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Small Rocks Do Occasionally Float; It Doesn't Make Me Wrong About Everything

by Eric Hall

August 24, 2015

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I was wrong. I am wrong often. As an educator of science, I try to be careful about avoiding speaking in absolute terms. When the rule holds a majority of the time, it is hard not to just say something is true, instead of saying it is true in most cases or under normal conditions. For example, Newton's Laws only work in an inertial frame of reference. We observe Newton's Laws working on Earth, yet Earth is not an inertial frame. But because it is close, we state the Earth is assumed to be an inertial frame because the effect is so small at the speeds and distances of everyday objects. I'll say more on this a little later in the post.

So what did I get wrong? In my post about oil pulling, I made a joke about small rocks floating. I included a link to a YouTube clip of the scene in Monty Python and the Holy Grail where the angry mob wants to burn a witch and they use bad logic to decide if the woman in question is a witch. When asked what else floats in water, one of the mob answers "very small rocks." While this is false in nearly every case, it is possible there is an exception, namely pumice.

Pumice is a very low density rock that forms in the expanding gas of magma in a volcano. Some of the stones can have large pockets of gas trapped inside relative to the size of the stone, thus making their average density less than that of water. Thus, the stone itself can float. They tend not to float forever, as the water eventually infiltrates the stone, and the mineral material, being denser than water, will cause it to sink.

In my attempt at humor, I made a flippant remark and a reference to a classic movie which resulted in an inaccurate scientific statement. I am not sure how I would have corrected it in my case. Because the humor is in the fact most rocks do sink in water, which is what makes it a funny line. When someone conjures an image of a rock thrown in a pond, we don't think of it as floating.

So, let me issue an apology for what might be taken as a misleading scientific statement. There are rocks that do float—even small ones.

What I also want to point out is a mistake such as that doesn't negate the entire article. I've pointed out in the past that I didn't score 100% on all of my exams as a graduate student. Does this mean I don't understand physics at any level? No, it simply means physics isn't always easy. It means we make mistakes on the path to learning. A positive discussion of errors and a sharing of information and new learning is the correct path.

Another example of these flippant statements, or uncouched statements as it were, is one of the Coriolis Effect. The basic concept here is that because the Earth is not a true inertial reference frame (its spinning), objects will be deflected as they move along or near the Earth's surface. For weather systems for example, this is why high pressure systems spin in a clockwise direction in the northern hemisphere, and counter-clockwise in the southern hemisphere (but not the only reason). However, at smaller distance scales, such as toilets or sinks, the Coriolis Effect is overshadowed by other forces being put on the fluid. You don't deflect off the road you are driving on because the frictional forces of the tires, wind, etc. are all much larger than the Coriolis Effect.

This leads to statements which can be misleading because we often leave them incomplete with an assumed understanding. A physicist might say you need something much larger than a sink or pool to see the Coriolis Effect. This is because the assumption is the inherent turbulence, leftover motion from filling the pool, air currents creating motion on the water, and all sorts of other variables would make it impossible to see the Coriolis Effect under normal circumstances.

However, as Destin Sandlin (from Smarter Every Day) showed us, we need to be more careful with those statements. In his video about the Coriolis Effect, he teamed up with Derek Muller from Veritasium to show that when one controls all of those variables, the effect can be seen even on the scale of a kiddie pool. He and Muller set up kiddie pools under controlled conditions, and allowed all of the motion of filling to settle out of the water (via friction), and they were able to verify that the Coriolis Effect works, even at a scale of a couple meters. This isn't unexpected, but it is a good reminder to be more thorough in explaining our assumptions being made when explaining a concept.

The real issue here is the rotational motion is due to the net force, both "real" forces and "apparent" forces due to the non-inertial frame of the earth. As Dr. Alistair Fraser explains on his webpage:

It is correct that the Coriolis force causes a moving object to experience a force to the right (left) of its path in the northern (southern) hemisphere. It is not correct that this necessarily produces a clockwise rotation. The direction of rotation (if any at all) depends upon the net force, not just a single force.

One must distinguish between the direction of deviation caused by the Coriolis force (operating on its own) and the direction of rotation (when other forces are present). Both directions of rotation are evident in both hemispheres depending upon the whether the flow is around a high pressure area (the pressure gradient force points radially outward) or around a low (the pressure gradient force points radially inward).In a geophysical flow, such as motion in the atmosphere or oceans, there is always some other force operating (such as the pressure gradient force) or how else would the material have started to move.

You can see more on the Bad Coriolis page about how small this effect really is.

Another good way to think about the scale of some effect is to do an order of magnitude calculation. As Dave Van Domelen explains:

How slow is slow enough? Well, a quick order of magnitude calculation can be used here. Figure that after the first second of draining a sink has gotten set in whichever way it's going to spiral down the sink... it only gets stronger after it starts moving (since the velocity towards the drain picks up). Figure an average particle is at a radius of ten centimeters from the drain, so a micron per second corresponds to about 2 microradians per second angular velocity that can be changed before things get out of hand. Or about 100000 seconds per rotation per day, roughly. Give or take an order of magnitude and one full rotation per hour is all the Coriolis Effect can reverse. Even take two orders of magnitude and you still can have water spinning at once every few minutes and still be spinning the "wrong" direction enough to ignore the Coriolis Effect and go down the sink its own way. This is certainly "not visibly moving."

So again, it isn't that the Coriolis Effect doesn't have an influence on small scales, we normally just ignore it due to size. And as best we can, we should always be clear on this.

So what happens when we make mistakes, whether by omission, by assumption, or simply by an honest error? We acknowledge them. Does it mean that person's entire body of work is invalid? No. Just like someone's education, experience, past publications, etc., these are all things that should be used to evaluate someone's next publication. Maybe you will look a little more closely at the next thing they write or say. Errors do not invalidate someone's previous or future work. How the errors are handled is important, but even more important is the evidence presented.

How does it affect my stance on oil pulling? I still see no evidence of it being superior in any way to normal modern oral hygiene. It has a minor potential for harm, but probably no more than other oral hygiene methods. The largest harm would seem to be the waste of time because it requires an extended swishing time, and the waste of money investing in expensive oils. There is also the potential for harm in overselling the benefits in that people may delay medical treatment and develop a more serious problem. Oil pulling is still mostly nonsense, even the modern spin on it. Maybe ask your dentist about taking care of your teeth—not some blogger (including me).

And most rocks will still sink in water.

by Eric Hall

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