Category: simplifying

Surface tension is due to everybody trying to get into the water

Surely you are joking, Prof. Feynman? 1

Keith S. Taber

Photo of Richard Feynman, taken in 1984 © Tamiko Thiel (accessed from Wikipedia and shared under Creative Commons Attribution-Share Alike 3.0 Unported)

The late, great, Richard Feynman

Richard Feynman was special. Any one who wins the Nobel prize has to be pretty special, but physics laureate Feynman was even more remarkable as he was an exceptionally high achieving research physicist also known for his…teaching. No one gets a Nobel for being a good teacher, and it is often considered in Academia that teaching (that is, if one tries to give teaching the time and energy required to do it well – as students deserve) distracts from research to such an extent that it is rare to excel in both.

Feynman had something a lot of scientists do not not: great charisma. (That is no insult to fellow scientists – most plumbers and greengrocers and bus drivers and accountants and hairdressers do not – that is what makes it notable). He might be considered the Albert Einstein of the second half of the twentieth century, and because of that timescale we are lucky to have quality recordings of him talking and teaching in a way that could not have happened with previous generations. (A great shame in many cases: if perhaps a blessing with some – Isaac Newton's lectures were apparently avoided by most of his own students.)

Like many people, I find Feynman bewitching – he had a sparkle about him – almost a permanent mischievous twinkle in the eye – and an ability to somehow express the excitement of science (of working out why things are as they are) whilst being able to talk in ways that could be understood by people that lacked his expertise. That is perhaps one trait of a great teacher – being able to talk at the level of the audience, despite personally understanding at a higher, more complex and subtle, level.

That is by way of preamble – as I want to consider an explanation Feynman once offered of surface tension.

Screenshot of Richard Feynman explaining why water forms into drops.

Why does it rain in drops?

The extract I am discussing is taken from a 1983 BBC series of short episodes in a series called 'Fun to Imagine'. Although, at the time of writing, the episodes are "not currently available" from the BBC site, there is a compilation on YouTube. One of the topics Feynman discusses is the origin of surface tension – although he only introduces the technical term after explaining the phenomenon that water forms into droplets,

"you see a little drop of water, a tiny drop
And the atoms [sic, molecules] attract each other, they like to be next to each other
They want as many partners as they can get
Now the guys that are at the surface have only partners on one side
here, in the air on the other side, so they're trying to get in
And you can imagine…this teeming people, all moving very fast
all trying to have as many partners as possible and the guys at the edge are very unhappy and nervous and they keep pounding in
trying to get in, and that makes it a tight ball instead of a flat
and that's what, you know, surface tension
When you realise when you see how sometimes a water drop sits like this on a table then you start to imagine why it's like that
because everybody is trying to get into the water"

Richard Feynman speaking in 1983

Is this a good explanation?

Well, we might suggest Feynman makes a schoolchild error – water is not an atomic substance, but molecular. It does not contain discrete atoms, so he should be referring to the molecules attracting each other. But I do not think this is an error in the sense that Feynman was mistaken, simply that although the distinction is of great importance in chemistry, physicists sometimes use the term 'atom' generically to refer to the individual particles in a gas, for example. That might be unhelpful to a secondary school student studying for examinations, but if Feynman thought of his television audience for the recording as lay people, the general public, then perhaps the distinction between atoms (arguably a more familiar term in everyday discourse) and molecules would be considered an unhelpful detail? I am certainly prepared to give him that. I think it was the wrong choice, but not that Feynman was in error.

But what about the overall argument here. The 'atoms' want to have partners all around them 2 so they try to get inside the volume of the liquid. The overall effect of everyone, including these guys at the edge, trying to get inside the water is that it forms a sphere-like shape: "a tight ball instead of [something more] flat". Is that a convincing explanation – and is it a valid one?

What makes for a good explanation?

If anything is central to both science and science teaching, it is explanation.

"Explanation would seem to be central to the essence of science. A naïve view might claim that science discovers knowledge about the World, although it might be more accurate to suggest that science creates knowledge through the development of theories. The theories are used in turn to understand, predict and sometimes control the world, and in these activities, scientific explanations play the key role. We might consider theories and models to be the resources of science, but explanations to be the active processes through which theory is applied to contexts of interest…

An explanation is an answer to a 'why' question: but that in itself neither makes for a good explanation, nor for a scientific one. There is no simple answer to what does count as a good explanation, in science or elsewhere. Explanations have audiences, and to some extent, a good explanation is one that satisfied its audience – in other words it meets the explainee's purpose in seeking an explanation. Additionally, it has been known since at least Aristotle's time that we can talk of different kinds of causes, which suggests that many 'why questions' might have different types of acceptable responses, depending on the type of cause being sought."

Taber, 2007, p.159 [Download the chapter]

That passage is taken from a chapter where I described some activities used with secondary school students to help teach them about the nature of scientific explanation. (Read about the classroom activities here.) In that context, working with learners who were about 14 years of age, students were told that a good scientific explanation would be logical, and would draw upon scientific theory,

"pupils were told that scientific explanations needed to take into account logic and theory, i.e., that the explanation needs to be rational, and the explanation needs to draw upon accepted scientific ideas. As the notion of 'theory' is itself known to be difficult for students, they were also told that scientific theories are ideas about the world which are well supported by evidence; are internally consistent; and which usually fit with other accepted theories."

Taber, 2007, p.159 [Download the chapter]

Feynman's explanation is logical (if incomplete)

In that regard, Feynman's explanation can be considered logical, even if it omits (i.e., he takes as assumed) an important step* that is needed to explain the (approximately) spherical shape of the water drop.

If water quanticles (let's leave aside whether they are atoms or molecules) want to have many partners 2, and so try to get inside the volume, then we can understand* that the water drop will tend to the smallest surface area possible, so as few quanticles end up at the surface (with the tenuous air, rather than congregating water partners, on one side) where they will be nervous, and as many quanticles as possible are in the interior of the drop where they will be happy.

* The missing step is to state that a spherical drop will have a smaller surface area than any other shape with the same volume and so fewest quanticles at the surface. Perhaps Feynman assumed everyone would know/see that. Probably there is no such thing as a totally complete explanation.

So, is this a good explanation?

Explanations can have different purposes. Scientific explanations allow us to make effective predictions (and so often to control situations – the application of science through technology). But, in everyday life, explanations have a more subjective purpose ("explanations have audiences, and to some extent, a good explanation is one that satisfied its audience").

If, as a result of hearing Feynman's explanation, the viewers of the BBC televison programme

  • felt they now understood why sphere-like drops of water form, and
  • considered they had made sense of some science, and so
  • appreciated the value of science in explaining everyday phenomena,

then perhaps the explanation achieved its purpose?

Was Feynman's explanation scientific?

Of course, if I am being my usual pedantic self, I could point out that although Feynman's explanation was logical, that does not make it scientific unless it also drew upon accepted scientific principles. It was logical because the explicandum (what was to be explained – here, the drop shape) followed from the premise (i.e., if water quanticles want to have many partners, and act accordingly, then…)

But, in science, quanticles are not understood as sentient actors, but as inanimate entities that are not (and cannot be) aware of their situation and cannot act deliberately to work towards personal goals. Therefore, no matter how convincing someone may have found this explanation, it does not qualify as a scientific explanation as it is not based on accepted scientific principles (…or at least, not directly).

