Category: teaching analogy

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!

Neuroadaptation gremlins on the see-saw in your brain

The brain's reward pathway is like a teeter-totter because…

Keith S. Taber

in your brain there is a teeter-totter like in a kids' playground…these neuroadaptation gremlins hopping on the pain side of the balance…the gremlins hop off …But if we …accumulate so many gremlins on the pain side of our balance …we've crossed over into the disease of addiction…we are craving because …it's the gremlins jumping up and down

Dr Anna Lembke talking on 'All in the mind'
Is there a see-saw in your brain?
(Original images by Image by mohamed Hassan and OpenClipart-Vectors from Pixabay) 

Dr Anna Lembke, Professor of Psychiatry at Stanford University explained how addiction relates to dopmaine and the brain's reward pathway with an analogy of a see-saw. She was talking to Sana Qadar for an episode of the the ABC programme 'All in the Mind' called 'How dopamine drives our addictions'.

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 science analogies

A fried brain

During the programme the interviewer (Qadar) uses a metaphor for how addiction influences brain chemistry:

Sana Qadar: "The problem is when we are becoming addicted to something, our brain's ability to naturally produce dopamine gets fried."

Anna Lembke: "So essentially what happens in the brain as we tip toward the compulsive cycle of overconsumption or addiction is that we start to down-regulate our own dopamine production and dopamine transmission in order to compensate for the ways that we are bombarding our brain's reward pathway with too much dopamine through ingestion of these incredibly potent and rewarding substances and behaviours."

What does Sana Qadar mean by 'fried'? Presumably not destroyed, as the subsequent interview suggests that recovery is possible (see below) – although the brain's ability to naturally produce dopamine would surely not recover from actual frying. So, perhaps, fried means disturbed, or damaged? Given the following dialogue it might mean thrown out of balance.

Perhaps Qadar was thinking of the brain as circuitry as the term is commonly applied to damaged circuits (I think the term derives from damage caused by overheating, as can happen when there is a 'short' for example, which does stop the 'fried' components functioning permanently). So, perhaps for Qadar this is a dead metaphor – a term which started as a metaphor but which, with habitual use, has come to be treated as having literal meaning – at least in relation to electrical circuits and, by analogy, brain circuitry?

A fried brain?
(Images by OpenClipart-Vectors and y Roger YI from Pixabay)

Balancing those gremlins

What I found especially interesting is the way Dr Lembke made extensive use of an analogy in her explanation, much in the way teacher might keep referring back to the same metaphor or analogy or model when introducing an abstract topic.

Sana Qadar tells listeners that "to explain how this process unfolds in the brain's reward pathway, Dr Lembke uses the analogy of a teeter-totter or seesaw":

"Because pleasure and pain are processed in the same part of the brain and work like opposite sides of the balance, it means for every pleasure there is a cost and that cost is pain.

So, if you imagine that in your brain there is a teeter-totter like in a kids' playground, that teeter-totter will tip to one side when we experience pleasure, and the opposite side when we experience pain.

But no sooner has that balance tipped to the side of pleasure, for example when I eat a piece of chocolate, then my brain will work very hard to restore a level balance or what neuroscientists call homeostasis. And it does that not just by bringing the balance level again but first by tipping it an equal and opposite amount to the to the side of pain, that is the after-effect, the come-down. I imagine that as these neuroadaptation gremlins hopping on the pain side of the balance to bring it level again.

Now, if we wait long enough, the gremlins hop off and homeostasis is restored as we go back to our baseline tonic level of dopamine firing. But if we continue to ingest addictive substances or behaviours over very long periods of time, we essentially accumulate so many gremlins on the pain side of our balance that we are in a chronic dopamine deficit state, and that is essentially where we get when we've crossed over into the disease of addiction.

Dr Anna Lembke talking on 'All in the mind'

As part of the programme of treatment Dr Lembke has developed for those suffering from additions she often recommends a period of complete abstinence – asking her clients to abstain for at least 30 days

Because 30 days is about the minimum amount of time it takes for the brain to restore baseline dopamine firing. Another way of saying this is 30 days is about the minimum amount of time it takes for the gremlins to hop off the pain side of the balance so that homeostasis or balance can be restored.

… I think in many people it is possible with abstinence to reset the reward pathway, the brain has an enormous amount of plasticity.

Dr Anna Lembke talking on 'All in the mind'

Abstinence is obviously not easy when the person is constantly faced with relevant triggers, as

"…what happens when we are triggered is that we release a little bit of dopamine in the reward pathway. … But if we wait long enough, those gremlins will hop off the pain side of the balance, and balance is restored….we are craving because we are in a dopamine deficit state, it's the gremlins jumping up and down on the pain side of the balance. But if we can just wait a few more moments, they will get off, homeostasis will be restored and that feeling will pass."

"…It's a fine line between pleasure and pain
You've done it once you can do it again
Whatever you've done don't try to explain
It's a fine, fine line between pleasure and pain.."

From the lyrics of the song 'Pleasure and Pain' (covered by Manfred Mann's Earth Band), by Holly Knight & Michael Donald Chapman

It's a fine line between pleasure and pain

Sana Qadar suggests that certain kinds of pain can actually be good for us. From a biological perspective this is clearly so, as pain provides signals to motivate us to change our behaviour (move away from the fire, put down the very heavy object), but that is not what she is referring to. Rather, that "Dr Lembke says it has to do with the fact that pleasure and pain are processed in the same part of the brain":

Well, just like when we press on the pleasure side of the balance the gremlins hop on the pain side and ultimately shift our hedonic setpoint or our joy setpoint to the side of pain, it's also true that when we press on the pain side of the balance, so we intentionally invite psychologically or physically painful experiences into our lives, that those neuroadaptation gremlins will then hop on the pleasure side of the balance and we will start to up-regulate our own endogenous dopamine, not as the primary response to the stimulus but as the after-response

…I'm absolutely not talking about extreme forms of pain like cutting [which is] not a healthy way to get dopamine

…[For example] Michael was somebody who was addicted to cocaine and alcohol, and got into recovery and immediately experienced the dopamine deficit state, those gremlins on the pain side of the balance, he was anxious, he was irritable, and he also felt very numb, kind of an absence of emotions, which was really scary for him.

And he serendipitously discovered in early recovery that if he took a very cold shower, that created for him the same kinds of feelings, in a muted way, that he used to get from drugs, so he got into this practice of every morning taking a cold shower, and it worked great for him."

Dr Anna Lembke talking on 'All in the mind'

Gremlins, indeed?

Of course there is no see-saw in the brain, but a see-saw is a familiar everyday object that people understand can be balanced – or not. And that if more children (of similar size) load up one side than the other it will be out of balance – and it will only level up once the loads are balanced.

Strictly, there are some complications here with the analogue. If the children are at different distances from the fulcrum that will change their turning effect (so two children could balance one of similar mass according to where they are positioned). Similarly, when the moments are balanced the see-saw will not necessarily be level: as 'balance' means no overall turning effect. So, if the see-saw was already at an angle to the horizontal, loading it up in a balanced way should not shift it back to being level.

Perhaps there is something comparable in the reward system to whereabouts children sit on the see-saw – (perhaps some synapses are more sensitive to the effects of dopamine than others?), but this would be over-complicating an analogy that is intended to offer a link to a simple everyday phenomenon.

Are gremlins like children – do they come in different sizes? Perhaps it seems a little childish even to talk of such things in the brain. But there was once a strong (if discouraged these days 1) tradition of considering a homunculus, a little observer, inside the brain as if in a control room. Moreover, if the lauded physicist James Clerk Maxwell could invoke his famous demon to explain aspects of thermodynamics, we should not censure Lembke's metaphorical gremlins.

If this comparison was being used as a teaching analogy in a formal course, then we might want a more careful setting out of the positive and negative aspects of the analogy (those things that do, and do not, map across from the see-saw to the reward system). But Dr Lembke is not trying to teach her clients to pass tests about brain science, but rather give them a way of thinking about their problems that can help them plan and change behaviour – that is, a useful and straightforward model they can apply in overcoming their addictions.

An episode of the radio progrmme/podcast 'All in the mind'
To find out more

Prof. Lembke was talking about a very important topic and here I have only abstracted particular comments to illustrate her use of the analogy. For a fuller account of the topic, and in particular Prof. Lembke's clinical work to help people struggling with addiction, please refer to the full interview.

Work cited:
Note

1 The term is still use, but in a somewhat different sense:

"in neuroanatomy, the cortical homunculus represents either the motor or the sensory distribution along the cerebral cortex of the brain. The motor homunculus is a topographic representation of the body parts and its correspondents along the precentral gyrus of the frontal lobe. While the sensory homunculus is a topographic representation of the body parts along the postcentral gyrus of the parietal lobe."

Nguyen and Duong, 2021

So, nowadays we each have two 'little men' in our brains.

COVID is like photosynthesis because…

An analogy based on a science concept

Keith S. Taber

Photosynthesis illuminating a plant?
(Image by OpenClipart-Vectors from Pixabay)

Analogies, metaphors and similes are used in communication to help make the unfamiliar familiar by suggesting that some novel idea or phenomena being introduced is in some ways like something the reader/listener is already familiar with. Analogies, metaphors and similes are commonly used in science teaching, and also in science writing and journalism.

An analogy maps out similarities in structure between two phenomena or concepts. This example, from a radio programme, compared the COVID pandemic with photosynthesis.

Read about science analogies

Photosynthesis and the pandemic

Professor Will Davies of Goldsmiths, University of London suggested that:

"So, what we were particularly aiming to do, was to understand the collision between a range of different political economic factors of a pre-2020 world, and how they were sort of reassembled and deployed to cope with something which was without question unprecedented.

We used this metaphor of photosynthesis because if you think about photosynthesis in relation to plants, the sun both lights things up but at the same time it feeds them and helps them to grow, and I think one of the things the pandemic has done for social scientists is to serve both as a kind of illumination of things that previously maybe critical political economists and heterodox scholars were pointing to but now became very visible to the mainstream media and to mainstream politics. But at the same time it also accentuated and deepened some of those tendencies such as our reliance on various digital platforms, certain gender dynamics of work in the household, these sort of things that became acute and undeniable and potentially politicised over the course of 2020, 2021."

Prof. Will Davies, talking on 'Thinking Allowed' 1
This image has an empty alt attribute; its file name is Screenshot-2022-06-12-at-21.47.47.png
Will Davies, Professor in Political Economy at Goldsmiths, University of London was talking to sociologist Prof. Laurie Taylor who presents the BBC programme 'Thinking Aloud' as part of an episode called 'Covid and change'

A scientific idea used as analogue

Prof. Davies refers to using "this metaphor of photosynthesis". However he goes on to suggest how the two things he is comparing are structurally similar – the pandemic has shone a light on social issues at the same time as providing the conditions for them to become more extreme, akin to how light both illuminates plants and changes them. A metaphor is an implicit comparison where the reader/listener is left to interpret the comparison, but a metaphor or simile that is explicitly developed to explain the comparison can become an analogy.

Read about science metaphors

Often science concepts are introduced by analogy to more familiar everyday ideas, objects or events. Here, however, a scientific concept, photosynthesis is used as the analogue – the source used to explain something novel. Prof. Davies assumes listeners will be familiar enough with this science concept for it to helpful in introducing his research.

Mischaracterising photosynthesis?

A science teacher might not like the notion that the sun feeds plants – indeed if a student suggested this in a science class it would likely be judged as an alternative conception. In photosynthesis, carbon dioxide (from the atmosphere) and water (usually absorbed from the soil) provide the starting materials, and the glucose that is produced (along with oxygen) enables other processes – such as growth which relies on other substances also being absorbed from the soil. (So-called 'plant foods', which would be better characterised as plant nutritional supplements, contain sources of elements such as nitrogen, phosphorus and potassium). Light is necessary for photosynthesis, but the sunlight is not best considered 'food'.

One might also argue that Prof. Davies has misidentified the source for his analogy, and perhaps he should rather have suggested sunlight as the source metaphor for his comparison as sunlight both illuminates plants and enables them to grow. Photosynthesis takes place inside chloroplasts within a plant's tissues, and does not illuminate the plant. However, Prof. Davies' expertise is in political economy, not natural science, and it was good to see a social scientist looking to use a scientific idea to explain his research.

Baking fresh electrons for the science doughnut

Faster-than-light electrons race from a sitting start and are baked to give off light brighter than millions of suns that can be used to image tiny massage balls: A case of science communication

Keith S. Taber

(The pedantic science teacher)

Ockham's razor

Ockham's razor (also known as Occam's razor) is a principle that is sometimes applied as a heuristic in science, suggesting that explanations should not be unnecessarily complicated. Faced with a straightforward explanation, and an alternative convoluted explanation, then all other things being equal we should prefer the former – not simply accept it, but to treat is as the preferred hypothesis to test out first.

Ockham's Razor is also an ABC radio show offering "a soap box for all things scientific, with short talks about research, industry and policy from people with something thoughtful to say about science". The show used to offer recorded essays (akin to the format of BBC's A Point of View), but now tends to record short live talks.

