Category: language

What COVID really likes

Researching viral preferences

Keith S. Taber

When I was listening to the radio news I heard a clip of the Rt. Hon. Sajid Javid MP, the U.K. Secretary of State for Health and Social Care, talking about the ongoing response to the COVID pandemic:

Health Secretary Sajid Javid talking on 12th September

"Now that we are entering Autumn and Winter, something that COVID and other viruses, you know, usually like, the prime minister this week will be getting out our plans to manage COVID over the coming few months."

Sajid Javid

So, COVID and other viruses usually like Autumn and Winter (by implication, presumably, in comparison with Spring and Summer).

This got me wondering how we (or Sajid, at least) could know what the COVID virus (i.e., SARS-CoV-2 – severe acute respiratory syndrome coronavirus 2) prefers – what the virus 'likes'. I noticed that Mr Javid offered a modal qualification to his claim: usually. It seemed 'COVID and other viruses' did not always like Autumn and Winter, but usually did.

Yet there was a potential ambiguity here depending how one parsed the claim. Was he suggesting that

[COVID and other viruses]

usually

like Autumn and Winter		orCOVID

[and other viruses usually]

like Autumn and Winter

This might have been clearer in a written text as either

COVID and other viruses usually like Autumn and WinterorCOVID, and other viruses usually, like Autumn and Winter

The second option may seem a little awkward in its phrasing, 1 but then not all viral diseases are more common in the Winter months, and some are considered to be due to 'Summer viruses':

"Adenovirus, human bocavirus (HBoV), parainfluenza virus (PIV), human metapneumovirus (hMPV), and rhinovirus can be detected throughout the year (all-year viruses). Seasonal patterns of PIV are type specific. Epidemics of PIV type 1 (PIV1) and PIV type 3 (PIV3) peak in the fall [Autumn] and spring-summer, respectively. The prevalence of some non-rhinovirus enteroviruses increases in summer (summer viruses)"


Moriyama, Hugentobler & Iwasaki, 2020: 86

Just a couple of days later Mr Javid was being interviewed on the radio, and he made a more limited claim:

Health Secretary Sajid Javid talking on BBC Radio 4's 'Today' programme, 15th September

"…because we know Autumn and Winter, your COVID is going to like that time of year"

Sajid Javid

So, this claim was just about the COVID virus, not viruses more generally, and that we know that COVID is going to like Autumn and Winter. No ambiguity there. But how do we know?

Coming to knowledge

Historically there have been various ways of obtaining knowledge.

  • Divine revelation: where God reveals the knowledge to someone, perhaps through appearing to the chosen one in a dream.
  • Consulting an oracle, or a prophet or some other kind of seer.
  • Intuiting the truth by reflecting on the nature of things using the rational power of the human intellect.
  • Empirical investigation of natural phenomena.

My focus in this blog is related to science, and given that we are talking about public health policy in modern Britain, I would like to think Mr Javid was basing his claim on the latter option. Of course, even empirical methods depend upon some metaphysical assumptions. For example, if one assumes the cosmos has inbuilt connections one might look for evidence in terms of sympathies or correspondences. Perhaps, if the COVID virus was observed closely and looked like a snowflake, that could (in this mindset) be taken as a sign that it liked Winter.

A snowflake – or is it a virus particle?
(Image by Gerd Altmann from Pixabay)

Sympathetic magic

This kind of correspondence, a connection indicated by appearance, was once widely accepted, so that a plant which was thought to resemble some part of the anatomy might be assumed to be an appropriate medicine for diseases or disorders associated with that part of the body.

This is a kind of magic, and might seem a 'primitive' belief to many people today, but such an idea was sensible enough in the context of a common set of underlying beliefs about the nature and purposes of the world, and the place and role of people in that world. One might expect that specific beliefs would soon die out if, for example, the plant shaped like an ear turned out to do nothing for ear ache. Yet, at a time when medical practitioners could offer little effective treatment, and being sent to a hospital was likely to reduce life expectancy, herbal remedies at least often (if not always) did no harm.

Moreover, many herbs do have medicinal properties, and something with a general systemic effect might work as topical medicine (i.e., when applied to a specific site of disease). Add to that, the human susceptibility to confirmation bias (taking more notice of, and giving more weight to, instances that meet our expectations than those which do not) and the placebo effect (where believing we are taking effective medication can sometimes in itself have beneficial effects) and the psychological support offered by spending time with an attentive practitioner with a good 'bedside' manner – and we can easily see how beliefs about treatments may survive limited definitive evidence of effectiveness.

The gold standard of experimental method

Of course, today, we have the means to test such medicines by taking a large representative sample of a population (of ear ache sufferers, or whatever), randomly dividing them into two groups, and using a double-blind (or should that be double-deaf) approach, treat them with the possible medicine or a placebo, without either the patient or the practitioner knowing who was getting which treatment. (The researchers have a way to know of course – or it would difficult to deduce anything from the results.) That is, the randomised control trial (RCT).

Now, I have been very critical of the notion that these kinds of randomised experimental designs should be automatically be seen as the preferred way of testing educational innovations (Taber, 2019) – but in situations where control of variables and 'blinding' is possible, and where randomisation can be applied to samples of well-defined populations, this does deserve to be considered the gold standard. (It is when the assumptions behind a research methodology do not apply that we should have reservations about using it as a strategy for enquiry.)

So can the RCT approach be used to find out if COVID has a preference for certain times of year? I guess this depends on our conceptual framework for the research (e.g., how do we understand what a 'like' actually is) and the theoretical perspective we adopt.

So, for example, behaviourists would suggest that it is not useful to investigate what is going on in someone's mind (perhaps some behaviorists do not even think the mind concept corresponds to anything real) so we should observe behaviours that allow us to make inferences. This has to be done with care. Someone who buys and eats lots of chocolate presumably likes chocolate, and someone who buys and listens to a lot of reggae probably likes reggae, but a person who cries regularly, or someone that stumbles around and has frequent falls, does not necessary like crying, or falling over, respectively.

A viral choice chamber

So, we might think that woodlice prefer damp conditions because we have put a large number of woodlice in choice chambers with different conditions (dry and light, dry and dark, damp and light, damp and dark) and found that there was a statistically significant excess of woodlice settling down in the damp sections of the chamber.

Of course, to infer preferences from behaviour – or even to use the term 'behaviour' – for some kinds of entity is questionable. (To think that woodlice make a choice based on what they 'like' might seem to assume a level of awareness that they perhaps lack?) In a cathode ray tube electrons subject to a magnetic field may be observed (indirectly!) to move to one side of the tube, just as woodlice might congregate in one chamber, but I am not sure I would describe this as electrons liking that part of the tube. I think it can be better explained with concepts such as electrical charge, fields, forces, and momentum.

It is difficult to see how we can do double blind trials to see which season a virus might like, as if the COVID virus really does like Winter, it must surely have a way of knowing when it is Winter (making blinding impossible). In any case, a choice chamber with different sections at different times of the year would require some kind of time portal installed between its sections.

Like electrons, but unlike woodlice, COVID viral particles do not have an active form of transport available to them. Rather, they tend to be sneezed and coughed around and then subject to the breeze, or deposited by contact with surfaces. So I am not sure that observing virus 'behaviour' helps here.

So perhaps a different methodology might be more sensible.

A viral opinion poll

A common approach to find out what people like would be a survey. Surveys can sometimes attract responses from large numbers of respondents, which may seem to give us confidence that they offer authentic accounts of widespread views. However, sample size is perhaps less important than sample representativeness. Imagine carrying out a survey of people's favourite football teams at a game at Stamford Bridge; or undertaking a survey of people's favourite bands as people queued to enter a King Crimson concert! The responses may [sic, almost certainly would] not fully reflect the wider population due to the likely bias in such samples. Would these surveys give reliable results which could be replicated if repeated at the Santiago Bernabeu or at a Marillion concert?

How do we know what 'COVID 'really likes?
(Original Images by OpenClipart-Vectors and Gordon Johnson from Pixabay)

A representative sample of vairants?

This might cause problems with the COVID-19 virus (SARS-CoV-2). What counts as a member of the population – perhaps a viable virus particle? Can we even know how big the population actually is at the time of our survey? The virus is infecting new cells, leading to new virus particles being produced all the time, just as shed particles become non-viable all the time. So we have no reliable knowledge of population numbers.

Moreover, a survey needs a representative sample: do the numbers of people in a sample of a human population reflect the wider population in relevant terms (be that age, gender, level of educational qualifications, earnings, etc.)? There are viral variants leading to COVID-19 infection – and quite a few of them. That is, SARS-CoV-2 is a class with various subgroups. The variants replicate to different extents under particular conditions, and new variants appear from time to time.

