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August 21, 2023

Mothers shouldn't have favorites, but Mother Nature is partial to designs that exhibit simplicity and symmetry. Common non-biological examples would be the the symmetry of crystals and snowflakes, a consequence of the angles of atomic bonds. Symmetry also abounds in the biological world, as the mostly mirror symmetry of the human body demonstrates. Biological symmetry occurs more often than expected, and a recent study published in the Proceedings of the National Academy of Sciences suggests that this is a consequence of genetic efficiency.[1-2]

Researchers ran an evolutionary computer simulation on a protein cluster with 13,079,255 possible structure shapes for which just five shapes had the symmetry of a square. There would be a five in thirteen million chance of evolutionary forces selecting a square, but the evolutionary algorithm returned a square 30% of the time.[1-2] The conjecture is that it's easier to have a process repeat a simple instruction multiple times than having a detailed and more complex process. The basis of this conjecture is algorithmic information theory.[1-2]

Physics has multiple examples of symmetry, most being too difficult to easily explain, that have lead to important discoveries, such as the Omega-minus (Ω-) particle. The Ω- was discovered at Brookhaven National Laboratory in 1964. This discovery confirmed the 1961 theory of the quark model by American physicist Murray Gell-Mann (1929-2019) and Israeli physicist Yuval Ne'eman (1925-2006). The quark theory proposed the classification of hadrons through a symmetry named SU(3). Gell-Mann was awarded the 1969 Nobel Prize in Physics for his work.

Baryon decuplet

A baryon decuplet of Delta (Δ), Sigma (Σ), Xi (Ξ), and Omega (Ω) baryons.

This is a nice graphical example of symmetry in physics.

In this illustration, Q is electric charge and S is strangeness.

(Created using Inkscape, and also at Wikimedia Commons. Click for larger image.)

Leon Chua, famous for his eponymous chaotic oscillator circuit,[3] discovered a symmetry in passive electrical devices that led to discovery of a new circuit element, the memristor.[4] This device complements the trio of traditional passive devices, the resistor, the capacitor and the inductor. The memristor is simply a device with resistance that depends on current flow. Its resistance increases when current flows through it in one direction, and decreases when current flows through it in the other direction. A memristor exhibits non-volatility in that it remembers its most recent resistance when current is removed.

Passive electrical circuit elements

The four passive electrical circuit elements are defined by the following equations:

Resistor: dv = R⋅di
Capacitor: dq = C⋅dv
Inductor: dφ = L⋅di
Memristor: dφ = M⋅dq

in which v is the voltage, i is the current, φ is the magnetic flux, and q is the electric charge. R, C, L and M are the resistance, capacitance, inductance and memristance, respectively.

(Created using Inkscape, and also at Wikimedia Commons. Click for larger image.)

The first actual device to be named a memristor was described in a 2008 paper in Nature.[5] However, this Hewlett Packard device acts by ionic migration in a 5 nanometer film of titanium dioxide and not the faster, and more useful, electromagnetic effect involving magnetic flux.[5] Although Chua changed his view of memristors to conform to such devices, there was immediate controversy about whether the memristor had actually been discovered.[6] I personally believe that a true memristor is yet to be discovered.

In a chapter in a 2013 book, Jean-Marc Ginoux and Bruno Rossetto of the Universitè du Sud (La Garde Cedex, France) discuss a 19th century device that they suggest was the first memristor.[7] While this device, the singing arc of William Du Bois Duddell (1872-1917),[8] has some properties analogous to those of a memristor, their argument is not quite convincing to me.

The <em>singing arc</em> of William Du Bois Duddell (1872-1917).

The singing arc of William Du Bois Duddell (1872-1917).

In graduate school, I suppressed the electromagnetic interference of arcing relay contacts in a high temperature furnace controller by using a similar circuit.

(Created using Inkscape. Click for larger image.)

The invention of the singing arc was devised as a solution to the practical problem that carbon arc lamps used for lighting before the introduction of practical incandescent light bulbs emitted an annoying hissing sound.[7] In 1899, Duddell, a physicist, was commissioned by the British government to find a way to stop this noise.[7] He found that the addition a capacitor and inductor as a tuned circuit produced a musical tone.[7] As Duddell wrote,

"A direct-current arc of suitable length and current between solid carbons, will give out a musical note if it be shunted with a condenser in series with a self-induction..."[8]

It was found subsequently by Danish engineer, Valdemar Poulsen (1869-1942) that selected values of these produced radio waves, and this arc circuit was used in wireless communication for several decades.[7]

Ginoux and Rossetto write that the voltage-current characteristic curve of the singing arc can be expressed by the same hyperbolic function as a memristor, and both devices exhibit a closed loop hysteresis.[7] For those reasons, they conclude that the singing arc could be considered to be the oldest memristor.[7]


  1. Iain G. Johnston, Kamaludin Dingle, Sam F. Greenbury, Chico Q. Camargo, Jonathan P. K. Doye, Sebastian E. Ahnert, Ard A. Louis, "Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution," Proceedings of the National Academy of Science, vol. 119, no. 11 (March 11, 2022), Article no. e2113883119, https://doi.org/10.1073/pnas.2113883119.
  2. Nature prefers symmetry and simplicity, Oxford University Press Release, 31 March 31, 2022.
  3. T. Matsumoto, "A chaotic attractor from Chua's circuit," IEEE Transactions on Circuits and Systems, vol. 31, no. 12, (December, 1984), pp. 1055-1058, DOI: 10.1109/TCS.1984.1085459.
  4. Leon O. Chua, "Memristor - The Missing Circuit Element," IEEE Transactions on Circuit Theory, vol. 18, no. 5 (September 1971), pp. 507-519.
  5. Dmitri B. Strukov, Gregory S. Snider, Duncan R. Stewart, and R. Stanley Williams, "The missing memristor found," Nature, vol. 453 (May 1, 2008), pp. 80-83, https://doi.org/10.1038/nature06932.
  6. Sascha Vongehr, "Missing the Memristor," Advanced Science Letters, vol. 17, no. 1 (October 1, 2012), pp. 285-290, https://doi.org/10.1166/asl.2012.4241. Also at Sascha Vongehr, "The Missing Memristor: Novel Nanotechnology or rather new Case Study for the Philosophy and Sociology of Science?" arXiv, March 1, 2012, https://doi.org/10.48550/arXiv.1205.6129.
  7. Jean-Marc Ginoux and Bruno Rossetto, "The Singing Arc: The Oldest Memristor?" in Chaos, CNN, Memristors and Beyond, pp. 494-507 (World Scientific Publishing, 2013), https://doi.org/10.1142/9789814434805_0040. Also at Jean-Marc Ginoux and Bruno Rossetto, "The singing arc: the oldest memristor?," arXiv, August 21, 2014, https://doi.org/10.48550/arXiv.1408.5103.
  8. W. Du Bois Duddell, "On Rapid Variations in the Current through the Direct-Current Arc," Journal Inst. Elec. Eng., vol. 30 (December 13, 1900), pp.232-283.

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