An anthropomorphic explanation

Feynman's explanation uses anthropomorphism, which from a scientific perspective makes it a pseudo-explanation. A pseudo-explanation takes the form of an explanation in that it is presented as if an answer to a why question, but does meet the requirements for a formal explanation (e.g., it does "not logically fit the phenomenon to be explained into a wider conceptual scheme", Taber & Watts, 2000.)

There are various kinds of pseudo-explanations such as tautology (circular explanations that rely on the conclusions as premises) and simply offering a label for the explicandum (e.g., water absorbs a lot of heat for a small change in its temperature because it has a high heat capacity – this is a kind of disguised tautology, as a 'high heat capacity' is a way of characterising something that absorbs a lot of heat for a small change in its temperature).

Read about pseudo-explanations

Anthropomorphism explains by assuming that the entities involved can be considered to be like people, and, so, to be sentient, have feelings and opinions and preferences, and be able to plan and carry out actions that are intended to being about desired consequences.

It relies on an analogy that may not be appropriate:

  • if people were in a situation like this, they are likely to behave in a certain way
  • if we treat these entities as if they were people then we might expect them to behave as people would, therefore…

It is an open question to what extent we can assume animals (chimpanzees, dogs, birds, etc.) can be considered to share aspects of human-like experiences, emotions, thoughts, etcetera. Perhaps it is reasonable to suggest a dog can be sad or a chimp can be jealous. It may not be stretching credibility to suggest that members of some species of animals want to be in large groups, like to be in large groups, and perhaps may even get nervous when isolated? However, it stretches credibility when we are told that viruses are clever or that a bacterium can be happy.

And, there is a pretty strong scientific consensus that at the level of individual molecules there is no possibility of emotions, opinions, desires, thoughts, or deliberate actions. Atoms do not want to fill their electron shells, and genes cannot be selfish, except in a figurative sense.

Read about anthropomorphism

So, in order to accept Feynman's explanation as valid, we would have to assume that the quanticles in water, water molecules,

  • like to be next to each other
  • want as many partners as they can get 2
  • can be unhappy and nervous
  • try to have as many partners as possible 2
  • try to get into the inside of the volume

So, to find this explanation convincing, we have to accept (contrary to science) that something like a water molecule is able to

  1. have desires and preferences,
  2. be aware of the extent to which is current situation matches its preferences, and,
  3. deliberately act to bring about desired outcomes

[Feynman does not explicitly state that the quanticles know about their situation (point 2), but clearly this is implied as otherwise they would have no reason to be nervous and unhappy, nor to act to bring about change.]

These requirements are clearly not met. A being with a central nervous system as complex as a human can meet these requirements, but there is no conceivable mechanism by which molecules can be considered sentient, or to be deliberate agents in the world.

So, even if Feynman's explanation of surface tension satisfies viewers of the recording (i.e., is is subjectively an effective explanation) it fails as an objective, scientific, explanation. Feynman may indeed have been a 'genius' (Gleick, 1994), and a great physicist, but his explanation here is invalid and simply fails as good science.

Now a reader may suspect I have gone after a 'straw man' target here. Surely, Feynman was speaking figuratively, and not literally. Of course he was, but figurative language cannot support a logical explanation, except through an analogy we suspect to hold.

Consider the following hypothetical claim and two possible consequences if the claim was true

ClaimConsequence 1Consequence 2
"I managed to get tickets for Toyah and Fripp's sold out concert in Bury St Edmunds, and these tickets are gold dust.""I could sell these tickets at quite a mark up""I could put a sample of these tickets in a mass spectrometer and would find they had an atomic mass of 197."

If the claim was literally true, then consequence 2 would follow. But of course, it is meant as a figurative claim, where 'gold dust' is a metaphor for something of high value because it is rare. So, actually consequence 1 might follow, but not consequence 2.

In the same way, if water particles do not have likes, and do not try to do things, Fenyman's argument seems to fall apart…

A teaching model?

Now I would not presume to know better than Richard Feynman, and I am pretty sure (i.e., about as certain as I can be of anything) that Feynman would not have fallen into the mistake of thinking that atoms or molecules actually act like humans and want things, or try to do things. He surely knew this was not a scientific explanation, but he clearly thought this was a useful way of explaining (to his audience) why water forms into a drop.

Now, I suggested above that Feynman's narrative account of the origin of surface tension "is not based on accepted scientific principles (…or at least, not directly)". But near the outset of this account Feynman states that the water particles "attract each other":

"the [molecules] attract each other, they like to be next to each other"

Feynman was not only a researcher, but a teacher, and teachers use teaching models. I think this is what Feynman is doing here:

"[according to science] the [molecules] attract each other [and we can think of this as if] they like to be next to each other"

Affinity in the sense of human experience is used as a kind of analogy for the affinity between water molecules (which leads to hydrogen bonding and dipole-dipole interactions). Once we model inter-molecular forces as being like attractions between people, we can extend the analogy in terms of how people feel when they do not get what they want, and how they respond by acting in ways that they hope will get them what they want.

Looked at this way, Feynman is doing something that good teachers often do when they judge a scientific model is too abstract, sophisticated, complex, subtle, for their audience; they simplify by substituting a teaching model which represents the scientific model in terms more familiar and accessible to the learners.

Read about making the unfamiliar familiar

From this perspective, Feynman's explanation may not have been a valid scientific explanation, but we might ask if it was an effective intermediate explanation set out in terms of a teaching model. That is, perhaps Feynman's explanation may have satisfied viewers, and also potentially acted as a possible foundation for building up to a more technical, scientifically acceptable explanation.

Teachers and other science communicators often use anthropomorphism as a way of offering accounts of complex scientific topics that will appeal and make sense to learners of a public audience.

Read about anthropomorphism in accounts of science

This can be effective to the extent that it engages learners, leaves the audience with a subjective sense of making sense of the science, and provides accounts that are often remembered later.

Of course that is not so helpful if the audience is studying a science course, and think they have learnt an account which will get them credit in formal examinations! I know from my own teaching career that learners often find anthropomorphic explanations readily come to mind, even when then they have been taught more technical accounts they are expected to apply when assessed.

In public science communication, then, anthropomorphic accounts may be valuable in offering people some sense of the science. But in formal education we need to be careful as even if anthropomorphism offers a useful way of getting learners familiar with some abstract topic (what might be called 'weak' anthropomorphism: Taber & Watts, 1996), we need to avoid them learning and committing to that metaphoric 'social' account thinking it is a valid scientific account ('strong' anthropomorphism).

Mapping Feynman's explanation

If we see Feynman as offering an analogy as a teaching model then we might seek to 'translate' his terms into more scientific concepts. He tells us that attraction is 'liking', and we can perhaps think of 'wanting' and being 'nervous' as indicating a higher (excited) energy state, 'pounding' as being subject to unbalanced forces, and 'trying to get in' as tending to evolving toward a lower energy configuration. At least, someone who already understood the scientific account could suggest such mappings. It seems unlikely any one who did not appreciate the science already could interpret it that way without a knowing and careful guide.

And like all anthropomorphic explanations, it 'suffers' from the very quality that it offers a narrative which is likely to be more easily understood, better related to, and more readily recalled, than the scientific account. This is why I have very mixed feelings about the use of anthropomorphism in formal science teaching, as even when it (a) does a great job of engaging learners and offering them some level of understanding, this may be at the cost of (b) offering an account which many students will find it hard to later let go of and progress beyond.