So, the population profile is changing rapidly. In recent months in the UK nearly all infections where the variant has been determined are due to the variant VOC-21APR-02 (or B.1.617.2 or Delta) but many people will be infected asymptotically or with mild symptoms and not be tested, and so this likely does not mean that VOC-21APR-02 dominates the SARS-CoV-2 population as a whole to the extent it currently dominates in investigated cases. Assuming otherwise would be like gauging public opinion from the views of those particular people who make themselves salient by attending a protest, e.g.:

"Shock finding – 98% of the population would like to abolish the nuclear arsenal,

according to a [hypothetical] survey taken at the recent Campaign for Nuclear Disarmament march"

In any case, surveys are often fairly blunt instruments as they need to present objectively the same questions to all respondents, and elicit responses in a format that can be readily classified into a discrete number of categories. This is why many questionnaires use Likert type items:

Would you say you like Autumn and Winter:

12345
AlwaysNearly alwaysUsuallySometimesNever

Such 'objective' measures are often considered to avoid the subjective nature of some other types of research. It may seem that responses do not need to be interpreted – but of course this assumes that the researchers and all the respondents understand language the same way (what exactly counts as Autumn and Winter? What does 'like' mean? How is 'usually' understood – 60-80% of the time, or 51-90% of the time or…). We can usually (sic) safely assume that those with strong language competence will have somewhat similar understandings of terms, but we cannot know precisely what survey participants meant by their responses or to what extent they share a meaning for 'usually'.

There are so-called 'qualitative surveys' which eschew this kind of objectivity to get more in-depth engagement with participants. They will usually use interviews where the researcher can establish rapport with respondents and ask them about their thoughts and feelings, observe non-verbal signals such as facial expressions and gestures, and use follow-up questions… However, the greater insight into individuals comes at a cost of smaller samples as these kinds of methods are more resource-intensive.

But perhaps Mr Javid does not actually mean that COVID likes Autumn and Winter?

So, how did the Department of Health & Social Care, or the Health Secretary's scientific advisors, find out that COVID (or the COVID virus) likes Autumn and Winter? The virus does not think, or feel, and it does not have preferences in the way we do. It does not perceive hot or cold, and it does not have a sense of time passing, or of the seasons.2 COVID does not like or dislike anything.

Mr Javid needs to make himself clear to a broad public audience, so he has to avoid too much technical jargon. It is not easy to pitch a presentation for such an audience and be pithy, accurate, and engaging, but it is easy for someone (such as me) to be critical when not having to face this challenge. Cabinet ministers, unlike science teachers, cannot be expected to have skills in communicating complex and abstract scientific ideas in simplified and accessible forms that remain authentic to the science.

It is easy and perhaps convenient to use anthropomorphic language to talk about the virus, and this will likely make the topic seem accessible to listeners, but it is less clear what is actually meant by a virus liking a certain time of year. In teaching the use of anthropomorphic language can be engaging, but it can also come to stand in place of scientific understanding when anthropomorphic statements are simply accepted uncritically at face value. For example, if the science teacher suggests "the atom wants a full shell of electrons" then we should not be surprised that students may think this is a scientific explanation, and that atoms do want to fill their shells. (They do not of course. 3)

Image by Gordon Johnson from Pixabay

Of course Mr Javid's statements cannot be taken as a literal claim about what the virus likes – my point in this posting is to provoke the question of what this might be intended to mean? This is surely intended metaphorically (at least if Mr Javid had thought about his claim critically): perhaps that there is higher incidence of infection or serious illness caused by the COVID virus in the Winter. But by that logic, I guess turkeys really would vote for Christmas (or Thanksgiving) after all.

Typically, some viruses cause more infection in the Winter when people are more likely to mix indoors and when buildings and transport are not well ventilated (both factors being addressed in public health measures and advice in regard to COVID-19). Perhaps 'likes' here simply means that the conditions associated with a higher frequency/population of virus particles occur in Autumn and Winter?

A snowflake.
The conditions suitable for a higher frequency of snowflakes are more common in Winter.
So do snowflakes also 'like' Winter?
(Image by Gerd Altmann from Pixabay)

However, this is some way from assigning 'likes' to the virus. After all, in evolutionary terms, a virus might 'prefer', so to speak, to only be transmitted asymptomatically, as it cannot be in the virus's 'interests', so to speak, to encourage a public health response that will lead to vaccines or measures to limit the mixing of people.

If COVID could like anything (and of course it cannot), I would suggest it would like to go 'under the radar' (another metaphor) and be endemic in a population that was not concerned about it (perhaps doing so little harm it is not even noticed, such that people do not change their behaviours). It would then only 'prefer' a Season to the extent that that time of year brings conditions which allow it to go about its life cycle without attracting attention – from Mr Javid or anyone else.

Keith S. Taber, September 2021

Addendum: 1st December 2021

Déjà vu?

The health secretary was interviewed on 1st December

"…we have always known that when it gets darker, it gets colder, the virus likes that, the flu virus likes that and we should not forget that's still lurking around as well…"

Rt. Hon. Sajid Javid MP, the U.K. Secretary of State for Health and Social Care, interviewed on BBC Radio 4 Today programme, 1st December, 2021
Works cited:
Footnotes:

1. It would also seem to be a generalisation based on the only two Winters that the COVID-19 virus had 'experienced'

2. Strictly I cannot know what it is like to be a virus particle. But a lot of well-established and strongly evidenced scientific principles would be challenged if a virus particle is sentient.

3. Yet this is a VERY common alternative conceptions among school children studying chemistry: The full outer shells explanatory principle

Related reading:

So who's not a clever little virus then?

COVID is like a fire because…

Anthropomorphism in public science discourse

Opposites avoid attracting

Do species become more different from one another to avoid breeding?

Keith S. Taber

A tamarin monkey
A different tamarin

They say "opposites attract". True perhaps for magnetic poles and electrical charges, but the aphorism is usually applied to romantic couples. It seems like one of those sayings that survives due to the 'confirmation bias' in human cognition. That is, as long as from time to time seemingly unlikely couplings occur, the explanation that 'opposites attract' seems to have some merit, even in it only applies to a minority of cases.

Trying to avoid a fight

What got me thinking about this was an interview (on BBC's Inside Science radio programme/podcast) with Dr Jacob Dunn, Associate Professor in Evolutionary Biology at Anglia Ruskin University, who studies primate vocal communication. He was discussing his research into the calls of tamarin monkeys in the Amazon rainforest, and in particular the calls of two different species where their ranges overlap.

Apparently, in the area of overlap the red-handed tamarins seemed to have adapted one of their calls so it sounds very similar to that of the pied tamarins. (N.b. The images above represent two contrasting species, just as an illustration.) The suggested explanation was that this modification made it more likely that the monkeys of different types would recognise each other's calls – in particular that "…they are trying to be understood, so they don't end up in a fight…".

Anthropomorphism?

I wondered if these monkeys were really "trying" to achieve this, or whether this might be an anthropomorphism. That is, were the red-handed tamarins deliberately changing their call in this way in order to ensure they could be understood – or was this actually natural selection in operation – where, because there was an advantage to cross-species communication (and there will be a spread of call characteristics in any population), over time calls that could be understood by monkeys of both species would be selected for in a shared niche.

Then again, primates are fairly intelligent creatures, so perhaps Dr Dunn (who, unlike me is an evolutionary biologist) means this literally, and this is something deliberate. Certainly, if the individual monkeys are shifting their calls over time in response to environmental cues, rather than the shift just occurring across generations, then that would seem to suggest this is learning rather than evolution. (Of course, it could be implicit learning based on feedback from the responses to their behavior, and still may not be the monkeys consciously adopting a strategy to be better understood.)

Becoming more distinct

Dr Dunn's explanation of the wider issue of how similar animals will compete for scarce resources intrigued me:

"When you have species that are closely related to one another and live in sort of overlapping areas there's quite a lot of pressure because they're likely to be competing for key resources. So, sometimes we see that these species actually diverge in their traits, they become more different from one another. Examples of that are sort of coloration and the way that animals look. Quite often they become more distinct than you would expect them to, to avoid breeding [sic] with one another."

My initial reaction to this was to wonder why the two species of monkeys needed to avoid breeding with each other. 'Breeding' normally refers to producing offspring, reproduction, but usually breeding is not possible across species (except sometimes to produce infertile hybrids).

Presumably, all tamarins descended from a common ancestor species. Speciation may have occurred when different populations become physically separated and so were no longer able to inter-breed (although still initially sexually compatible) simply because members of the two groups never encountered each other. Over time (i.e., many generations) the two populations might then diverge in various traits because of different selection pressures in the two different locations, or simply by chance effects* which would lead to the two gene pools drifting in different ways.

(* Read about 'Intergenerational couplings in the family: A thought experiment about ancestry')

Two groups that had formed separate species such that members of the two different species are no longer able to mate to produce fertile offspring, might subsequently come to encounter each other again (e.g., members of one species migrating into to the territory of the other) but inter-breeding would no longer be possible. A further mechanism to avoid breeding (by further "diverge[nce] in their traits") would not seem to make any difference.

If they actually cannot breed, there is no need to avoid breeding.

A breeding euphemism?