I've just listened to an episode called The 'science donut' – in fact I listened several time as I thought it was fascinating – as in a few minutes there was much to attend to.

The 'Science Donut': a recent episode of Ockham's Razor

I approached the episode as someone with an interest in science, of course, but also as an educator with an ear to the ways in which we communicate science in teaching. Teachers do not simply present sequences of information about science, but engage pedagogy (i.e., strategies and techniques to support learning). Other science communicators (whether journalists, or scientists themselves directly addressing the public) use many of the same techniques. Teaching conceptual material (such as science principles, theories, models…) can be seen as making the unfamiliar familiar, and the constructivist perspective on how learning occurs suggests this is supported by showing the learner how that which is currently still unfamiliar, is in some way like something familiar, something they already have some knowledge/experience of.

Science communicators may not be trained as teachers, so may sometimes be using these techniques in a less considered or even less deliberate manner. That is, people use analogy, metaphor, simile, and so forth, as a normal part of everyday talk to such an extent that these tropes may be generated automatically, in effect, implicitly. When we are regularly talking about an area of expertise we almost do not have to think through what we are going to say. 1

Science communicators also often have much less information about their audience than teachers: a radio programme/podcast, for example, can be accessed by people of a wide range of background knowledge and levels of formal qualifications.

One thing teachers often learn to do very early in their careers is to slow down the rate of introducing new information, and focus instead on a limited number of key points they most want to get across. Sometimes science in the media is very dense in the frequency of information presented or the background knowledge being drawn upon. (See, for example, 'Genes on steroids? The high density of science communication'.)

A beamline scientist

Dr Emily Finch, who gave this particular radio talk, is a beamline scientist at the Australian Synchrotron. Her talk began by recalling how her family visited the Synchrotron facility on an open day, and how she later went on to work there.

She then gave an outline of the functioning of the synchrotron and some examples of its applications. Along the way there were analogies, metaphors, anthropomorphism, and dubiously fast electrons.

The creation of the god particle

To introduce the work of the particle accelerator, Dr Finch reminded her audience of the research to detect the Higgs boson.

"Do you remember about 10 years ago scientists were trying to make the Higgs boson particle? I see some nods. They sometimes call it the God particle and they had a theory it existed, but they had not been able to prove it yet. So, they decided to smash together two beams of protons to try to make it using the CERN large hadron collider in Switzerland…You might remember that they did make a Higgs boson particle".

This is a very brief summary of a major research project that involved hundreds of scientists and engineers from a great many countries working over years. But this abbreviation is understandable as this was not Dr Finch's focus, but rather an attempt to link her actual focus, the Australian Synchrotron, to something most people will already know something about.

However, aspects of this summary account may have potential to encourage the development of, or reinforce an existing, common alternative conception shared by many learners. This is regarding the status of theories.

In science, theories are 'consistent, comprehensive, coherent and extensively evidenced explanations of aspects of the natural world', yet students often understand theories to be nothing more than just ideas, hunches, guesses – conjectures at best (Taber, Billingsley, Riga & Newdick, 2015). In a very naive take on the nature of science, a scientist comes up with an idea ('theory') which is tested, and is either 'proved' or rejected.

This simplistic take is wrong in two regards – something does not become an established scientific theory until it is supported by a good deal of evidence; and scientific ideas are not simply proved or disproved by testing, but rather become better supported or less credible in the light of the interpretation of data. Strictly scientific ideas are never finally proved to become certain knowledge, but rather remain as theories. 2

In everyday discourse, people will say 'I have a theory' to mean no more that 'I have a suggestion'.
A pedantic scientist or science teacher might be temped to respond:
"no you don't, not yet,"

This is sometimes not the impression given by media accounts – presumably because headlines such as 'research leads to scientist becoming slightly more confident in theory' do not have the same impact as 'cure found', 'discovery made, or 'theory proved'.

Read about scientific certainty in the media

The message that could be taken away here is that scientists had the idea that Higgs boson existed, but they had not been able to prove it till they were able to make one. But the CERN scientists did not have a Higgs boson to show the press, only the data from highly engineered detectors, analysed through highly complex modelling. Yet that analysis suggested they had recorded signals that closely matched what they expected to see when a short lived Higgs decayed allowing them to conclude that it was very likely one had been formed in the experiment. The theory motivating their experiment was strongly supported – but not 'proved' in an absolute sense.

The doughnut

Dr Finch explained that

"we do have one of these particle accelerators here in Australia, and it's called the Australian Synchrotron, or as it is affectionately known the science donut

…our synchrotron is a little different from the large hadron collider in a couple of main ways. So, first, we just have the one beam instead of two. And second, our beam is made of electrons instead of protons. You remember electrons, right, they are those tiny little negatively charged particles and they sit in the shells around the atom, the centre of the atom."

Dr Emily Finch talking on Ockham's Razor

One expects that members of the audience would be able to respond to this description and (due to previous exposure to such representations) picture images of atoms with electrons in shells. 'Shells' is of course a kind of metaphor here, even if one which with continual use has become a so-called 'dead metaphor'. Metaphor is a common technique used by teachers and other communicators to help make the unfamiliar familiar. In some simplistic models of atomic structure, electrons are considered to be arranged in shells (the K shell, the L shell, etc.), and a simple notation for electronic configuration based on these shells is still often used (e.g., Na as 2.8.1).

Read about science metaphors

However, this common way of talking about shells has the potential to mislead learners. Students can, and sometimes do, develop the alternative conception that atoms have actual physical shells of some kind, into which the electrons are located. The shells scientists refer to are abstractions, but may be misinterpreted as material entities, as actual shells. The use of anthropomorphic language, that is that the electrons "sit in the shells", whilst helping to make the abstract ideas familiar and so perhaps comfortable, can reinforce this. After all, it is difficult to sit in empty space without support.

The subatomic grand prix?

Dr Finch offers her audience an analogy for the synchrotron: the electrons "are zipping around. I like to think of it kind of like a racetrack." Analogy is another common technique used by teachers and other communicators to help make the unfamiliar familiar.

Read about science analogies

Dr Finch refers to the popularity of the Australian Formula 1 (F1) Grand Prix that takes place in Melbourne, and points out

"Now what these race enthusiasts don't know is that just a bit further out of the city we have a race track that is operating six days a week that is arguably far more impressive.

That's right, it is the science donut. The difference is that instead of having F1s doing about 300 km an hour, we have electrons zipping around at the speed of light. That's about 300 thousand km per second.

Dr Emily Finch talking on Ockham's Razor

There is an interesting slippage – perhaps a deliberate rhetoric flourish – from the synchrotron being "kind of like a racetrack" (a simile) to being "a race track" (a metaphor). Although racing electrons lacks a key attraction of an F1 race (different drivers of various nationalities driving different cars built by competing teams presented in different livery – whereas who cares which of myriad indistinguishable electrons would win a race?) that does not undermine the impact of the mental imagery encouraged by this analogy.

This can be understood as an analogy rather than just a simile or metaphor as Dr Finch maps out the comparison:

target conceptanalogue
a synchotrona racetrack
operates six days a week[Many in the audience would have known that the Melbourne Grand Prix takes place on a 'street circuit' that is only set up for racing one weekend each year.]
racing electronsracing 'F1s' (i.e., Grand Prix cars)
at the speed of light at about 300 km an hour
An analogy between the Australian Synchrotron and the Melbourne Grand Prix circuit

So, here is an attempt to show how science has something just like the popular race track, but perhaps even more impressive – generating speeds orders of magnitude greater than even Lewis Hamilton could drive.

They seem to like their F1 comparisons at the Australian Synchrotron. I found another ABC programme ('The Science Show') where Nobel Laureate "Brian Schmidt explains, the synchrotron is not being used to its best capability",

"the analogy here is that we invested in a $200 million Ferrari and decided that we wouldn't take it out of first gear and do anything other than drive it around the block. So it seems a little bit of a waste"

Brian Schmidt (Professor of Astronomy, and Vice Chancellor, at Australian National University)
A Ferrari being taken for a spin around the block in Melbourne (Image by Lee Chandler from Pixabay )

How fast?

But did Dr Finch suggest there that the electrons were travelling at the speed of light? Surely not? Was that a slip of the tongue?

"So, we bake our electrons fresh in-house using an electron gun. So, this works like an old cathode ray tube that we used to have in old TVs. So, we have this bit of tungsten metal and we heat it up and when it gets red hot it shoots out electrons into a vacuum. We then speed up the electrons, and once they leave the electron gun they are already travelling at about half the speed of light. We then speed them up even more, and after twelve metres, they are already going at the speed of light….

And it is at this speed that we shoot them off into a big ring called the booster ring, where we boost their energy. Once their energy is high enough we shoot them out again into another outer ring called the storage ring."

Dr Emily Finch talking on Ockham's Razor

So, no, the claim is that the electrons are accelerated to the speed of light within twelve metres, and then have their energy boosted even more.

But this is contrary to current physics. According to the currently accepted theories, and specifically the special theory of relativity, only entities which have zero rest mass, such as photons, can move at the speed of light.

Electrons have a tiny mass by everyday standards (about 0.000 000 000 000 000 000 000 000 001 g), but they are still 'massive' particles (i.e., particles with mass) and it would take infinite energy to accelerate a single tiny electron to the speed of light. So, given our current best understanding, this claim cannot be right.

I looked to see what was reported on the website of the synchrotron itself.

The electron beam travels just under the speed of light – about 299,792 kilometres a second.

https://www.ansto.gov.au/research/facilities/australian-synchrotron/overview

Strictly the electrons do not travel at the speed of light but very nearly the speed of light.

The speed of light in a vacuum is believed to be 299 792 458 ms-1 (to the nearest metre per second), but often in science we are working to limited precision, so this may be rounded to 2.998 ms-1 for many purposes. Indeed, sometimes 3 x 108 ms-1 is good enough for so-called 'back of the envelope' calculations. So, in a sense, Dr Finch was making a similar approximation.

But this is one approximation that a science teacher might want to avoid, as electrons travelling at the speed of light may be approximately correct, but is also thought to be physically impossible. That is, although the difference in magnitude between

  • (i) the maximum electron speeds achieved in the synchrotron, and
  • (ii) the speed of light,

might be a tiny proportional difference – conceptually the distinction is massive in terms of modern physics. (I imagine Dr Finch is aware of all this, but perhaps her background in geology does not make this seem as important as it might appear to a physics teacher.)

Dr Finch does not explicitly say that the electrons ever go faster than the speed of light (unlike the defence lawyer in a murder trial who claimed nervous impulses travel faster than the speed of light) but I wonder how typical school age learners would interpret "they are already going at the speed of light….And it is at this speed that we shoot them off into a big ring called the booster ring, where we boost their energy". I assume that refers to maintaining their high speeds to compensate for energy transfers from the beam: but only because I think Dr Finch cannot mean accelerating them beyond the speed of light. 3

The big doughnut

After the reference to how "we bake our electrons fresh in-house", Dr Finch explains

And so it is these two rings, these inner and outer rings, that give the synchrotron its nick name, the science donut. Just like two rings of delicious baked electron goodness…

So, just to give you an idea of scale here, this outer ring, the storage ring, is about forty one metres across, so it's a big donut."

Dr Emily Finch talking on Ockham's Razor
A big doughnut? The Australian Synchrotron (Source Australia's Nuclear Science and Technology Organisation)

So, there is something of an extended metaphor here. The doughnut is so-called because of its shape, but this doughnut (a bakery product) is used to 'bake' electrons.

If audience members were to actively reflect on and seek to analyse this metaphor then they might notice an incongruity, perhaps a mixed metaphor, as the synchrotron seems to shift from being that which is baked (a doughnut) to that doing the baking (baking the electrons). Perhaps the electrons are the dough, but, if so, they need to go into the oven.

But, of course, humans implicitly process language in real time, and poetic language tends to be understood intuitively without needing reflection. So, a trope such as this may 'work' to get across the flavour (sorry) of an idea, even if under close analysis (by our pedantic science teacher again) the metaphor appears only half-baked.

Perverting the electrons

Dr Finch continued

"Now the electrons like to travel in straight lines, so to get them to go round the rings we have to bend them using magnets. So, we defect the electrons around the corners [sic] using electromagnetic fields from the magnets, and once we do this the electrons give off a light, called synchrotron light…

Dr Emily Finch talking on Ockham's Razor

Now electrons are not sentient and do not have preferences in the way that someone might prefer to go on a family trip to the local synchrotron rather than a Formula 1 race. Electrons do not like to go in straight lines. They fit with Newton's first law – the law of inertia. An electron that is moving ('travelling') will move ('travel') in a straight line unless there is net force to pervert it. 4

If we describe this as electrons 'liking' to travel in straight lines it would be just as true to say electrons 'like' to travel at a constant speed. Language that assigns human feelings and motives and thoughts to inanimate objects is described as anthropomorphic. Anthropomorphism is a common way of making the unfamiliar familiar, and it is often used in relation to molecules, electrons, atoms and so forth. Sadly, when learners pick up this kind of language, they do not always appreciate that it is just meant metaphorically!

