The complicated social lives of stars

Stealing, escaping, and blowing-off in space


Keith S. Taber


"After a lecture on cosmology and the structure of the solar system, James [William James] was accosted by a little old lady.

'Your theory that the sun is the centre of the solar system, and the earth is a ball which rotates around it has a very convincing ring to it, Mr. James, but it's wrong. I've got a better theory,' said the little old lady.

'And what is that, madam?' inquired James politely.

'That we live on a crust of earth which is on the back of a giant turtle.'

Not wishing to demolish this absurd little theory by bringing to bear the masses of scientific evidence he had at his command, James decided to gently dissuade his opponent by making her see some of the inadequacies of her position.

'If your theory is correct, madam,' he asked, 'what does this turtle stand on?'

'You're a very clever man, Mr. James, and that's a very good question,' replied the little old lady, 'but I have an answer to it. And it's this: The first turtle stands on the back of a second, far larger, turtle, who stands directly under him.'

'But what does this second turtle stand on?' persisted James patiently.

To this, the little old lady crowed triumphantly,

'It's no use, Mr. James – it's turtles all the way down.'

Ross, 1967, iv

"The Hindoos [sic] held the earth to be hemispherical, and to be supported like a boat turned upside down upon the heads of four elephants, which stood on the back of an immense tortoise. It is usually said that the tortoise rested on nothing, but the Hindoos maintained that it floated on the surface of the universal ocean. The learned Hindoos, however, say that these animals were merely symbolical, the four elephants meaning the four directions of the compass, and the tortoise meaning eternity." (The Popular Science Monthly, March, 1877; image via Wikipedia)

It's metaphors all the way down

A well-known paper in the journal 'Cognitive Science' is entitled 'The metaphorical structure of the human conceptual system' (Lakoff & Johnson, 1980). What the authors meant by this was that metaphor, or perhaps better analogy, was at the basis of much of our thinking, and so our language.

This links to the so-called 'constructivist' perspective on development and learning, and is of great significance in both the historical development of science and in science teaching and learning. Consider some of the concepts met in a science course (electron, evolution, magnetic flux, hysteresis, oxidation state, isomerism…the list is enormous) in comparison to the kind of teaching about the world that parents engage in with young children:

  • That is a dog
  • That is a tree
  • That is round
  • This is hot
  • This is aunty
  • etc.

Pointing out the names of objects is not a perfect technique – just as scientific theories are always underdetermined by the available data (it is always possible to devise another scheme that fits the data, even if such a scheme may have to be forced and convoluted), so the 'this' that is being pointed out as a tree could refer to the corpse of trees, or the nearest branch, or a leaf, or this particular species of plant, or even be the proper name of this tree, etc. 1


Pointing requires the other person to successfully identify what is being pointed at
(Images by Joe {background} and OpenClipart-Vectors {figures} from Pixabay)


But, still, the 'this' in such a case is usually more salient than the 'this' when we teach:

  • This is an electron
  • This is reduction
  • This is periodicity
  • This is electronegativity
  • This is a food web
  • This is a ᴨ-bond
  • This is a neurotransmitter
  • etc.

Most often in science teaching we are not holding up a physical object or passing it around, but offering a 'this' which is at best a model (e.g., of a generalised plant cell or a human torso) or a complex linguistic structure (a definition in terms of other abstract concepts) or an abstract representation ('this', pointing to a slope of an a graph, is acceleration; 'this', pointing to an image with an arrangement of a few letters and lines, is a transition state…).

So, how do we bridge between the likes of dogs and trees on one hand and electrons and the strong nuclear force on the other (so to speak!)? The answer is we build using analogy and we talk about those constructions using a great deal of metaphor.2 That is, we compare directly, or indirectly, with what we can experience. This refers to relationships as well as objects. We can experience being on top of, beneath, inside, outside, next to, in front of, behind, near to, a long way from (a building, say – although hopefully not beneath in that case), and we assign metaphorical relationships in a similar way to refer to abstract scenarios. (A chloroplast may be found in a cell, but is sodium found in (or on) the periodic table? Yes, metaphorically. And potassium is found beneath it!)


In a wall, the bricks on the top layer are supported by the bricks in the layer beneath – but those are in turn supported by those beneath them.

In building, we have to start at the foundations, and build up level by level. The highest levels are indirectly supported by the foundations.