Screenshot of Richard Feynman explaining why water forms into drops.

As a good teacher, Feynman would know to pitch his teaching for particular audiences depending on their likely level of background knowledge. The explanation discussed here was not how Feynman taught about surface tension in his undergraduate classes at the California Institute of Technology (Feynman, Leighton & Sands, 1963). We can imagine that had he told students at Caltech that water formed into spherical drops because all the molecular guys are trying to get into the water, he might indeed had heard the retort: Surely you are joking, Prof. Feynman? 1

Work cited:

Notes:

1 My subtitle is a reference to the book 'Surely you're Joking Mr Feynman: Adventures of a Curious Character' in which Feynman tells anecdotes from his life.

2 Water was perhaps a poor example to choose as there is extensive hydrogen bonding in liquid water,

"I suspect even some experienced chemists may underestimate the extent of hydrogen bonding in water. According to one source…, in liquid water at the freezing point, the typical water molecule is at any time bonded by three or four hydrogen bonds – compared with the four bonds in the solid ice structure."

Taber, 2020, p.98

So, in Feynman's analogy, a water molecules does not become happy (lower energy state) when it is surrounded by as many other water molecules as possible, but when it is aligned with 3 or 4 other molecules to hydrogen bond, if only transiently. Without the hydrogen bonding, the drop would still be approximately spherical, but it would be smaller and denser as the molecules could get even closer together, but it would evaporate away more readily.

Cells are buzzing cities that are balloons with harpoons

What can either wander door to door, or rush to respond; and when it arrives might touch, sniff, nip, rear up, stroke, seal, or kill?

Keith S. Taber

a science teacher would need to be more circumspect in throwing some of these metaphors out there, without then doing some work to transition from them to more technical, literal, and canonical accounts

BBC Radio 4's 'Start the week' programme is not a science programme, but tends to invite in guests (often authors of some kind) each week according to some common theme. This week there was a science theme and the episode was titled 'Building the Body, Opening the Heart', and was fascinating. It also offers something of a case study in how science gets communicated in the media.

Building the Body, Opening the Heart

The guests all had life-science backgrounds:

Their host was geneticist and broadcaster Adam Rutherford.

Communicating science through the media

As a science educator I listen to science programmes both to enhance and update my own science knowledge and understanding, but also to hear how experts present scientific ideas when communicating to a general audience. Although neither science popularisation nor the work of scientists in communicating to the public is entirely the same as formal teaching (for example,

  • there is no curriculum with specified target knowledge; and
  • the audiences
    • are not well-defined,
    • are usually much more diverse than found in classrooms, and
    • are free to leave at any point they lose interest or get a better offer),

they are, like teachers, seeking to inform and explain science.

Science communicators, whether professional journalists or scientists popularising their work, face similar challenges to science teachers in getting across often complex and abstract ideas; and, like them, need to make the unfamiliar familiar. Science teachers are taught about how they need to connect new material with the learners' prior knowledge and experiences if it is to make sense to the students. But successful broadcasters and popularisers also know they need to do this, using such tactics as simplification, modelling, metaphor and simile, analogy, teleology, anthropomorphism and narrative.

Perhaps one of the the biggest differences between science teaching and science communication in the media is the ultimate criterion of success. For science teachers this is (sadly) usually, primarily at least, whether students have understood the material, and will later recall it, sufficiently to demonstrate target knowledge in exams. The teacher may prefer to focus on whether students enjoy science, or develop good attitudes to science, or will consider working in science: but, even so, they are usually held to account for students' performance levels in high-stakes tests.

Science journalists and popularisers do not need to worry about that. Rather, they have to be sufficiently engaging for the audience to feel they are learning something of interest and understanding it. Of course, teachers certainly need to be engaging as well, but they cannot compromise what is taught, and how it is understood, in order to entertain.

With that in mind, I was fascinated at the range of ways the panel of guests communicated the science in this radio show. Much of the programme had a focus on cells – and these were described in a variety of ways.

Talking about cells

Dr Rutherford introduced cells as

  • "the basic building blocks of life on earth"; and observed that he had
  • "spent much of my life staring down microscopes at these funny, sort of mundane, unremarkable, gloopy balloons"; before suggesting that cells were
  • "actually really these incredible cities buzzing with activity".

Dr. Mukherjee noted that

"they're fantastical living machines" [where a cell is the] "smallest unit of life…and these units were built, as it were, part upon part like you would build a Lego kit"

Listeners were told how Robert Hooke named 'cells' after observing cork under the microscope because the material looked like a series of small rooms (like the cells where monks slept in monasteries). Hooke (1665) reported,

"I took a good clear piece of Cork, and with a Pen-knife sharpen'd as keen as a Razor, I cut a piece of it off, and…cut off from the former smooth surface an exceeding thin piece of it, and…I could exceeding plainly perceive it to be all perforated and porous, much like a Honey-comb, but that the pores of it were not regular; yet it was not unlike a Honey-comb in these particulars

…these pores, or cells, were not very deep, but consisted of a great many little Boxes, separated out of one continued long pore, by certain Diaphragms, as is visible by the Figure B, which represents a sight of those pores split the long-ways.

Robert Hooke
Hooke's drawing of the 'pores' or 'cells' in cork

Components of cells

Dr. Mukherjee described how

"In my book I sort of board the cell as though it's a spacecraft, you will see that it's in fact organised into rooms and there are byways and channels and of course all of these organelles which allow it to work."

We were told that "the cell has its own skeleton", and that the organelles included the mitochondria and nuclei ,

"[mitochondria] are the energy producing organelles, they make energy in most cells, our cells for instance, in human cells. In human cells there's a nucleus, which stores DNA, which is where all the genetic information is stored."

A cell that secretes antibodies which are like harpoons or missiles that it sends out to kill a pathogen?

(Images by by envandrare and OpenClipart-Vectors from Pixabay)

Immune cells

Rutherford moved the conversation onto the immune system, prompting 'Sid' that "There's a lovely phrase you use to describe T cells, which is door to door wanderers that can detect even the whiff of an invader". Dr. Mukherjee distinguished between the cells of the innate immune system,

"Those are usually the first responder cells. In humans they would be macrophages, and neutrophils and monocytes among them. These cells usually rush to the site of an injury, or an infection, and they try to kill the pathogen, or seal up the pathogen…"

and the cells of the adaptive system, such as B cells and T cells,

"The B cell is a cell that eventually becomes a plasma cell which secretes antibodies. Antibodies, they are like harpoons or missiles which the cell sends out to kill a pathogen…

[A T cell] goes around sniffing other cells, basically touching them and trying to find out whether they have been altered in some way, particularly if they are carrying inside them a virus or any other kind of pathogen, and if it finds this pathogen or a virus in your body, it is going to go and kill that virus or pathogen"

A cell that goes around sniffing other cells, touching them? 1
(Images by allinonemovie and OpenClipart-Vectors from Pixabay)

Cells of the heart

Another topic was the work of Professor Harding on the heart. She informed listeners that heart cells did not get replaced very quickly, so that typically when a person dies half of their heart cells had been there since birth! (That was something I had not realised. It is believed that this is related to how heart cells need to pulse in synchrony so that the whole organ functions as an effective pumping device – making long lasting cells that seldom need replacing more important than in many other tissues.)