Read about anthropomorphism

The brilliant light

Dr Finch tells her audience that

"This synchrotron light is brighter than a million suns, and we capture it using special equipment that comes off that storage ring.

And this equipment will focus and tune and shape that beam of synchrotron light so we can shoot it at samples like a LASER."

Dr Emily Finch talking on Ockham's Razor

Whether the radiation is 'captured' is a moot point, as it no longer exists once it has been detected. But what caught my attention here was the claim that the synchrotron radiation was brighter than a million suns. Not because I necessarily thought this bold claim was 'wrong', but rather I did not understand what it meant.

The statement seems sensible at first hearing, and clearly it means qualitatively that the radiation is very intense. But what did the quantitative comparison actually mean? I turned again to the synchrotron webpage. I did not find an answer there, but on the site of a UK accelerator I found

"These fast-moving electrons produce very bright light, called synchrotron light. This very intense light, predominantly in the X-ray region, is millions of times brighter than light produced from conventional sources and 10 billion times brighter than the sun."

https://www.diamond.ac.uk/Home/About/FAQs/About-Synchrotrons.html#

Sunlight spreads out and its intensity drops according to an inverse square law. Move twice as far away from a sun, and the radiation intensity drops to a quarter of what it was when you were closer. Move to ten times as far away from the sun than before, and the intensity is 1% of what it was up close.

The synchrotron 'light' is being shaped into a beam "like a LASER". A LASER produces a highly collimated beam – that is, the light does not (significantly) spread out. This is why football hooligans choose LASER pointers rather than conventional torches to intimidate players from a safe distance in the crowd.

Comparing light with like

This is why I do not understand how the comparison works, as the brightness of a sun depends how close you are too it – a point previously discussed here in relation to NASA's Parker solar probe (NASA puts its hand in the oven). If I look out at the night sky on a clear moonlight night then surely I am exposed to light from more "than a million suns" but most of them are so far away I cannot even make them out. Indeed there are faint 'nebulae' I can hardly perceive that are actually galaxies shining with the brightness of billions of suns. 5 If that is the comparison, then I am not especially impressed by something being "brighter than a million suns".

How bright is the sun? it depends which planet you are observing from. (Images by AD_Images and Gerd Altmann from Pixabay)

We are told not to look directly at the sun as it can damage our eyes. But a hypothetical resident of Neptune or Uranus could presumably safely stare at the sun (just as we can safely stare at much brighter stars than our sun because they are so far away). So we need to ask :"brighter than a million suns", as observed from how far away?

How bright is the sun? That depends on viewing conditions
(Image by UteHeineSch from Pixabay)

Even if referring to our Sun as seen from the earth, the brightness varies according to its apparent altitude in the sky. So, "brighter than a million suns" needs to be specified further – as perhaps "more than a million times brighter than the sun as seen at midday from the equator on a cloudless day"? Of course, again, only the pedantic science teacher is thinking about this: everyone knows well enough what being brighter than a million suns implies. It is pretty intense radiation.

Applying the technology

Dr Finch went on to discuss a couple of applications of the synchrotron. One related to identifying pigments in art masterpieces. The other was quite timely in that it related to investigating the infectious agent in COVID.

"Now by now you have probably seen an image of the COVID virus – it looks like a ball with some spikes on it. Actually it kind of looks like those massage balls that your physio makes you buy when you turn thirty and need to to ease all your physical ailments that you suddenly have."

Dr Emily Finch talking on Ockham's Razor
Coronavirus particles and massage balls…or is it…
(Images by Ulrike Leone and Daniel Roberts from Pixabay)

Again there is an attempt to make the unfamiliar familiar. These microscopic virus particles are a bit like something familiar from everyday life. Such comparisons are useful where the everyday object is already familiar.

By now I've seen plenty of images of the coronavirus responsible for COVID, although I do not have a physiotherapist (perhaps this is a cultural difference – Australians being so sporty?) So, I found myself using this comparison in reverse – imagining that the "massage balls that your physio makes you buy" must be like larger versions of coronavirus particles. Having looked up what these massage balls (a.k.a. hedgehog balls it seems) look like, I can appreciate the similarity. Whether the manufacturers of massage balls will appreciate their products being compared to enormous coronavirus particles is, perhaps, another matter.

Work cited:
  • Taber, K. S., Billingsley, B., Riga, F., & Newdick, H. (2015). English secondary students' thinking about the status of scientific theories: consistent, comprehensive, coherent and extensively evidenced explanations of aspects of the natural world – or just 'an idea someone has'. The Curriculum Journal, 1-34. doi: 10.1080/09585176.2015.1043926
Notes:

1 At least, depending how we understand 'thinking'. Clearly there are cognitive processes at work even when we continue a conversation 'on auto pilot' (to employ a metaphor) whilst consciously focusing on something else. Only a tiny amount of our cognitive processing (thinking?) occurs within conscousness where we reflect and deliberate (i.e., explicit thinking?) We might label the rest as 'implicit thinking', but this processing varies greatly in its closeness to deliberation – and some aspects (for example, word recognition when listening to speech; identifying the face of someone we see) might seem to not deserve the label 'thinking'?

2 Of course the evidence for some ideas becomes so overwhelming that in principle we treat some theories as certain knowledge, but in principle they remain provisional knowledge. And the history of science tells us that sometimes even the most well-established ideas (e.g., Newtonian physics as an absolutely precise description of dynamics; mass and energy as distinct and discrete) may need revision in time.

3 Since I began drafting this article, the webpage for the podcast has been updated with a correction: "in this talk Dr Finch says electrons in the synchrotron are accelerated to the speed of light. They actually go just under that speed – 99.99998% of it to be exact."

4 Perversion in the sense of the distortion of an original course

5 The term nebulae is today reserved for clouds of dust and gas seen in the night sky in different parts of our galaxy. Nebulae are less distinct than stars. Many of what were originally identified as nebulae are now considered to be other galaxies immense distances away from our own.

A discriminatory scientific analogy

Animals and plants as different kinds of engines

Keith S. Taber

Specimens of two different types of natural 'engines'.
Portrait of Sir Kenelm Digby, 1603-65 (Anthony van Dyck: From Wikimedia Commons, the free media repository)

In this post I discuss a historical scientific analogy used to discuss the distinction between animals and plants. The analogy was used in a book which is said to be the first major work of philosophy published in the English language, written by one of the founders of The Royal Society of London for Improving Natural Knowledge ('The Royal Society'), Sir Kenelm Digby.

Why take interest in an out-of-date analogy?

It is quite easy to criticise some of the ideas of early modern scientists in the light of current scientific knowledge. Digby had some ideas which seem quite bizarre to today's reader, but perhaps some of today's canonical scientific ideas, and especially more speculative theories being actively proposed, may seem equally ill-informed in a few centuries time!

There is a value in considering historical scientific ideas, in part because they help us understand a little about the path that scientists took towards current scientific thinking. This might be valuable in avoiding the 'rhetoric of conclusions', where well-accepted ideas become so familiar that we come to take them for granted, and fail to appreciate the ways in which such ideas often came to be accepted in the face of competing notions and mixed experimental evidence.

For the science educator there are added benefits. It reminds us that highly intelligent and well motivated scholars, without the value of the body of scientific discourse and evidence available today, might sensibly come up with ideas that seem today ill-conceived, sometimes convoluted, and perhaps even foolish. That is useful to bear in mind when our students fail to immediately understand the science they are taught and present with alternative conceptions that may seem illogical or fantastic to the teacher. Insight into the thought of others can help us consider how to shift their thinking and so can make us better teachers.

Read about historical scientific conceptions

Analogies as tools for communicating science

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 scientific analogies

Nature made engines

Digby presents his analogy for considering the difference between plants and animals in his 'Discourse on Bodies', the first part of his comprehensive text known as his 'Two Discourses' completed in 1644, and in which he sets out something of a system of the world.1 Although, to a modern scientific mind, many of Digby's ideas seem odd, and his complex schemes sometimes feel rather forced, he shared the modern scientific commitment that natural phenomena should be explained in terms of natural causes and mechanisms. (That is certainly not to suggest he was an atheist, as he was a committed Roman Catholic, but he assumed that nature had been set up to work without 'occult' influences.)

Before introducing an analogy between types of living things and types of engines, Digby had already prepared his readers by using the term 'engine' metaphorically to refer to living things. He did this after making a distinction between matter dug out of the ground as a single material, and other specimens which although highly compacted into single bodies of material clearly comprised of "differing parts" that did not work together to carry out any function, and seemed to have come together by "chance and by accident"; and where, unlike in living things (where removed parts tended to stop functioning), the separate parts could be "severed from [one] another" without destroying any underlying harmonic whole. He contrasted these accidental complexes with,

"other bodies in which this manifest and notable difference of parts, carries with it such subordination of one of them unto another, as we cannot doubt but that nature made such engines (if so I may call them) by design; and intended that this variety should be in one thing; whole unity and being what it is, should depend of the harmony of the several differing parts, and should be destroyed by their separation".

Digby emphasising the non-accidental structure of living things (language slightly tidied for a modern reader).

Digby was writing long before Charles Darwin's work, and accepted the then widely shared idea that there was design in nature. Today this would be seen as teleological, and not appropriate in a scientific account. A teleological account can be circular (tautological) if the end result of some process is explained as due to that process having a purpose. [Consider the usefulness as an 'explanation' that 'oganisms tend to become more complex over time as nature strives for complexity'. 2]

Read about teleology

Scientists today are expected to offer accounts which do not presuppose endpoints. That does not mean that a scientists cannot believe there is purpose in the world, or even that the universe was created by a purposeful God – simply that scientific accounts cannot 'cheat' by using arguments that something happens because God wished it, or nature was working towards it. That is, it should not make any difference whether a scientist believes God is the ultimate cause of some phenomena (through creating the world, and setting up the laws of nature) as science is concerned with the natural 'mechanisms' and causes of events.

Read about science and religion

Two types of engines

In the part of his treatise on bodies that concerns living things, Digby gives an account of two 'engines' he had seen many years before when he was travelling in Spain. This was prior to the invention of the modern steam engine, and these engines were driven by water (as in water mills). 3

Digby introduces two machines which he considers illustrate "the natures of these two kinds of bodies [i.e., plants and animals]"

He gives a detailed account of one of the engines, explaining that the mechanism has one basic function – to supply water to an elevated place above a river.

  • 1/4
  • 2/4
  • 3/4
  • 4/4

His other engine example (apparently recalled in less detail – he acknowledges having a "confused and cloudy remembrance" ) was installed in a mint in a mine where it had a number of different functions, including:

  • producing metal of the correct thickness for coinage
  • stamping the metal with the coinage markings
  • cutting the coins from the metal
  • transferring the completed coins into the supply room.

These days we might see it as a kind of conveyor belt moving materials through several specialist processes.

Different classes of engine

Digby seems to think this is a superior sort of engine to the single function example.

For Digby, the first type of engine is like a plant,

"Thus then; all sorts of plants, both great and small, may be compared to our first engine of the waterwork at Toledo, for in them all the motion we can discern, is of one part transmitting unto the next to it, the juice which it received from that immediately before it…"

Digby comparing a plant to a single function machine

The comments here about juice may seem a bit obscure, as Digby has an extended explanation (over several pages) of how the growth and structure of a plant are based on a single kind of vascular tissue and a one-way transport of liquid. 4 Liquid rises up through the plant just as it was raised up by the mechanism at Toldeo

The multi-function 'engine' (perhaps ironically better considered in today's terms as an industrial plant!) is however more like an animal,

"But sensible living creatures, we may fitly compare to the second machine of the mint at Segovia. For in them, though every part and member be as it were a complete thing of itself, yet every one requires to be directed and put on in its motion by another; and they must all of them (though of very different natures and kinds of motion) conspire together to effect any thing that may be for the use and service of the whole. And thus we find in them perfectly the nature of a mover and a moveable; each of them moving differently from one another, and framing to themselves their own motions, in such sort as is more agreeable to their nature, when that part which sets them on work hath stirred them up.

And now because these parts (the movers and the moved) are parts of one whole; we call the entire thing automaton or…a living creature".

Digby comparing animals to more complex machines (language slightly tidied for a modern reader)

So plants were to animals as a single purpose mechanism was to a complex production line.

Animals as super-plants

Digby thought animals and plants shared in key characteristics of generation (we would say reproduction), nutrition, and augmentation (i.e., growth), as well as suffering sickness, decay and death. But Digby did not just think animals were different to plants, but a superior kind.

He explains this both in terms of the animal having functions that be did not beleive applied to plants,

And thus you see this plant [sic] has the virtue both of sense or feeling; that is, of being moved and affected by external objects lightly striking upon it; as also of moving itself, to or from such an object; according as nature shall have ordained.

but he also related to this as animals being more complex. Whereas the plant was based on a vascular system involving only one fluid, this super-plant-like-entity, had three. In summary,

this plant [sic, the animal] is a sensitive creature, composed of three sources, the heart, the brain, and the liver: whose are the arteries, the nerves, and the veins; which are filled with vital spirits, with animal spirits, and with blood: and by these the animal is heated, nourished, and made partaker of sense and motion.

