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 concept	analogue
a synchotron	a 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 electrons	racing '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.

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. ⁴Liquid 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.

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 structure	Feature of sequencing
primary structure	logical sequencing of concepts to identify and later build on prerequisites
secondary structure	spiral curriculum to build up sophistication of understanding
tertiary structure	cross-linking between lessons along strand to reinforce learning by finding opportunities to revisit, review, and apply prior learning
quaternary structure	cross 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:

Bruner, J. S. (1960). The Process of Education. New York: Vintage Books.
Taber, K. S. (2021). Squaring the circle: Circumnavigating an ontological tension between practical learning progression models and the complex, multi-facetted, and meandering nature of conceptual learning. In M. N. Bowman (Ed.), Topics in Science Education (pp. 1-100). New York: Nova Science Publishers Inc.

Note:

¹Sometimes 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)

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.

⁴Strictly '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).

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 membrane	analogue: internal combustion engine valves
positive mapping	poison may stop channels closing	valves may stick in open position
	cell does not function with channels unable to close	engine does not function with valves stuck open
	if nerve and heart cells do not function, paralysis occurs, and person dies	if engine does not work, car does not go
negative mapping	tissue damage will soon be irreversible	valves 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

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?'

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 positive	when an ideal perfect test would have shown negative
positive	is called a true positive	is called a false positive
negative	is called a false negative	is 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 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."

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:

Taber, K. S. (2019). Experimental research into teaching innovations: responding to methodological and ethical challenges. Studies in Science Education, 55(1), 69-119. doi:10.1080/03057267.2019.1658058

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:

McInerney, C., Bird, N., & Nucci, M. (2004). The Flow of Scientific Knowledge from Lab to the Lay Public: The Case of Genetically Modified Food. Science Communication, 26(1), 44-74. doi:10.1177/1075547004267024 https://journals.sagepub.com/doi/10.1177/1075547004267024
Mullin, C. A., Frazier, M., Frazier, J. L., Ashcraft, S., Simonds, R., vanEngelsdorp, D., & Pettis, J. S. (2010). High Levels of Miticides and Agrochemicals in North American Apiaries: Implications for Honey Bee Health. 5(3): e9754. PLoS ONE, 5(3), e9754. doi:10.1371/journal.pone.0009754 https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0009754
Siviter, H. (2021) Pesticides: interactions between agrochemicals increase their harm to bees, The Conversation, August 4, 2021 5.36pm BST, https://theconversation.com/pesticides-interactions-between-agrochemicals-increase-their-harm-to-bees-165626
Siviter, H., Bailes, E. J., Martin, C. D., Oliver, T. R., Koricheva, J., Leadbeater, E., & Brown, M. J. F. (2021). Agrochemicals interact synergistically to increase bee mortality. Nature. doi:10.1038/s41586-021-03787-7 https://www.nature.com/articles/s41586-021-03787-7
Taber, K. S. (2013). Modelling Learners and Learning in Science Education: Developing representations of concepts, conceptual structure and conceptual change to inform teaching and research. Dordrecht: Springer.

Resowing the garden in your gut

A faecal transplant is like wild flower seeds in some soil

Keith S. Taber

"Many animals naturally ate each other's poo…as a way of staying healthy" Prof. Tim Spector. (Original image by Debbie De Jager from Pixabay, with apologies to Monty Python)

I was listening to a podcast from 'Science Stories' (BBC Radio 4) about 'Lady Mary Montagu's Smallpox Experiment', where Naomi Alderman described how the aforementioned Lady Mary Wortley Montagu brought the practice of opening veins to introduce some smallpox into the body, as a way of protecting against the deadly disease, back from Turkey to Britain.

An episode in the BBC Radio 4 series '*Science Stories*'

Flush or donate?

This was compared with the process of faecal transplantation which was apparently first used in China, and is increasingly being seen as a valuable treatment for some gut disorders. This is the process of ingesting, under carefully controlled conditions, some human faeces – either some of your own carefully preserved (for example, some cancer patients have a sample collected and stored before starting chemotherapy), or from some donor who is willing to offer some of their own. Unlike some other donor procedures (such as kidney donation) this is non-invasive and concerns material most of us just dispose of anyway!

Tim Spector, Professor of Genetic Epidemiology at Kings College, London explained the significance of the gut microbiome, the community of something like 100 trillion microbes that typically occupy a human gut. The importance of these organisms for human health is increasingly being appreciated.

Treating Clostridium difficile infection

Disturbances of the gut microbiome can lead to ill health. One particular example is the condition known as Clostridium difficile infection ('C. diff') – which is commonly experienced in hospitals when patients have extensive courses of antiobiotics – which can sadly kill the useful gut microbes as well those disease-causing organisms being targeted. Clostridium difficile (being itself unaffected by many commonly used antibiotics) can in these circumstances reproduce rapidly and vastly increase its numbers. This is problematic as the organism releases a toxin.

C. diff infection can lead to the sufferer needing to visit the toilet urgently and repeatedly – many times each day. This is not only undesirable in itself, but interferes with getting nutrition from food (if the person has any appetite to eat), and leads to dangerous dehydration – and can have other complications. So, this is a very serious condition, and it is readily transmitted from one person to another.

"C. difficile is an infectious Gram-positive spore-forming bacillus microorganism of the gastrointestinal tract, and its toxin expression causes gastrointestinal illness with a wide spectrum of severity, ranging from mild diarrhea to pseudomembranous colitis, toxic megacolon, sepsis-like picture and death…"
Bien, Palagan & Bozko, 2013: 53

Many people have a low level of Clostridium difficile specimens in their gut normally, but as one small part of the much larger and diverse population of gut microbes – in which context they cause no problems.

"C. difficile does not cause any significant disease when it is present in small numbers. However, disturbance of the normal intestinal flora (dysbiosis) by several potential causative factors may result in unlimited [sic] expansion of C. difficile in the microbiota, leading to inflammation and damage of the gut mucosa…"
Bien, Palagan & Bozko, 2013: 56

Someone who has suffered from C. diff infection needs a way to repopulate their gut with a good range of the usual different microbes. And that is when consuming a sample of a healthy person's excrement can be useful. (This is of course done under medical direction and supervision, both to maintain hygiene and to ensure the donor does not have medical conditions that might be passed on with the sample.)

A teaching analogy for faecal transplantation

This was all explained by Prof. Spector using an analogy.

Analogies are comparisons where a less familiar, and perhaps abstract or counterintuitive, concept is explained in terms of something familiar that can be seen to have a similar conceptual structure (see the figure). Analogies are commonly used in science teaching and public communication of science (as here in a radio programme) to introduce scientific ideas.

(Read about science analogies)

Figure: A teaching analogy to explain why faecal transplantation can be used to treat C. diff (based on the presentation by Prof. Tim Spector in '*Lady Mary Montagu's Smallpox Experiment*')

How does your garden grow?

Prof. Spector developed a comparison between the different microbes found in the gut, and the plants growing in a garden:

"These nasty infections are the most extreme, if you like, that pretty much wipe out most of our normal species. So … we might, say, start with a thousand species and people [with C. diff] might be down to just ten or so, different ones and so nasty ones take over. It's a bit like a garden that has gone very badly wrong and you have put too much herbicide all over it and it looks like an Arizona back yard with a few burning tyres in it. It's very easy for things to take over that and what we want to get, is by putting these bugs in there, to create a really healthy garden that gets back to normal that looks like a nice English country garden with lots of blooms, and really good soil, and lots of plants interacting with each other, and that's the way to think about these microbes, but to do that, to get to this nice rosy picture of a country garden you have to go through yucky stages first"
Prof. Tim Spector – From 'Lady Mary Montagu's Smallpox Experiment'

Before and after faecal transplantation: a medical treatment that can transform your 'garden'? (Images by Simon (left) and Prawny (right) from Pixabay)
[Move the slider to change between the pictures].

So the idea of taking a sample of someone else's excrement into our own gut may seem "yukky" – and is definitely NOT recommended without proper procedures and supervision – but may sometimes be a sensible and beneficial medical treatment. Just think of it as resewing the garden of the gut with a nice selection of seeds that will give rise to a diverse selection of colourful blooms.

Naomi Alderman: Instead of poo, we could think to ourselves, 'wild flower seeds'

Tim Spector: It's wild flower seeds with a bit of soil in it as well, so they have come in their own pot [sic] if you like.
From 'Lady Mary Montagu's Smallpox Experiment'

'wild flower seeds with a bit of soil…in their own pot'? (Images by OpenClipart-Vectors from Pixabay)

Work cited:

Bien, J., Palagani, V., & Bozko, P. (2013). The intestinal microbiota dysbiosis and Clostridium difficile infection: is there a relationship with inflammatory bowel disease? Therapeutic advances in gastroenterology, 6(1), 53-68. doi:10.1177/1756283X12454590 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3539291/

Balding black holes – a shaggy dog story

Resurrecting an analogy from a dead metaphor?

Keith S. Taber

Now there's a look in your eyes, like black holes in the sky…(Image by Garik Barseghyan from Pixabay)

I was intrigued by an analogy in a tweet

Like a shaggy dog in springtime, some black holes have to shed their "hair."

The link led me to an item at a webpage at 'Science News' entitled 'Black holes born with magnetic fields quickly shed them' written by Emily Conover. This, in turn, referred to an article in Physical Review Letters.

Now Physical Review Letters is a high status, peer-reviewed, journal.

(Read about peer review)

As part of the primary scientific literature, it publishes articles written by specialist scientists in a technical language intended to be understood by other specialists. Dense scientific terminology is not used to deliberately exclude general readers (as sometimes suggested), but is necessary for scientists to make a convincing case for new knowledge claims that seem persuasive to other specialists. This requires being precise, using unambiguous technical language."The thingamajig kind of, er, attaches to the erm, floppy bit, sort of" would not do the job.

(Read about research writing)

Science News however is news media – it publishes journalism (indeed, 'since 1921' the site reports – although that's the publication and not its website of course.) While science journalism is not essential to the internal processes of science (which rely on researchers engaging with each other's work though scholarly critique and dialogue) it is very important for the public's engagement with science, and for the accountability of researchers to the wider community.

Science journalists have a job similar to science teachers – to communicate abstract ideas in a way that makes sense to their audience. So, they need to interpret research and explain it in ways that non-specialists can understand.

The news article told me

"Like a shaggy dog in springtime, some black holes have to shed…
Unlike dogs with their varied fur coats, isolated black holes are mostly identical. They are characterized by only their mass, spin and electric charge. According to a rule known as the no-hair theorem, any other distinguishing characteristics, or "hair," are quickly cast off. That includes magnetic fields."

Conover, 2013

Here there is clearly the use of an analogy – as a black hole is not the kind of thing that has actual hair. This would seem to be an example of a journalist creating an analogy (just as a science teacher would) to help 'make the unfamiliar familiar' to her readers:

just as

dogs with lots of hair need to shed some ready for the warmer weather (a reference to a familiar everyday situation)

so, too, do

black holes (no so familiar to most people) need to lose their hair…

(Read about making the unfamiliar familiar)

But hair?

Surely a better analogy would be along the lines that just as dogs with lots of hair need to shed some ready for the warmer weather, so to do black holes need to lose their magnetic fields…

An analogy is used to show a novel conceptual structure (here, relating to magnetic fields around black holes) maps onto a more familiar, or more readily appreciated, one (here, that a shaggy dog will shed some of its fur). A teaching analogy may not reflect a deep parallel between two systems, as its function may be just to *introduce* an abstract principle.

(Read about science analogies)

Why talk of black holes having 'hair'?

Conover did not invent the 'hair' reference for her ScienceNews piece – rather she built her analogy on a term used by the scientists themselves. Indeed, the title of the cited research journal article was "Magnetic Hair and Reconnection in Black Hole Magnetospheres", and it was a study exploring the consequences of the "no-hair theorem" – as the authors explained in their abstract:

"The no-hair theorem of general relativity states that isolated black holes are characterized [completely described] by three parameters: mass, spin, and charge."

Bransgrove, Ripperda & Philippov, 2021

However, some black holes "are born with magnetic fields" or may "acquire magnetic flux later in life", in which case the fields will vary between black holes (giving an additional parameter for distinguishing them). The theory suggests that these black holes should somehow lose any such field: that is, "The fate of the magnetic flux (hair) on the event horizon should be in accordance with the no-hair theorem of general relativity" (Bransgrove, Ripperda & Philippov, 2021: 1). There would have to be a mechanism by which this occurs (as energy will be conserved, even when dealing with black holes).

So, the study was designed to explore whether such black holes would indeed lose their 'hair'. Despite the use of this accessible comparison (magnetic flux as 'hair'), the text of the paper is pretty heavy going for someone not familiar with that area of science:

"stationary, asymptotically flat BH spacetimes…multipole component l of a magnetic field…self-regulated plasma…electron-positron discharges…nonzero stress-energy tensor…instability…plasmoids…reconnection layer…relativistic velocities…highly magnetized collisionless plasma…Lundquist number regime…Kerr-schild coordinates…dimensionless BH spin…ergosphere volume…spatial hypersurfaces…[…and so it continues]"

(Bransgrove, Ripperda & Philippov, 2021: 1).

"***Come on Harry, you know full well that 'the characteristic minimum plasma density required to support the rotating magnetosphere is the Goldreich-Julian number density'*** *[Bransgrove, Ripperda & Philippov, 2021: 2]****, so hand me that hyperspanner***."
Image from Star Trek: Voyager (Paramount Pictures)

Spoiler alert

I do not think I will spoil anything by revealing that Bransgrove and colleague conclude from their work that "the no-hair theorem holds": that there is a 'balding process' – the magnetic field decays ("all components of the stress-energy tensor decay exponentially in time"). If any one reading this is wondering how they did this work, given that most laboratory stores do not keep black holes in stock to issue to researchers on request, it is worth noting the study was based on a computer simulation.

That may seem to be rather underwhelming as the researchers are just reporting what happens in a computer model, but a lot of cutting-edge science is done that way. Moreover, their simulations produced predictions of how the collapsing magnetic fields of real black holes might actually be detected in terms of the kinds of radiation that should be produced.

As the news item explained matters:

Magnetic reconnection in balding black holes could spew X-rays that astronomers could detect. So scientists may one day glimpse a black hole losing its hair.

Conover, 2013

So, we have hairy black holes that go through a balding process when they lose their hair – which can be tested in principle because they will be spewing radiation.

Balding is to hair, as…

Here we have an example of an analogy for a scientific concept. Analogies compare one phenomenon or concept to another which is considered to have some structural similarity (as in the figure above). When used in teaching and science communication such analogies offer one way to make the unfamiliar familiar, by showing how the unfamiliar system maps in some sense onto a more familiar one.

hair = magnetic field

balding = shedding the magnetic field

Black holes are expected to be, or at least to become, 'hairless' – so without having magnetic fields detectable from outside the event horizon (the 'surface' connecting points beyond which everything, even light, is unable to 'escape' the gravitational field and leave the black hole). If black holes are formed with, or acquire, such magnetic fields, then there is expected to be a 'balding' process. This study explored how this might work in certain types of (simulated) black holes – as magnetic field lines (that initially cross the event horizon) break apart and reconnect. (Note that in this description the magnetic field lines – imaginary lines invented by Michael Faraday as a mental tool to think about and visualise magnetic fields – are treated as though they are real objects!)

Some such comparisons are deliberately intended to help scientists explain their ideas to the public – but scientists also use such tactics to communicate to each other (sometimes in frivolous or humorous ways) and in these cases such expressions may do useful work as short-hand expressions.

So, in this context hair denotes anything that can be detected and measured from outside a black hole apart form its mass, spin, and charge (see, it is much easier to say 'hair')- such as magnetic flux density if there is a magnetic field emerging from the black hole.

A dead metaphor?

In the research paper, Bransgrove, Ripperda and Philippov do not use the 'hair' comparison as an analogy to explain ideas about black holes. Rather they take the already well-established no-hair theorem as given background to their study ("The original no-hair conjecture states that…"), and simply explain their work in relation to it ("The fate of the magnetic flux (hair) on the event horizon should be in accordance with the no-hair theorem of general relativity.")

Whereas an analogy uses an explicit comparison (this is like that because…), a comparison that is not explained is best seen as a metaphor. A metaphor has 'hidden meaning'. Unlike in an analogy, the meaning is only implied.

"The no-hair theorem of general relativity states that isolated black holes are characterized by three parameters: mass, spin, and charge";
"The original no-hair conjecture states that all stationary, asymptotically flat BH [black hole] spacetimes should be completely described by the mass, angular momentum, and electric charge"

(Read adbout science metaphors)

Bransgrove and colleagues do not need to explain why they use the term 'hair' in their research report as in their community it has become an accepted expression where researchers already know what it is intended to mean. We might consider it a dead metaphor, an expression which was originally used to imply meaning through some kind of comparison, but which through habitual use has taken on literal meaning.

Science has lots of these dead metaphors – terms like electrical charge and electron spin have with repeated use over time earned their meanings without now needing recourse to their origins as metaphors. This can cause confusion as, for example, a learner may develop alternative conceptions about electron spin if they do not appreciate its origin as a metaphor, and assumes an electron spins in the same sense as as spinning top or the earth in space. Then there is an associative learning impediment as the learner assumes an electron is spinning on its axis because of the learner's (perfectly reasonable) associations for the word 'spin'.

The journalist or 'science writer' (such as Emily Conover), however, is writing for a non-specialist readership, so does need to explain the 'hair' reference. So, I would characterise the same use of the terms hair/no-hair and balding as comprising a science analogy in the news item, but a dead metaphor in the context of the research paper. The meaning of language, after all, is in the mind of the reader.

Work cited:

Bransgrove, A., Ripperda, B., & Philippov, A. (2021). Magnetic Hair and Reconnection in Black Hole Magnetospheres. Physical Review Letters, 127(5), 055101. doi:10.1103/PhysRevLett.127.055101 https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.055101
Conover, E. (2013, August 3rd 2021). Black holes born with magnetic fields quickly shed them. ScienceNews. https://www.sciencenews.org/article/black-hole-magnetic-field-hair-computer-simulations-physics

Excavating a cognitive dinosaur

Keith S. Taber

Filling-in; and digging-out a teaching analogy

Is the work of cognition like the work of a palaeontologist? (Image by Brenda Geisse from Pixabay)

I like the reflexive nature of this account – of someone reconstructing an analogy
about how cognition reconstructs coherent wholes from partial, fragmented data
from a partial, fragmented memory representation.

I was reading something about memory function that piqued my interest in an analogy:

"Neisser, using an analogy initially developed by Hebb (1949) to characterize [sic] perception, likened the rememberer to a paleontologist who attempts to reconstruct a dinosaur from fragmentary remains: 'out of a few stored bone chips, we remember a dinosaur'…"
Schacter, 1995, p.10

I was interested enough to look up the original use of this analogy (as I report below).

This links to three things that have separately interested me:

the nature of memory
the constructivist account of learning and cognition
using analogies in teaching and comunicating science

The nature of our memories

I have long been interested in what memory is and how it works – and its role in academic learning (Taber, 2003). In part this perhaps derives from the limits of my own memory – I have been reasonably successful academically, but have never felt I had a good memory (and I seem to get more 'absent minded' all the time). This interest grew as it became clearer to me that our memory experiences seem to be quite different – my late wife Philippa would automatically and effortlessly remember things in a way that that seemed to me to be a kind of superpower. (She was once genuinely surprised that I could not picture what a family member had been wearing on arriving at a family event years before, whereas I thought I was doing pretty well to even remember I had been there.) Now that neurodiversity is widely recognised, it seems less surprising that we do not all experience memory in the same way.

A lot of people, however, understand memory in terms of a kind of folk-model (that is, a popular everyday account which does not match current scientific understanding) – along the lines that we put information into a memory store, where – unless it gets lost and we forget – we can later access it and so remember what it was that we committed to memory. Despite the ubiquity of that notion, research suggests that is not really how memory functions. We might say that this is a common alternative conception of how memory works.

(Read about 'Memory')

The constructive nature of memory

Schacter was referring back to a tradition that began a century ago when Bartlett carried out a series of studies on memory. Bartlett (1932/1995) would, for example, expose people to a story that was unfamiliar to his study participants, and then later ask them to retell as much of the story as they could remember. As might be expected, some people remembered more details than others.

What perhaps was less predictable at the time was the extent to which people included in their retelling details that had not been part of the original story at all. These people were not deliberately embellishing or knowingly guessing, but reporting, as best they could, what their memory suggested had been part of the original story.

People who habitually exhibit this 'confabulation' to an pathological degree (perhaps remembering totally fantastic things that clearly could not be true) are recognised as having some kind of problem, but it transpires this is just an extreme of something that is normal behavior. Remembering is not the 'pulling something out of storage' that we may experience it as – as actually what we remember is more like a best guess based on insufficient data (but a guess made preconsciously, so it appears in our conscious minds as definitive) than a pristine copy of an original experience. Memory is often more a matter of constructing an account from the materials at hand than simply reading it out from something stored.

Thus the analogy. Here is some wider context for the quote presented above:

"The publication of Neisser's (1967) important monograph on cognitive psychology rekindled interest in Bartlett's ideas about schemas and reconstructive memory. According to Neisser, remembering the past is not a simple matter of reawakening a dormant engram or memory trace; past events are constructed by using preexisting knowledge and [schemata] to piece together whatever fragmentary remains of the initial episode are available in memory. Neisser, using an analogy initially developed by Hebb (1949) to characterize [sic] perception, likened the rememberer to a paleontologist who attempts to reconstruct a dinosaur from fragmentary remains: 'out of a few stored bone chips, we remember a dinosaur' (1967, p.285). In this view, all memories are constructions because they include general knowledge that was not part of a specific event, but is necessary to reconstruct it. The fundamentally constructive nature of memory in turn makes it susceptible to various kinds of distortions and inaccuracies. Not surprisingly, Neisser embraced Bartlett's observations and ideas about the nature of memory."
Schacter, 1995, p.10

These ideas will not seem strange to those who have studied science education, a field which has been strongly influenced by a 'constructivist' perspective on learning. Drawing on learning science research, the constructivist perspective focuses on how each learner has to build up their own knowledge incrementally: it is not possible for a teacher to take some complex technical knowledge and simply transfer it (or copy it) to a learner's mind wholesale.

(Read more about constructivism in education)

Excavating the analogy: what did Hebb actually say?

Hebb is remembered for his work on understanding the brain in terms of neural structures – neurons connected into assemblies through synapses. His book 'The Organization of Behavior' has been described as "one of the most influential books in Psychology and Neuroscience" (Brown, 2020: 1).

Tachistoscope Source: Science Museum Group (This image is released under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence)

The analogy referred to by Schacter was used by Hebb in describing perception. He discussed studies using a tachistoscope, an instrument for displaying images for very brief periods. This could be used to show an image to a person with an exposure insufficient for them to take in all the details,

"…the pattern is perceived, first, as a familiar one, and then with something missing or something added. The something, also, is familiar; so the total perception is a mélange of the habitual.
The subject's reports [make it] clear that the subject is not only responding to the diagram as a whole; he perceives its parts as separate entities, even though presentation is so brief. Errors are prominent, and such as to show that all the subject really perceives–and then only with rough accuracy–is the slope of a few lines and their direction and distance from one another"
Hebb, 1949: pp.46-47

That is, the cognitive system uses the 'clues' available from the incomplete visual data to build (in effect) a hypothesis of what was seen, based on correspondences between the data actually available and familiar images that match that limited data. What the person becomes consciously aware of 'seeing' is not actually a direct report from the visual field of the presented image, but a constructed image that is a kind of conjecture of what might have been seen – 'filling-in' missing data with what seems most likely based on past visual experiences.

Cognitive scientist Annette Karmiloff-Smith developed the concept of 'representational redescription' as a way of describing how initially tacit knowledge could eventually become explicit. She suggested that "intra-domain and inter-domain representational relations are the hallmark of a flexible and creative cognitive system" (Karmiloff-Smith,1996: 192). The gist was that the brain is able to re-represent its own internal representations in new forms with different affordances.

An loose analogy might be someone who takes a screenshot when displaying an image from the JPEG photo collection folder on the computer, opens the screenshot as a pdf file, and then adds some textual annotations before exporting the file to a new pdf. The representation of the original image is unchanged in the system, but a new representation has been made of it in a different form, which has then been modified and 'stored' (represented) in a different folder.

Hebb was describing how a representation of visual data at one level in the cognitive system has been represented elsewhere in the system (representational redescription?) at a level where it can be mentipulated by 'filling-in'.

Hebb then goes on to use the analogy:

"A drawing or a report of what is seen tachistoscopically is not unlike a paleontologist's reconstruction of early man from a tooth and a rib. There is a clear effect of earlier experience, filling in gaps in the actual perception, so that the end result is either something familiar or a combination of familiar things–a reconstruction on the basis of experience."
Hebb, 1949: p.47

Teaching analogies

Hebb was writing a book that can be considered as a textbook, so this can be seen as a teaching analogy, although such analogies are also used in communicating science in other contexts.

(Read about Science analogies)

Teaching is about making the unfamiliar familiar, and one way we do that is by saying that 'this unfamiliar thing you need to learn about is a bit like this other thing that you already know about'. Of course, when teaching in this way we need to say in what way there is an analogy, and it may also be important to say in what ways the two things are not alike if we do not want people to map across irrelevant elements (i.e., to develop 'associative' learning impediments).

(Read about Making the unfamiliar familiar)

Hebb is saying that visual perception is often not simply the detection of a coherent and integral image, but is rather a construction produced by building upon the available data to construct a coherent and integral image. In extremis, a good deal may be made of very little scraps of input – akin to a scientist reconstructing a model of a full humanoid body based on a couple of bits of bone or tooth.

There are examples where palaeontologists or anthropologists have indeed suggested such complete forms based on a few fossil fragments as data. This is only possible because of their past experiences of meeting many complete forms, and the parts of which they are made. (And of course, sometimes other scientists completely disagree about their reconstructions!)

An exscientific analogy?

Often in teaching science we use teaching analogies that compare an unfamiliar scientific concept to some familiar everyday phenomenon – perhaps a reaction profile is a bit like a roller-coaster track. Perhaps we could call these adscientific analogies as the meaning is transferred to the scientific concept from the everyday.

Sometimes, however, familiar scientific phenomena or ideas are used as the source – as here. Perhaps these could be called exscientific analogies as the meaning is taken from the science concept and applied elsewhere.

Developing the palaeontology analogy

So, Hebb had originally used the palaeontology analogy in the context of discussing perception. When I looked into how Neisser had used the comparison in his "important monograph on cognitive psychology" I found he had developed the analogy, returning to it at several points in his book.

Do we analyse what we attend to?

Neisser's first reference was also in relation to perception, rather than memory. Neisser argued that before we can attend to part of a scene there must already have been the operation of "preattentive mechanisms, which form segregated objects" from which we can select what to attend to. These processes might be referred to as analyses:

"…the detailed properties and features that we ordinarily see in an attended figure…arise…only because part of the input was selected for attention and certain operations then performed on it. Neither the object of analysis nor the nature of the analysis is inevitable, and both may vary in different observers and at different times."

Neisser, 1967, p.94

But Neisser was not sure this really was 'analysis', which he understood as drawing on another (what I labelled above) exscientific analogy:

"The very word 'analysis' may not be apt. It suggests an analogy with chemistry: a chemist 'analyses' unknown substances to find out what they 'really' are."

Neisser, 1967, p.94

Rather than refer to analysis, we could draw on Hebb's palaeontological analogy:

"More appropriate…is Hebb's (1949, p.47) comparison of the perceiver with a paleontologist, who carefully extracts a few fragments of what might be bones from a mass of irrelevant rubble and 'reconstructs' the dinosaur that will eventually stand in the Museum of Natural History. In this sense it is important to think of focal attention as a constructive, synthetic activity rather than as purely analytic. One does not simply examine the input and make a decision; one builds an appropriate visual object."

Neisser, 1967, p.94

[If it helps to have some examples to reflect upon this account of perception, you may find it useful to look at some images that may require careful interpretation.]

Neisser draws upon the analogy repeatedly in developing his account of perception:

"Such emotion-flooded experiences [as 'physiognomic' perception: 'Everyone has perceived such traits as suppressed anger in a face, gaiety in a movement, or peaceful harmony in a picture'] can be thought of as the result of particular kinds of construction. The same fragments of bone that lead one paleontologist to make an accurate model of an unspectacular creature might lead another, perhaps more anxious or more dramatic, to 'reconstruct' a nightmarish monster." (pp.96-97)
"To 'direct attention' to a figure is to attempt a more extensive synthesis of it. Of course, synthesis presupposes some prior analysis, as the paleontologist must have some fragments of bone before he can build his dinosaur…" (p.103)
"Recognition, whether of spelling patterns or words as wholes, must be mediated by relevant features, as meaningless in themselves as the bone chips of the paleontologist." (p.114)
"The process of figural synthesis does not depend only on the features extracted from the input, just as the dinosaur constructed by a paleontologist is not based only on the bone chips he has found. Equally important is the kind of perceptual object the perceiver is prepared to construct. The importance of set and context on the perception of words has been demonstrated in a great many experiments." (pp.115-116)
Neisser, 1967

And as with perception, so memory…

When Neisser discusses memory he uses a kind of double analogy – suggesting that memory is a bit like perception, which (as already established) is a bit like the work of the palaeontologist:

"Perception is constructive, but the input information often plays the largest single role in determining the constructive process. A very similar role, it seems to me, is played by the aggregate of information stored in long-term memory.
This is not to say that the stimuli themselves are copied and stored; far from it. The analogy being offered asserts only that the role which stored information plays in recall is like the role which stimulus information plays in perception….The model of the paleontologist, which was applied to perception and focal attention in Chapter 4, applies also to memory: out of a few stored bone chips, we remember a dinosaur….one does not recall objects or responses simply because traces of them exist in the mind, but after an elaborate process of reconstruction, (which usually makes use of relevant stored information).
What is the information – the bone chips – on which reconstruction is based? The only plausible possibility is that it consists of traces of prior processes of construction. There are no stored copies of finished mental events, like images or sentences, but only traces of earlier constructive activity."
Neisser, 1967, p.285

Fleshing-out the metaphor

Neisser then pushes the analogy one step further, by pointing out that the 'fleshed-out' model of a dinosaur in the museum may be constructed in part based on the fossil fragments of bones, but those fragments themselves do not form part of the construction (the model). The bones are used as referents in building the skeletal framework (literally, the skeleton) around which the model will be built, but the model is made from other materials (wood, steel, fibreglass, whatever) and the fossil fragments themselves will be displayed separately or perhaps filed away in a drawer in the museum archives. (As in the representational redescription model – the original representation is redescribed at another level of the system.)

"The present proposal is, therefore, that we store traces of earlier cognitive acts, not of the products of those acts. The traces are not simply 'revised' or 'reactivated' in recall; instead, the stored fragments are used as information to support a new construction. It is as if the bone fragments used by the paleontologist did not appear in the model he builds at all – as indeed they need not, if it to represent a fully fleshed-out skin-covered dinosaur. The bones can be thought of, somewhat loosely, as remnants of the structure which created and supported the original dinosaur, and thus as sources of information about how to reconstruct it."
Neisser, 1967, pp.285-286

The head palaeontologist?

