Aristotelian aerosols?

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Kasha Patel, "Covid-19 may have seasons for different temperature zones, study suggests", WaPo 1/28/2022:

Aerosol researcher and co-author Chang-Yu Wu explained that local humidity and temperature play vital roles in the size of the virus’s particles, which can influence its life span in the air. Drier atmospheres in colder regions will induce water evaporation from the particles, shrinking their size and allowing them to float in the air for longer periods. People also tend to seek shelter inside in colder environments and expose themselves to recirculated air that potentially contains the virus.

The air in humid, hotter environments contains more water, which can condense onto the virus particles, make them bigger and theoretically fall to the ground faster. Wu compares the particles to a rock in this case — the more mass, the faster it falls.

Readers who remember Galileo's Leaning Tower of Pisa experiment from long-ago science classes will find this explanation puzzling. As Wikipedia explains,

Between 1589 and 1592, the Italian scientist Galileo Galilei (then professor of mathematics at the University of Pisa) is said to have dropped two spheres of different masses from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass. […] According to the story, Galileo discovered through this experiment that the objects fell with the same acceleration, proving his prediction true, while at the same time disproving Aristotle's theory of gravity (which states that objects fall at speed proportional to their mass).

Dr. Wu was interviewed for background on the scientific paper that's featured in the article — Moiz Usmani, Yusuf Jamal, Mayank Gangwar, Bailey Magers, Juan Chaves-Gonzalez, Chang-Yu Wu, Rita Colwell, and Antarpreet Jutla, "Asymmetric Relationship between Ambient Air Temperature and Incidence of COVID-19 in the Human Population", The American Journal of Tropical Medicine and Hygiene, 2022.

The effect of temperature and humidity on the "aerosolization of virus" is a key concept in that paper:

But the scientific publication, needless to say, has nothing like the WaPo's "the more mass, the faster it falls" explanation.

The Wikipedia article on aerosols tells us that "Particle size has a major influence on particle properties, and the aerosol particle radius or diameter (dp) is a key property used to characterise aerosols", but does not suggest (for good reasons!)  that the mass of the individual particles plays an Aristotelian role in aerosolization. It's true that an increase in the size of a particles means an increase in its mass, but that's not why smaller-particle aerosols are more durable. And the analogy to the falling rate of different-sized rocks is a double failure, since the different-sized rocks will fall at the same rate.

(Well, small effects due to air resistance aside. I have a vivid memory of discussing that very aspect of Galileo's legendary experiment with Dick Oehrle, as an undergraduate, while eating lunch in a diner.  A brilliant physicist, then employed at the Harvard Observatory, overheard us. She intervened, introduced herself, and scrawled equations on three or four napkins to calculate exactly what the effect would be on rocks of different plausible sizes over leaning-tower-ish distances. The estimated effects of course were very small — and not dependent on the difference in mass, at least for objects of rock-like density.)

As often in the interpretation of reported interviews in news articles, the WaPo article leaves us with a problem in abductive reasoning. Did the interviewee really say that? or did the writer (or one of their editors) misunderstand, misremember, or invent it?



  1. Theophylact said,

    January 30, 2022 @ 10:15 am

    Air resistance has a far greater effect on small particles than on rocks. Stokes' Law quantifies the effect.

    [(myl) Sort of. The Wikipedia article on aerosols continues:

    For low values of the Reynolds number (<1), true for most aerosol motion, Stokes' law describes the force of resistance on a solid spherical particle in a fluid. However, Stokes' law is only valid when the velocity of the gas at the surface of the particle is zero. For small particles (< 1 μm) that characterize aerosols, however, this assumption fails. To account for this failure, one can introduce the Cunningham correction factor, always greater than 1.


  2. Giles said,

    January 30, 2022 @ 10:28 am

    "[S]mall effects due to air resistance aside" is the relevant bit here. Aerosol particles are so small that those effects are no longer something you can disregard. With larger rocks of roughly the same size as each other, it might be irrelevant, but imagine a "rock" so small that it's essentially a spec of dust — it would float on the breeze, gradually tending downwards. A slightly larger spec would tend downwards faster, while a pebble would, um, plummet like a rock.

