speech Under Stress Before and After OM Chant Using MATLAB 7.’ International Journal of Emerging Technologies and Applications in Engineering, Technology and Sciences 2 (2): 713–18.

–– (2009). ‘Time-Domain Analysis of “OM” Mantra to Study It’s [sic] Effect on Nervous System.’ International Journal of Engineering Research and Industrial Applications 2 (3): 233–42.

Gurjar, Ajay Anil (2009). ‘Multi-Resolution Analysis of Divine Sound “OM” Using Discrete Wavelet Transform.’ International Journal of Emerging Technologies and Applications in Engineering, Technology and Sciences 2 (2): 468–72.

Gurjar, Ajay Anil, Siddharth A. Ladhake, Ajay P. Thakare (2009). ‘Analysis of Acoustic [sic] of “OM” Chant to Study It’s [sic] Effect on Nervous System.’ International Journal of Computer Science and Network Security 9 (1): 363–67.

Humming in the Key of Bee

Norman E. Gary is the rare academic who plays clarinet while he is covered with live bees, and often does so in public.

An emeritus professor of apiculture at the University of California (Davis), Gary also plays Dixieland music in a human ensemble called the Beez Kneez Jazz Band. He generally goes solo – he alone with his instrument – for the bee-encrusted gigs.

Hollywood has used Gary’s bee-wrangling talents and sometimes his acting ability, though seldom his clarinet, in more than a dozen films. Among them: The X Files, Fried Green Tomatoes, Invasion of the Bee Girls, and Candyman: Farewell to the Flesh.

Several of Gary’s scientific activities involve vibration, a general physics phenomenon of which music is just a part. He has microwaved bees. He has also analysed one of the lesser-known (to most humans) sounds that bees produce. Details appear in a 1984 monograph published with colleague S. S. Schneider in the Journal of Apicultural Research. They gave their article the title ‘“Quacking”: A Sound Produced by Worker Honeybees after Exposure to Carbon Dioxide’.

Gary has vacuumed bees. He has also made it easier and more efficient for others who want or need to vacuum the insects, by inventing a purpose-built bee vacuum with his colleague Kenneth Lorenzen. The wording in their patent could, with a bit of work, be set to hummable music: ‘By the operation of the mechanism in the fashion disclosed, the bees on the opposite sides of a comb, and eventually of a plurality of combs and frames, are removed therefrom by a concomitant vacuuming and brushing operation.’

The professor has published more than one hundred academic papers, many of them about bees. In one of the earliest, called ‘The Case of Utter vs. Utter’, he took a fond look back at a court case decided in 1901 in Goshen, New York, starring two brothers from a family named Utter.

The brothers disagreed – Utterly, of course – about many things. The question here was: did the bees associated with one brother, a beekeeper, eat the peaches growing on trees owned by the other brother, a fruit grower? Perhaps the most enjoyable account appeared soon after the trial, in the Rocky Mountain Bee Journal. The anonymous writer says: ‘It was amusing to see the plaintiff try to mimic the bee, on the witness stand as he swayed his head from one side to the other, raised up on his legs and flopped his arms. His motions were so utterly ridiculous and so contrary to the real acts and achievements of the bees, that everyone in the courtroom, including the jury, laughed, and laughed heartily.’

The court ruled against that Utter, and for the other. This established a legal precedent favourable to wandering bees. It also inspired, almost sixty years later, the young Norman Gary as he began his more-than-sixty-year-long career of collaborating with and studying tiny, honey-making musicians.

Schneider. S. S., and Norman E. Gary (1984). ‘“Quacking”: A Sound Produced by Worker Honeybees After Exposure to Carbon Dioxide.’ Journal of Apicultural Research 23 (1): 25–30.

Gary, Norman E., and Kenneth Lorenzen (1981). ‘Bee Vacuum Device and Method of Handling Bees.’ US Patent no. 4,288,880.

Gary, Norman E. (1959). ‘The Case of Utter vs. Utter.’ Gleanings in Bee Culture 87 (6): 336–37.

N. A. (1901).‘Bees in Court: History of the Celebrated Case of Peach Utter versus Bee-Keeper Utter.’ Rocky Mountain Bee Journal 1 (1): 6.