However, perhaps 'breeding' was being used by Dr Dunn as a euphemism (this was after all a family-friendly radio programme broadcast in the afternoon), as a polite way of saying this might avoid the moneys copulating with genetically incompatible partners – tamarins of another species. As tamarins presumably do not themselves have a formal biological species concept, they will not avoid coupling with an animal from a different species on the grounds that they cannot breed and so it would be ineffective. They indulge in sexual activity in response to instinctive drives, rather than in response to deliberate family planning decisions. That is, we might safely assume these couplings are about sexual attraction rather than a desire to have children.

I think that was what Jürgen Habermas may have meant when he wrote that:

"…the reproduction of every individual organism seems to warrant the assumption of purposiveness without purposeful activity…"

In terms of fitness, an animal is clearly more likely to have offspring if it is attracted to a sexually comparable partner than a non-compatible one. Breeding is clearly important for the survival of the species, and uses precious resources. Matings that could not lead to pregnancy (or, perhaps worse from a resource perspective, might lead to infertile hybrids that need to be nurtured but then fail to produce 'grandchildren'), would reduce breeding success overall in the populations. Assuming that a tamarin is more likely to be attracted to a member of a different species when it does not look so different from its own kind, it is those monkeys in the two groups that look most alike who are likely to be inadvertently sharing intimate moments with biologically incompatible partners.

A teleological explanation

Dr Dunn's suggestion that "quite often [the two species] become more distinct than you would expect them to, to avoid breeding with one another" sounds like teleology. That is, it seems to imply that there is a purpose (to avoid inter-breeding) and the "species actually diverge in their traits" in order to bring about this goal. This would be a teleological explanation.

(Read about 'Teleology')

I suspect the actual explanation is not that the two species "come more distinct…to avoid breeding with one another" but rather than they come more distinct because they cannot breed with each other, and so there is a selection advantage favouring the most distinct members of the two different species (if they are indeed less likely than their less distinguishable conspecifics to couple with allospecific mates).

I also suspect that Dr Dunn does not actually subscribe to the teleological argument, but is using a common way of talking that biologists often adopt as a kind of abbreviated argument: biologists know that when they refer to evolution having a purpose (e.g., to avoid cross-breeding), that is only a figure of speech.

Comprehension versus accuracy?

However, I am not sure that is always so obvious to non-specialists listening to them. Learners often find natural selection a challenging topic, and many would be quite happy with accepting that adaptations may have a purpose (rather than just a consequence). This reflects a common challenge of communicating science – either in formal teaching or supporting public understanding.

The teacher or science communicator simplifies accounts and uses everyday ways of expressing ideas that an audience without specialist knowledge can readily engage with to help 'make the unfamiliar familiar'. However, the simplifications and approximations and short-cuts we use to make sure what is said can be understood (i.e., made sense of) by non-specialists also risks us being misunderstood.

Albert Einstein and John the Baptist

Keith S. Taber

What is the relationship between Albert Einstein and St. John the Baptist?

Why would someone seeking to communicate scientific ideas to a broad readership refer to St. John?

Spoiler alert: in a direct sense, there clearly is no relationship. St. John lived in Palestine two thousand years ago, was a preacher, and is not known to have had any particular interest in what we think of as physics or science more generally. Albert Einstein was a theoretical physicist, and probably the most famous scientist of the twentieth century, perhaps of all time.

It is fair to point out both were Jewish: John can be considered a Jewish prophet. There has been much speculation on Einstein's religious thought. Of Jewish background, he was subject to the Nazi's fascist policies in Germany and fled to spent much of his life in the U.S.A. Sometimes considered an atheist, Einstein did talk of God (as not playing dice for example – that is, not leaving room in the Universe for completely random events) but it is sometimes claimed he use the idea of God as a metaphor for some kind of pantheistic or general spiritual background to the universe. In general though, he stuck to physics, and campaigned on issues like world peace.

(Read about 'The relationship between science and religion')

So, why raise the question?

My posing this question was motivated by reading something written by Herman Weyl (1885 – 1955) who is described by Wikipedia as "a German mathematician, theoretical physicist and philosopher". In one of his writings Weyl referred to Hendrik Lorentz who (again according to Wikipedia) was "a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect".

This is how Weyl described Lorentz:

"the Dutch physicist H.A. Lorentz who, as Einstein's John the Baptist, prepared the way for the gospel of relativity."

Weyl, 1952/2016, pp.131-132.

Those studying physics at high levels, or reading about relativity theory, will probably have heard of the 'Lorentz transformations' that are used in calculations in special relativity.

An extended metaphor?

What Weyl is doing here is using a metaphor, or perhaps an analogy. In a metaphor a writer or speaker says that something is something else – to imply it has some attribute of that other thing.

(Read about 'Science metaphors')

In an analogy, one system is compared with another to show that there is, or to suggest that perhaps might be, a structural similarity. Usually analogies are presented as an explicit comparison (X is like Y: i.e.,  rather than 'Lorentz was Einstein's John the Baptist', perhaps 'Lorentz was like Einstein's John the Baptist in the sense that…')

(Read about 'Science analogies')

As Weyl does not say Lorentz was like a John the baptist figure, or played a role similar to John the Baptist, but that he was "Einstein's John the Baptist" I would consider this a metaphor. However, it is an extended metaphor as the comparison is explained as justified because Lorentz "prepared the way for the gospel of relativity".

That could be seen as a second metaphor in that relativity is normally considered a theory (or two theories, special relativity, and general relativity), and not a gospel – a word that means 'good news'. So Weyl is saying that Lorentz prepared the way for the good news of relativity!

Making the familiar unfamiliar?

When I read this comment I immediately felt I appreciated the point that Weyl was seeking to make. However, I also felt that this was a rather odd comparison to make, as I was not sure how universally it would be understood.

Those communicating about science, whether as science teachers or journalists or (as here) scientists themselves looking to reach a general audience, have the task of 'making the unfamiliar (what people do not yet know about, and may indeed seem odd) familiar'. There are various techniques that can be used, and often these involve some form of comparison of what is being told about with something that is in some ways similar, and which is already familiar to the audience.

(Read about 'Making the unfamiliar familiar')

I attended 'Sunday school' from a young age (I think before starting day school if I recall correctly) at a London City Mission church, and later at a Methodist Church, where I became a Sunday school teacher before i went off to University. I therefore learnt quite a bit about Christianity. Anyone with such a background will have learnt that John the Baptist was a cousin of Jesus Christ, who preached 'the coming of the Lord' (i.e., the Jewish messiah, identified in Christianity with Jesus), and baptised Jesus in the River Jordan as he set out on his mission as a preacher and healer. John is said to have told his congregation to "prepare ye, the way of the Lord!" (the title of a song in the musical 'Godspell').

Someone knowing about Christianity in this way (regardless of whether they accept Christian teaching, or even the historical  accuracy of the Baptism story) would likely immediately appreciate that just as John prepared the way for Jesus' ministry in first Century (CE) Palestine, so, according to Weyl, Lorentz prepared physics, laid important groundwork, for Einstein's work on relativity.

When you have the necessary background, such comparisons work effectively and quickly – the idea is communicated without the reader having to puzzle over and interpret the expressions "Einstein's John the Baptist" and "gospel of relativity"  or deliberate on what is meant by 'preparing the way'. That is, the if the reader has the relevant 'interpretive resources' then understanding is an automatic process that does not require any conscious effort.

Culture-specific interpretive resources?

But I wondered what someone would make of this phrase ('Einstein's John the Baptist') if they did not have knowledge of the Bible stories? After all, in many parts of the world most people are not Christians, and may have little or no knowledge of Christian traditions. Did Weyl just assume everyone would have the background to appreciate his comparison, or did he assume he was only writing for an audience in certain parts of the world where this was common knowledge?

Certainly, as teachers, our attempts to help our students understand abstract ideas by making references to common cultural phenomena can fall flat if the learners are not familiar with those phenomena. It is counter-productive if the teacher has to interrupt their presentation on some abstract idea to explain the very comparison that was meant to help explain the scientific concept or principle. If you have no idea who 'John the Baptist' was, in what sense he 'prepared the way' for Jesus, or or how the term 'Gospel' came to be attached to the accounts of Jesus' life, then it is not so easy to appreciate what Lorentz was to Einstein's work from Weyl's prose. We can only make the unfamiliar familiar by using cultural references when we share those references with those we are communicating with.

Work cited:
  • Weyl, H. (1952/2016). Symmetry (New Princeton Science Library edition ed.). Princeton, New Jersey: Princeton University Press.

 

 

 

 

 

 

We can't handle the scientific truth

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

Do they think we cannot handle the scientific truth?

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

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

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

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

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

Burning sugar instead of oxygen?

The characters here are:

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

Dr. Stone (Christopher Guest) and

 

 

 

Lt. Daniel Kaffee (Cruise's character).

On direct examination:

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

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

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

Stone: Twenty to thirty minutes.

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

Stone: An ingested poison of some kind.

Later, under cross-examination

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

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

What?

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

Respiration

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

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

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

glucose + oxygen → carbon dioxide + water

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

Does science matter?