At least, this relates to the cardiomyocytes – the cells that pulse when the heart beats (a pulse that can now be observed in single cells in vitro). Professor Harding described how in the heart tissue there are also other 'supporting' cells, such as "resident macrophages" (immune cells) as well as other cells moving around the cardiomyocytes. She describe her observations of the cells in Petri dishes,

"When you look at them in the dish it's incredible to see them interact. I've got a… video [of] cardiomyocytes in a dish. The cardiomyocytes pretty much just stay there and beat and don't do anything very much, and I had this on time lapse, and you could see cells moving around them. And so, in one case, the cell (I think it was a fibroblast, it looked like a fibroblast), it came and it palpated at the cardiomyocyte, and it nipped off bits of it, it sampled bits of the cardiomyocyte, and it just stroked it all the way round, and then it was, it seemed to like it a lot.

[In] another dish I had the same sort of cardiomyocyte, a very similar cell came in, it went up to the cardiomyocyte, it touched it, and as soon as it touched it, I can only describe it as it reared up and it had, little blobs appeared all over its surface, and it rushed off, literally rushed off, although it was time lapse so it was two minutes over 24 hours, so, it literally rushed off, so what had it found, why did one like it and the other one didn't?"

Making the unfamiliar, familiar

The snippets from the broadcast that I have reported above demonstrate a wide range of ways that the unfamiliar is made familiar by describing it in terms that a listener can relate to through their existing prior knowledge and experience. In these various examples the listener is left to carry across from the analogue features of the familiar (the city, the Lego bricks, human interactions, etc.) those that parallel features of the target concept – the cell. So, for example, the listener is assumed to appreciate that cells, unlike Lego bricks, are not built up through rigid, raised lumps that fit precisely in depressions on the next brick/cell. 2

Analogies with the familiar

Hooke's original label of the cell was based on a kind of analogy – an attempt to compare what we has seeing with something familiar: "pores, or cells…a great many little Boxes". He used the familiar simile of the honeycomb (something directly familiar to many more people in the seventeenth century when food was not subject to large-scale industrialised processing and packaging).

Other analogies, metaphors and similes abound. Cells are visually like "gloopy balloons", but functionally are "building blocks" (strictly a metaphor, albeit one that is used so often it has become treated as though a literal description) which can be conceptualised as being put together "like you would build a Lego kit" (a simile) although they are neither fixed, discrete blocks of a single material, nor organised by some external builder. They can be considered conceptually as the"smallest unit of life"(though philosophers argue about such descriptions and what counts as an individual in living systems).

The machine description ("fantastical living machines") reflects one metaphor very common in early modern science and cells as "incredible cities" is also a metaphor. Whether cells are literally machines is a matter of how we extend or limit our definition of machines: cells are certainly not actually cities, however, and calling them such is a way of drawing attention to the level of activity within each (often, apparently from observation, quite static) cell. B cells secrete antibodies, which the listener is old are like (a simile) harpoons or missiles – weapons.

Skeletons of the dead

Whether "the cell has its own skeleton" is a literal or metaphorical statement is arguable. It surely would have originally been a metaphoric description – there are structures in the cell which can be considered analogous to the skeleton of an organism. If such a metaphor is used widely enough, in time the term's scope expands to include its new use – and it becomes (what is called, metaphorically) a 'dead metaphor'.

Telling stories about cells

A narrative is used to help a listener imagine the cell at the scale of "a spacecraft". This is "organised into rooms and there are byways and channels" offering an analogy for the complex internal structure of a cell. Most people have never actually boarded a spacecraft, but they are ubiquitous in television and movie fiction, so a listener can certainly imagine what this might be like.

Endoplastic reticulum? (Still from Star Trek: The Motion Picture, Paramount Pictures, 1979)
Oversimplification?

The discussion of organelles illustrates how simplifications have to be made when introducing complex material. This always brings with it dangers of oversimplification that may impede further learning, or even encourage the development of alternative conceptions. So, the nucleus does not, strictly, 'store' "all the genetic information" in a cell (mitochondria carry their own genes for example).

More seriously, perhaps, mitochondria do not "make energy". 'More seriously' as the principle of conservation of energy is one of the most basic tenets of modern science and is considered a very strong candidate for a universal law. Children are often taught in school that energy cannot be created or destroyed. Science communication which is contrary to this basic curriculum science could confuse learners – or indeed members of the public seeking to understand debates about energy policy and sustainability.

Anthropomorphising cells

Cells are not only compared to inanimate entities like balloons, building bricks, cities and spaceships. They are also described in ways that make them seem like sentient agents – agents that have experiences, and conscious intentions, just as people do. So, some immune cells are metaphorical 'first responders' and just as emergency services workers they "rush to the site" of an incident. To rush is not just to move quickly, buy to deliberately do so. (By contrast, Paul McAuley refers to "innocent" amoeboid cells that collectively form into the plasmodium of a slime mould spending most of their lives"bumbling around by themselves" before they "get together". ) The immune cells act deliberately – they "try" to kill. Other immune cells "send out" metaphorical 'missiles' "to kill a pathogen". Again this language suggests deliberate action (i.e., to send out) and purpose.

That is, what is described is not just some evolved process, but something teleological: there is a purpose to sending out antibodies – it is a deliberate act with an aim in mind. This type of language is very common in biology – even referring to the 'function' of the heart or kidney or a reflex arc could be considered as misinterpreting the outcome of evolutionary developments. (The heart pumps blood through the vascular system, but referring to a function could suggest some sense of deliberate design.)

Not all cells are equal

I wonder how many readers noticed the reference above to 'supporting' cells in the heart. Professor Harding had said

"When you look inside the [heart] tissue there are many other cells [than cardiomyocytes] that are in there, supporting it, there are resident macrophages, I think we still don't know really what they are doing in there"

Why should some heart cells be seen as more important and others less so? Presumably because 'the function' of a heart is to beat, to pump, so clearly the cells that pulse are the stars, and the other cells that may be necessary but are not obviously pulsing just a supporting cast. (So, cardiomyocytes are considered heart cells, but macrophages in the same tissue are only cells that are found in the heart, "residents" – to use an analogy of my own, like migrants that have not been offered citizenship!)3

That is, there is a danger here that this way of thinking could bias research foci leading researchers to ignore something that may ultimately prove important. This is not fanciful, as it has happened before, in the case of the brain:

"Glial cells, consisting of microglia, astrocytes, and oligodendrocyte lineage cells as their major components, constitute a large fraction of the mammalian brain. Originally considered as purely non-functional glue for neurons, decades of research have highlighted the importance as well as further functions of glial cells."

Jäkel and Dimou, 2017
The lives of cells

Narrative is used again in relation to the immune cells: an infection is presented as a kind of emergency event which is addressed by special (human like) workers who protect the body by repelling or neutralising invaders. "Sniffing" is surely an anthropomorphic metaphor, as cells do not actually sniff (they may detect diffusing substances, but do not actively inhale them). Even "touching" is surely an anthropomorphism. When we say two objects are 'touching' we mean they are in contact, as we touch things by contact. But touching is sensing, not simply adjacency.

If that seems to be stretching my argument too far, to refer to immune cells "trying to find out…" is to use language suggesting an epistemic agent that can not only behave deliberately, but which is able to acquire knowledge. A cell can only "find" an infectious agent if it is (i.e., deliberately) looking for something. These metaphors are very effective in building up a narrative for the listener. Such a narrative adopts familiar 'schemata', recognisable patterns – the listener is aware of emergency workers speeding to the scene of an incident and trying to put out a fire or seeking to diagnose a medical issue. By fitting new information into a pattern that is familiar to the audience, technical and abstract ideas are not only made easier to understand, but more likely to be recalled later.