Vacuum Travel

The journey between London and Edinburgh would be much quicker had the London and Edinburgh Vacuum Tunnel Company been allowed and able to build a breathtaking new piece of technology, back when land was cheap and all things seemed possible. The 29 January 1825 issue of the Mechanics Register presents the scheme in detail: ‘The London and Edinburgh Vacuum Tunnel Company is proposed to be established, with a capital of Twenty Millions Sterling, divided into 200,000 shares, of £100 each, for the purpose of forming a Tunnel or Tube of metal between Edinburgh and London, to convey Goods and Passengers between these cities and the other towns through which it passes.’

The plan is simple. There are two long tunnels or tubes, side by side, one reserved for trips northbound to Edinburgh, the other for London-bound traffic. Boilers, located every two miles along the approximately 390-mile length of the tunnel or tube, supply steam that, through a clever bit of engineering, creates a vacuum.

At departure time, the vacuum seal is broken at the departure end, right behind the train. Thanks to the difference in pressure, the train is thus immediately impelled into the tunnel or tube.

To maintain pressure all through the journey, to keep a tight seal behind the train, there’s a ‘very strong air-tight sliding door, running on several small cylindrical rollers, to lessen the friction’. The inrushing air pushes the slick-sliding door. That whizzing, roller-riding door pushes the amassed railway cars onwards, onwards, faster and faster into the airless tunnel or tube.

These cars carry only freight. People never enter the tube, which, being four feet tall, is too short for most of them.

Passengers instead ride in traditional railway carriages on tracks affixed on top of the tunnel or tube. These passenger cars are coupled by strong magnets to the freight-carrying cars. As the freight train zooms through the tunnel or tube, its magnetic field drags the passenger train along on what is sure to be a rapid and exciting ride. The acceleration is such that the train travels ‘altogether, in the first five minutes’ of its journey, ‘480 miles 4448 feet’.

This would have been a considerable advance over the standard railway capabilities of the time. A dispatch in the same issue of the Mechanics Register allows that ‘the practicality of [conventional] steam carriages for the conveyance of passengers is fully established, and we have as little doubt that the conveyance of goods at the rate of seven or eight miles an hour, will soon be as easily accomplished’.

The London and Edinburgh Vacuum Tunnel Company report is accompanied by a small notice: ‘The foregoing Jeu d’Esprit appeared in a recent number of the Edinburgh Star, and being well calculated to throw ridicule upon some of the preposterous plans now before the public for the investment of money, we insert it in the Register.’

Nonetheless, in subsequent decades, engineers in Ireland, America, and Britain did build short stretches of pneumatic passenger railway. None spanned great distances or lasted more than a few years. Isambard Kingdom Brunel, designer of England’s first great railways (and of London’s Paddington station), built about twenty miles of pneumatic railway between Exeter and Newton before abandoning it as impractical.

N. A. (1825). ‘London and Edinburgh Vacuum Tunnel Company, Capital 90,000 Sterling.’ Mechanics Register 1 (13): 205–7.

May We Recommend

‘Effects of Horizontal Whole-Body Vibration on Reading’

by Michael J. Griffin and R. A. Hayward (published in Applied Ergonomics, 1994)

Very Special Topics

The global nature of football (a/k/a soccer in the US) varies measurably from city to city because of down-to-Earth differences in the air pressures, temperatures, and other physical conditions. But those differences are slight in comparison to the ones described in a University of Leicester study called ‘Association Football on Mars’.

Calum James Meredith, David Boulderstone, and Simon Clapton published the analysis in the university’s Journal of Physics Special Topics, which takes up topics that seldom find their way into the better-known physics journals. The journal is produced by and for university students, which makes it a bit unusual. Its unusualness quotient increases with the knowledge that the current head of the department of physics and astronomy at the University of Leicester is Professor Lester.

‘Association Football on Mars’ methodically calculates the altered basics of play on the red planet. ‘It would be possible to retain the game in a familiar but slightly changed form’, the authors say.

On the Martian surface, the gravitational pull and the air pressure are less than we’re used to. The ball would encounter substantially less drag in its journeying from foot to foot to head to foot to goal. On many a kick, the ball would travel about four times as far as it would on Earth. These impressive distances come with a straightforward cost: ‘the inability to “bend” the ball due to a lack of air resistance would seem to decrease the skill involved in football’.

Height vs. distance for footballs kicked on Earth (solid line) and Mars (dashed line)

In the same issue of the journal, one finds other monographs by the team of Meredith, Boulderstone, and Clapton. Two of those consider a solution to our era’s most pressing environmental problem.

In ‘None Like It Hot’, the trio propose and describe a method ‘to help combat global warming by moving the Earth further [sic] away from the Sun to reduce its surface temperature’. A companion paper, ‘None Like It Hot II’, investigates whether this feat ‘would be plausible given conventional rocket technology’. They conclude that the mass of fuel needed to perform the manoeuvre ‘is only a few orders of magnitude smaller than the mass of the Earth. The number of rockets will make only a small difference due to the nature of the relationship between the two values.’

Meredith, Calum James, David Boulderstone, and Simon Clapton (2011). ‘Association Football on Mars.’ Journal of Physics Special Topics 9 (1).

–– (2010). ‘None Like It Hot.’ Journal of Physics Special Topics 9 (1).

–– (2010). ‘None Like It Hot II.’ Journal of Physics Special Topics 9 (1).

Basic Black Dress: Hot or Not?

Why do Bedouins wear black robes in hot deserts? The question so intrigued four scientists – all non-Bedouins – that they ran an experiment. Their study, called ‘Why Do Bedouins Wear Black Robes in Hot Deserts?’, was published in the journal Nature in 1980.

‘It seems likely’, the scientists wrote, ‘that the present inhabitants of the Sinai, the Bedouins, would have optimised their solutions for desert survival during their long tenure in this desert. Yet, one may have doubts on first encountering Bedouins wearing black robes and herding black goats. We have therefore investigated whether black robes help the Bedouins to minimise solar heat loads in a hot desert.’

The research team – C. Richard Taylor and Virginia Finch of Harvard University, and Amiram Shkolnik and Arieh Borut of Tel Aviv University – quickly discovered that, as you might suspect, a black robe does convey more heat inward than a white robe does. But they doubted that this was the whole story.

They found inspiration and guidance in a 1969 report about cattle. John Hutchinson and Graham Brown of the Ian Clunies Ross Animal Research Laboratory, in Prospect, New South Wales, Australia, worked with Friesian dairy cows. The Australian team discovered that light and heat penetrate deeper into white cattle hair than into black. The saving grace for cattle is that even a tiny amount of wind whisks away that extra heat.

However, cattle are not people. So, what of man (and woman)?

Taylor, Finch, Shkolnik, and Borut measured the overall heat gain and loss suffered by a brave volunteer. They described the volunteer as ‘a man standing facing the Sun in the desert at mid-day while he wore: (1) a black Bedouin robe; (2) a similar robe that was white; (3) a tan army uniform; and (4) shorts (that is, he was semi-nude)’.

Each of the test sessions (black-robed, white-robed, uniformed, and half-naked) lasted thirty minutes. It was hot there in the Negev Desert at the bottom of the rift valley between the Dead Sea and the Gulf of Elat. The volunteer stood in temperatures that ranged from a just-semi-sultry 35 degrees Celsius (95 degrees Fahrenheit) to a character-building 46 degrees Celsius (115 degrees Fahrenheit). Though he is now nameless, this was his day in the sun.

The results were clear. As the report puts it: ‘The amount of heat gained by a Bedouin exposed to the hot desert is the same whether he wears a black or a white robe. The additional heat absorbed by the black robe was lost before it reached the skin.’

Bedouins’ robes, the scientists noted, are worn loose. Inside, the cooling happens by convection – either through a bellows action, as the robes flow in the wind, or by a chimney sort of effect, as air rises between robe and skin.

Thus it was conclusively demonstrated that, at least for Bedouin robes, black is as cool as any other colour.

Shkolnik, Amiram, C. Richard Taylor, Virginia Finch, and Arieh Borut (1980). ‘Why Do Bedouins Wear Black Robes in Hot Deserts?’ Nature 283: 373–75.

Hutchinson, John C. D., and Graham D. Brown (1969). ‘Penetrance of Cattle Coats by Radiation.’ Journal of Applied Physiology 26 (4): 454–64.

Capacity of the Nose

‘What is the Air-Conditioning Capacity of the Human Nose?’ Spring this question the next time you find yourself at a party where everybody else is an HVAC engineer. HVAC engineers specialize in heating, ventilating, and air conditioning. But, as a group, HVAC engineers are surprisingly ignorant about the air-conditioning capacity of their own noses.

Your question might throw the engineers into a two-part frenzy: first measuring each other’s nasal cavity dimensions, temperatures, and vapour concentrations; and then competitively calculating, calculating, calculating until the party ends.

You could save them the trouble. Tell them about a report called ‘The Air-Conditioning Capacity of the Human Nose’, which was published in the Annals of Biomedical Engineering. There, Sara Naftali and her colleagues at Tel Aviv University tell how they attacked the question by using three artificial noses.

None of these artificial noses are ones that a mother would love if she saw one installed on her child. The first, which the scientists call ‘nose-like’, would seem anything but if it were mounted on someone’s face. This rough-hewn product of a machine shop has internal ductwork that corresponds to ‘averaged data of human nasal cavities’. A later version is called, unappealingly, ‘nose-like with valve’.

The third artificial nose is a mechanically detailed reproduction of one individual’s nose, with lots of twisty, bumpy idiosyncrasies. Because this nose – like most noses – is far from average, the scientists used it mostly in a sort of ‘reality check’ to compare against the performance of the nose-like nose and the nose-like with valve.

The ensuing artificial huffing and puffing taught them two things. First, that the nose-like noses behave realistically enough for scientists not to have to do too many uncomfortable experiments using actual people’s actual noses. And second, that the basic ductwork appears to handle ninety percent or so of a person’s air-conditioning needs – it delivers air of usable temperature and humidity to the lungs no matter how cold, hot, humid, or dry the atmosphere happens to be.

Now, should you happen to be introduced to one of the very few party-going HVAC engineers who does know the air-conditioning capacity of the human nose, do not despair. You can still stimulate a good conversation. Simply ask: what is the cooling power of the pigeon head?

For years, birders disagreed as to how their favourite animals manage to keep from overheating. More than a decade ago, Robert St. Laurent and Jacques Larochelle of the Université Laval in Quebec, Canada, wrote ‘The Cooling Power of the Pigeon Head’. It describes how they inserted electronic temperature probes, via the rear exhaust openings, up into the intestines of several birds; then body-wrapped the birds; then put them into a wind tunnel.

They discovered that simply opening one’s beak, without making a sound, is sufficient to keep things from getting overheated. It remains for others to see if this applies to partygoers in conversation, as well as to birds in flight.

Naftali, Sara, Moshe Rosenfeld, Michael Wolf, and David Elad (2005). ‘The Air-Conditioning Capacity of the Human Nose.’ Annals of Biomedical Engineering 33 (4): 545–53.

St. Laurent, Robert, and Jacques Larochelle (1994). ‘The Cooling Power of the Pigeon Head.’ Journal of Experimental Biology 194: 329–39.

Moving Violations

Historically, Europe’s washing machines tended to walk across a room, while America’s did not. Daniel Conrad and Werner Soedel explained why, in a study called ‘On the Problem of Oscillatory Walk of Automatic Washing Machines’. Conrad and Soedel, based at the School of Mechanical Engineering at Purdue University in West Lafayette, Indiana, published their work in 1995 in the Journal of Sound and Vibration. Their explanation has been recognized by authority figures for its power to inspire youths.

The fear of ambling machinery resonated with modern times. One could feel it in the 1995 Japanese science-fiction film Mechanical Violator Hakaider. Critic Jason Buchanan later described what happens once the title character, a cyborg, is loosed upon the land: ‘Once Hakaider sets on the path of destruction there is little that can be done to stop him from destroying all of Jesus Town.’

Washing machines of that era sometimes contained frightful things. A 1993 detective thriller called Vortice Mortale (English title: The Washing Machine) cinematically depicted a dismembered man inside an Italian unit.

Conrad and Soedel eschewed the sensational, restricting themselves to the engineering basics. ‘The problem of walk in automatic washing machines is becoming more and more of interest to appliance manufacturers’, they wrote. ‘The current trend is towards lightweight plastic and composite components. The reduction of mass associated with these changes in materials increases the possibility that a washing machine will walk.’

In washing machines, the propensity to waddle is the consequence of a particular design choice. While steadfast American machines rotated their dirty clothes about a vertical axis, European designs typically made the internal machinery twirl around horizontally.

Conrad and Soedel saw this as a mechanical and business blunder. They wrote: ‘The horizontal axis washer has innate unbalance problems associated with the design. This unbalance can typically create a force in excess of 19 kilonewtons during the spin cycle.’

Four years after the publication of ‘On the Problem of Oscillatory Walk of Automatic Washing Machines’, two officers at the US Military Academy in West Point, New York, used it as a major source for their paper ‘Basic Vibration Design to Which Young Engineers Can Relate: The Washing Machine’.

Lt. Col. Wayne Whiteman and Col. Kip Nygren pointed out that ‘virtually every campus has laundry facilities for students. Most students are therefore familiar with the unwanted vibrations that occur when an unbalance of clothes accumulates during the spin cycle.’

Young engineers thrill at bad vibrations. Keying on that, Whiteman and Nygren sketched out, in terms designed to resonate with their audience, the story of how to prevent oscillatory walk. These terms are lyrical, if you are a certain type of engineer, and perhaps someone will use them in a hip-hop hit: Mass of the Entire Machine; Mass of Inner Housing and Rotating Drum; Mass of Unbalanced Clothes; Coefficient of Static Friction with Floor; Radial Distance to Unbalanced Clothes; Spin Speed; Suspension Spring Constant; Suspension Damping Ratio.

Conrad, Daniel C., and Werner O. Soedel (1995). ‘On the Problem of Oscillatory Walk of Automatic Washing Machines.’ Journal of Sound and Vibration 188 (3): 301–14.

Whiteman, Wayne E. and Kip P. Nygren (1999). ‘Basic Vibration Design to Which Young Engineers Can Relate: The Washing Machine.’ Paper presented at the annual meeting of the American Society for Engineering Education, Charlotte, N.C., 20–23 June, session 3268.

The Threat of the Robo-Toaster

Which kind of robot will be the first to arise and smite us? A study called ‘Experimental Security Analysis of a Modern Automobile’ suggests we keep an eye on the family car.

Written by Karl Koscher and a team of ten other researchers at the University of Washington and at the University of California, San Diego, the paper was presented at the 2010 IEEE (Institute of Electrical and Electronics Engineering) Symposium on Security and Privacy, in Berkeley, California.

Unlike the mindless jalopies of the past, the paper points out, ‘Today’s automobile is no mere mechanical device, but contains a myriad of computers.’

This myriad has powers to do good things for us humans, as well as bad things to us. Already, in some cases, the microchip hordes quietly, beneficently take control from the driver. The Lexus LS460 luxury sedan can automatically parallel-park itself. Many General Motors cars will soon have what the study calls ‘integration with Twitter’. Other abilities are just around the corner.

The team’s goal was to look past the goodness, and see how hard it would be to cause trouble.

Limiting themselves to the here and now (‘we concern ourselves solely with the vulnerabilities in today’s commercially available automobiles’), they tell, in professionally dull, let’s-remember-we’re-engineers fashion, how they conducted an experimental reign of terror: ‘We have demonstrated the ability to systematically control a wide array of components including engine, brakes, heating and cooling, lights, instrument panel, radio, locks, and so on. Combining these we have been able to mount attacks that represent potentially significant threats to personal safety. For example, we are able to forcibly and completely disengage the brakes while driving, making it difficult for the driver to stop. Conversely, we are able to forcibly activate the brakes, lurching the driver forward and causing the car to stop suddenly.’

They played other sorts of dangerous tricks, too, with the greatest of ease. At their behest, speeding cars shot windscreen-washing fluid continuously, popped the trunk, blared the horn, and, in a grim sense, had a high old time.

The study focuses on cars. But indirectly, it foresees the day when our very toasters and teapots might turn or be turned against us. On that question there is mystery, if not much dread, in part because there’s little publicly available research about the threat of hijackable household appliances. In 1996, security experts based partly at the RAND Corporation wrote a report called ‘Information Terrorism: Can You Trust Your Toaster?’ Mainly they (1) recommend hiring lots of ‘information warriors’, but warn that (2) law enforcement agencies sometimes squabble, and so (3) ‘information terrorists’ could inflict damage ‘in the time it takes to argue about whose job it is to respond’. More mundanely, Austin Houldsworth of the Royal College of Art in London created what may be the world’s most dangerous teapot, and the quickest. Houldsworth tells how it works: ‘The heating elements within the kettle contain thermite, which ... burns at 2500 degrees.’ (See it in action at http://vimeo.com/5043742.)

Koscher, Karl, Alexei Czeskis, Franziska Roesner, Shwetak Patel, Tadayoshi Kohno, Stephen Checkoway, Damon McCoy, Brian Kantor, Danny Anderson, Hovav Shacham, and Stefan Savage (2010). ‘Experimental Security Analysis of a Modern Automobile.’ Paper presented at the 2010 IEEE Symposium on Security and Privacy, Berkeley, Calif., 16–19 May, http://www.autosec.org/pubs/cars-oakland2010.pdf.

Dress Stress Engineering

Charles Seim is project engineer of the Gibraltar Bridge, the somewhat whimsically proposed megagigantic structure that would join Spain and Morocco, spanning a distance of five miles across the Strait of Gibraltar. He prepared for this perilous task, early in his career, by writing a report entitled ‘Stress Analysis of a Strapless Evening Gown’.

‘Effective as the strapless evening gown is in attracting attention’, Seim wrote in 1956, ‘it presents tremendous engineering problems to the structural engineer. He is faced with the problem of designing a dress which appears as if it will fall at any moment and yet actually stays up with some small factor of safety.’

The study includes two technical drawings. The first is a front view of the torso of a woman wearing a strapless gown. It will be familiar in kind, if not in all its details, to anyone who has studied physics on any level.

Seim’s prose fleshes out the fine points. Here is a typical passage: ‘If a small elemental strip of cloth from a strapless evening gown is isolated as a free body in the area of plane A in Figure 1, it can be seen that the tangential force F1 is balanced by the equal and opposite tangential force F2. The downward vertical force W (weight of the dress) is balanced by the force V acting vertically upward due to the stress in the cloth above plane A. Since the algebraic summation of vertical and horizontal forces is zero and no moments are acting, the elemental strip is at equilibrium.’

Figure 2 offers a detailed side view of the bust. Seim uses it to illustrate the kind of daunting technical challenge that good engineers relish. His prose brings vivacity to the spare draftsmanship and simple mathematical notation. This is how he introduces the chief difficulty posed by the upper surface of the breast: ‘Exposure and correspondingly more attention can be had by moving the dress line from a toward b. Unfortunately, there is a limit stress defined by S = F/2A (A being the area over which the stress acts). Since F/2 is constant, if the area A is decreased, the bearing stress must increase. The limit of exposure is reached when the area between b and c is reduced to a value of “danger point”.’

Over the past fifty years, Charles Seim’s concept of an engineering danger point has inspired many people to see the drama inherent in the analysis of tension, compression, stress, and strain. In 1992, it inspired an homage from jazz harpist and singer Deborah Henson-Conant, a five-movement orchestral composition called Stress Analysis of a Strapless Evening Gown. Henson-Conant performs this technical gem regularly with symphony orchestras. Each time, she wears a well-engineered strapless evening dress, which she loves. Her hope is to keep it up.

Seim, Charles E. (1956). ‘Stress Analysis of a Strapless Evening Gown.’ The Indicator November.

Pecker Bang Analysis

While others tried to build a better computer or teapot or mousetrap, Julian F. V. Vincent, Mehmet Necip Sahinkaya, and W. O’Shea of the department of mechanical engineering at the University of Bath tried to build a better hammer. Unlike most previous hammer smiths, they studied woodpeckers. Why? Because to mechanical engineers, when they are in a certain frame of mind, a woodpecker is nature’s finest version of a hammer.

The trio published ‘A Woodpecker Hammer’ in a scholarly journal with the unwieldy name Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science.

There they begin with a nod to the Ig Nobel Prize-winning research of Dr Ivan Schwab of the University of California-Davis School of Medicine, who in 2002 wrote a monograph that explains why woodpeckers don’t get headaches. Schwab was fascinated by the mechanical properties of the woodpecker’s head – especially why its brain doesn’t homogenize during all that pummelling, and why its eyes don’t pop out of their sockets. The Bath scientists take a more holistic approach. They explore how the bird’s entire body, from head to toes, feathers included, effectively function as a simple mechanical tool for pounding wood.

Vincent, Sahinkaya, and O’Shea examined a green woodpecker (Picus viridis) that was in the terminal state known as ‘road kill’. They measured the remains using old-fashioned methods and also with X-ray equipment, thus determining the values for several parameters: head mass, body mass, and the relative lengths of the parts. Using these, and also video of a living, pecking woodpecker of similar size, the scientists estimated the bird’s head inertia, body inertia, neck stiffness, neck damping, and body spring stiffness. They wrote equations to describe a woodpecker’s motions as it moves through all phases of the drum-drum-drum-on-wood cycle. To keep the mathematics fairly simple, there were a few engineering simplifications. The woodpecker’s vertebrae and neck tendons together behave as a spring. The tree is, essentially, a stiff spring with a damper.