A historical analogy to explain the superiority of animals to plants

[The account here does not seem entirely consistent with other parts of the book, especially if the reader is supposed to associate a different fluid with each of the three systems. Later in the treatise, Digby refers to Harvey's work about circulation of the blood (including to the liver), leaving the heart through arteries, and to veins returning blood to the heart. His discussion of sensory nerves suggest they contain 'vital spirits'.]

Some comments on Digby's analogy

Although some of this detail seems bizarre by today's standards, Digby was discussing ideas about the body that were fairly widely accepted. As suggested above, we should not criticise those living in previous times for not sharing current understandings (just as we have to hope that future generations are kind to our reasonable mistakes). There are, however, two features of this use of analogy I thought worth commenting on from a modern point of view.

The logic of making the unfamiliar familiar

If such analogies are to be used in teaching and science communication, then they are a tactic we can use to 'make the unfamiliar familiar', that is to help others understand what are sometimes difficult (e.g., abstract, counter-intuitive) ideas by pointing out they are somewhat like something the person is already familiar with and feels comfortable that they understand.

Read about teaching as 'making the unfamiliar familiar'

In a teaching context, or when a scientist is being interviewed by a journalist, it is usually important that the analogue is chosen so it is already familiar to the audience. Otherwise either the analogy does not help explain anything, or time has to be spent first explaining the analogy, before it can be employed.

In that sense, then, we might question Digby's example as not being ideal. He has to exemplify the two types of machines he is setting up as the analogue before he can make an analogy with it. Yet this is not a major problem here for two reasons.

Firstly, a book affords a generosity to an author that may not be available to a teacher or a scientist talking to a journalist or public audience. Reading a book (unlike a magazine, say) is a commitment to engagement in depth and over time, and a reader who is still with Digby by his Chapter 23 has probably decided that continued engagement is worth the effort.

Secondly, although most of his readers will not be familiar with the specific 'engines' he discusses from his Spanish travels, they will likely be familiar enough with water mills and other machines and devices to readily appreciate the distinction he makes through those examples. The abstract distinction between two classes of 'engine' is therefore clear enough, and can then be used as an analogy for the difference between plants and animals.

A biased account

However, today we would not consider this analogy to be applicable, even in general terms, leaving aside the now discredited details of plant and animal anatomy and physiology. An assumption behind the comparison is that animals are superior to plants.

In part, this is explained in terms of the plants apparent lack of sensitivity (later 'irritability' would be added as a characteristic of living things, shared by plants) and their their lack of ability in getting around, and so not being able to cross the room to pick up some object. In part, this may be seen as an anthropocentric notion: as humans who move around and can handle objects, it clearly seems to us with our embodied experience of being in the world that a form of life that does not do this (n.b., does not NEED to do this) is inferior. This is a bit like the argument that bacteria are primitive forms of life as they have evolved so little (a simplification, of course) over billions of years: which can alternatively be understood as showing how remarkably adapted they already were, to be able to successfully occupy so many niches on earth without changing their basic form.

There is also a level of ignorance about plants. Digby saw the plant as having a mechanism that moved moisture from the soil through the plant, but had no awareness of the phloem (only named in the nineteenth century) that means that transport in a plant is not all in one direction. He also did not seem to appreciate the complexity of seasonal changes in plants which are much more complex than a mechanism carrying out a linear function (like lifting water to a privileged person who lives above a river). He saw much of the variation in plant structures as passive responses to external agents. His idea of human physiology are also flawed by today's standards, of course.

Moreover, in Digby's scheme (from simple minerals dug from the ground, to accidentally compacted complex materials, to plants and then animals) there is a clear sense of that long-standing notion of hierarchy within nature.

The great chain of being

That is, the great chain of being, which is a system for setting out the world as a kind of ladder of superior and inferior forms. Ontology is sometimes described as the study of being , and typologies of different classes of entities are sometimes referred to as ontologies. The great chain of being can be understood as a kind of ontology distinguishing the different types of things that exist – and ranking them.

Read about ontology

In this scheme (or rather schemes, as various versions with different levels of detail and specificity had been produced – for example discriminating the different classes of angels) minerals come below plants, which come below animals. To some extent Digby's analogy may reflect his own observations of animals and plants leading him to think animals were collectively and necessarily more complex than plants. However, ideas about the great chain of being were part of common metaphysical assumptions about the world. That is, most people took it for granted that there was such hierarchy in nature, and therefore they were likely to interpret what they observed in those terms.

Digby made the comparison between increasing complexity in moving from plant to animal as being a similar kind of step-up as when moving from inorganic material to plants,

But a sensitive creature, being compared to a plant, [is] as a plant is to a mixed [inorganic] body; you cannot but conceive that he must be compounded as it were of many plants, in like sort as a plant is of many mixed bodies.

Digby, then, was surely building his scheme upon his prior metaphysical commitments. Or, as we might say these days, his observations of the world were 'theory-laden'. So, Digby was not only offering an analogy to help discriminate between animals and plants, but was discriminating against plants in assuming they were inherently inferior to animals. I think that is a bias that is still common today.

Work cited:
  • Digby, K. (1644/1665). Two Treatises: In the one of which, the nature of bodies; In the other, the nature of mans soule, is looked into: in ways of the discovery of the immortality of reasonable soules. (P. S. MacDonald Ed.). London: John Williams.
  • Digby, K. (1644/2013). Two Treatises: Of Bodies and of Man's Soul (P. S. MacDonald Ed.): The Gresham Press.
  • Taber, K. S. & Watts, M. (2000) Learners' explanations for chemical phenomena, Chemistry Education: Research and Practice in Europe, 1 (3), pp.329-353. [Free access]
Notes:

1 This is a fascinating book with many interesting examples of analogies, similes, metaphor, personification and the like, and an interesting early attempt to unify forces (here, gravity and magnetism). (I expect to write more about this over time.) The version I am reading is a 2013 edition (Digby, 1644/2013) which has been edited to offer consistent spellings (as that was not something many authors or publishers concerned themselves with at the time). The illustrations, however, are from a facsimile of an original publication (Digby, 1644/1645: which is now out of copyright so can be freely reproduced).

2 Such explanations may be considered as a class of 'pseudo-explanations': that give the semblance of explanation without actually explaining very much (Taber & Watts, 2000).

3 The aeolipile (e.g., Hero's engine) was a kind of steam engine – but was little more than a novelty where water boiled in a vessel with suitably directed outlets and free to rotate, causing it to spin. However, the only 'useful' work done was in turning the engine itself.

4 This relates to his broader theory of matter which still invokes the medieval notion of the four elements, but is also an atomic theory involving tiny particles that can pass into apparently solid materials due to pores and channels much too small to be visible.

How is a well-planned curriculum like a protein?

Because it has different levels of structure providing functionality

Keith S. Taber

I have been working on a book about pedagogy, and was writing something about sequencing teaching. I was setting out how well-planned teaching has a structure that has several levels of complexity – and I thought a useful analogy here (as the book is primarily aimed at chemistry educators) might be protein structure.

Proteins can have very complex structures. (Image by WikimediaImages from Pixabay )

Proteins are usually considered to have at least three, or often four, levels of structure. Protein structure is not just of intellectual interest, but has critical functional importance. It is the shape, conformation, of the protein molecule which allows it to have its function. Now, I should be careful here, as I am well aware (and have discussed on the site) how the language we often use when discussing organisms can seem teleological.

Read about teleology

We analyse biological structures and processes, and when considering the component parts can see them as having some function in relation to that overall structure or process. That can give the impression of purpose – as though someone designed the shape of the protein with a particular function in mind. That can give the impression of teleological thinking – seeing nature as having a purpose. The scientific understanding is that proteins with their complex shapes that are just right for their observed functions have been subject to natural selection over a very long period – evolving along with the structures and processes they are part of.

The importance of protein shape

The shape of a protein can allow it to act as a catalyst that will allow, say, a polysaccharide to break down into simple sugars at body temperature and at a rate that can support an organism's metabolism (when the rate without the enzyme would only give negligible amounts of product ). The shape of a protein, as in haemoglobin, may allow a complex to exist which either binds with oxygen or releases it depending on the local conditions in different parts of the body. And so forth.

Now, chemically, proteins are of the form of polyamides – substances that can be understood to have a molecular structure of connected amide units (above left, source: Wikipedia) in a long chain that results from polymerising amino acid units (amino acid structure shown above right, source: Wikipedia). An amino acid molecule has two functional groups – an amide group (-NH2) which allows the compounds to react with carboxylic acids (including amino acids for example), and a carboxylic acid group (-COOH) that allows the compound to react with amides (including amino acids for example). So, amino acids can polymerise as each amino acid molecule has two sites that can be loci for the reaction.

Molecular structure of a compound formed by four amino acids – the peptide linkage (highlighted orange) is formed from part (-CO-) of the acid group (-COOH, as outlined in red) of one amino acid molecule with part (-NH-) of the amine group (-NH2, as outlined in cyan) of another amino acid molecule (which may be of the same or a different amino acid). In proteins the chains are much longer. Original image from Wikipedia

Special examples of polyamides

So, proteins are polyamides. But this does not mean that polyamides are proteins. In the same way that chemistry Nobel prize winners are scientists – but not all scientists are Nobel laureates. So, being a polyamide is a necessary, but not a sufficient, condition for being a protein. For examples, nylons are also polyamides, but are not proteins. 1

Proteins tend to be very complex polyamides, which are built up from a number of different amino acids (of which 20 are found in proteins). Each amino acid has a different molecular structure – there is the common feature which allows the peptide linkages to form, but each amino acid also has a different side chain or 'residue' as part of its molecule. But just being a large, complex, polypeptide built from a selection of those 20 amino acids does not necessarily lead to a protein found in livings things. The key point about the protein is that its very specific shape allows it to have the function it does. Indeed there are many billions of polyamide structures of similar complexity to naturally found proteins which could exist (and perhaps do somewhere), but which have no role in living organisms (on this planet at least!)

A simple teaching analogy often used to explain enzyme specificity is that of a lock and key. Whilst somewhat simplistic, if we consider that the protein has to have just the right shape to 'fit' the 'substrate' molecule then it is clear that the precise shape is important. A key that opens a door lock has to be precisely shaped. (The situation with an enzyme is actually more demanding, as the molecule can change its shape according to whether a substrate is bound – so it needs to be the right shape to bind to the substrate molecular and then the right shape to release the product molecule.)

So a functioning protein molecule has a very specific shape, indeed sometimes a specific profile of shapes as it interacts with other molecules, and this can be understood to arise from several levels of structure.

Four levels of structure

The primary structure is the sequence of amino acid residues along the polypeptide skeleton.

The amino acid sequence in polypeptide chains in human insulin (with the amino acids represented by conventional three letter abbreviations) – image from Saylor Academy, 2012 open access text: The Basics of General, Organic, and Biological Chemistry

The chain is not simply linear, or a zigzag shape (as we might commonly represent an organic molecules based on a chain of carbon atoms). Rather the interactions between the peptide units, causes the chain to form a more complex three-dimensional structure, such as a helix. This is the secondary structure.

Protein chains tend to form into shapes such as helices (This example: Crystal structure of the DNA-binding protein Sso10a from Sulfolobus solfataricus; from the protein data base PDB DOI: 10.2210/pdb4AYA/pdb.)

Because the secondary structure allows the amino acid residues on different parts of the chain to be close, interactions, forms of bonding, form between different points on the chain. (As shown in the representation of the insulin structure above.) This depends on the amino acid sequence as the different residues have different sizes, shapes and functional groups – so interactions will occur between particular residue pairs. This adds another level of structure.

A coiled cable can take on various overall shapes (Image by Brett Hondow from Pixabay )

Imagine taking a coiled cable somewhat like the helical secondary structure), such as used for some headphone, and folding this into a more complex shape. This is the tertiary structure, and gives the protein its unique shape, which it turn makes it suitable to act as an enzyme or hormone or whatever.

Proteins may be even more complex, as they may comprise complexes of several chains, closely bound together by weak chemical bonds. Haemoglobin, for example, has four such subunits arranged in a quaternary structure.

A representation of the structure of a haemoglobin protein – with the four interlinked chains shown in different colours (Structure determination of haemoglobin from Donkey (equus asinus) at 3.0 Angstrom resolution, from the protein data base: PDB DOI: 10.2210/pdb1S0H/pdb)

But what has this got to do with sequencing curriculum?

When planning teaching, such as when developing a course or writing a 'scheme of work', one has to consider how to sequence the introduction of course material as well as learning activities. This can be understood to have different levels in terms of the considerations we might take into account.

A well-designed curriculum sequence has several levels of structure (ordering, building, cross-linking) affording more effective teaching

Primary structure and conceptual analysis

A fundamental question (once we have decided what falls within the scope of the course, and selected the subject matter) is how to order the introduction of topics and concepts. There is usually some flexibility here, but as some concepts are best understood in terms of other more fundamental ideas, there are more and less logical ways to go about this. 'Conceptual analysis' is the technique which is used to break down the conceptual structure of material to see what prerequisite learning is necessary before discussing new material.