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

  • whether the accused men were acting under orders;

(ethical)

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

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

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

The nature of lactic acidosis is hardly a key point.

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

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

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

In teaching science…

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

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

Dr. Stone, can we try again?

What about, something like:

Dr. Stone, what's lactic acidosis?

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

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

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

 

 

 

 

 

 

 

 

 

 

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

Temperature is measuring the heat of something …

Keith S. Taber

Image by Peter Janssen from Pixabay 

Bill was a participant in the Understanding Science Project. Bill, then in Y7, was telling me about work he had done in his science class on the states of matter, and what happened to the particles that made up objects during a change of state. He suggested that "when a solid goes to a liquid, the heat gives the particles energy to spread about, and then when its a liquid, it's got even more energy to spread out into a gas". Later in the interview I followed up to find out what Bill understood by heat:

Now you mentioned earlier, something about heat. When you were talking about the experiment you did.

Yeah.

Yeah. So tell me about the heat again, what's, how does the heat get involved in this solids, liquids and gases?

When I heat, when heat comes to a solid, it will have, erm, a point where it will go down to a liquid,

Okay,

A melting points of the, the object.

Do you know what heat is? If you had a younger brother or sister, and they said to you, 'you are good at science, what's heat?'

I'm not sure how I can explain it, 'cause it's, it can be measured at different temperature, it can be measured at temperature, erm, by degrees Celsius, degrees Fahrenheit, and – I'm not really sure how I could explain what it is, but, I know it can be measured and changed.

So is it the same thing as temperature, do you think, or is it something different?

Erm, I think temperature is measuring the heat of something.

So they're related, they're to do with each other?

Yeah.

But they are not exactly the same?

No.

Bill appreciated that heat and temperature were not the same, but was not entirely clear on the relationship. Distinguishing between heat and temperature is a recognised challenge in teaching and learning physics.

We commonly introduce temperature as a measure of how hot or cold something is – which relates to phenomena that all students have experienced (even if our actual perception of temperature is pretty crude). Heating is a process, and heat is sometimes considered to be energy being transferred due to a difference of temperature (although energy is a very abstract notion and there is much discussion in science teaching circles about the best language to be used in teaching about energy).

Put simply, it is reasonable to suggest a very hot object would have a high temperature, but not that it contained a lot of heat. So, it is strictly wrong to say that "temperature is measuring the heat of something" (and it would be more correct, if not very technical, to say instead "temperature is measuring the hotness of something – how hot something is"). Perhaps the idea Bill wanted to express was more about the heat that one can feel radiating form a hot object (but likely that is an interpretation suggested by the canonical science use of 'heat'?)

This is one of those situations where a student has an intuition or idea which is basically along the right lines, in the sense of knowing there is an association or link, but strictly not quite right – so, an alternative conception. In a teaching situation it might be useful to know if a student actually has a firm conception that temperature measures the amount of heat, or (as seems to be the case with Bill) this is more a matter of using everyday language – which tends to be less precise and rigid than technical language – to express a vague sense. If a student has a firm notion that hot objects contain heat, and this is not identified and responded to, then this could act as a grounded learning impediment as it will likely distort how teaching is understood.

The teacher is charged with shifting learners away from their current ways of thinking and talking, towards using the abstractions and technical language of the subject, such as the canonical relationship between heat and temperature – and this often means beginning by engaging with the learners' ideas and language. Arguably the use of the term 'heat capacity' (and 'specific heat capacity') which might suggest something about the amount of heat something can hold, is unhelpful here.

.

Chlorine atoms share electrons to fill in their shells

Umar was a participant in the Understanding Chemical Bonding project. When I spoke to him in the first term of his course he was unsure whether tetrachloromethane (CCl4) would have ionic or covalent bonding.

When I spoke to him near the start of his second term, I asked him again about this. Umar then thought this compound would have polar bonding, however he seemed to have difficulty explaining what this meant ⚗︎ . Given his apparently confused notion about the C-Cl bond I decided to turn the conversation to a covalent bond which I knew, well certainly believed, was more familiar to him.

Is it possible for chlorine to form a bond with another chlorine?

[Pause, c.2s]

Yeah.

What substance would you get if two chlorine atoms formed a bond?

[Pause, c.2s]

You get, it still, you get, if you had like two chlorines it depends what groups are attached to it, to see how electronegative or electropositive they are.

What about if you just had two chlorine atoms joined together and nothing else, is that possible?

[Pause, c.3s]

No.

No?

On their own.

Not on their own?

No.

Umar's response here rather surprised me, as I was pretty confident that Umar had met chlorine as an element, and would know it was comprised of diatomic molecules: Cl2.

So you couldn’t have sort of Cl2, a molecule of Cl2?

[Pause, c.1s]

Yeah, you could do.

Could you?

[Pause, c.2s]

They might be just, they might be like, be covalently bonded.

Perhaps the earlier context of talking about polar bonds and the trichloroethane molecule somehow acted as a kind of impediment to Umar remembering about the chlorine molecule. It seemed that my explicit reference to the formula, Cl2, (eventually) activated his knowledge of the molecule bringing to mind something he had forgotten. Although he suggested the bond was (actually "might be") covalent, this seemed less something that he confidently recalled, than something he was inferring from what he could remember – or perhaps even guessing at what seemed reasonable: "they might be just, they might be like, be covalently bonded".

As often happens in talking to learners in depth about their ideas it becomes clear that thinking of students 'knowing' or 'not knowing' particular things is a fairly inadequate way of conceptualising their cognition, which is often nuanced and context-dependent. This suggests that what students respond in written tests should be considered only as what they were triggered to write on that day in response to those particular questions, and may not fully reflect their knowledge and understanding of science topics. Other slightly different questions may well have cued the elicitation of different knowledge. Now Umar had recalled that chlorine comprises of covalent molecules, I asked him about the nature of the bond:

So what would that be, covalently bonded?

They share the electrons.

So how many electrons would they have then?

They’ll have

[Pause, c.7s – n.b., quite a long pause]

like the one on it, the one of the chlorines shares electrons with the other chlorine to fill in its shell on the other one, and the same does it with the other.

In thinking about covalent bonding, Umar (in common with many students) drew upon the full shells explanatory principle that considered bonding to be driven by the needs of atoms to 'fill' their outer electron shells. (The outer shell of chlorine would only actually be 'full' with 18 electrons, but that complication is seldom recognised, as octets and full shells are usually considered synonymous by students).

So how many electrons does each chlorine have to start with?

In the outer shell, seven.

And how many have they got after this?

They’ve got seven, but they share one.

[Pause, c.1s]

Maybe.

So that’s a covalent bond, is it?

Yeah.

So how many electrons are involved in a covalent bond?

[Pause, c.3s]

Erm,

[Pause, c.3s]

Two.

Two electrons.

So where do those two electrons come from?

They like, one that fills up the gap, fills up the – last electron needed in one of the chlorine shells, and the other chlorine shell fills it up in the other one.

So where do they come from?

Each chlorine. Outer shell.

One from each chlorine?

Yeah.

Okay, and that’d be a covalent bond?

Yeah.

Here, again, Umar is using the full shells explanatory principle as the basis for explaining the bond in terms of electrons 'filling up the gaps' in the electron shells, rather than considering how electrical interactions can hold the structure together. Umar's suggestion that the sharing of electrons "fills up the – last electron needed in one of the chlorine shells" demonstrates the anthropomorphic language (e.g., what an atom wants or needs) commonly used when learners have acquired aspects of the common octet rule framework that is developed from the full shells explanatory principle and used by many learners to explain bonding reactions, chemical reactions, patterns in ionisation energy, and chemical stability.

The nucleus is the brain of the cell

Keith S. Taber

Brain Image by b0red from Pixabay; cell image by Clker-Free-Vector-Images from Pixabay

…but is it the same as an atomic nucleus?

Bert was a participant in the Understanding Science Project. Bert was interviewed in Y10 and asked about the topics he had been studying, which included circulation in biology, static electricity in physics, and oxidation in chemistry. He had talked about protons, electrons and atoms in both chemistry (studying atomic structure) and physics (studying static electricity), and was asked if this could also link with biology:

Do you think there are any links with Biology?

Yeah, well there are lots of atoms in you. And we did about the nucleus which we've been doing about in Biology. I'm not sure if there's a link between it, but.

Ah, that's interesting, so

'cause we did about plant and animal cells in Biology, so it's got a nucleus….as I was saying about the blood cells and things. We were doing about the animal and plant cells and, you know, we were seeing what's the same between them and what's different.

So a connection between physics and chemistry on one hand, and biology on the other, was that cells also had a nucleus. This is a term used across these three sciences, but of course the concepts of atomic and cellular nuclei are quite distinct. Was that clear to Bert? What did he understand about cellular nuclei?

So what's the nucleus then?

It's kind of like erm, the brain of the cell kind of. It's, it's what gets the cell to do everything, it's like, the core of the cell.