Again, an anthropomorphic narrative is used to describe interactions between heart cells. So, a fibroblast that "palpates at" a cardiomyocyte seems to be displaying deliberate behaviour: if "nipping" might be heard as some kind of automatic action – "sampling" and "stroking" surely seem to be deliberate behaviour. A cell that "came in, it went up [to another]" seems to be acting deliberately. "Rearing up" certainly brings to mind a sentient being, like a dog or a horse. Did the cell actually 'rear up'? It clearly gave that impression to Professor Harding – that was the best way, indeed the "only" way, she had to communicate what she saw.

Again we have cells "rushing" around. Or do we? The cell that had reared up, "rushed off". Actually, it appeared to "rush" when the highly magnified footage was played at 720 times the speed of the actual events. Despite acknowledging this extreme acceleration of the activity, the impression was so strong that Professor Harding felt justified in claiming the cell "literally rushed off, although it was time lapse so it was two minutes over 24 hours, so, it literally rushed off…". Whatever it did, that looked like rushing with the distortion of time-lapse viewing, it certainly did not literally rush anywhere.

But the narrative helps motivate a very interesting question, which is why the two superficially similar cells 'behaved' ('reacted', 'responded' – it is actually difficult to find completely neutral language) so differently when in contact with a cardiomyocyte. In more anthropomorphic terms: what had these cells "found, why did one like it and the other one didn't?"

Literally speaking?

Metaphorical language is ubiquitous as we have to build all our abstract ideas (and science has plenty of those) in terms of what we can experience and make sense of. This is an iterative process. We start with what is immediately available in experience, extend metaphorically to form new concepts, and in time, once those have "settled in" and "taken root" and "firmed up" (so to speak!) they can then be themselves borrowed as the foundation for new concepts. This is true both in how the individual learns (according to constructivism) and how humanity has developed culture and extended language.

So, should science communicators (whether scientists themselves, journalists or teachers) try to limit themselves to literal language?

Even if this were possible, it would put aside some of our strongest tools for 'making the unfamiliar familiar' (to broadcast audiences, to the public, to learners in formal education). However these devices also bring risks that the initial presentations (with their simplifications and metaphors and analogies and anthropomorphic narratives…) not only engage listeners but can also come to be understood as the scientific account. That is is not an imagined risk is shown by the vast numbers of learners who think atoms want to fill their shells with octets of electrons, and so act accordingly – and think this because they believe it is what they have been taught.

Does it matter if listeners think the simplification, the analogy, the metaphor, the humanising story,… is the scientific account? Perhaps usually not in the case of the audience listening to a radio show or watching a documentary out of interest.

In education it does matter, as often learners are often expected to progress beyond these introductory accounts in their thinking, and teachers' models and metaphors and stories are only meant as a starting point in building up a formal understanding. The teacher has to first establish some kind of anchor point in the students' existing understandings and experiences, but then mould this towards the target knowledge set out in the curriculum (which is often a simplified account of canonical knowledge) before the metaphor or image or story becomes firmed-up in the learners' minds as 'the' scientific account.

'Building the Body, Opening the Heart' was a good listen, and a very informative and entertaining episode that covered a lot of ideas. It certainly included some good comparisons that science teachers might borrow. But I think in a formal educational context a science teacher would need to be more circumspect in throwing some of these metaphors out there, without then doing some work to transition from them to more technical, literal, and canonical accounts.

Read about science analogies

Read about science metaphors

Read about science similes

Read about anthropomorphism

Read about teleology

Work cited:

Notes:

1 The right hand image portrays a mine, a weapon that is used at sea to damage and destroy (surface or submarine) boats. The mine is also triggered by contact ('touch').

2 That is, in an analogy there are positive and negative aspects: there are ways in which the analogue IS like the target, and ways in which the analogue is NOT like the target. Using an analogy in communication relies on the right features being mapped from the familiar analogue to the unfamiliar target being introduced. In teaching it is important to be explicit about this, or inappropriate transfers may be made: e.g., the atom is a tiny solar system so it is held together by gravity (Taber, 2013).

3 It may be a pure coincidence in relation to the choice of term 'resident' here, but in medicine 'residents' have not yet fully qualified as specialist physicians or surgeons, and so are on placement and/or under supervision, rather than having permanent status in a hospital faculty.

A corny teaching analogy

Pop goes the comparison

Keith S. Taber

The order of corn popping is no more random than the roll of a dice.

I was pleased to read about a 'new' teaching analogy in the latest 'Education in Chemistry' (the Royal Society of Chemistry's education magazine) – well, at least it was new to me. It was an analogy that could be demonstrated easily in the school science lab, and, according to Richard Gill (@RGILL_Teach on Twitter), went down really well with his class.

Teaching analogies

Analogies are used in teaching and in science communication to help 'make the unfamiliar familiar', to show someone that something they do not (yet) know about is actually, in some sense at least, a bit like something they are already familiar with. In an analogy, there is a mapping between some aspect(s) of the structure of the target ideas and the structure of the familiar phenomenon or idea being offered as an analogue. Such teaching analogies can be useful to the extent that someone is indeed highly familiar with the 'analogue' (and more so than with the target knowledge being communicated); that there is a helpful mapping across between the analogue and the target; and that comparison is clearly explained (making clear which features of the analogue are relevant, and how).

Read about analogies in science

The analogy is discussed in the July 2022 Edition of Education in Chemistry, and on line.

Richard Gill suggests that 'Nuclear decay is a tough concept' to teach and learn, but after making some popcorn he realised that popping corn offered an analogy for radioactive decay that he could demonstrate in the classroom.

Richard Gill describes how

"I tell the students I'm going to heat up the oil; I'm going to give the kernels some energy, making them unstable and they're going to want to pop. I show them under the visualiser, then I ask, 'which kernel will pop first?' We have a little competition. Why do I do this? It links to nuclear decay being random. We know an unstable atom will decay, but we don't know which atom will decay or when it will decay, just like we don't know which kernel will pop when."

Gill, 2022

In the analogy, the corn (maize) kernels represents atoms or nuclei of an unstable isotope, and the popped corn the decay product, daughter atoms or nuclei. 1

'Parents' before 'decay
(Image by Paulo Marcos pmarcos6821 from Pixabay)
'Daughters' after 'decay'
(Image by Leonardo Alvarado from Pixabay)

Richard Gill homes in on a key feature of radioactive decay which may seem counter-intuitive to learners, but which is actually a pattern found in many different phenomena – exponential decay. The rate of radioactive decay falls (decays, confusingly) over time. Theoretically the [radioactive] decay rate follows a very smooth [exponential] decay curve. Theoretically, because of another key feature of radioactive decay that Gill highlights – its random nature!

It may seem that something which occurs by random will not lead to a regular pattern, but although in radioactivity the behaviour of an individual nucleus (in terms of when it might decay) cannot be predicted, when one deals with vast numbers of them in a macroscopic sample, a clear pattern emerges. Each different type of unstable atom has an associated half-life which tells us when half of a sample will have decayed. These half-lives can vary from fractions of a second to vast numbers of years, but are fixed for a particular nuclide.