For example, if we wish to teach for understanding then it probably does not make sense to introduce double bonds before the concept of covalent bonds, or neutralisation before teaching something about acids, or d-level splitting before introducing ideas about atomic orbitals, or the rate determining step of a reaction before teaching about reaction rate. In biology, it would not make sense to teach about mitochondria before the concept of cells had been introduced. In physics, one would not seek to teach about conservation of momentum, before having introduced the concept of momentum. The reader can probably think of many more examples. The sequence of quanta of subject matter in the curriculum sequence can be considered a first level of curriculum structure.

Secondary structure and the spiral curriculum

We also revise topics periodically at different levels of treatment. We introduce topics at an introductory level – and later offer more sophisticated accounts (atomic structure, acidity, oxidation…). We distinguish metals form non-metals and later introduce electronegativity. We distinguish ionic and covalent bonds and later introduce degrees of bond polarity. In recent years this has been reflected in the work on developing model 'learning progressions' that support students in more sophisticated scientific thinking over several grade levels.

From Taber, 2021

This builds upon the well-established idea of a 'spiral curriculum' (Bruner, 1960) where the learner resists topics in increasing levels of sophistication over their student career. So, here is a level of structure beyond the linear progression of topics covered in different sessions, encompassing revisiting the same topic at different turns of the 'spiral' (perhaps like the alpha helices formed in may proteins).

This already suggests there will be linkages across the 'chain' of teachings units (whether seen as lectures/lesson or lesson episodes) as references are made back to earlier teaching in order to draw upon more fundamental ideas in building up more complex ideas, and building on simplified accounts to develop more nuanced and sophisticated accounts.

Tertiary structure – drip feeding to reinforce learning

The skilled teacher will also be making other links that are not strictly* essential but are useful unless the students have exemplary study skills usually ARE essential!]

To support students in consolidating learning (something that is usually essential if we want them to remember the material and be able to apply it months later) the teacher will 'drip feed' reinforcement of prior learning by looking for opportunities to revise key points form earlier teaching.

We have defined what we mean by 'compound' or 'oxidising agent' or 'polymer', so now we spot opportunities to reinforce this whenever it seems sensible to do so in teaching other material. We have taught students to calculate molecular mass, or assign oxidation states, or recognise a Lewis acid – so we look for opportunities to ask students to rehearse and apply this knowledge in contexts that arise in later teaching. At the end of a previous lesson everyone seemed to understand the difference between respiration and breathing – but it sensible to find opportunity for them to rehearse the distinction. 2

There is then a level of structure due to linkages back and forth between the components of the teaching sequence.

So where the 'primary structure' is necessary to build up knowledge in a logical way in order that the teaching scheme functions to provide a coherent learning experience (teaching makes sense at the time), and the secondary structure allows progression toward more sophisticated accounts and models as students develop, the 'tertiary structure' offers reinforcement of learning to ensure the course functions as an effective long term learning experience (that what was taught is not just understood at the time, but is retained, and readily brought to mind in relevant contexts, and can be applied, over the longer term).

Quaternary structure – locating the course in the wider curriculum experience

What about quaternary structure? Well, commonly a student is not just attending one class or lecture course. Their curriculum consists of several different strands of teaching experiences. At upper secondary school level, for example, the learner may attend chemistry classes interspersed with physics classes, biology classes and mathematics classes. Their experience of the curriculum encompasses these different strands. Likely, there are both salient and other less obvious potential linkages between these different courses. Conservation of energy from physics applies in chemistry and biology. Enzymes are catalysts, so the characteristics of catalysts apply to them. The nature of hydrogen bonds may be taught in chemistry – and applied in biology. In that case, it would be useful for the learners if the topic was taught that concept in the chemistry class before it was needed in biology.

And just as there may be aspects of logical sequencing of ideas across the strands to be considered, there may be other potential links where the teacher in one subject can draw upon, exemplify, or provide opportunities to review, what has been taught in the other.

Level of structureFeature of sequencing
primary structurelogical sequencing of concepts to identify and later build on prerequisites
secondary structurespiral curriculum to build up sophistication of understanding
tertiary structurecross-linking between lessons along strand to reinforce learning by finding opportunities to revisit, review, and apply prior learning
quaternary structurecross links between courses to build up integrated (inter-*)disciplinary knowledge
levels of structure in well-designed curriculum

(* in a degree course this may be coordinating different lecture courses within a discipline; in a school context this may be relating different curriculum subjects)

Afterword

How seriously do I intend this comparison? Of course this is just an analogy. It is easy to see that it does not hold up to detailed analysis – there are more ways that curricular structure is quite unlike protein structure, and the kinds of units and links being discussed in the two cases are of very different nature.

Is there any value in such a comparison if the analogy is somewhat shallow? Well, devices such as analogies operate as thinking tools. Most commonly we use teaching analogies to help 'make the unfamiliar familiar' by showing how something unfamiliar is somewhat like something familiar. This can be a useful first stage in helping someone understand some new phenomena or concept.

In teaching science we commonly make analogies with everyday phenomena to help introduce abstract science concepts. Here I am using a scientific concept (protein structure) as the analogue for the target idea about sequencing teaching.

Read about scientific analogies

My motivation here was to prompt teachers (and others who might read the book when it is finished) who are already familiar with general ideas about curriculum and schemes of work to think about a parallel (albeit, perhaps a somewhat forced one?) with something rather different but likely already very familiar – protein structure. Chemists and science teachers are likely to already appreciate the different levels of structure in proteins, and how the different aspects of the nature of polypeptide chains and the links formed between amino acid residues inform the overall shape, and therefore the functionality, of the structure.

Perhaps this thinking tool will entice readers to think about how conceptual links within and between courses of study can support the functionality of teaching? Perhaps they will dismiss the comparison, pointing out various ways in which the level of structure in a well-planned curriculum are quite different from the levels of structure in a protein. Of course, if they can do that insightfully, I might suspect that this 'teaching analogy' will have done its job.

Work cited:
Note:

1 Sometimes the term polyamide is reserved for synthetic compounds and contrasted with polypeptides as natural products.

2 This can be useful even when students 'seem' to have grasped key ideas. When they remember that 'everything is made of atoms' we may not appreciate they think that implies chemical bonds contain atoms. When they seem to have understood that cellular metabolism depends upon respiration, we may not appreciate they think that this does not apply to plants when the sun is shining.

How fat is your memory?

A chemical analogy for working memory

Keith S. Taber

This posting has nothing to do with the chemical composition of your brain (where lipids do play an important part), nor about diet – such as those claims of the merits of 'omega-3 fatty acids' in a healthy diet.

Rather, I am going to suggest how a chemical structure can provide an analogy for thinking about working memory.

In a sense, working memory is a bit like triglyceride structure (which is only a useful comparison for those who already know about the chemistry being referenced)

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).

So, the similarly is in terms of conceptual structures. Consider the figure above, which suggests there are similarities between aspects of the concept of working memory and aspects of the concept of triglyceride structure. In this case the analogy is at quite an abstract level – so is only likely to be useful for more advanced learners (such as science graduates preparing for teaching for example).

In relation to science, we might distinguish between several classes of analogy. In teaching we are most likely to be explaining some target scientific idea in terms of an everyday idea or phenomenon. However, sometimes one scientific idea which is already well-established is used as the analogue by which to explain about a less familiar scientific idea. This can happen in science teaching or science communication to the public – but can also be employed by scientists themselves when communication new ideas to their peers. It is also possible that sometimes a scientific idea may be useful as an analogue for explaining some target idea from outside science (as long, of course, as the science is familiar to the audience for the analogy).

Read about science analogies

An analogy for science teachers

My professional life has basically encompassed teaching about three broad areas – teaching natural science (mainly chemistry and physics) to school and college learners; teaching educational ideas to those preparing for school teaching; and teaching about research to those setting out on research projects.

The analogy I am discussing here came to me when preparing the manuscript for a book aimed at teachers of chemistry (an audience of readers that I can reasonably assume have a high level of chemistry knowledge) and broadly about pedagogy. So, what came to mind was an analogy from science to put across an idea about what is known as working memory.

Working memory

Working memory is the name given to the faculty or apparatus we all have to support conscious thinking – when we plan, assess and evaluate, problem solve, and so forth. It is absolutely critical to our nature as deliberate thinkers. We probably do MUCH more thinking (if you allow that term in this context, if not, say, cognitive processing) pre-consciously, so without any awareness. This is the 'thinking' [or cognitive processing] that goes on in the background, much of which is quite low level, but also includes the kind of incubation of problems that leads to those sudden insights where a solution comes to us (i.e., to our conscious awareness) in a 'flash'. It is also the basis of those intuitions that we describe as 'gut feelings' and which are often powerful (and often turn out to be correct) even though we are not sure what we are basing them on.

Yet working memory is where we do the thinking that we are aware of, and supports the stream of consciousness that is the basis of our awareness of ourselves as thinking beings. Given its importance, a very interesting finding is that although the brain potentially has a virtually inexhaustible capacity for learning new information (through so called 'long-term memory'), the working memory itself where we process material we are trying to learn and memorise has a very limited capacity. Indeed, it is often said that typical working memory capacity in a normal adult is 7±2. And some think that may be an overestimate. So, a typical person can juggle no more than about seven items in mind at once.

There is a very important question of why such an important aspect of cognition is so limited. Is there some physical factor which has limited this, or some evolution contingency that is in effect an unlucky break in human evolution? There is also the intriguing suggestion that actually this very limited capacity may have survival value and so be considered an adaptation increasing fitness.1 Whatever the reason – we have a working memory that can be considered to only have about half a dozen slots for information. (Of course, 'slots' is here a metaphor, but a useful one.)

Chunking

Each slot will take one item of information, except that we have to be careful what we mean by one 'item', as the brain acts to treat such 'items' subjectively. That is, what counts as one item for your brain may not work as one item for mine. Consider the following example:

1s22s22p63s1

How many 'items' is that string of symbols? If we consider someone who only saw this as a series of numbers and letters and who had never come across this before they would need to remember:

  • the number 1,
  • is followed by the lower-case letter s,
  • followed by the number 2,
  • which is a superscript,
  • then the number 2,
  • then the lower-case letter s,
  • then the number 2,
  • which is a superscript,
  • …

and quite likely we have exceeded memory capacity when only half way through!

But for a chemist who already knows that this particular string could be seen as the electronic structure of a sodium atom,2 this can be treated as one unit – the whole string is already available represented as an integrated structure in long-term memory form where it can be copied as 'a chunk' into working memory to occupy a single slot. So, a chemistry teacher using this information in an argument or calculation has other 'slots' for the other relevant information whereas a student may be struggling.

Triglycerides as an analogue for working memory

It struck me that an analogy that would be familiar to many chemists and science teachers is that of triglycerides which are considered esters of glycerol (with its three alcohol groups) with fatty acids. Although this class of compounds has some commonalities, there are a great many possible different specific structures (each strictly reflecting a distinct compound). What is common is the short chain of three carbons each bonded to an ester linkage (left hand figure below). However, what those ester linkages actually link to can vary. In human milk, for example, there are a great many different triglycerides (at least of the order of hundreds) comprising a wide range of fatty acids (Winter, Hoving & Muskiet, 1993).3

The triglycerides are members of a class of compounds with common features. They can be considered to be the result of glycerol (propane-1,2,3-triol) reacting with fatty acids, where the compounds formed will depend upon the specific fatty acids. The first figure uses R as a generic symbol to show the common structure. The second figure is the simplest triglyceride type structure formed when the acid is methanoic acid. If a mixture of acids is reacted with the glycerol, the side chains need not be the same – as in the third example. Actual triglycerides found in fats and oils in organisms usually have much longer chains than in this example.

In the image above, meant to be a simple representation of the structure of triglyceride molecules, the first figure has Rs to represent any of a great many possible side chains. The shortest possible structure here just has hydrogen atoms for Rs (triformin – the second figure), but more commonly there are long aliphatic chains as suggested by the third figure – although usually the chains would be even longer. In relation to diet, a key feature of interest is whether the fats consumed are saturated, or have some degree of 'unsaturation' (i.e., the double bond shown in the middle chain of the third figure) – unsaturated fats tend to be seen as more healthy, and tend to come from plant sources.

We might consider that the molecular structures consists of the common component with three 'slots' for side chains. In principle the slots could be occupied by hydrogens (hydrogen 'atoms') or chains based on any number of carbons (carbon 'atoms').4 So the total mass of a triglyceride molecule can vary considerably, as can the number of carbon centres in a molecule.

Fixed 'slots', variable content

Working memory is sometimes said to have 'slots' as well (again, to be understood metaphorically) into which information from perception or memory can be 'slotted'. We can consciously operate on the information in working memory, for example forming associations between the material in different slots. The number of slots in a person's working memory is fixed, but as information that has been well learnt can be 'chunked' into quite extensive conceptual structures, the total amount of information that can be engaged with is highly variable.