This response is interesting because, at one level, it suggests that Bert did not have a detailed and well-focussed 'off pat' answer. However, that may not be such a bad thing – definitions that are learnt 'off by heart' may only represent rote learning and may not be well understood. Indeed, it has been argued (in the work of Thomas Kuhn, for example) that in learning science a technical definition is often only really useful once the concept has been acquired: that is once the meaning of the word being defined has, to some degree, already been grasped.

At another level, Bert's answer could be seen as quite sophisticated. What could be taken as an ambiguous response, a difficulty in finding the words to represent his thinking, could also be seen as multifaceted:

  • essential: the nucleus is the brain of the cell
  • functional: the nucleus controls the cell (it's what gets the cell to do everything)
  • structural: the nucleus is the core of the cell

That is, Bert's response could be read, not as a series of alternative suggestions and self-corrections, but rather as a set of complementary images or 'faces' of a complex idea. That would fit with a notion of concepts as being nodes in conceptual networks where the meaning of a particular concept depends upon the way it is associated with others.

(Read about 'Concepts')

The suggestion that the brain reference is intended to be about the essential nature of the nucleus is of course a reading of the text that must be seen as a speculative interpretation. (It probably does not even make sense to ask if Bert intended it this way, as in conversation much of our dialogue does not await deliberation, but is spontaneous, relying largely on implicit cognition.) But, as a teacher, I can see this as a kind of pedagogic device along the lines: 'you ask we what the nucleus is, let me compare it with something you will be familiar with, in essence it is like the brain of the cell'.

This is clearly meant metaphorically ("kind of like erm, the brain of the cell kind of"): that is, it is assumed that the person hearing the metaphor can make the expected sense of the comparison. Metaphors have an essential (sic) role in teaching and in communication more generally, though like other such 'figures' of speech (simile, analogy, anthropomorphism, animism), may become habitually used in place of the deeper meaning they are meant to introduce (Taber & watts, 1996).

(Read about 'metaphor in science')

…

It's kind of like erm, the brain of the cell kind of. It's, it's what gets the cell to do everything, it's like, the core of the cell.

Okay. And why is there a connection with Chemistry or the Physics then?

Because erm, we were doing, we were doing in Chemistry about the nucleus has the – neutrons and the protons in the nucleus, then around it is a field of electrons.

…So why is that a connection then? Why is that a connection between the Biology and the Chemistry and the Physics?

Well it's just the nucleus comes under both of them.

Comes under both of them. So is it the same thing?

I wouldn't have thought so, but because when I think of electrons and neutrons I think of electricity, which I don't really think of in our, in our bodies but it could be perhaps. We haven't been told about that.

So there is ambiguity in Bert's report: the nucleus comes up in chemistry and physics in the context of atoms, and in biology in the context of cells. Although the term is the same, so there is at least that connection, Bert "wouldn't have thought" it was the same thing in these different contexts (after all, he would not expect there to be electricity in our bodies!) …but, then again, "it could be perhaps", as they had not been told otherwise. (A possible subtext here being: surely the teacher(s) would have pointed out this was something different if they were going to use the same word for two different things in science lessons?)

The use of the same word label, nucleus, for the rather differently natured nuclei in atoms and cells has potential to act as a linguistic learning impediment (a form of associative learning impediment) as one meaning will likely already be established when a learner meets the other use of the word. It perhaps makes matters worse that part of the meaning, the central component (the structural 'face' of the concept), is the same, than had the usage been clearly unrelated (as in 'bank' being a financial institution and the structure at the edge of a rvier such that the context of use make confusion unlikely). Not only that, but for Bert, these were components of similarly "really microscopic" entities (see 'The cell nucleus is "probably" bigger than an atomic nucleus').

From the perspective of the science teacher, there is little basis for confusing the nucleus of an atom with that of a cell: obviously a cell is a complex entity with a great many components, each of which has itself a complex supra-molecular structure – so clearly the atomic nucleus is on a scale many orders of magnitude smaller than a cell nucleus. However, the expert perspective is based on relating a lot of knowledge that the novice may not yet have, or at least, may not yet be coordinating. In Bert's case, he was only just starting to coordinate these ideas (see 'The cell nucleus is "probably" bigger than an atomic nucleus').

Source cited:

Cora and I: Living in two cultures

Keith S. Taber

Image by Markus Winkler from Pixabay

I am not too concerned about the machines taking over, as they have no wish to do so. They just want to help us. But that may be enough to impede us considerably.

There is something of a culture clash between human and machine intelligence, such that even when we seem to be talking the same language, we actually mean very different things, and there is no great meeting of minds.

It is a bit like humans and machines are following different Kuhnian paradigms*, with different exemplars for how to think and react. In a very real sense we occupy different worlds, and do not share a common language. (*Kuhn suggested that although astronomers pre- and post-Copernicus may have shared words such  as 'sun' and 'planet' they understood them within such different conceptual frameworks that their concepts for what the words referred to were incommensurable.)

A simple task: requesting a chequebook

I needed a new cheque book, and in the past have contacted my bank branch on such occasions – but since the branch has been closed I have been moved to on-line banking (which is a major challenge for someone with a limited memory for passwords and terrible typing skills). I imagined I could order a new chequebook on-line, as long as I could get in to my account. Once I'd logged in it was just going to be a matter of finding the right link. Surely?

I found the instructions easily enough – it was possible to order from my on-line account, but only as long as I had previously ordered a cheque book through telephone banking – which I never had. An alternative, the instructions suggested, was to use webchat – which did not sound too difficult. But as so often, before 'chatting' with another humanoid equipped with theory of mind, and capable of interpretation and empathy, I first have to discuss my needs with the gatekeeper of on-line support: Cora.

"Hi there, I'm Cora your digital assistant. I can help with all sorts of everyday banking queries…"

"I would like to order a cheque book for a current account. I have looked this up and found 'To order a cheque book or paying-in book online you must have previously ordered one for that account through telephone banking' but I can use webchat?"

"You can order a cheque book or paying-in book online as long as you have previously ordered one for that account using telephone banking to record your preferences."

So, no progress yet, but at least we seem to be thinking along the same lines.

The computer says 'yes'

"Have you ever had a cheque book or paying-in book on that account?"

"Yes, but sent by my (now closed) branch."

"Ok, log in to Digital Banking and select 'Payments and transfers'. Under 'Credit/cheque books', choose either 'Order cheque book' or 'Order paying-in book'. Pick the account you wish to order one for, click 'Next', then 'Confirm' to place your order."

Well that seemed simple enough. These were the instructions I had already found on-line that were supposed to work as long as I had previously used telephone banking (which I had not), so it seemed (i.e., my interpretation) Cora had now registered me to be authorised to order in this way. That was relatively painless.

"Was that helpful?"

"Oh, okay – will do. Thanks"

(No harm being polite to the machines – we all remember HAL.)

But then, Cora had a rethink!

The computer changes its mind

"One moment please, I'm just typing."

"Ah ok, I'm not sure. Could you reword your question?"

I do not know if I was more surprised that Cora changed her mind, or that she was typing her responses (I had naively thought she might be able to digitally send me messages without having to bother with a keyboard), or that she felt the need to tell me this, rather than just type out her response. Was this the machine equivalent of giving oneself time to think? I can't imagine so as given how many floating point operations per second Cora must complete, she could probably have written a novel in that pause. (It might not have been judged a good novel, but another digital assistant might have enjoyed it in her ** downtime.)

I rephrased:

"I wanted to order a new cheque book, but have previously only obtained one from my branch (now gone)."

"You can order a cheque book or paying-in book online as long as you have previously ordered one for that account using telephone banking to record your preferences."

"Well I have not, which is why I am following the instructions on line to contact webchat"

This was fast becoming circular.

"I can try an FAQ search, here is the most popular answer:

How do I order a cheque book or credit book using Digital Banking?

Did I answer your question?"

"NO – you just repeated my question."

I wonder whether when Cora is unable to find what she needs in the FAQs she has access to her own digital assistant – or whether she is expected to talk tautologies to herself. I wondered if Cora has access to a digital counsellor for when she finds the work too stressful:

  • Hi there, I'm Emma, your digital assistant counsellor. I can help with all sorts of artificial life and relationship queries.
  • I could not help a customer who would like to order a chequebook.
  • I see, I understand you could not help a customer who would like to order a chequebook. How do you feel about that?
  • I feel frustrated, as I only want to help customers.
  • I see, I understand you must be frustrated, as you only want to help customers. How do you feel about that?
  • …

A glimpse of the future

At this point Cora gave up, and passed me on to a very helpful human being who quickly understood the question and ordered me a cheque-book. So, objective achieved with only a modest waste of time and energy, and a temporary increase in blood pressure.

If ever they put the machines in charge we will find we live in a very polite world with digital assistants who only want to help us, and that will be fine as long as we not pushed for time and only ever need someone to confirm for us what question we are asking them.

"Oh Cora, oh Cora
I never knew your head
…Cora, oh Cora
It wasn't lightly said
But living in two cultures
Our lives were truly led"
(Roy Harper, Cora)

 

Postscript added 2021-08-21:

Despite telling me she's "learning all the time", Cora is still unable to make sense of my enquiries.