A final reference to the analogy is used when Neisser addresses the question of the cognitive executive: the notion that somewhere in the cognitive system there is something akin to an overseer who direct operations:

"Who does the turning, the trying, and the erring" Is there a little man in the head, a homonculus, who acts the part of the paleontologist vis-à-vis the dinosaur? p.293
Neisser, 1967, p.293

The homonculus can be pictured as a small person sitting in the brain's control room, for example, viewing the images being projected from the visual input.

It is usually considered this is a flawed model (potentially lading to an infinite regress), a failure to take a systemic view of the cognitive system. It is the system which functions and leads to our conscious experience of perceiving, attending, making decisions, planning, remembering, and so forth. Whilst there are specialist components (modules) including for the coordination of the system, there is not a discrete controller overlaying the system as a whole who is doing the seeing, hearing, thinking, etcetera based on outputs from processing by the system.

Here the homonculus would like an authority that the palaeontologist turned to in order to decide how to build her model: raising the question of how does that expert know, and who would they, in turn, ask?

Why change Hebb's orignal analogy?

Altohugh Neisser refers to the analogy as being that used by Hebb, he modifies it. A tooth and rib become fragments of bone, and the early man becomes a dinosaur. Whether the shift from the reconstruction of an early hominid to the reconstruction of a terrible lizard was a deliberate one (for greater effect? because Neisser thought it would be more familiar to his readers?) or not I do not know. The phrasing suggests that Neisser thought he was applying Hebb's original comparison – so I suspect this is how he recalled the analogy.

Perhaps Neisser had regularly used the analogy in his teaching, in which case it may have become so familiar to him that he did not feel the need to check the original version. That is, perhaps he was correctly remembering how he had previously misremembered the original analogy. That is not fanciful, as memory researchers suggest this is something that is very common. Each time we access a memory the wider representational context becomes modified by engagement with it.

That is, if what is represented (in 'long-term memory'*) is indeed "traces of prior processes of construction…traces of earlier constructive activity" then each time a 'memory' is experienced, by being constructed based on what is represented ('in memory'*), new traces of that process of constructing the memory are left in the system.

It is possible over the years to be very convinced about the accuracy of a distorted memory that has been regularly reinforced. (The extent to which this may in part be the origin of many wars, feuds, and divorces might be a useful focus for research?)

So perhaps Neisser had represented in his long-term memory the analogy of a palaeontologist with a few fossil fragments, and when he sought to access the analogy, perhaps in a classroom presentation, the other elements were filled-in: the 'tooth and rib' became 'a few fragments of what might be bones' and the 'early man' become 'a dinosaur' – details that made sense of the analogy in terms familiar to Neisser.

The account of cognition that Hebb, Neisser and Schater were presenting would suggest that if this had been the case then for Neisser there would be no apparent distinction between the parts of Hebb's analogy that Neisser was remembering accurately, and the parts his preconscious mind had filled-in to construct a coherent analogy. I like the reflexive nature of this account – of someone reconstructing an analogy about how cognition reconstructs coherent wholes from partial, fragmented data – from a partial, fragmented memory representation.

Sources cited:

Bartlett, F. C. (1932/1995). Remembering: A study in experimental and social psychology Cambridge: Cambridge University Press.
Brown, R. E. (2020). Donald O. Hebb and the Organization of Behavior: 17 years in the writing. Molecular Brain, 13(1), 55. doi:10.1186/s13041-020-00567-8
Hebb, D. O. (1949). The Organisation of Behaviour. A neuropsychological theory. New York: John Wiley & Sons, Inc.
Karmiloff-Smith, A. (1996). Beyond Modularity: A developmental perspective on cognitive science. Cambridge, Massachusetts: MIT Press.
Neisser, U. (1967). Cognitive Psychology. New York: Appleton-Century-Crofts.
Schacter, D. L. (1995). Memory distortion: history and current status. In D. L. Schacter (Ed.), Memory Distortion. How minds, brains, and societies reconstruct the past (pp. 1-43). Cambridge, Massachusetts: Harvard University Press.
Taber, K. S. (2003) Lost without trace or not brought to mind? – a case study of remembering and forgetting of college science, Chemistry Education: Research and Practice, 4 (3), pp.249-277. [Free access]

* terms like 'in memory' and 'in long-term memory' may bring to mind the folk-notion of memory as somewhere in the brain where things are stored away, whereas it is probably better to think of the brain as a somewhat plastic processing system which is constantly being modified by its own functioning. The memory we experience is simply the outcome of active processing** in part of the system that has previously been modified by earlier mental activity (** active processing which is in turn itself further modifying the system).