Working memory has a very limited number of 'slots' – but where extensive conceptual frameworks are already well established from prior learning a great deal of information can be engaged with as a single chunk

If student in class is keeping in mind information that is not directly related to the task in hand then this will 'use up' slots that are not then available for problem-solving or other tasks. Indeed, one of the skills someone with expert knowledge in a field has, but not novices, is determining which information available is likely to be peripheral or incidental rather that important to the task in hand, and indeed which of the important features need to be considered initially, and which can be ignored until later.

The perceived complexity of a learning task then always has to be considered in relation to the background knowledge and experience of the individual. So, at one time a person may be watching a documentary on a subject they know nothing about, in which case the information they perceive may seen unconnected, such that working memory may be occupied by very small chunks (such as individual names of unfamiliar people that are bring discussed). If that same person sits down to revise course notes they have developed over an extended time time, and have reviewed regularly, they may be bringing to mind quite extensive conceptual structures to slot into working memory. The same working memory, with the same nominal capacity, is now engaging with a much more extensive body of information.

Work cited:
  • Winter, C. H., Hoving, E. B., & Muskiet, F. A. J. (1993). Fatty acid composition of human milk triglyceride species: Possible consequences for optimal structures of infant formula triglycerides. Journal of Chromatography B: Biomedical Sciences and Applications, 616(1), 9-24. doi:https://doi.org/10.1016/0378-4347(93)80466-H
Footnotes

1 The logic here is that, because of chunking, working memory biases cognition towards what is already familiar, which may be an advantage in a context where although change is important there is a largely stable environment so that developing and then following a stable set of survival strategies is generally advantageous.

The kind of fruit that was edible yesterday is probably edible today, and the animal that attacked the group last week is best assumed to be dangerous today as well. The peer who helped us yesterday may help us again in future if we reciprocate, and the person who tried to cheat us before is best not trusted too far today.

2 There is a strong case that the familiar designation of electronic structures in terms of discrete s, p, d and f orbitals is only strictly valid for hydrogenic (single electron) species – but the model is commonly taught and used in chemical explanations relating to multi-electron atoms.

3 Strictly there are no fatty acids 'in' the triglycerol just as strictly there are no atoms in a molecule.4 I am here using economy of language which will be clear to the expert, though we risk misleading novice students if we are not careful to be precise. The triglycerides have various chain segments corresponding to a wide range of fatty acids; a wide range of fatty acids are generated by hydrolysing the triglyceride.

4 Strictly 'atomic centres', as molecules do not contain atoms, as atoms are by definition discrete structures with only one nucleus – and the atomic centres in molecules are bound into a molecular structure. Again, chemists and teachers may refer to carbon atoms in the side chain knowing this is not precisely what they mean, but we should perhaps be careful to be clear when talking to learners.

NASA puts its hand in the oven

A tenuous analogy

Keith S. Taber

The Parker Solar Probe

I recently listened to NASA's Nicky Fox being interviewed about the Parker Solar Probe which (as the name suggests) is being used to investigate the Sun.

Screenshot from http://parkersolarprobe.jhuapl.edu (© 2019 The Johns Hopkins University Applied Physics Laboratory LLC. All rights reserved. Permission for use requested.)

There is a website for the project which, when I accessed it (28th December 2021), suggested the spacecraft was 109 279 068 km from the Sun's surface (which I must admit would have got a marginal comment on one of my own student's work along the lines "is the Sun's surface so distinctly positioned that this level of precision can be justified?") and travelling at 57 292 kph (kilometers per hour). This unrealistic precision derives from the details being based on "mission performance modeling [sic] and simulation and not real-time data…" Real-time data is not necessarily available to the project team itself – the kind of shielding needed to protect the spacecraft from such extreme conditions also creates a challenge in transmitting data back to earth.

But the serious point is that returning to the website at another time it is possible to see how the probe's speed and position have changed (as shown on 'the Mission' webpage – indeed by the time I took the 'screenshot' it had moved about 7000 km), as the spacecraft moves through a sequence of loops in space orbiting the Sun on a shifting elliptical path that takes it periodically very close (very close, in solar system terms, that is) to the sun. Like any orbiting body, the probe will be moving faster when closest to the sun and slowest when furthest from the sun. (The balance shifts between its kinetic and potential energy – as it works to move away against the sun's gravity when receding from it 1.)

Touching the Sun

Publicity still from the Danny Boyle film 'Sunshine'

Getting too close the Sun – with its high temperature, the 'solar wind' of charged particles emitted into space, occasional solar flares, and the high flux of radiation from across the electromagnetic spectrum – is very dangerous, making the design and engineering of any craft intended to investigate our local star up close very challenging. A key feature is a protective heat shield facing the Sun . This was the premise of the sci-fi film 'Sunshine' 2.

For the Parker probe

"the spacecraft and instruments will be protected from the Sun's heat by a …11.43 cm carbon-composite shield, which will need to withstand temperatures outside the spacecraft that reach nearly …1,377 degrees Celsius"

"At closest approach to the Sun, while the front of Parker Solar Probe' solar shield faces temperatures approaching … 1,400° Celsius, the spacecraft's payload will be near room temperature, at about [29˚C.]."

http://parkersolarprobe.jhuapl.edu

Note: Dr Fox is NOT reporting from the Parker Solar Probe – just pictured in front of an image of the sun (Dr Fox's profile on NASA website)

Dr Fox, who is Director of NASA's Heliophysics [physics of the Sun] Division, was being interviewed about data released from an earlier close approach on a BBC Science in Action podcast.

Science in Action episode broadcast 2021-12-19

"The Parker Solar probe continues its mission of flying closer and closer to the sun. Results just published show what the data the probe picked up when it dipped into the surrounding plasma. NASA's Nicky Fox is our guide."

Item on BBC Science in Action

The project is framing that event as when, "For the first time in history, a spacecraft has touched the Sun". Although the visible surface of the sun has a temperature of about 6000K (incredibly hot by human standards), the temperature of the 'atmosphere' or corona around it is believed to reach several million Kelvins. On the programme, Dr Fox was asked about how the spacecraft could survive in the sun's corona, given its extremely high temperatures.

A teaching analogy?

In response she used an analogy from everyday experience:

"We talk about the plasma being at a couple of million degrees, it's like putting your hand inside an oven, and you don't touch anything. You won't burn your hand, you'll feel some heat but you won't actually burn your hand, and so the solar wind itself, or the corona, is a very tenuous plasma, there are just not that many particles there. So, even though the whole atmosphere is at about two million degrees, the number of particles that are coming into contact with the spacecraft are [sic] very small.

The temperatures that we have to deal with are about fourteen, fifteen hundred degrees Celsius, at the maximum, which is still hot, don't…let me kid you, that's still hot, but it is not two million degrees."

Dr Fox interviewed on Science in Action

Analogies are commonly used in science, science communication and science education as one means of 'making the unfamiliar familiar' by showing how something novel or surprising is actually like something the audience is already aware of and comfortable with.

Read about science analogies

Read about making the unfamiliar familiar

If the probe had been dipped in a molten vat of some hypothetical refractory liquid at two million degrees it would have quickly been destroyed. But because the Corona is not only a plasma (an 'ionised gas')3, but a very tenuous one, this does not happen. NASA sending the probe into the corona is similar to putting one's hand in the oven when cooking. If you touch the metal around the outside you will burn yourself, but you are able to reach inside without damage as long as you do not touch the sides – as although the air in the oven can get as hot as the metal structure, it has a very low particle density compared with a solid metal. So, your hand is in a hot place, but is not in contact with much of the hot material.

Do not try this at home – at least not unless you are quick

Of course, this is not the whole story. You can reach in the oven to put something in or (with suitable protection) take something out, but you cannot safely leave your hand in there for any length of time.

When two objects at different temperature are placed in contact, heating will occur with 'heat' passing from the hotter to colder object until they are in thermal equilibrium (i.e., at the same temperature). But this is not instantaneous – it takes time.4 If the Parker Solar Probe had been flown into the Sun's atmosphere and left there it would have been heated till it eventually matched the ambient temperature (not 'just' 1400˚C) regardless of how effective a heat shield it had been given. Or rather, it would have been heated till its substance reached the ambient temperature, as it would have lost structural integrity long before this point.

Of course, the probe has been designed to spend some time in the coronal atmosphere collecting data, but to only dip in for short visits, as NASA is well aware that it would not be wise to leave one's hand in the oven for too long.

Note:

1 This at least is the description based on Newtonian physics. There is an attractive, gravitational force between the Sun and the probe. As the spacecraft moves towards the sun it accelerates, and then its momentum takes it away, being decelerated by gravity.In this model gravity is a force between two bodies. (The path is actually more complex than this, as it has been designed to fly past Venus several times to adjust its trajectory round the Sun.)

In the model offered by general relativity the probe simply moves in a straight line through space which has a complex geometry due to the presence of matter/energy: a straight line which seems to us to be a shifting series of ellipses. Gravity here is best understood as a distortion from a 'flat' space. Perhaps it is clear why for most purposes scientists stick with the Newtonian description even though it is no longer the account considered to best describe nature.

2 The movie poster gives a slight clue to the hazards involved in taking a manned mission to the Sun!

3 Plasma is considered a fourth state of matter: solid, liquid, gas, plasma. The expression that 'a plasma is an ionised gas' may suggest plasma is a kind of gas, but then we might also say that a gas is a boiled liquid or that a liquid is melted solid! So, perhaps what we should say is that a plasma [gas/liquid] is what you get when you ionise [boil/melt] a gas [liquid/solid].

4 In theory, modelling of such a process suggests it takes an infinite time for this to occur. 5 In practice, the temperatures become close enough that for practical purposes we consider thermal equilibration to have occurred.

5 This is an example of a process that can be understood as having a negative feedback cycle: temperature difference drives the heat flow, which reduces temperature difference, which therefore also reduces the driver for heat flow; so the rate of heat flow is reduced, so therefore the rate of temperature change is reduced… This is a similar pattern to radioactive decay – both follow an 'exponential decay' law.

The heart-stopping queen

An analogy for a paralysing poison

Keith S. Taber

By the light of day…in the dead of night

It was nice to have a sunny and warm day in October to sit in the garden and do some reading. Looking at Chemistry World, I came across an article by Raychelle Burks (2021) on the the natural poison aconitine, extracted from plants collectively known as aconite. The article was punningly called 'The dead of aconite'.

An article in October's Chemistry World

Regular readers of this blog (if that is not a null set) may have noticed my interest in analogies used in teaching and communicating science, and so I was intrigued with the comparison between the effect of the poison and a damaged car engine:

Aconitine likely serves as a defensive tool for the plants that produce it, discouraging [!] predators with its deadly action. It acts quickly on sodium ion signalling channels, opening them and preventing their closure. 'To use a car analogy, if the valves in your car's engine open up, but then won't close, it's dead in the water', wrote toxicologist Justin Bower [sic]. 'Just like aconitine victims.'

Burks, 2021: 69

I was quite interested in following this up, but no citation was given. A little searching around the web led to the a blog called 'Nature's Poisons' written by forensic toxicologist  Justin Brower [sic], and an entry on 'the queen of the poisons'.

Making the unfamiliar familiar

Analogy is just one technique used by teachers and others communicating technical or abstract ideas to assist in introducing those ideas – by suggesting that what is unfamiliar and is to be communicated is actually somewhat like something that the listeners(s) or reader(s) already know(s) about.

For this to work, the analogue needs to actually be more familiar than the target idea being communicated. Dr Brower's analogy relies upon people knowing enough about car engines to be familiar with the possibility of engine valves getting stuck open and preventing the car operating.

That the function and operation of the two systems are quite different means that knowing about car engines only offers limited support in learning about the effects of the poison on body cells, but this kind of superficial mapping between systems is true of many teaching analogies. Their role is more about initial familiarisation with the novel concept or phenomenon than providing a detailed explanation. We might almost see their primary role as affective rather than cognitive – making something quite technical seem less alien (and potentially less inaccessible).

Posting at Justin Brower's blog

Dr Brower explained in his blog that aconitine is found in the plant Monkshood (a.k.a. Wolfsbane), "in every part…from its pretty flowers right down to its dirty roots", and therefore

When any part of the plant is ingested, the aconitine is absorbed through the gut and goes to work. It binds to receptors that help regulate the muscle cells' sodium-ion channels, key components of the nervous system and cardiac cells (i.e. the heart). This action keeps the channels open, allowing sodium to flow freely into the cell. Unable to repolarize, the cells are stuck in a state of "open", and paralysis sets in. To use a car analogy, if the valves in your car's engine open up, but then won't close, it's dead in the water. Just like aconitine victims.

Brower, 2014

Cell membranes have to both prevent the unrestrained ingress and egress of materials, and yet also allow transport of particular substances across the barrier. Sodium ion channels are structures in the cell membrane that are specifically suited to allowing sodium ions (but not, say, calcium ions) to pass through. Moreover these channels do not remain open all the time. (They act as metaphorical 'gates' that can be closed.) The channels depend on specific proteins embedded in the membrane – substances that can have relatively 'large' molecules (that is, large for molecules!) with complex structures. The shapes of proteins can be very complicated.