Richard Gill notes that he can use the popping corn demonstration as background for teaching about half-life,

I usually follow this lesson with the idea of half-lives. The concept of half-lives now makes sense. Why are there fewer unpopped kernels over time? Because they're popping. Why do radioactive materials become less radioactive over time? Because they're decaying.

Gill, 2022

Perhaps he could even develop his demonstration to model the half-life of decay?

Modelling the popcorn decay curve

The Australian Earth Science Education blog suggests

"Popcorn can be used to model radioactive decay. It is a lot safer than using radioactive isotopes, as well as much tastier"

and offers instructions for a practical activity with a bag of corn and a microwave to collect data to plot a decay curve (see https://ausearthed.blogspot.com/2020/04/radioactive-popcorn.html). Although this seems a good idea, I suspect this specific activity (which involves popping the popping corn in and out of the oven) might be too convoluted for learners just being introduced to the topic, but could be suitable for more advanced learners.

However, The Association of American State Geologists suggests an alternative approach that could be used in a class context where different groups of students put bags of popcorn into the microwave for different lengths of time to allow the plotting of a decay curve by collating class results (https://www.earthsciweek.org/classroom-activities/dating-popcorn).

Another variants is offered by The University of South Florida's' Spreadsheets Across the Curriculum' (SSAC) project. SSAC developed an activity ("Radioactive Decay and Popping Popcorn – Understanding the Rate Law") to simulate the popping of corn using (yes, you guessed) a spreadsheet to model the decay of corn popping, as a way of teaching about radioactive decay!

This is more likely to give a good decay curve, but one cannot help feeling it loses some of the attraction of Richard Gill's approach with the smell, sound and 'jumping' of actual corn being heated! One might also wonder if there is any inherent pedagogic advantage to simulating popping corn as a model for simulating radioactive decay – rather than just using the spreadsheet to directly model radioactive decay?

Feedback cycles

The reason the popping corn seems to show the same kind of decay as radioactivity, is because it can be represented with the same kind of feedback cycle.

This pattern is characteristic of simple systems where

  • a change is brought about by a driver
  • that change diminishes the driver

In radioactive decay, the level of activity is directly proportional to the number of unstable nuclei present (i.e., the number of nuclei that can potentially decay), but the very process of decay reduces this number (and so reduces the rate of decay).

So,

  • when there are many unstable nuclei
  • there will be much decay
  • quickly reducing the number of unstable nuclei
    • so reducing the rate of decay
    • so reducing the rate at which unstable nuclei decay
      • so reducing the rate at which decay is reducing
      • …

and so forth.

Exponential decay is a characteristic of systems with a simple negative feedback cycle
(source: ASCEND project)

Recognising this general pattern was the focus of an 'enrichment' activity designed for upper secondary learners in the Gatsby SEP supported ASCEND project which presented learners with information about the feedback cycle in radioactive decay; and then had them set up and observe some quite different phenomena (Taber, 2011):

  • capacitor discharge
  • levelling of connected uneven water columns
  • hot water cooling

In each case the change driven by some 'driver' reduced the driver itself (so a temperature difference leads to heat transfer which reduces the temperature difference…).

Read about the classroom activity

In Richard Gill's activity the driver is the availability of intact corn kernels being heated such that water vapour is building up inside the kernel – something which is reduced by the consequent popping of those kernels.

A negative feedback cycle

Mapping the analogy

A key feature of an analogy is that it can be understood as a kind of mapping between two conceptual structures. The making popcorn demonstration seems a very simple analogue, but mapping out the analogy might be useful (at least for the teacher) to clarify it. Below I present a representation of a mapping between popping corn and radioactive decay, suggesting which aspects of the analogue (the popping corn) map onto the target scientific concept.

Mapping an analogy between making pop-corn and radioactive decay

In this mapping I have used colour to highlight differences between the two (conceptual) structures. Perhaps the most significant difference is represented by the blue (target concept) versus red (analogue) features.

Most analogies only map to a limited extent

There will be aspects of an analogue that do not map onto anything on the target, and sometimes there will be an important feature of the target which has no analogous feature in the analogue. There is always the possibility that irrelevant features of an analogue will be mapped across by learners.

As one example, the comparison of the atom with a tiny solar system was once an image often used as a teaching analogy, yet it seems learners often have limited understandings of both analogue and target, and may be transferring across inappropriately – such as assuming the electrons are bound to the atom by gravity (Taber, 2013a). Where students have an alternative conception of the analogue (the earth attracts the sun, but not vice versa) they will often assume the same pattern in the target (the nucleus is not attracted to the electrons).

Does this matter? Well, yes and no. A teaching analogy is used to introduce a technical scientific concept by making it seem familiar. This is a starting point to be built upon (so, Richard Gill tells us that he will build upon the diminishing activity of cooking corn in his his popcorn demonstration to introduce the idea of half-life), so it does not matter if students do not fully understand everything immediately. (Indeed, it is naive to assume most learners could acquire a new complex set of ideas all at once: learning is incremental – see Key ideas for constructivist teaching).

Analogies can act as 'scaffolds' to help learners venture out from their existing continents of knowledge towards new territory. Once this 'anchor' in learners' experience is established one can, so to speak, disembark from the scaffolding raft the onto the more solid ground of the shore.

Read about scaffolding learning

However, it is important to be careful to make sure

  • (a) learners appreciate the limitations of models (such an analogies) – that they are thinking and learning tools, and not absolute accounts of the natural word; and that
  • (b) the teacher helps dismantle the 'scaffolding' once it is not needed, so that it is not retained as part of the learners 'scientific' account.
Weak anthropomorphism

An example of that might be Gill's use of anthropomorphism.

…unstable atoms/nuclei need to become stable…

…I'm going to give the kernels some energy, making them unstable and they're going to want to pop…

Anthropomorphism

This type of language is often used to offer narratives that are more readily appreciated by learners (making the unfamiliar familiar, again) but students can come to use such language habitually, and it may come to stand in place of a more scientific account (Taber & Watts, 1996). So, 'weak' anthropomorphism used to help introduce something abstract and counter-intuitive is useful, but 'strong' anthropomorphism that comes to be adopted as a scientific explanation (e.g., nuclei decay because they want to be stable) is best avoided by seeking to move beyond the figurative language as soon as students are ready.

Read about anthropomorphism

The 'negative' analogy

The mapping diagram above may highlight several potential teaching points that may be considered (perhaps not to be introduced immediately, but when the new concepts are later reinforced and developed).

Where does the energy come from?

One key difference between the two systems is that radioactive decay is (we think) completely spontaneous, whereas the corn only pops because we cook it (Gill used a Bunsen burner) and left to its own devices remains as unpopped kernels.

Related to this, the source of energy for popping corn is the applied heat, whereas unstable nuclei are already in a state of high energy and so have an 'internal' source for their activity. This a key difference that will likely be obvious to some, but certainly not all learners in most classes.

When is random, random?

A more subtle point relates to the 'random' nature of the two events. I suggest subtle, because there are many published reports written by researchers in science education which suggests even supposed experts can have a pretty shaky ideas of what counts as random (Taber, 2013b).

Read 'Nothing random about a proper scientific evaluation?'

Read about the randomisation criterion

As far as scientists understand, the decay of one unstable nucleus in a sample of radioactive material (rather than another) is a random process. It is not just that we are not yet able to predict when a particular nucleus will decay – according to current scientific accounts it is not possible to predict in principle. This is an idea that even Einstein found difficult to accept.

