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Kai Ryssdal and Maria Hollenhorst, "What a magnetized iron screwdriver can teach us about the post-COVID economy", NPR Marketplace 12/2/2020:

There’s a scientific demonstration you may have seen in grade school, in which an iron nail or screwdriver is transformed into a temporary magnet by striking it repeatedly with an actual magnet. It demonstrates “hysteresis,” a term meaning “delayed” or “lagging behind” in both physics and economics. We won’t delve deeply into the science of why that works here, but the concept itself is important to understanding the economic damage caused by COVID-19.

“If you’re holding a piece of iron, the piece of iron itself is not likely to be magnetized,” said Elizabeth Green, a condensed-matter physicist at the National High Magnetic Field Laboratory in Tallahassee, Florida. “But when we do start applying an external parameter, in this case, an external magnetic field, we can start magnetizing this piece of iron, and if we remove that external field, the iron will still remain magnetized.”

It shows how once a piece of iron has been magnetized by something external, it will remain magnetized even when the thing that caused the change is gone. “Nature is lazy,” Green said. “It likes to stay in a particular state, it does not like change. So when we change the direction of this external field, what happens is everything lags behind.”

Perhaps thanks to this piece, the question of what hysteresis is, anyway, has been batted around on social media recently.

One of the tweets, by James Munns, gets to the point much more clearly than the Marketplace magnetism business does:

The OED defines hysteresis as "A phenomenon, observed in some physical, biological, and ecological systems, in which changes in a property lag behind changes in the agent or influence which causes them; esp. one for which the response of the property depends not only on the current state of the system, but also the states it has previously occupied."

My favorite example of hysteresis is not from magnetism or economics or electronics, but from phonetics. It explains why small, gradient changes in articulatory control sometimes turn into large, quantal differences in acoustical output. One notable example is from voicing, where the larynx exhibits two qualitatively different states. In one state the vocal folds are moved apart — "abducted" — so that air can pass freely from the lungs out through the superglottal vocal tract. In the other state, the vocal folds are moved together — "adducted" — so as to block the flow of air; but pressure builds up behind the seal, forcing the flexible tissue apart, and releasing a flow of air. The resulting flow generates Bernoulli forces, which pull the vocal folds together again, recreating the seal; and the process repeats, generating the oscillatory flow that we perceive as "voicing" (and pitch). (Here's a video showing the larynx changing state; and another one showing the voiced state in slow motion.)

In order to articulate a voiceless consonant in between two voiced vowels, obviously the vocal folds need to be moved apart and then moved together again. This opening-and-closing gesture can be stronger (and longer) or weaker (and shorter). As the vocal folds move apart, they continue their oscillation until the opening reaches a certain threshold, at which point the oscillation stops. And as they come together again, there's another threshold at which the oscillation starts again. But these two change-of-state thresholds are different — the value depends on the history — hence hysteresis. The threshold at which oscillating vocal folds stop oscillating as they move apart (labelled Threshold 1 below, in red) is different from the threshold at which open vocal folds start oscillating as they move together (labelled Threshold 2 in green).

Schematically, it looks something like this:

This creates a quantum jump in the duration of the devoiced region — if it happens at all, it happens for a certain minimal amount of time:

As a result, gradual lenition (= weakening) of the voiceless consonant can result in a quantal shift to a complete loss of voicelessness — the voiceless consonant becoming voiced — not because there's been a quantal change in the underlying articulation, but because of this non-linearity in the mapping from articulation to sound. This is surely the history, and maybe the current reality, of (the voicing part of) American English "flapping and voicing" of intervocalic non-syllable-initial /t/.


  1. Robot Therapist said,

    December 5, 2020 @ 4:20 am

    My own preferred example of hysteresis may date me. With early rotational dimmer switches for domestic lights, the mapping from rotational position to brightness was quite different when turning up and when turning down. So to get a low level of lighting, you couldn't just "fade up", you had to turn it up high then fade down. I imagine what with bluetooth and LED bulbs and AI, that will all have been fixed now.

  2. Jerry Friedman said,

    December 5, 2020 @ 11:28 am

    When I tell my physics students about hysteresis, I tell them that some scientists and engineers like to use it in other contexts, but maybe it has escaped or it's escaping to the fadosphere.

    I always mention that it's not etymologically related to "history". I may have added that it's related to "hysteria" and "hysterectomy", but that's apparently wrong too.

  3. Gregory Kusnick said,

    December 5, 2020 @ 3:18 pm

    The bimetal "jumping disks" sold in my youth by Edmund Scientific provided a fun demonstration of hysteresis. Warm one between your hands and its slight curvature flips from concave to convex. Set it down and let it cool to room temperature and it spontaneously snaps back, sending it flying into the air. Between the two critical temperatures its shape depends on how it got there.

  4. Garrett Wollman said,

    December 5, 2020 @ 10:25 pm

    The canonical example of hysteresis for me has always been thermostats. You wouldn't want a thermostat to turn the heat on and off at exactly the same temperature, because that would cause wasteful and frequent cycling. So instead you have a window of a few degrees, and turn the heat on when the ambient temperature crosses the low threshold and turn the heat off when the temperature crosses the high threshold. (In Fahrenheit units, typically four or five degrees.) This is effectively a low-pass filter, but it's one that can be implemented mechanically in a bimetallic strip, no fancy logic required. (The classic round Honeywell thermostat does this, implemented using a glass bulb partially filled with mercury at the end of a coiled bimetallic strip: the mercury, which serves as the actual switch, provides the hysteresis.)

  5. Jerry Friedman said,

    December 6, 2020 @ 12:02 am

    Gregory Kusnick and Garrett Wollman: The discontinuous changes in those jumping disks and thermostats seem especially similar to Prof. Liberman's example of voicing and devoicing.

    However, the one and only canonical example of hysteresis is the phenomenon the word was coined for (according to the OED), namely ferromagnetism. In my humble opinion.

    Off-topic: I like Elizabeth Green's explanation, but her generalization that "Nature is lazy" and "does not like change" is very dubious. For instance, paramagnetic materials and diamagnetic materials, which there are a great many of, have no hysteresis in their response to an applied magnetic field.

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