Molecular shapes

The shapes of simple molecules are understood in terms of the electrical forces within the molecule (and at upper secondary school level the VSEPRT – the valance shell electron pair repulsion theory – model is often taught). Put very simply, the distribution of charges attracting and repelling each other (positive atomic cores, negative electrons) leads to the conformation of lowest potential energy.

The simple molecules can be considered to have one 'central' atomic centre (O in H2O; N in NH3; C in CH4; P in PCl5, and so forth) and the shape decided by considering the electronic distribution around that atom.  In a molecule like propane (CH3CH2CH3) the shape can be considered by considering the situation around each of the of the C centres in turn, but taking into account that free rotation around the C-C bonds means that the molecule has a dynamic conformation. In larger molecules, there may be interactions (such as hydrogen bonding) between different parts of the molecule which influence and constrain the shape. Proteins may be very large molecules with many such interactions, often leading to a convoluted shape as the molecule 'folds' according to these interactions. Such protein folding can very difficult to predict.

Two views of a voltage-gated sodium channel. (Source: Protein Data Bank). The second view shows the protein located in the membrane (represented in grey).

VSEPRT is used to consider isolated molecules, and ignores the influence of other charges from outside the molecule (such as interactions with solvent molecules). The protein in a context such as a cell membrane may have quite a different shape than the same protein had it been isolated. Moreover, a change in the environment may affect the protein shape. In cells, when the membrane potential changes, the electric field around the ion channel proteins change, and they may change shape. The changes 'open' or 'close' the channels.

The same protein molecule, showing sites where two different toxins (shown as green and yellow) are known to bind and change the conformation of the structure preventing the 'gate' functioning. (Source: Protein Data Bank).

If a poison interferes with this process, the channels can no longer control the transport of sodium ions across the membrane in a way that enables the cell's normal functioning. Without this process nerve cells are unable to transmit electrical signals, and heart cells called myocytes (muscle cells) do not beat. That is important, as the beating of the heart is due to the synchronised beating of these cells. And the beating heart keeps the blood flowing, and with it the critical movement of substances (glucose, carbon dioxide, oxygen, etc.) around the body. Aconitine, then, acts as a cardiotoxin and neurotoxin (a heart poison and nerve poison).

Individual heart cells beat in this YouTube video from Wake Forest Baptist Medical Center's Institute for Regenerative Medicine

The car analogy breaks down in the sense that engine valves that are stuck open might later be closed again with some oil and a hammer and may then function again, and this restoration is not time critical; whereas after a heart has stopped beating, irreversible tissue damage will soon follow.

The first symptoms of aconitine poisoning appear approximately 20 min to 2 hr after oral intake and include paraesthesia [odd sensations], sweating and nausea. This leads to severe vomiting, colicky diarrhoea, intense pain and then paralysis of the skeletal muscles. Following the onset of life-threatening arrhythmia [irregular heartbeat], including ventricular tachycardia [fast, abnormal heartbeat] and ventricular fibrillation [loss of coordination in the muscle activity so there is no effective pumping1] death finally occurs as a result of respiratory paralysis or cardiac arrest.

Beike, Frommherz, Wood, Brinkmann & Köhler,2004: 289

In a worse case scenario for the car, the engine could be replaced, and the car made as good as new. Nonetheless, this is a useful analogy for anyone who knows a little of how the car engine works, as without working valves, the engine cycle (which I seem to recall summarised as 'suck-squeeze-bang-blow' on one course I once taught on) cannot occur, and the car goes nowhere.

Read about science analogies

Read about making the unfamiliar familiar

target: sodium channels in cell membraneanalogue: internal combustion engine valves
positive mappingpoison may stop channels closingvalves may stick in open position
cell does not function with channels unable to closeengine does not function with valves stuck open
if nerve and heart cells do not function, paralysis occurs, and person diesif engine does not work, car does not go
negative mappingtissue damage will soon be irreversiblevalves may sometimes be freed up, restoring engine function – a quick response is not critical
Mapping between target idea and analogue
Work cited:
  • Beike, J., Frommherz, L., Wood, M., Brinkmann, B., & Köhler, H. (2004). Determination of aconitine in body fluids by LC-MS-MS. International Journal of Legal Medicine, 118(5), 289-293. doi:10.1007/s00414-004-0463-2
  • Brower, J. (2014). Aconitine: Queen of poisons. Nature's poisons. Retrieved from https://naturespoisons.com/2014/02/20/aconitine-queen-of-poisons-monkshood/
  • Burks, R. (2021). The dead of aconite. Chemistry World (October), 69.
Footnote:

1 An interactive 3D simulation of ventricular fibrillation can be found at https://www.msdmanuals.com/en-gb/home/heart-and-blood-vessel-disorders/abnormal-heart-rhythms/ventricular-fibrillation

Easter eggs?

We didn't start the fire (it was the virus)

A simile for viral infection

Keith S. Taber

Could an oral Covid-19 treatment be available soon?

There was an item on the BBC radio programme/podcast 'Science in Action' (23rd September 2021) about anti-viral agents being used in response to the COVID-19 pandemic: 'Could an oral Covid-19 treatment be available soon?'

Science in Action – 23/09/2021

In discussing early trials of a new potential treatment, Molnupiravir 1, Daria Hazuda (Vice President of Infectious Disease and Vaccines at Merck Research Labs and Chief Scientific Officer of MRL Cambridge) made the point that in viral infections the virus may trigger an immune response which is responsible for aspects of the illness, and which may continue even when there is no longer active virus present. As part of her interview comments she said:

"But even after someone is infected, the host actually mounts, for all these [respiratory] viruses, a really dramatic immune and inflammatory response. So it sort of lights a fire. And even when the virus stops replicating, you know that fire continues to burn, and in a lot of cases that's what lands people in the hospital. And so you want to prevent the virus from igniting that fire, that is what really ends up causing a huge amount of damage to the patient. …

the greatest benefit [of the antiviral drug being tested] is in the outpatient setting before that fire gets ignited."

Daria Hazuda being interviewed on 'Science in Action'

A scientific simile

Science communicators, such as teachers, but also scientists and journalists presenting science in the public media, often use techniques to 'make the unfamiliar familiar', to get across abstract or difficult ideas in ways that their audience can relate to.

These techniques can include analogies, metaphors and similes. Here Dr Hazuda used an analogy between the damage to tissue that can occur in disease, and the damage a fire can do. In particular, she was suggesting that the virus may be seen as like something which ignites a fire (such as a match or a spark) but which is not needed to keep the fire going once it had taken hold.

She introduced this idea by suggesting that the virus "sort of lights a fire". This can be considered a simile, which is a figure of speech which is a kind of explicit comparison where one thing is said to be like or similar to another.2 Dr Hazuda did not suggest that the virus actually lights a fire, but rather it has an effect which can be considered somewhat like ('sort of') igniting a fire.

"We didn't start the fire
It was always burning, since the world's been turning
We didn't start the fire
No, we didn't light it, but we tried to fight it"

Billy Joel

Viruses triggering long term disease

The symptoms we experience when ill can be the results of our immune system reacting to illness, rather than the direct effect of the disease causing agent. That does not mean the disease itself would not harm us (infectious agents may be destroying cells which would not be obvious until extensive damage was done), but that in some conditions what we notice – perhaps sneezing, coughing, a raised temperature – is due to the immune response.

The immediate context of the Science in Action interview was the current COVID-19 pandemic caused by infection with the SARS-CoV-2 virus. However, the idea that a viral infection may trigger ('ignite') a longer term immune response (the 'fire') is not new with COVID. The syndrome sometimes known as chronic fatigue syndrome has unknown cause(s), but viruses are among the suspects. Viruses have been suspected as being a possible trigger (if perhaps in combination with other factors) in a range of autoimmune conditions. In autoimmune conditions the mechanisms that usually protect a person from infectious agents such as (some) bacteria and viruses attack and destroy the person's own cells leading to inflammation and potentially serious tissue damage.

People might commonly say that the immune system is 'meant' or 'intended' to protect us from diseases and that it sometimes 'goes wrong' leading to autoimmune disease – but strictly this is not a scientific way of thinking. The immune system has no purpose as such (this would be 'teleological' thinking), but has just evolved in ways such that it has on balance increased fitness.

From that perspective, it might not seem so strange that our immune systems are sometimes insufficient to protect us from harm, and yet can also sometimes be over-sensitive and start doing damage – as that surely is what we might expect if evolution has (through natural selection) led to a system which has tended on the whole to be protective.

The admirable HLA-B27?

"HLA B27 plays an admirable, perhaps outstanding role in the immune response to viruses, however, it is also directly involved in the pathogenesis of the spondyloarthropathies"

Bowness, 2002: 866

My late wife Philippa was diagnosed with a complex autoimmune condition – she was told that she had atypical Wegener's granulomatosis (a disease now usually called Granulomatosis with polyangiitis 2), a form of vasculitis (a disease leading to inflammation in the blood vessels), and that she might have been genetically susceptible to autoimmune diseases because she produced a particular type of human leukocyte antigen, HLA-B27. HLA is an important component of human immune systems, but the precise antigens a person produces varies, depending on their genes (just as we all have blood but people can be assigned into different blood groups). It was also suggested to her that an otherwise minor infection may have acted as a trigger in setting off the autoimmune problems.

Medicine today has some effective agents such as steroids that help 'dampen down' the 'fires' that damage tissues in autoimmune diseases. But these conditions can be very serious. Fifty years ago, most people found to have Wegener's granulomatosis were dead from that damage within a year of their diagnosis.

HLA-B27 is only found in a minority of people in most populations and is associated with a higher prevalence of certain immune conditions such as ankylosing spondylitis (an inflammatory condition especially affecting the spine), inflammatory bowel disease, and some forms of arthritis. It might seem odd that evolution has not led to the elimination of HGLA-B27 if it is associated with serious medical conditions. Yet, again, it may be that something which can make people prone to some conditions may also be better at protecting them from others.

People with HLA-B27 may be better at mounting an effective immune response to some viral infections (the fire is more readily ignited, we might say) and this might be enough of an advantage to balance its unfortunate role in autoimmune conditions. Over human history, HLA-B27 might have protected a great many people from dangerous infections, if also being responsible for a smaller number becoming very ill.

"HLA-B27 appears to excel at its natural function of binding and presenting viral peptide epitopes to cytotoxic T cells. We have suggested that HLA-B27 may, however, act as a 'double-edged sword'. Thus, certain features of its peptide binding ability or cell biology (perhaps those favouring excellent antiviral responses) might also lead to autoimmunity."

McMichael & Bowness, 2002: S157

That is, what makes this immune component so good at attacking certain viruses (as if the immune system had been doused in petrol so that the slightest spark might initiate a response) may also be responsible for its association with autoimmune diseases. HLA-B27 may (metaphorically) be the can of petrol that means that a viral spark starts not just a fire, but a conflagration.

Read about science in public discourse and the media

Read about making the unfamiliar familiar

Read about science similes

Read about teleological explanations


Work cited:

Bowness, P. (2002). HLA B27 in health and disease: a double‐edged sword? Rheumatology, 41(8), 857-868. doi:10.1093/rheumatology/41.8.857

McMichael, A., & Bowness, P. (2002). HLA-B27: natural function and pathogenic role in spondyloarthritis. Arthritis research, 4 Suppl 3(Suppl 3), S153-S158. doi:10.1186/ar571

Footnotes:

1: "the first oral, direct-acting antiviral shown to be highly effective at reducing nasopharyngeal SARS-CoV-2 infectious virus" according to a preprint reported at medRχiv). A preprint is a paper written to report scientific research but NOT yet tested through peer review and formally published, and so treated as reporting more provisional and uncertain findings than a peer-reviewed paper.

2 By comparison, a metaphor may be considered an implicit comparison presented as if an identity: e.g., the nucleus is the brain of the cell.

2. The disease was named after the German physician Friedrich Wegener who described the condition. After Wegener was identified as a Nazi and likely war criminal (suspected, but not convicted) it was decided to rename the disease.

Shortlisting for disease

False positives on screening tests can be understood in relation to job applications

Keith S. Taber

I rather liked an analogy used by Dr Kit Yates of Bath University comparing medical screening to being shortlisted for a job. The context was a Royal Institution podcast entitled: Can We Trust Maths? 1

Ri Podcast available at https://soundcloud.com/royal-institution/maths-trust

This was a very informative discussion of aspects of statistics, and one of the questions addressed was:

How often do false positive and false negative test results occur in medical screenings?

Screening for disease

Screening programmes test apparently healthy members of the population for serious medical issues in order to catch problems at an early stage when treatment offers the best prognosis.

Screening programmes can quickly test many people…
(Image by Ahmad Ardity from Pixabay)

No tests are perfect, so tests will sometimes give misleading results – called false positives and false negatives.

a test result that is:when an ideal perfect test would have shown positivewhen an ideal perfect test would have shown negative
positiveis called a true positiveis called a false positive
negativeis called a false negativeis called a true negative
…but definitive diagnoses may require more sophisticated follow-up investigation
(Image by Michal Jarmoluk from Pixabay)

Sometimes tests can be tuned to avoid many false negatives by tolerating a higher rate of false positive (or vice versa). This is similar to what happens in statistical hypothesis testing when the choice of 'confidence level' (the p {for probability} value used as a cut-off criterion for 'statistical significance') can be chosen according to whether it is more important to avoid false positives or to avoid false negatives.