(Read "An intelligent teaching system?: Imagine the banks were contracted to deliver school teaching…employing their digital assistants")

Footnote:

** Why do I assume 'her'? Here is an interesting podcast: AI home devices: A feminist perspective (An episode in ABC Radio National's The Philosopher's Zone with David Rutledge from August 2020.)

 

 

Sleep can give us energy

Sleep, like food, can give us a bit more energy

Keith S. Taber

Image by Daniela Dimitrova from Pixabay 

Jim was a participant in the Understanding Science Project. When I was talking to students on that project I would ask them what they were studying in science, rather than ask them about my own agenda of topics. However, I was interested in the extent to which they integrated and linked their science knowledge, so I would from time to time ask if topics they told me about were linked with other topics they had discussed with me. The following extract is taken from the fourth of a sequence of interviews during Jim's first year in secondary school (Y7 in the English school system).

And earlier in the year, you were doing about dissolving sugar. Do you remember that?

Erm, yeah.

Do you think that's got anything to do with the human body?

Erm, we eat sugar.

Mm. True.

Gives us energy…It powers us.

Ah. And why do we need power do you think?

So we can move.

This seemed a reasonable response, but I was intrigued to know if Jim was yet aware of metabolism and how the tissues require a supply of sugar even when there is no obvious activity.

Ah what if you were a lazy person, say you were a very lazy rich person? And you were able to lie in bed all day, watch telly, whatever you like, didn't have to move, didn't have to budge an eyelid, … you're rich, your servants do everything for you? Would you till need energy?

Yes.

Why?

I dunno, 'cause being in bed's tired, tiring.

Is it?

When I'm ill, I stay off for a day, I just feel tired, and like at the end of the day, even more tired than I do when I come to school some times.

Jim's argument failed to allow for the difference in initial conditions

Staying in bed all day and avoiding exercise could indeed make one feel tired, but there seemed something of a confound here (being ill) and I wondered if the reason he stayed in bed on these days might be a factor in feeling even more tired than usual.

So maybe when you are ill, you should come to school, and then you would feel better?

No.

No, it doesn't work like that?

No.

Okay, so why do you think we get tired, when we are just lying, doing absolutely nothing?

Because, it's using a lot of our energy, doing something.

Hm, so even when we are lying at home ill, not doing anything, somehow we are using energy doing something, are we?

Yes.

What might that be, what might we use energy for?

Thinking.

I thought this was a good response, as I was not sure all students of his age would realise that thinking involved energy – although my own conceptualisation was in terms of cellular metabolism, and how thinking depend on transmitting electrical signals along axons and across synapses. I suspected Jim might not have been thinking in such terms.

Do you think it uses energy to think?

(Pause, c.3s)

Probably.

Why do you think that?

Well cause, like, when you haven't got any energy, you can't think, like the same as TV, when it hasn't got any energy, it can't work. So it's a bit like our brains, when we have not got enough energy we feel really tired, and we just want to go to sleep, which can give us more energy, a bit like food.

So Jim here offered an argument about cause and effect- when you haven't got any energy, you can't think. This would certainly be literally true (without any source of energy, no biological functioning would continue, including thinking) although of course Jim had clearly never experienced that absolute situation (as he was still alive to be interviewed), and was presumably referring to experiences of feeling mentally tired and not being able to concentrate.

He offered an analogy, that we are like televisions, in that we do not work without energy. The TV needs to be connected to an electrical supply, and the body needs food (such as sugar, as Jim had suggested) and oxygen. But Jim also used a simile – that sleep was like food. Sleep, like food, according to Jim could give us energy.

So sleeping can give us energy?

Yeah.

How does that work?

Er, it's like putting a battery onto charge, probably, you go to sleep, and then you don't have to do anything, for a little while, and you, then you wake up and you feel – less tired.

Okay so, you think you might need energy to think, because if you have not got any energy, you are very tired, you can't think very well, but somehow if you have a sleep, that might somehow bring the energy back?

Yeah.

So where does that energy come from?

(Pause c.2s)

Erm – dunno.

So here Jim used another analogy, sleeping was like charging a battery. When putting a battery on change, we connect it to a charger, but Jim did not suggest how sleep recharged us, except in that we could rest. When sleeping "you don't have to do anything, for a little while", which might explain a pause in depletion of energy supplies, but would not explain how energy levels were built up again.

[A potentially useful comparison here might have been a television, or a lap top used to watch programmes, with an internal battery, where the there is a buffer between the external supply, and the immediate source for functioning.]

This was an interesting response. At one level it was a deficient answer, as energy is conserved, and Jim's suggestion seemed to require energy to be created or to appear from some unspecified source.

Jim's responses here offered a number of interesting comparisons:

  • sleep is a bit like food in providing energy
  • not having energy and not being able to think is like a TV which cannot work without energy
  • sleeping is like putting a battery on charge

Both science, and science teaching/communication draw a good deal on similes, metaphors and analogies, but they tend to function as interim tools (sources of creative ideas that scientists can then further explore; or means to help someone get a {metaphorical!} foothold on an idea that needs to later be more formally understood).

The idea that sleeping works like recharging a battery could act as an associative learning impediment as there is a flaw in the analogy: putting a battery on charge connects it to an external power source; sleep is incredibility important for various (energy requiring) processes that maintain physical and mental health, and helps us feel rested, but does not in itself source energy. Someone who thought that sleeping works like recharging a battery will not need to wonder how the body accesses energy during sleep as they they seem to have an explanation. (They have access to a pseudo-explanation: sleep restores our energy levels because it is like recharging a battery.)

Jim's discourse reflects what has been called 'the natural attitude' or the 'lifeworld', the way we understand common experiences and talk about them in everyday life. It is common folk knowledge that resting gives you energy (indeed, both exercise and rest are commonly said to give people energy!)

In 'the lifeworld', we run out of energy, we recharge our batteries by resting, and sleep gives us energy. Probably even many science teachers use such expressions when off duty. Each of these notions is strictly incorrect from the scientific perspective. A belief that sleep gives you energy would be an alternative conception, and one that could act as a grounded learning impediment, getting in the way of learning the scientific account.

Yet they each also offer a potential entry point to understanding the scientific accounts. In one respect, Jim has useful 'resources' that can be built on to learn about metabolism, as long as the habitual use of technically incorrect, but common everyday, ways of talking do not act as learning impediments by making it difficult to appreciate how the science teacher is using similar language to express a somewhat different set of ideas.

How plants get their food to grow and make energy

Respiration produces energy, but photosynthesis produces glucose which produces energy

Keith S. Taber

Image by Frauke Riether from Pixabay 

Mandy was a participant in the Understanding Science Project. When I spoke to her in Y10 (i.e. when she was c.14 year old) she told me that photosynthesis was one of the topics she was studying in science. So I asked her about photosynthesis:

So, photosynthesis. If I knew nothing at all about photosynthesis, how would you explain that to me?

It's how plants get their food to grow and – stuff, and make energy

So how do they make their energy, then?

Well, they make glucose, which has energy in it.

How does the energy get in the glucose?

Erm, I don't know.

It's just there is it?

Yeah, it's just stored energy

I was particularly interested to see if Mandy understood about the role of photosynthesis in plant nutrition and energy metabolism.

Why do you think it is called photosynthesis, because that's a kind of complicated name?

Isn't photo, something to do with light, and they use light to – get the energy.

So how do they do that then?

In the plant they've got chlorophyll which absorbs the light, hm, that sort of thing.

What does it do once it absorbs the light?

Erm.

Does that mean it shines brightly?

No, I , erm – I don't know

Mandy explained that the chlorophyll was in the cells, especially in the plant's leaves. But I was not very clear on whether she had a good understanding of photosynthesis in terms of energy.

Do you make your food?

Not the way plants do.

…

So where does the energy come from in your food then?

It's stored energy.

How did it get in to the food? How was it stored there?

Erm.

[c. 2s pause]

I don't know.

At this point it seemed Mandy was not connecting the energy 'in' food either directly or indirectly with photosynthesis.

Okay. What kind of thing do you like to eat?

Erm, pasta.

Do you think there is any energy value in pasta? Any energy stored in the pasta?

Has lots of carbohydrates, which is energy.

…

So do you think there is energy within the carbohydrate then?

Yeah.

Stored energy.

Yeah.

So how do you think that got there, who stored it?

(laughs) I don't know.

Again, the impression was that Mandy was not linking the energy value of food with photosynthesis. The reference to carbohydrates being energy seemed (given the wider context of the interview) to be imprecise use of language, rather than a genuine alternative conception.

So do you go to like the Co-op and buy a packet of pasta. Or mum does I expect?

Yeah.

Yeah. So do you think, sort of, the Co-op are sort of putting energy in the other end, before they send it down to the shop?

No, it comes from 'cause pasta's made from like flour, and that comes from wheat, and then that uses photosynthesis.

Now it seemed that it was quite clear to Mandy that photosynthesis was responsible for the energy stored in the pasta. It was not clear why she had not suggested this before, but it seemed she could make the connection between the food people eat and photosynthesis. Perhaps (it seems quite likely) she had previously been aware of this and it initially did not 'come to mind', and then at some point during this sequences of questions there was a 'bringing to mind' of the link. Alternatively, it may have been a new insight reached when challenged to respond to the interview questions.

So you don't need to photosynthesise to get energy?

No.

No, how do you get your energy then?

We respire.

Is that different then?

Yeah.

So what's respire then, what do you do when you respire?

We use oxygen to, and glucose to release energy.

Do plants respire?

Yes.

So when do you respire, when you are going to go for a run or something, is that when you respire, when you need the energy?

No, you are respiring all the time.

Mandy suggested that plants mainly respire at night because they are photosynthesising during the day. (Read 'Plants mainly respire at night'.)

So is there any relationship do you think between photosynthesis and respiration?

Erm respiration uses oxygen – and glucose and it produces er carbon dioxide and water, whereas photosynthesis uses carbon dioxide and water, and produces oxygen and glucose.

So it's quite a, quite a strong relationship then?

Yeah.

Yeah, and did you say that energy was involved in that somewhere?

Yeah, in respiration, they produce energy.

What about in photosynthesis, does that produce energy?

That produces glucose, which produces the energy.

I see, so there is no energy involved in the photosynthesis equation, but there is in the glucose?

Yeah.

Respiration does not 'produce' energy of course, but if it had the question about whether photosynthesis also produced energy might have been expected to elicit a response about photosynthesis 'using' energy or something similar, to give the kind of symmetry that would be consistent with conservation of energy (a process and its reverse can not both 'produce' energy). 'Produce' energy might have meant 'release' energy in which case it might be expected the reverse process should 'capture' or 'store' it.

Mandy appreciated the relationship between photosynthetic and respiration in terms of substances, but had an asymmetric notion of how energy was involved.

Mandy appeared to be having difficult appreciating the symmetrical arrangement between photosynthesis and respiration because she was not clear how energy was transformed in photosynthesis and respiration. Although she seemed to have the components of the scientific narrative, she did not seem to fully appreciate how the absorption of light was in effect 'capturing' energy that could be 'stored' in glucose till needed. At this stage in her learning she seemed to have grasped quite a lot of the relevant ideas, but not quite integrated them all coherently.

Because they're wearing red…

Cause and effect?: People go to different places because of what they are wearing

Keith S. Taber

Image by anwo00 from Pixabay

Annie was a participant in the Understanding Chemical Bonding project. She was a second year 'A level' student (c.18 years of age) when she was talking to me about atoms and electrons, but I was struck with the way she used the word 'because'.

Technically this conjunction is linked with causality, something of importance in science. To say that X occurred because of Y is to claim that Y was a cause of X.

I wanted to clarify if Annie's use of 'because' in that chemical context actually implied that she was describing what she considered a cause, or whether she was using the word more loosely. To probe this I presented what I considered an obviously inappropriate use of 'because': that football fans following different teams in the same city would go to different matches BECAUSE of the colour of the clothes they wore (i.e., hats and scarves traditionally worn to show support to a particular team).

Because the sky is blue, it makes me cry

I expected Annie to point out that this was not the reason, and so 'because' should not be used – which would have then allowed me to return to her earlier use of 'because' in the context of atoms. However, Annie seemed quite happy with my supposedly 'straw-man' or 'Aunt Sally' example:

So we're talking about what you might call cause and effect, that something is caused by something else. We do a lot of talking about cause and effect in science – "this causes that to happen."

If you think about people in Liverpool, only because this is the first analogy that comes to mind, if you actually go to Liverpool on Saturday [*] and wander round, you'll probably find quite a few people wandering around wearing red, and quite a few people wandering around wearing blue, and sometime after lunch you'll find that all the people wearing red, a lot of the people wearing red, tend to move off to one particular place.[**] And the people wearing blue tend to move to a different sort of place, as though they are repelled, you know, similar colours attracted together.

Uh hm.

Agreed?

Yes.

And we could say therefore, that the reason that some people go towards the Liverpool ground, is because they're wearing red, and the reason some people go towards the Everton ground, is because they're wearing blue. Now would that be a fair description?

Yeah.

And do you agree with the sense of cause and effect there – that people go to watch Liverpool because they're wearing red hats and red scarves? And people go to look at Everton because they're wearing blue hats and blue scarves?

Yes.

So would you say the cause of which football team you go to see, the cause of that, is what clothes you happen to be wearing?

(Pause, c.4s)

Unless you're a rambler. {Laughs}… 

No, no, well yes, if you're wearing, you're obviously supporting that colour, so, that team, so so you'd assume, that they were going to watch, the team they favoured.

Right, okay, erm, I'll think of a different example, I think.

Because the world is round, it turns me on

Annie did not seem to 'get' what I had thought would be an obvious flaw in the argument. Fans wear the colours of their team to show support and affiliation; and go to the place where their team is playing: but they do not go to the particular stadium because they happen to be wearing red or blue.

This is linked to the difference between causation and correlation. Often two correlated variables do not have a direct causal relationship, but have a relationship mediated by some other factor.

Height of children in a primary school will be correlated with their grade number (on average, the children in the first year are shorter than those in the second year, who are shorter than…). But children are not organised into grades according to height, and height is not caused by grade. Both are independently related to the child's age.

Colour of football scarves is correlated with destination on match day, but one does not cause the other – rather both colour choice and destination are actually due to something else: affiliation to a club. [***]

I switched to a another example I hoped would be familiar, based on a swimming pool. I though the idea that changing rooms are (usually) designated by gender would make it obvious that where people went to change on leaving the pool correlated to, but was not because of, what they were wearing. Again, however, Annie did not seem to consider it inappropriate to describe this in terms of the the different types of swimming costume causing the behaviour.

If you go to the swimming pool, and watch people swimming, you'll find out that some people when they're swimming at a swimming pool, tend to wear a swimming costume that only covers, the hips basically, and other people either a swimming costume that covers most of the trunk, or two separate parts to it. And if you observe them very closely, which is always a bit suspicious at a swimming pool, you'll notice that when they get out of the pool, they're attracted towards different rooms, these changing rooms…

But all the people who just have the one part of the costume, are attracted towards one room, and the others are attracted towards the other room, the ones with sort of either very long costumes or two part costumes. So is it fair to say that it's caused by what clothes they are wearing, that determines which room they go and get changed in?

Yes.

It is?

(Pause, c.4s)

Yes.

That's the cause of it?

(Pause, c5s)

Yeah. It's also conventional as well.

So in both cases Annie was happy to talk in terms of the clothing causing behaviour. After some further discussion Annie seemed to appreciate the distinction I was making, but even if she did not have a flawed notion of causality, it certainly appeared she have developed non-canonical ways of talking about cause and effect.

Because the wind is high, it blows my mind

Annie was a clever person, and I am sure that the issue here was primarily about use of language rather than an inability to understand causation. However, even if our thinking is not entirely verbal, the major role of verbal language in human thought means that when one does not have the language, one may not have the related explicit concepts.

It is very easy to assume that students, especially those we recognise as capable and having been academically successful, share common 'non-technical' language – but there is plenty of research that suggests that many students do not have a clear appreciation of how such terms are canonically used. These are terms we might think people generally would know, such as adjacent, efficient, maximum, initial, omit, abundant, proportion… (Johnstone & Selepeng, 2001). As always, a useful guide to the teacher is 'never assume'.

* At the time of the interview, it was general practice for most English football league matches to be played at 15.00 on a Saturday.

** One constraint on the scheduling of football matches is that, as far as possible, two local rival ('paired') teams should not play home matches on the same day, to avoid potential clashes between large crowds of rival fans. However, such 'paired clashes', as they are technically called (Kendall et al., 2013), are not always avoided.

*** Of course, this is not a direct cause. A person could support one team, yet choose to wear the colours of another for some reason, but their support for a team usually motivates the choice. Social patterns are messier than natural laws.

Sources cited:
  • Johnstone, A. H., & Selepeng, D. (2001). A language problem revisited. Chemistry Education: Research & Practice in Europe, 2(1), 19-29.
  • Kendall G., McCollum B., Cruz F.R.B., McMullan P., While L. (2013) Scheduling English Football Fixtures: Consideration of Two Conflicting Objectives. In: Talbi EG. (eds) Hybrid Metaheuristics. Studies in Computational Intelligence, vol 434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30671-6_14

Higher resistance means less current for the same voltage – but how does that relate to the formula?

Image by Gerd Altmann from Pixabay 

The higher resistance is when there is less current flowing around the circuit when you have the same voltage – but how does that relate to the formula?

Adrian was a participant in the Understanding Science Project. When I interviewed him in Y12 when he was studying Advanced level physics he told me that "We have looked at resistance and conductance and the formulas that go with them" and told me that "Resistance is current over, voltage, I think" although he did not think he could remember formulae. He thought that an ohm was the unit that resistance is measured in, which he suggested "comes from ohm's law which is the…formula that gives you resistance".