That is not true with the corn. Presumably there are subtle differences between kernels – some have slightly more water content, or slightly weaker casings. Perhaps more significantly, some are heated more than others due to their position in the pan and the position of the heat source, or due differential exposure to the cooking oil… In principle it would be possible to measure relevant variables and model the set up to make good predictions. (In principle, even if in practice a very complex task.) The order of corn popping is no more random than…say…the roll of a dice. That is, physics tells us it follows natural laws, even if we are not in a position to fully model the phenomenon.

(We might suggest that a student who considered the corn popping as a random event because she saw apparently identical kernels all being heated in the same pan at the same time is simply missing certain 'hidden variables'. Einstein wondered if there were also 'hidden variables' that science had not yet uncovered which could explain random events such as why one nucleus rather than another decays at a particular moment.)

On the recoil

Perhaps a more significant difference is what is observed. The corn are observed 'jumping' (more anthropomorphic language?) Physics tells us that momentum must always be conserved, and the kernels act like tiny jet propelled rockets. That is, as steam is released when the kernel bursts, the rest of the kernel 'jumps' in the opposite direction. (That is, by Newton's third law, there is a reaction force to the force pushing the steam out of the kernel. Momentum is a vector, so it is possible for a stationary object to break up into several moving parts with conservation of momentum.)

Something similar happens in radioactive decay. The emitted radiation carries away momentum, and the remaining 'daughter' nucleus recoils – although if the material is in the solid state this effect is dissipated by being spread across the lattice. So, the radioactivity which is detected is not analogous to the jumping corn, but to the steam it has released.

Is this important? That likely depends upon the level being taught. If the topics is being introduced to 14-16 years-olds, perhaps not. If the analogy is being explored with post-compulsory students doing an elective course, then maybe. (If not in chemistry; then certainly in physics, where learners are expected to to apply the principle of conservation of momentum across various scenarios.)

Will this be on the exam?

When I drafted this, I suspected most readers might find my caveats above about the limitations of the analogy, a bit pernickety (the kind of things an academic who's been out of the school classroom too long and forgotten the realities of working with pupils might dream up), but then I found what claims to be an Edexcel GCE Physics paper from 2012 (paper reference 6PH05/01) on line. In this paper, one question begins:

"In a demonstration to her class, a teacher pours popcorn kernels onto a hot surface and waits for them to pop…".

Much to my delight, I found the first part of this question asked learners:

"How realistic is this demonstration as an analogy to radioactive decay?

Consider aspects of the demonstration that are similar to radioactive decay and aspects that are different"

Examination paper asking physics students to identify positive and negative aspects of the analogy.

Classes of radioactivity

One further difference did occur to me that may be important. At some level this analogy works for radioactivity regardless of what is being emitted from an excited nucleus. However, the analogy seems clearer for the emission of an alpha particle, or a beta particle, or a neutron, than in the case of gamma radiation.

Although in gamma decay an excited nucleus relaxes to a lower energy state emitting a photon, it may not be as obvious to learners that the nucleus has changed (arguably, it has not 'substantially' changed as there is no change of substance) – as it has the same mass number and charge as before. This may be a point to be raised if moving on later to discuss different classes of radioactivity.

Or, perhaps, with gamma decay one can use a different version of the analogy?

Another corny analogy

Although I do not think I had never come across this analogy before reading the Education in Chemistry piece (perhaps because I do not make myself popcorn), Richard Gill does not seem to be the only person to have noticed this comparison. (They say 'great minds think alike' – and not just physicist Henri Poincaré thinking like Kryten from'Red Dwarf'). When I looked around the world-wide web I found there were two different approaches to using corn kernels to model radioactivity.

Some people use a similar demonstration to Mr Gill.2 However, there was also a different approach to using the corn. There were variations on this 3, but the gist was that

  • one starts with a large number of kernels
  • they are agitated (e.g., shaken in a box with different cells, poured onto the bench…)
  • then inspected to see which are pointing in some arbitrary direction designated as representing decay
  • the 'decayed' kernels are removed and counted
  • the rest of the sample is agitated again
  • etc.
Choose a direction to represent decay, and remove the aligned kernels as the 'activity' in that interval.
(Original image by Susie from Pixabay)

This lacks the excitement of popping corn, but could be a better model for gamma decay where the daughter nucleus is at a different energy after decay, but is otherwise unchanged.

Perhaps this version of the analogy could be improved by using a tray with an array of small dips (like tiny spot tiles) just the right size to stand corn kernels in the depressions with their points upwards. Then, after a very gentle tap on the bench next to the tile, those which have 'relaxed' from the higher energy state (i.e., fallen onto their sides) would be considered decayed. This would more directly model the change in potential energy and also avoid the need to keep removing kernels from the context (just as daughter atoms usually remain in a sample of radioactive material), as further gentle tapes are unlikely to excite them back to the higher energy state. 4

Or, dear reader, perhaps I've just been thinking about this analogy for just a little too long now.

Sources:
Notes

1 Referring to the nuclei before and after radioactive decay as 'parents' and 'daughters' seems metaphorical, but this use has become so well established (in effect, these are now technical terms) that these descriptors are now what are known (metaphorically!) as 'dead metaphors'.

Read about metaphors in science

2 Here are some examples I found:

Jennifer Wenner, University of Wisconsin-Oshkosh uses the demonstration in undergraduate geosciences:

"I usually perform it after I have introduced radioactive decay and talked about how it works. It only takes a few minutes and I usually talk while I am waiting for the "decay" to happen 'Using Popcorn to Simulate Radioactive Decay'"

https://serc.carleton.edu/quantskills/activities/popcorn.html

The Institute of Physics (IoP) include this activity as part of their 'Modelling decay in the laboratory Classroom Activity for 14-16' but suggest the pan lid is kept on as a safety measure. (Any teacher planing on carrying out any activity in the lab., should undertake a risk assessment first.)

I note the IoP also suggests care in using the term 'random':

Teacher: While we were listening to that there didn't seem to be any fixed pattern to the popping. Is there a word that we could use to describe that?

Lydia: Random?

Teacher: Excellent. But the word random has a very special meaning in physics. It isn't like how we think of things in everyday life. When do you use the word random in everyday life?

Lydia: Like if it's unpredictable? Or has no pattern?

https://spark.iop.org/modelling-decay-laboratory

Kieran Maher and 'Kikibooks contributors' suggests readers of their 'Basic Physics of Nuclear Medicine' could "think about putting some in in a pot, adding the corn, heating the pot…" and indeed their readers "might also like to try this out while considering the situation", but warn readers not to "push this popcorn analogy too far" (pp.20-21).

3 Here are some examples I found:

Florida High School teacher Marc Mayntz offers teachers' notes and student instructions for his 'Nuclear Popcorn' activity, where students are told to "Carefully 'spill' the kernels onto the table".

Chelsea Davis (a student?) reports her results in 'Half Life Popcorn Lab' from an approach where kernels are shaken in a Petri dish.

Redwood High School's worksheet for 'Radioactive Decay and Half Life Simulation' has students work with 100 kernels in a box with its sides labelled 1-4 (kernels that have the small end pointed toward side 1 after "a sharp, single shake (up and down, not side to side)" are considered decayed). Students are told at the start to to "Count the popcorn kernels to be certain there are exactly 100 kernels in your box".

This activity is repeated but with (i) kernels pointing to either side 1 or 2; and in a further run (ii) any of sides 1, 2, or 3; being considered decayed. This allows a graph to be drawn comparing all three sets of results.

The same approach is used in the Utah Education network's 'Radioactive Decay' activity, which specifies the use of a shoe box.

A site called 'Chegg' specified "a square box is filled with 100 popcorn kernels". and asked "What alteration in the experimental design would dramatically change the results? Why?" But, sadly, I needed to subscribe to see the answer.

The 'Lesson Planet' site offers 'Nuclear Popcorn' where "Using popcorn kernels spread over a tabletop, participants pick up all of those that point toward the back of the room, that is, those that represent decayed atoms".

'Anonymous' was set a version of this activity, but could not "seem to figure it out". 'Jiskha Homework Help' (tag line: "Ask questions and get helpful responses") helpfully responded,

"You ought to have a better number than 'two units of shake time…'

Read off the graph, not the data table."

(For some reason this brought to mind my sixth form mathematics teacher imploring us in desperation to "look at the ruddy diagram!")

4 Consider the challenge of developing this model to simulate nuclear magnetic resonance or laser excitation!

We can't handle the scientific truth

"If the muscles and other cells of the body burn sugar instead of oxygen…"

Do they think we cannot handle the scientific truth?

I should really have gone to bed, but I was just surfing the channels in case there was some 'must watch' programme I might miss, and I came across a screening of the film 'A few good men'. This had been a very popular movie at one time, and I seem to recall watching it with my late wife. I remembered it as an engaging film, and as an example of the 'courtroom drama' genre: but beyond that I could really only remember Tom Cruise as defence advocate questioning Jack Nicholson's as a commanding officer – and the famous line from Nicholson – "You can't handle the truth!".

This became something of a meme – I suspect now there are a lot of people who 'know' and use that line, who have never even seen the film and may not know what they are quoting from.

So, I  though I might watch a bit, to remind myself what the actual case was about. In brief, a marine stationed at the U.S. Guantánamo Bay naval base and detention camp had died at the hands of two of his comrades. They had not intended to kill, but admitted mistreating him – their defence was they were simply obeying orders in subjecting a colleague who was not measuring up, and was letting the unit down, to some unpleasant, but ultimately (supposedly) harmless, punishment.

The film does not contain a lot of science, but what struck me was the failure to get some science that was invoked right.  I was so surprised at what I thought I'd heard being presented as science, that I went back and replayed a section, and I then decided to see if I  could find the script (by Aaron Sorkin*, screenplay adapted from his own theatre play) on the web, to see if what was said had actually been written into the script.

One of the witnesses is a doctor who is asked by the prosecuting counsel to explain lactic acidosis.

Burning sugar instead of oxygen?

The characters here are:

Capt. Jack Ross (played by Kevin Bacon) the prosecuting counsel,

Dr. Stone (Christopher Guest) and

 

 

 

Lt. Daniel Kaffee (Cruise's character).

On direct examination:

Ross: Dr. Stone, what's lactic acidosis?

Stone: If the muscles and other cells of the body burn sugar instead of oxygen, lactic acid is produced. That lactic acid is what caused Santiago's lungs to bleed.

Ross: How long does it take for the muscles and other cells to begin burning sugar instead of oxygen?

Stone: Twenty to thirty minutes.

Ross: And what caused Santiago's muscles and other cells to start burning sugar? [In the film, the line seems to be: And what caused this process to be speed up in Santiago's muscles?]

Stone: An ingested poison of some kind.

Later, under cross-examination

Kafee: Commander, if I had a coronary condition, and a perfectly clean rag was placed in my mouth, and the rag was accidentally pushed too far down, is it possible that my cells would continue burning sugar after the rag was taken out?

Stone: It would have to be a very serious condition.

What?

If a student suggested that lactic acid is produced when the muscles burn sugar instead of oxygen we would likely consider this an alternative conception (misconception). It is, at best, a clumsy phrasing, and is simply wrong.

Respiration

Metabolism is a set of processes under very fine controls, so whether we should refer to metabolism as burning or not, is a moot point. Combustion tends to be a vigorous process that is usually uncontrolled. But we can see it as a metaphor: carbohydrates are 'burnt' up in the sense that they undergo reactions analogous to burning.

But burning requires oxygen (well, in the lab. we might burn materials in chlorine, but, in general, and in everyday life, combustion is a reaction with oxygen), so what could burning oxygen mean?

In respiration, glucose is in effect reacted with oxygen to produce carbon dioxide and water. However, this is not a single step process, but a complex set of smaller reactions – the overall effect of which is

glucose + oxygen → carbon dioxide + water

Breaking glucose down to lactic acid also acts as an energy source, but is no where near as effective. Our muscles can undertake this ('anaerobic') process when there is insufficient oxygen supply –  for example when undertaking high stamina exercise – but this is best seen as a temporary stop-gap, as lactic acid build up causes problems (cramp for example) – even if not usually death.

Does science matter?

Now clearly the science is not central to the story of 'A few good men'. The main issues are (factual)

  • whether the accused men were acting under orders;

(ethical)

  • the nature of illegal orders,
  • when service personal should question and ignore orders (deontology) given that they seldom have the whole picture (and in this film one of the accused men is presented as something of a simpleton who viewer may suspect should not be given much responsibility for decision making),
  • whether it is acceptable to use corporal or cruel punishment on an under-performing soldier (or marine) given that the lives of many may depend upon their high levels of performance (consequentialism, or perhaps pragmatics)…

There is also a medical issue, regarding whether the torture of the soldier was the primary cause of death, or whether there was an underlying health issue which the medical officer (Stone) had missed and which might also explain the poor performance. [That is a theme which featured large in a recent very high profile real murder case.]

Otherwise the film is about the characters of, and relationships among, the legal officers. Like most good films – this is film about people, and being human in the world, and how we behave towards and relate to each other.

The nature of lactic acidosis is hardly a key point.

But if it is worth including in the script as the assumed cause of death, and its nature relevant – why not get the science right?

Perhaps, because science is complicated and needs to be simplified for the cinema-goer who, after all, wants to be entertained, not lectured?

Perhaps there is no simple account of lactic acidosis which could be included in the script without getting technical, and entering into a long and complicated explanation.

In teaching science…

But surely that is not true. In teaching we often have to employ simplifications which ignore complexity and nuance for the benefit of getting the core idea across to learners. We seek the optimal level of simplification that learners can make good sense of, but which is true to the core essence of the actual science being discussed (it is 'intellectually honest') and provides a suitable basis for later more advanced treatments.

It can be hard to find that optimum level of simplification – but I really do not think that explaining lactic acidosis as burning sugar instead of oxygen could be considered a credit-worthy attempt.

Dr. Stone, can we try again?

What about, something like:

Dr. Stone, what's lactic acidosis?

It occurs when the body tissues do not have sufficient oxygen to fully break down sugar in the usual way, and damaging lactic aid is produced instead of carbon dioxide and water.

I am sure there are lots of possible tweaks here. The point is that the script did not need to go into a long medical lecture, but by including something that was simply nonsensical, and should be obviously wrong to anyone who had studied respiration at school (which should be everyone who has been to school in the past few decades in many countries), it distracts, and so detracts, from the story.

All images from 'A few good men' (1992, Columbia Pictures)

 

 

 

 

 

 

 

 

 

 

* I see that ("acclaimed screenwriter") Aaron Sorkin is planning a new live television version of 'A Few Good Men' – so perhaps the description of lactic acidosis can be updated?