Choice of confidence level reflects a balance between admitting false positives (due to chance events) and false negatives (where real effects are not distinguished from chance events).
After, Taber, 2019, Fig. 7.

The notion of 'beyond reasonable doubt' used in criminal trials can be understood as based on the principle that it is better that some guilty perpetrators are not convicted at trial than to risk miscarriages of justice where innocent people may lose their liberty (or indeed in some jurisdictions, perhaps their lives). That is, it is better to have false negatives than false positives in criminal convictions.

In medical screening programmes, it is common to have an initial test which might give quite a few positive results (but hopefully not produce many false negatives, where a person with a disease appears to be clear according to the test), even though most of the positive results will prove to be false alarms (false positives) when followed up by a more sophisticated test that it is impractical or too expensive to use for mass screening.

The bias towards false positives built into some medical screening trials means that a person should not be too despondent at getting a positive result in the initial screen. Dr Yates worked through one example to show that based on the rates of false positives on certain screening tests, a person called for regular screenings over a number of years was actually more likely than not to get at least one positive screening result – but still unlikely to be unlucky enough to have the disease.

A teaching analogy

What I most liked was the use of an analogy to compare the logic of the screening process with a familiar everyday situation. Teaching can be seen as a process of making the unfamiliar familiar, and teachers often do this by comparing the unfamiliar they are charged with teaching about with something already familiar to the their students. That is only a starting point for supporting a developing understanding of the new concept or phenomenon, but it often is very useful in making abstract new ideas seem less threatening or inaccessible.

Read about making the unfamiliar familiar

One common way of making the unfamiliar familiar is through analogy: showing that what is new has a familiar conceptual structure – mapping onto a set of ideas already understood.

Read about teaching analogies

An 'outreaching' analogy?

Scientists charged with giving talks to a public audience as part of 'public communication' of science ('outreach') or attempts to improve 'public understanding' of science also have the job of making the unfamiliar familiar and may also use teaching analogies – as Dr Yates did here:

"I would make the analogy to screenings with a job interview. So, when a company wants to hire someone for a job, they send out an advert, and people send in their c.v.s. And the company can read those c.v.s quickly and make a shortlist. And that's a really cheap way, just as the first screen is a really cheap way of identifying people, who might be suitable for the job, people who might have breast cancer. And then for the job interview you call people in and you interview them and you throw 'assessment centres' at them, you do tests which are too expensive to do to the whole population at large to identify someone good for the job, but you can do it to this smaller population. And in the same way, with the screen we invite people in and we throw more expensive, more accurate tests at them to give them a diagnosis. And the point is, just because you would get invited to an interview for a job you had applied for, you wouldn't assume that you had got the job, right? So, in the same way, just because you get invited for further tests after a screen, you shouldn't assume you have the disease that is being screened for. You should wait and go to the follow-up test and see what that follow-up test says."

Dr Kit Yates explaining the logic of screening programmes
Based on an analogy used by Dr Kit Yates

This seemed a well-considered analogue, one that would be very accessible to most people in the audience. It is a common experience to have applied for jobs: perhaps sometimes not being shortlisted; sometimes called in for interview but not appointed; and sometimes being offered the job. 2

The explanations flowed nicely between the target concept (screening) and the analogue (shortlisting) – as can be seen in the tabulated version below.

"I would make the analogy to screeningswith a job interview.
So, when a company wants to hire someone for a job, they send out an advert, and people send in their c.v.s.
And the company can read those c.v.s quickly and make a shortlist.
And that's a really cheap way,
just as the first screen is a really cheap way of identifying people,
who might be suitable for the job,
people who might have breast cancer.
And then for the job interview you call people in and you interview them and you throw 'assessment centres' at them, you do tests which are too expensive to do to the whole population at large to identify someone good for the job, but you can do it to this smaller population.
And in the same way, with the screen we invite people in and we throw more expensive, more accurate tests at them to give them a diagnosis.
And the point is, just because you would get invited to an interview for a job you had applied for, you wouldn't assume that you had got the job, right?
So, in the same way, just because you get invited for further tests after a screen, you shouldn't assume you have the disease that is being screened for.
You should wait and go to the follow-up test and see what that follow-up test says."

An effective teaching analogy needs to have an analogue that is sufficiently familiar for an audience to appreciate its conceptual structure – and that structure must fit well when mapped across to the target concept. 'Medical screening is like job shortlisting' seems to work well on both these criteria.

Work cited:

Footnotes:

1: "If you see a newspaper headline with a big, bold statistic, how do you know that you can trust it? How often do false positive and false negative test results occur in medical screenings? And how do you safely bet whether or not 2 people in any room will share a birthday?
This month we hear from Kit Yates about the maths of medicine, crime and the media, exploring real-world data from his book, 'The Maths of Life and Death'.
This talk was recorded from our theatre at the Royal Institution, on 21 January 2020." https://soundcloud.com/royal-institution/maths-trust

2. It might be suggested that this process reflects a middle class /professional/white collar employment experiences, whereas for many jobs, such as much shop or factory work, an employer is likely to employ the first apparently suitable candidate that applies, rather than using a slower and more expensive two stage process. This is so, but the situation of short-listing is still generally familiar through story lines in fiction, such as in television dramas.

Shock! A typical honey bee colony comprises only six chemicals!

Is it half a dozen of one, or six of the other?

Keith S. Taber

Bee-ware chemicals!
(Images by PollyDot and Clker-Free-Vector-Images from Pixabay)

A recent episode of the BBC Inside science radio programme and podcast was entitled 'Bees and multiple pesticide exposure'. This discussed a very important issue that I have no wish to make light of. Researchers were looking at the stressors which might be harming honey bees, very important pollinators for many plants, and concluded that these likely act synergistically. That is a colony suffering from, say a drought and at the same time a mite infection, will show more damage that one would expect from simply adding the typical harm of each as if independent effects.  Rather there are interactions.

This is hardly surprising, but is none-the-less a worrying finding.

Bees and multiple pesticide exposure episode of BBC Inside Science

However,  my 'science teacher' radar honed in on an aspect of the language used to explain the research. The researcher interviewed was Dr Harry Siviter of the University of Texas at Austin. As part of his presentation he suggested that…

"Exposure to multiple pesticides is the norm, not the exception. So, for example a study in North America showed that the average number of chemicals found in a honey bee colony is six, with a high of 42. So, we know that bees are exposed to multiple chemicals…"

Dr Harry Siviter

The phrase that stood out for me was "the average number of chemicals found in a honey bee colony is six" as clearly that did not make any sense scientifically. At least, not if the term 'chemical' was meant to refer to 'chemical substance'. I cannot claim to know just how many different substances would be found if one analysed honey bee colonies, but I am pretty confident the average would be orders of magnitude greater than six. An organism such as a bee (leaving aside for a moment the hive in which it lives) will be, chemically, 'made up' of a great many different proteins, amino acids, lipids, sugars, nuclei acids, and so forth.

"the average number of chemicals found in a honey bee colony is six"

From the context, I understood that Dr Siviter was not really talking about chemicals in general, but pesticides. So, I am (not for the first time) being a pedant in pointing out that technically he was wrong to suggest "the average number of chemicals found in a honey bee colony is six" as any suitably informed listener would have immediately, and unproblematically, understood what he meant by 'chemicals' in this context.

Yet, as a teacher, my instinct is to consider that programmes such as this, designed to inform the public about science, are not only heard by those who are already well-versed in the sciences. By its nature, BBC Inside Science is intended to engage with a broad audience, and has a role in educating the public about science. I also knew that this particular pedantic point linked to a genuine issue in science teaching.

A common alternative conception

The term chemical is not usually used in science discourse as such, but rather the term substance. Chemical substances are ubiquitous, although in most everyday contexts we do not come across many pure samples of single substances. Tap water is nearly all water, and table salt is usually about 99% sodium chloride, and sometimes metals such as copper or aluminium are used in more or less pure form. But these tend to be exceptions – most material entities we engage with are not pure substances ('chemicals'), rather being mixtures or even more complex (e.g., wood or carrot or hair).

In everyday life, the term chemical tends to be used more loosely – so, for example, household bleach may be considered 'a chemical'. More problematically 'chemicals' tends to be seen as hazardous, and often even poisonous. So, people object to there being 'chemicals' in their food – when of course their food comprises chemicals and we eat food to access those chemicals because we are also made up of a great many chemicals. Food with the chemicals removed is not food, or indeed, anything at all!

In everyday discourse 'chemical' is often associated with 'dangerous' (Image by Arek Socha from Pixabay)

So, science teachers not only have the problem that in everyday discourse the term 'chemical' does not map unproblematically on 'substance' (as it is often used also for mixtures), but even more seriously that chemicals are assumed to be bad, harmful, undesirable – something to be avoided and excluded. By contrast, the scientific perspective is that whilst some chemicals are potentially very harmful, others are essential for life. Therefore, it is unhelpful when science communicators (whether journalists, or scientists themselves) use the term 'chemical' to refer only to potentially undesirable chemicals (which even then tend to be undesirable only in certain contexts), such as pesticides which are found in, and may harm, pollinators.

I decided to dig into the background of the item.

The news item

I found a news item in 'the Conversation' that discuses the work.

Dr Siviter's Article in the Conversation

It began

"A doctor will always ask if you are on any other medication before they write you a prescription. This is because pharmaceuticals can interact with each other and potentially disrupt the treatment, or even harm the patient. But when agrochemicals, such as pesticides, are licensed for use on farms, little attention is paid to how they interact with one another, and so their environmental impact is underestimated."

Siviter, 2021

This seemed a very good point, made with an analogy that seemed very telling.

(Read about science analogies)

This was important because:

"We analysed data gathered in scientific studies from the last two decades and found that when bees are exposed to a combination of pesticides, parasites and poor nutrition, the negative impact of each is exacerbated. We say that the cumulative effect of all these things is synergistic, meaning that the number of bees that are killed is more than we would predict if the negative effects were merely added together."

Siviter, 2021

This seems important work, and raises an issue we should be concerned about. The language used here was subtly different from in the radio programme:

"Many agrochemicals, such as neonicotinoids, are systemic, meaning they accumulate in the environment over several months, and in some cases years. It is perhaps not surprising then that honeybee colonies across the US have on average six different agrochemicals present in their wax, with one hive contaminated with 39 [sic, not 42]. It's not just honeybees which are at risk, though: wild bees such as bumblebees are also routinely exposed."

Siviter, 2021

So, here it was not 'chemicals' that were being counted but 'agrochemicals' (and the average figure of 6 now referred not to the colony as a whole, but only to the beeswax.)

The meta-analysis

'Agrochemicals' was also the term used in the research paper in the prestigious journal Nature where the research had been first reported,

"we conducted a meta-analysis of 356 interaction effect sizes from 90 studies in which bees were exposed to combinations of agrochemicals, nutritional stressors and/or parasites."

Siviter, et al., 2021

A meta-analysis is a type of secondary research study which collects results form a range of related published studies and seeks to identify overall patterns.

The original research

Moreover, the primary study being referred to as the source of the dubious statistic (i.e., that "the average number of chemicals found in a honey bee colony is six") referred not to 'chemicals' but to "pesticides and metabolites" (that is, substances which would be produced as the bee's metabolism broke the pesticides down):

"We have found 121 different pesticides and metabolites within 887 wax, pollen, bee and associated hive samples….

Almost all comb and foundation wax samples (98%) were contaminated with up to 204 and 94 ppm [parts per million], respectively, of fluvalinate and coumaphos, and lower amounts of amitraz degradates and chlorothalonil, with an average of 6 pesticide detections per sample and a high of 39."

Mullin, et al., 2010

Translation and representation

Scientific research is reported in research journals primarily for the benefit of other researchers in the field, and so is formatted and framed accordingly – and this is reflected in the language used in primary sources.

A model of the flow of scientific to public knowledge (after McInerney et al., 2004)

Fig. 10.2 from Taber, 2013

It is important that science which impacts on us all, and is often funded from public funds, is accessible to the public. Science journalism, is an important conduit for the communication of science, and for his to be effective it has to be composed with non-experts in the public in mind.

(Read about science in public discourse and the media)

It is perfectly sensible and desirable for a scientist engaging with a public audience to moderate technical language to make the account of research more accessible for a non-specialist audience. This kind of simplification is also a core process in developing science curriculum and teaching.

(Read about representing science in the curriculum)

However, in the case of 'chemical' I would suggest scientists take care with using the term (and avoid it if possible), as science teachers commonly have to persuade students that chemicals are all around of us, are not always bad for us, are part of us, and are essential. That pesticides and their breakdown products have been so widely detected in bee colonies is a matter of concern, as pesticides are substances that are used because of their detrimental effects on many insects and other organisms that might damage crops.

Whilst that is science deserving public attention, there are a good many more than 6 chemicals in any bee colony, and – indeed – we would want most of them to be there.

References: