I am not that old, I think. Well, yet. However I am old enough to remember some old days when many groceries were purchased in bulk at the local shop around the corner. That was indeed the case for pasta, rice, beans, lentils, and in general all dry foods; wine and oil were also obtained from the counter by bringing in your own bottles to refill; meat and fish were chosen and hand-picked, usually after a long discussion with the shop owner that could also include updates about recent family matters on both sides, and packed in a thick brown paper; we called it “straw-paper” because it was so rough that you could see straw specks in the fabric, and this paper was kept and recycled, since very good to absorb any grease produced in the kitchen. At home, I remember my grandmother grabbing in her hands a bunch of spaghetti enough for the six or seven people that got at the table at lunchtime. Spaghetti at that time were much longer than the standard 25 cm of today, actually they were twice that length or more, and they needed to be cut in half to be cooked in a normal size pot of hot water. My grandmother squeezed the bunch of spaghetti with both hands near the middle, leaving a few centimeters gap between her clenched fists, and energically turned both hands clockwise, while breaking in half the thick bunch with a twisting-bending gesture. All spaghetti got split perfectly in half in that swift move, only every now and then you could see a few small debris floating in the boiling pot.

One evening Richard Feynman was having dinner with his friend Danny Hillis, the founder of Thinking Machines Corporation and inventor of the first massively parallel supercomputer (a project that he did for his PhD thesis…!). They wanted to cook spaghetti following some strange recipe that Hillis had just invented, but while preparing the pasta they started noticing that raw spaghetti when folded split into several parts, usually three or four, rather than simply breaking in two. According to Danny, who told the story in a 1993 TV program, they spent a couple of hours in making experiments, trying to put spaghetti underwater or cutting at different places, only to find themselves with the floor covered in spaghetti fragments without getting any sensible physical explanation for the weird phenomenon, to the scorn of Feynman who could not make up even an approximate theoretical model.

After Feynman-Hillis never-published efforts, however, Basile Audoly and Sebastien Neukirch in UPMC Jussieu quite seriously took over the question, and in 2005 they published the results of their research in PRL  (“Fragmentation of rods by cascading cracks: why spaghetti do not break in half”,  https://doi.org/10.1103/PhysRevLett.95.095505 ). Besides being generally correct, their results were so nicely fun that the two scientists were also awarded a Physics IgNobel Prize in 2006. In the work, the authors studied theoretically and experimentally the dynamics of a thin elastic rod held at one end, quasi-statically bent and suddenly released. They found that the sudden relaxation of the curvature at the new free ends produced by the initial break, leads to a burst of flexural waves that locally increase the curvature in the rod, that is, an increase in mechanical stress. The multiple breakage of bent rods, as it happens with dry spaghetti, can therefore be understood as a cascade succession of cracks followed by increases in stress, that lead to new cracks. The math behind the Audoly-Neukirch discovery is based on the Kirchhoff equations for elastic bars; when released, the spaghetti is subjected to three regimes in succession: 1) the released end quickly straightens, which causes 2) the generation of bending waves, which, in turn, travel along the spaghetti until the only fixed end, where 3) they are reflected and amplified, thereby leading to multiple breaks. Carefully done experiments confirmed the theoretical findings, and the IgNobel was theirs to enjoy.

But years later, there was still one point to clarify: once the physics behind this bizarre phenomenon is understood, would it be possible to put it under full control and eventually break one long spaghetti into exactly two pieces? That would be a meaningful problem, since the structural stability of elastic rods is ubiquitous in both natural and man-made materials, performing important physical and biological functions across a wide range of length and time scales. From Greek temple columns, trees and animal bones, to the legs of water striders, semiflexible polymer networks, and carbon nanotube composites, when placed under extreme stresses, the structural stability of such materials becomes ultimately limited by the fracture behavior of their individual fibrous or tubular constituents. Advances in video microscopy and microscale force manipulation have extended the scope of fracture studies to the microworld, revealing causes and effects of structural failure in the axonal cytoskeleton, fibroblasts, bacterial flagellar motors, active liquid crystals, and multiwalled carbon nanotubes.

Well then, it seems the answer to the fracture control could be “yes”, even if it took several years of work, a complicated experimental apparatus, and the commitment of no less than an entire team of MIT physicists. According to a reconstruction with interviews published by the Washington Post, the MIT graduate students Ronald Heisser and Edgar Gridello had been breaking spaghetti for about two months. They had taken on Feynman’s spaghetti enigma as a final project for a class. With the help of another friend, Vishal Patil, and using some more mathematical modeling, a one-of-a-kind spaghetti breaking machine, and a high-tech camera that can capture up to a million frames per second, the three students turned what began as a class project into the latest revelation for a famed puzzle. Once joined by the colleagues Norbert Stoop, Emmanuel Villermaux, and Jörn Dunkel their success was reported in the August 2018 issue of PNAS (“Controlling fracture cascades through twisting and quenching”, https://doi.org/10.1073/pnas.1802831115; the online paper also contains a number of beautiful videos of breaking spaghetti taken from the high-frame-rate camera).

The MIT researchers studied the breaking phenomenon by designing a machine that can simultaneously bend and rotate thin rods like spaghetti, under the fast camera. The highest time-resolution data show that already a basic fracture event involves several timescales, from initial crack nucleation and growth, to the catastrophic failure. The initial nucleation phase is relatively slow, lasting about 10 ms, and is followed by a fast catastrophic phase in the range of tens of microseconds, during which the cracks propagate rapidly at velocities close to the material speed of sound. However, when the bending of a thin spaghetti that has also been rotated by a large amount (even up to 360 deg) brings it to the breaking point, the flexural waves that are generated (as in the Audoly-Neukirch solution) are in fact dissipated with the rotational movement that brings the two fragments back to the initial torsion state. In practice, the rotational and flexural waves cancel each other out, avoiding new fractures and leaving just two fragments of spaghetti in our hands.

As for the mathematical model, they used again Kirchhoff’s theory but including also twisting and damping effects. The most refined of my dear readers (I know there are well-trained and sophisticated mathematicians among you J) may notice that coupled shear effects should also be included, as described in Timoshenko’s beam theory. According to the authors of the PNAS study, shear-coupling effects can be neglected in this case, since the form factor (diameter/length) of spaghetti is vanishingly small. The MIT model proved to be accurate in predicting the behavior of different varieties of spaghetti used in the experiments, specifically the Barilla N.5 and Barilla N.7, which have slightly different diameters). For other types of long pasta, however, things get more complicated. Linguini, for example, are very different, resembling more to a narrow flat stripe; the model only applies to ideally cylindrical bars, and even if commercial spaghetti do not have a perfectly regular shape, the theory manages to capture their behavior quite well. Further research therefore will be needed, to properly break linguini, bucatini, tagliatelle and pappardelle.

Well, lunchtime is approaching. But if everything that was needed were a bit of a twist, I must say my grandmother had solved the problem many years back already.

Feynman’s spaghetti sauce

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