    [(myl) Indeed — but again, it's not helpful to compare aerosol particles to rocks, and assert that "the more mass, the faster it falls". That's exactly the Aristotelian theory of gravity that Galileo aimed to disprove. And I'm skeptical that "Aerosol researcher and co-author Chang-Yu Wu" believes in Aristotelian gravity…]

  3. MattF said,

    January 30, 2022 @ 10:54 am

    Note, btw, that a Reynold’s number < 1 is quite a small Reynold’s number. Since the Reynold’s number is the ratio of inertial to frictional forces, it means that frictional forces on the particle are -larger- than inertial forces.

  4. MattF said,

    January 30, 2022 @ 11:10 am

    And ‘Reynolds’ doesn’t have an apostrophe.

  5. Gregory Kusnick said,

    January 30, 2022 @ 11:19 am

    Don't forget David Scott's feather v. hammer drop on the moon.

  6. Jerry Friedman said,

    January 30, 2022 @ 11:41 am

    The best I can do for Wu is to point out that even for rocks, heavier ones have higher terminal velocities.

    It's not that bad an approximation that falling objects accelerate at the same rate (the acceleration of gravity) till they reach terminal velocity, then stop accelerating. Using that, what are the mass and radius of a sphere of marble (density about 260 kg/m^3) dropped from the Leaning Tower that reaches its terminal velocity as it hits the ground? I'm getting a mass of 0.7 kg and a radius of 9 cm. So a piece of marble significantly smaller than that will feel a significant effect of air resistance.

    Whether you call that a rock may depend on your variety of English—I understand that for many Britons, a "rock" is too heavy to throw (except for Ajax), whereas many of us Americans have experienced the discomfort of a rock in our shoe. OK, that's a bit misleading, since we probably wouldn't call it a rock if it weren't in our shoe, but we do comfortably talk about throwing rocks.

    By the way, many rocks are denser (a lot of my students would say "more dense") than marble, so the dropped object would need to be smaller to be affected by air resistance.

    Sorry, I blew a perfect opportunity to use calculus in talking about pebbles.

  7. JosefE said,

    January 30, 2022 @ 11:45 am

    Or Frank Anstice’s (with apostrophe) piece of paper on the back of a coin drop

  8. Jerry Friedman said,

    January 30, 2022 @ 12:00 pm

    I'll add that if you want to imagine dropping the lithic object from 1.7 m, a height most people can reach without climbing a tower, the analogous mass is 20 mg and the radius is 2.6 mm, so we're approaching speck territory.

  9. tangent said,

    January 30, 2022 @ 12:05 pm

    I think people get that Aristotle was wrong about rocks and that a rock-based explanation is busted here, but are questioning where you're going with "It's true that an increase in the size of a particles means an increase in its mass, but that's not why smaller-particle aerosols are more durable."

    The lower mass does cause smaller particles in air to have slower gravitational settling. "The more mass, the faster it falls" is accurate within the aerosol and droplet regime Dr. Wu works in.

    My suspicion is that the reporter had that fact, and when Dr. Wu described "in this case" heavier particles as falling more like rocks: "The air in humid, hotter environments contains more water, which can condense onto the virus particles, make them bigger and theoretically fall to the ground faster. Wu compares the particles to a rock in this case …" — inserted the true and conceptually relevant fact in a textually bad way.

  10. Roscoe said,

    January 30, 2022 @ 3:16 pm

    Or the scene in the film version of "Rosencrantz and Guildenstern are Dead" where Rosencrantz drops a feather and a rock at the same time: "You would think that this would fall faster than this, wouldn't you?…And you'd be absolutely right."

  11. "A Rock ... — the More Mass, the Faster It Falls" - Fast trendings news said,

    January 30, 2022 @ 3:26 pm

    […] Prof. Mark Liberman (Language Log) notes this from the Washington Post Friday: […]

  12. "A Rock ... — the More Mass, the Faster It Falls" - TRUE NEWS AND REAL NEWS said,

    January 30, 2022 @ 3:45 pm

    […] Prof. Mark Liberman (Language Log) notes this from the Washington Post Friday: […]

  13. Jerry Friedman said,

    January 30, 2022 @ 5:05 pm

    tangent: I agree that nothing is wrong with the excerpt article except "compares the particles to a rock in this case—the more mass the faster it falls" (and some wording peeves, such as "shrinking their size"). And I agree with you and MYL that Wu isn't necessarily to blame, so I shouldn't have said he was.