X-ray of a road-kill green woodpecker (top); schematic of woodpecker at work (bottom)

The study proudly proclaims an intended payoff from this research: ‘One of the reasons for studying the woodpecker was to derive a design for a lightweight hammer. It was reasoned that the woodpecker is a bird, therefore has to fly and therefore is constructed as light as possible. The mechanism, which has emerged as a result of the model reported here – momentum transfer from body to head of the woodpecker – has been used in the design of a novel hammer [in which a] rotating crank is connected by means of a rod to the casing, so that the motor plus its mounting oscillates about a central pin.’

Vincent, Sahinkaya, and O’Shea say their original intent was to use this hammer in space exploration, ‘where it has no net inertia until it comes in contact with an object’. But its first use, they confide, probably will be in dentistry.

Vincent, Julian F. V., Mehmet Necip Sahinkaya, and W. O’Shea (2007). ‘A Woodpecker Hammer.’ Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science 221 (10): 1141–7.

The Physics of Skulking and Falling Cats

Cats may skulk, and cats may fall – but no matter what they do, cats must obey the laws of physics. Scientists have tried repeatedly to figure out how they manage to do it.

At the extreme, physicists analysed what happens to a dropped cat. That’s a cat in free-fall, a cat hurtling earthwards with nothing but kitty cunning to keep it from crashing.

In 1969, T. R. Kane and M. P. Scher of Stanford University published their monograph ‘A Dynamical Explanation of the Falling Cat Phenomenon’. It remains one of the few studies about cats ever published in the International Journal of Solids and Structures. Kane and Scher explain: ‘It is well known that falling cats usually land on their feet and, moreover, that they can manage to do so even if released from complete rest while upside-down … numerous attempts have been made to discover a relatively simple mechanical system whose motion, when proceeding in accordance with the laws of dynamics, possesses the salient features of the motion of the falling cat. The present paper constitutes such an attempt.’

And what an attempt it is!

Kane and Scher neither lifted nor dropped a single cat. Instead, they created a mathematical abstraction of a cat: two imaginary cylinder-like chunks, joined at a single point so the parts could (as with a feline spine) bend, but not twist. When they used a computer to plot the theoretical bendings of this theoretical falling chunky-cat, the motions resembled what they saw in old photographs of an actual falling cat. They conclude that their theory ‘explains the phenomenon under consideration’.

In 1993, a professor at the University of California, Santa Cruz, applied some heavier-duty mathematics and physics tools to the same question. Richard Montgomery’s study, called ‘Gauge Theory of the Falling Cat’, leaps and bends across twenty-six pages of a mathematics journal. Then it mutters that ‘the original solutions of Kane and Scher [are] both the optimal and the simplest solutions’.

But cats rarely fall from the sky. More commonly, they skulk. On the ground. And skulking cats are just as provocative, to a physics-minded scientist, as plummeting cats.

In 2008, Kristin Bishop of the University of California, Davis, together with Anita Pai and Daniel Schmitt of Duke University in North Carolina, published a report called ‘Whole Body Mechanics of Stealthy Walking in Cats’, in the journal PLoS One.

They studied six cats, three of which ‘were partially shaved and marked with contrasting, non-toxic paint to aid in kinematic analysis’. They discovered ‘a previously unrecognised mechanical relationship’ between ‘crouched postures’, ‘changes in footfall pattern’, and the amount of energy needed to produce those crouched-posture footfall patterns.

Cats that intend to skulk, in Bishop, Pai, and Schmitt’s view, are hemmed in by the laws of the physical universe. They must make ‘a tradeoff between stealthy walking’, which uses a lot of energy, and plain old, energy-efficient cat-walking.

Kane, T. R., and M. P. Scher (1969). ‘A Dynamical Explanation of the Falling Cat Phenomenon.’ International Journal of Solids and Structures 5: 663–70.

Montgomery, Richard (1993). ‘Gauge Theory of the Falling Cat.’ Fields Institute Communications 1: 193–218.

Bishop, Kristin L., Anita K. Pai, and Daniel Schmitt (2008). ‘Whole Body Mechanics of Stealthy Walking in Cats.’ PLoS One 3 (11): e3808.