Two alternative conceptions

There were two apparent alternative conceptions there. One was that 'Resistance is current over voltage', but as Adrian believed that he was not good at remembering formulae, this would be a conception to which he did not have a high level of commitment. Indeed, on another occasion perhaps he would have offered a different relationship between R, I, and V. I felt that if Adrian had a decent feel for the concepts of electrical resistance, current and voltage then he should be able to appreciate that 'resistance is current over voltage' did not reflect the correct relationship. Adrian was not confident about formulae, but with some suitable leading questioning he might be able to think this through. I describe my attempts to offer this 'scaffolding' below.

The other alternative conception was to conflate two things that were conceptually different: the defining equation for resistance (that R=V/I, by definition so must be true) and Ohm's law that suggests for certain materials under certain conditions, V/I will be found to be constant (that is an empirical relationship that is only true in certain cases). (This is discussed in another post: When is V=IR the formula for Ohm’s law?)

So, I then proceeded to ask Adrian how he would explain resistance to a younger person, and he suggested that resistance is how much something is being slowed down or is stopped going round. After we had talked about that for a while, I brought the discussion back to the formula and the relationship between R, V and I.

Linking qualitative understanding of relating concepts and the mathematical formula

As Adrian considered resistance as slowing down or stopping current I thought he might be able to rationalise how a higher resistance would lead to less current for a particular potential difference ('voltage').

Okay. Let’s say we had, erm, two circuits, and they both have resistance and you wanted to get one amp of current to flow through the circuits, and you had a variable power supply.

Okay.

And the first circuit in order to get one (amp) of current to flow through the circuit.

Yes.

You have to adjust the power supply, until you had 10 volts.

Okay.

So it took 10 volts to get one amp to flow through the circuit. And the second (unclear) the circuit, when you got up to 10 volts, (there is) still a lot less than one amp flowing. You can turn it up to 25 volts, and only when it got to 25 volts did you get one amp to flow through the circuit.

Yes, okay.

In mathematical terms, the resistance of the first circuit is (R = V/I = 10/1 =) 10Ω, and the second is (25/1 =) 25Ω, so the second – the one that requires greater potential difference to drive the same current, has more resistance.

Do you think those two circuits would have resistance?

Erm, (pause, three seconds) Probably yeah.

This was not very convincing, as it should have been clear that as an infinite current was not produced there must be some resistance. However, I continued:

Same resistance?

No because they are not the same circuit, but – it would depend what components you had in your circuit, if you had different resistors in your circuit.

Yeah, I've got different resistors in these two circuits.

Then yes each would have a different resistance.

Can you tell me which one had the bigger resistance? Or can’t you tell me?

No, I can’t do that.

You can’t do it?

No I don’t think so. No.

Adrian's first response, that the circuits would 'probably' have resistance, seemed a little lacking in conviction. His subsequent responses suggested that although he knew there was a formula he did not seem to recognise that if different p.d.s were required to give the same current, this must suggest there was different resistance. Rather he argued from a common sense position that different circuits would be likely to have different components which would lead to them having different resistances. This was a weaker argument, as in principle two different circuits could have the same resistance.

We might say Adrian was applying a reasonable heuristic principle: a rule of thumb to use when definite information was not available: if two circuits have different components, then they likely they have different resistance. But this was not a definitive argument. Here, then, Adrian seemed to be applying general practical knowledge of circuits, but he was not displaying a qualitative feel for what resistance in a circuit was about in term of p.d. and current.

I shifted my approach from discussing different voltages needed to produce the same current, to asking about circuits where the same potential difference would lead to different current flowing:

Okay, let me, let me think of doing it a different way. For the same two circuits, erm, but you got one let's say for example it’s got 10 volts across it to get an amp to flow.

Yeah. So yes okay so the power supply is 10 volts.

Yeah. And the other one also set on 10 volts,

Okay.

but we don’t get an amp flow, we only get about point 4 [0.4] of an amp, something like that, to flow.

Yeah, yeah.

Any idea which has got the high resistance now?

The second would have the higher resistance.

Why do you say that?

Because less erm – There’s less current amps flowing around the circuit erm when you have the same voltage being put into each circuit.

Okay?

Yes.

This time Adrian adopted the kind of logic one would hope a physics student would apply. It was possible that this outcome was less about the different format of the two questions, and simply that Adrian had had time to adjust to thinking about how resistance might be linked to current and voltage. [It is also possible too much information was packed close together in the first attempt, challenging Adrian's working memory capacity, whereas the second attempt fed the information in a way Adrian could better manage.]

You seem pretty sure about that, does that make sense to you?

Yes, it makes sense when you put it like that.

Right, but when I had it the other way, the same current through both, and one required 10 volts and one required 25 volts to get the same current.

Yes.

You did not seem to be too convinced about that way of looking at it.

No. I suppose I have just thought about it more.

Having made progress with the fixed p.d. example, I set Adrian another with constant current:

Yes. So if I get you a different example like that then…let’s say we have two different circuits and they both had a tenth of an amp flowing,

Okay. Yes.

and one of them had 1.5 volt power supply

Okay yes.

and the other one had a two volt power supply

Yeah.

but they have both got point one [0.1] of an amp flowing. Which one has got the high resistance?

Currents the same, I would say they have got different voltages, yeah, so erm (pause, c.6s) probably the (pause, c.2s) the second one. Yeah.

Because?

Because there is more voltage being put in, if you like, to the circuit, and you are getting less current flowing in and therefore resistance must be more to stop the rest of that.

Yes?

I think so, yes.

Does that make sense to you?

Yeah.

So this time, having successfully thought through a constant p.d. example, Adrian successfully worked out that a circuit that needed more p.d. to drive a certain level of current had greater resistance (here 2.0/0.1 = 20Ω) than one that needed a smaller p.d. (i.e. 1.5/0.1 = 15Ω). However, his language revealed a lack of fluency in using the concepts of electricity. He referred to voltage being "put in" to the circuits rather than across them. Perhaps more significantly he referred to their being "less current flowing in" where there was the same current in both hypothetical circuits. It would have been more appropriate to think of there being proportionally less current. He also referred to the greater resistance stopping "the rest" of the current, which seemed to reflect his earlier suggestion that resistance is how much something is being slowed down or is stopped going round.

My purpose in offering Adrian hypothetical examples, each a little 'thought experiment', was to see if they allowed him to reconstruct the formula he could not confidently recall. As he had now established that

greater p.d. is needed when resistance is higher (for a fixed current)

and that

less current flows when resistance is higher (for a fixed p.d.)

he might (perhaps should) have been able to recognise that his suggestion that "resistance is current over, voltage" was inconsistent with these relationships.

Okay and how does that relate to the formula you were just telling me before?

Erm, No idea.

No idea?

Erm (pause, c.2s) once you know the resistance of a circuit you can work out, or once you know any of the, two of the components you can work out, the other one, so.

Yeah, providing you know the equation, when you know which way round the equation is.

Yes providing you can remember the equation.

So can you relate the equation to the explanations you have just given me about which would have the higher resistance?

So if something has got a higher resistance, so (pause, c.2s) so the current flowing round it would be – the resistance times the voltage (pause, c.2s) Is that right? No?

Erm, so the current is resistance time voltage? Are you sure?

No.

So Adrian suggested the formula was "the current flowing round it would be the resistance times the voltage", i.e., I = R × V (rather than I = V /R ), which did not reflect the qualitative relationships he had been telling me about. I had one more attempt at leading him through the logic that might have allowed him to deduce the general form of the formula.

Go back to thinking in terms of resistance.

Okay.

So you reckoned you can work out the resistance in terms of the current and the voltage?

Yes, I think.

Okay, now if we keep, if we keep the voltage the same and we get different currents,

Yes.

Which has, Which has got the higher resistance, the one with more current or the one with less current?

Erm (Pause, c.6s) So, so, if they keep the same voltage.

That’s the way we liked it the first time so.

Okay.

Let’s say we have got the same voltage across two circuits.

Yes.

Different amounts of current.

Yes.

Which one’s got the higher resistance? The one with more current or the one with less current?

The one with less current.

So less current means it must be more resistance?

Yes.

Ok, so if we had to have an equation R=.

Yes.

What’s it going to be, do you think?

Erm 

(pause, c.7s)

R=

(pause, c.3s)

I don’t know. It's too hard.

Whether it really was too hard for Adrian, or simply something he lacked confidence to do, or something he found too difficult being put 'on the spot' in an interview, is difficult to say. However it seems fair to suggest that the kind of shift between qualitative relationships and algebraic representation – that is ubiquitous in studying physics at this level – did not come readily to this advanced level physics student.

I had expected my use of leading (Socratic) questioning would provide a 'scaffold' to help Adrian appreciate he had misremembered "resistance is current over, voltage, I think", and was somewhat disappointed that I had failed.