  14. Jerry Friedman said,

    January 30, 2022 @ 5:06 pm

    And if anyone wants more realistic numbers about dropping rocks off the Leaning Tower, I can provide them, if I haven't made any mistakes.

    *excerpt from the article

  15. Bloix said,

    January 30, 2022 @ 6:12 pm

    Not just air resistance. Anyone who has seen dust motes floating in a ray of sunlight coming through a window has seen how small objects can stay aloft indefinitely, held up by a rising column of air that has been heated by the sun. Similarly, the slightest current of air will push smaller virus-contaminated particles up and away from the person breathing them out, even as heavier particles gently coast down to the ground.

  16. RfP said,

    January 30, 2022 @ 7:14 pm

    Along the lines of the comment from Bloix, doesn’t Brownian motion gradually supplant gravitational effects as size diminishes?

  17. J.W. Brewer said,

    January 30, 2022 @ 8:08 pm

    The plausible rehabilitation of Aristotelian physics as applied to non-rock dust motes rather than actual rocks does not fit very well with the actual sentence: "Wu compares the particles to a rock in this case — the more mass, the faster it falls." Either Prof. Wu did not actually make that comparison and has been badly misrepresented by the journalist Ms. Patel, or Prof. Wu did make that comparison and is a refreshingly old-school Aristotelian, and/or has a pop-Kuhnian explanation ready to go that neither Aristotle nor Galileo/Newton is actually "right" in any objective sense here.

  18. Mildred Bonk said,

    January 30, 2022 @ 10:05 pm

    I thought this was Language Log, not Bullying Scientists for Trivial Errors in News Reports on Their Research Log.

  19. Andrew Usher said,

    January 31, 2022 @ 8:11 am

    Why would you not assume the journalist is to blame? It's been a frequent topic of posts here how the media are sloppy and distort science by that and ignorance rather than by intent. The sentence does not pretend to be a direct quote; and the most likely explanation has already been given: he said that heavier particles settled faster (true and uncontroversial) and made some mention of rocks, but did not explicitly say _of rocks_ 'the more mass, the faster it falls', though the article makes it seem so.

    There are obvious spam comments above that should be removed.

    On the concept of dropping weights from the tower, I remember having heard that that human being unconsciously compensates for air resistance by, if one object is held in each hand as usual, releasing the lighter first because the muscles are more able to.

    k_over_hbarc at

  20. Seth said,

    January 31, 2022 @ 10:24 am

    I think the intended point could have been put in snappy way as "In the air, the small particles act more like feathers, while the larger particles act more like rocks.".

    A plausible real-world analogy: Imagine a leaf falling off a tree on snowy day. If there's a lot of snow on the leaf, it'll tend to fall faster than if there is no snow on the leaf (not of course because of mass effect vs gravity in general, but because the atmospheric effects are significant here).

  21. Dara Connolly said,

    January 31, 2022 @ 4:07 pm

    Whether you call that a rock may depend on your variety of English—I understand that for many Britons, a "rock" is too heavy to throw (except for Ajax), whereas many of us Americans have experienced the discomfort of a rock in our shoe. OK, that's a bit misleading, since we probably wouldn't call it a rock if it weren't in our shoe, but we do comfortably talk about throwing rocks.

    I've noticed this difference in usage but never seen it remarked upon until today. One example is in a novel by John Irving where a character says "She threw rocks at you?", referring to pebbles from a gravel driveway. Another has a character (Tom) in the TV series "Succession" picking up a pebble on the beach and referring to it as a "sad rock" while throwing it into the sea.

    For me (Ireland) anything smaller than my fist is too small to be called a rock. However it's not the case that a rock is necessarily too heavy to throw. I would say that if someone threw pebbles at me, it would be extremely annoying, while if someone threw rocks at me it would be liable to cause serious injury.

  22. Philip Anderson said,

    January 31, 2022 @ 5:25 pm

    A rock is definitely bigger than a pebble (unless it’s a large diamond), but if it’s more than say fist size, smoothness and regularity become for me the primary distinction between rocks and stones – rocks are irregular, and may be an outcrop, whereas stones are more regular, whether naturally or worked (e.g. standing stones). Smaller than that, pebbles are rounder, normally water-worn, and stones are irregular, often sharp.

  23. Matt Sayler said,

    February 1, 2022 @ 7:40 pm

    "A rock is definitely bigger than a pebble" There's "a rock in my shoe," which could be a very tiny pebble, indeed.

  24. Philip Taylor said,

    February 2, 2022 @ 5:06 am

    Standing at the kitchen window this morning and idly scratching my eyebrows, I watched the motes of dead skin float gently to the floor. I then took a few grains of castor sugar and dropped them from the same height. The castor sugar fell at a rate of between five and ten times as fast as the motes of skin. In vacuo, of course, they would have fallen at exactly the same speed, but the SARS-CoV-2 virus, as far as we know, does not exist in vacuo, tho' it might well be capable of surving there, at least for a while..

  25. Jerry Friedman said,

    February 2, 2022 @ 10:51 am

    Philip Taylor: Did you time them with your pulse, like Galileo?

    If you'd dropped anything I can imagine you'd call a rock, it would have taken approximately the same time as any other rock to reach the kitchen floor from a given height, as air resistance would have a negligible effect. That's the basis of criticizing whoever said "the more mass [a rock has], the faster it falls." If they'd said it about grains of sugar or motes of dead skin, the comparison would have been valid.

  26. Bloix said,

    February 3, 2022 @ 6:23 pm

    The title of this post is "Aristotelian Aerosols."
    By definition, an aerosol is a particle or collection of particles suspended in a gas (usually air, hence the name). Fog is an aerosol. We are not troubled when we see fog rising, as we don't expect it to fall under the force gravity. Similarly, a corona-virus-containing water droplet small enough to be an aerosol — under <5 μm, or 2 10,000ths of an inch, in diameter – is not expected to fall to the ground. A warm droplet emerging from a person's respiratory tract can float around indefinitely just as a fog can linger until the sun burns it off or the wind disperses it.

    Water droplets larger than aerosols – larger than 5 μm – do tend to fall unless there's a force carrying them upward – a breeze, or a rising warm current of air, or the force of a cough or sneeze. And the larger and heavier they are, the the sooner they will fall. Even in a vacuum, a person can throw a baseball farther than a cinder block.

  27. Jerry Friedman said,

    February 4, 2022 @ 11:17 am

    Bloix: I agree with everything in your post, but the last sentence is irrelevant to falling objects. A person can throw a baseball farther than a cinder block (British "breeze block"?) because they can't exert any more force on the cinder block than on the ball. (In fact, probably less, because most or all people can't use an effective throwing motion on a cinder block.) However, the Earth pulls the cinder block more strongly than it pulls a baseball, with the non-Aristotelian result that objects take the same time to fall as long as air resistance is unimportant.

  28. Philip Taylor said,

    February 4, 2022 @ 12:25 pm

    I mis-understood Bloix's assertion until Jerry clarified it, which leads me to ask a question based on my mis-understanding — in a zero-gravity vacuum, can a person throw a baseball farther than a cinder block ?

  29. Jerry Friedman said,

    February 4, 2022 @ 1:12 pm

    In a situation with no gravity or air resistance or other forces, anything you throw will keep going forever (Newton's First Law). You could throw a less massive object faster, but that's the only difference.

  30. Jerry Friedman said,

    February 4, 2022 @ 1:16 pm

    I should probably add that since people and objects people can throw have mass, there's no such thing as a truly zero-gravity environment in which someone throws something, so Newton's First Law doesn't really apply. For my statement above to be true, the gravity between the person and the object has to be negligible compared to the force the person exerts. It's actually good enough for the person to be able to give the object a speed relative to the person greater than escape speed. So no throwing planets.

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