(Image by OpenClipart-Vectors from Pixabay)


In science, we initially form formal concepts based on direct experience of the world (including experience mediated by our interventions, i.e., experiments), and then we build more abstract concepts from those foundational concepts, and then we build even more abstract concepts by combining the abstract ones. In the early stages we refine 'common sense' or 'life-world' categories into formal concepts so we can more 'tightly' (and operationally, through standard procedures) define what count as referents for scientific terms (Taber, 2013). So, the everyday phenomenon of burning might be reconceptualised as combustion: a class of chemical reactions with oxygen.

This is not just substituting a technical term, but also a more rigid and theoretical (abstract) conceptualisation. So, in the 'life-world' we might admit the effects of too much sunshine or contact with a strong acid within the class of 'burning' by analogy with the effect of fire (it hurts and damages the skin); but the scientific categorisation is less concerned with direct perception, and more with explanation and mechanism. So, iron burning in chlorine (in the absence of any oxygen) is considered combustion, but an acid 'burn' is not.


Combustion without oxygen: A Royal Society of Chemistry video demonstrating the reactions of iron with the halogens.

This is what science has done over centuries, and is also what happens in science education. So, one important tool for the teacher is concept analysis, where we check which prerequisite concepts need to be part of a student's prior learning before we introduce some new concept that is built upon then (e.g., do not try to teach mass spectroscopy before teaching about atomic structure, and do not teach about atomic structure before introducing the notion of elements; do not try to teach about the photoelectric effect to someone who does not know a little about the structure of metals and the nature of electromagnetic radiation.)

This building up of abstract concepts, one on another, is reflected in the density of metaphor we find in our language. (That is a metaphorical 'building', metaphorically placed one upon another, with a metaphorical 'density' which is metaphorically 'inside' the language and which metaphorically 'reflects' the (metaphorical) building process! You can 'see' (a metaphor for understand) just how extensive (oops, another metaphorical reference to physical space) this is. Hopefully, the (metaphorical) 'point' is (metaphorically) 'made', and so I am going to stop now, before this gets silly. 3

A case study of using language in science communication: the death of stars

Rather, I am going to discuss some examples of the language used in a single science programme, a BBC radio programme/podcast in the long-running series 'In Our Time' that took as its theme 'The Death of Stars'. The programme was hosted by Melvyn Bragg, and The Lord Bragg's guests were Professors Carolin Crawford (University of Cambridge), the Astronomer Royal Martin Rees (University of Cambridge) and Mark Sullivan (University of Southampton). This was an really good listen (recommended to anyone with an interest in astronomy), so I have certainly not picked it out to be critical, but rather to analyse the nature of some of the language used from the perspective of how that language communicates technical ideas.


An episode of 'In Our Time' on 'The Death of Stars'
"The image above is of the supernova remnant Cassiopeia A, approximately 10,000 light years away, from a once massive star that died in a supernova explosion that was first seen from Earth in 1690"

A science teacher may be familiar with stars being born, living, and dying – but how might a young learner, new to astronomical ideas, make sense of what was meant?

The passing of stars: birth, death, and afterlife in the universe

The lives and deaths of stars

Now there is already a point of interest in the episode title. Are stars really the kind of entities that can die? Does this mean they are living beings prior to death?

There are a good many references in the talk of these three astronomers in the episode that suggests that, in astronomy at least, stars do indeed live and die. That is, this does not seem to be consciously used as a metaphor – even if the terminology may have initially been introduced that way a long time ago. The programme offered so much material on this theme, that I have separated it out for a post of its own:

"So, in the language of astronomy, stars are born, start young, live; sometimes living alone but sometimes not, sometimes have complicated lives; have lifetimes, reach the end of their lives, and die, so, becoming dead, eventually long dead; and indeed there are generations of stars with life-cycles."

The passing of stars: birth, death, and afterlife in the universe

In this post I am going to consider some of the other language used.

Making the unfamiliar familiar

Language is used in science communication to the public, as it is in teaching, to introduce abstract technical ideas in ways that a listener new to the subject can make reasonable sense of. The constructivist perspective on learning tells us that meaning is not automatically communicated from speaker (or author or teacher) to listener (or reader or student). Rather, a text (spoken or written, or even in some other form – a diagram, a graph, a dance!) has to be interpreted, and this relies on the interpretive resources available to the learner. 4 The learner has to relate the communication to something familiar, and the speaker can help by using ways to make the new idea seem like something already familiar.

Read about constructivism in education

This is why it it is so common in communicating science to simplify, to use analogies and similes, to gesture, to use anthropomorphism and other narrative devices. There was a good deal of this in the programme, and I expect I have missed some examples. I have divided my examples into

  • simplifications: where some details are omitted so not to overburden the listener;
  • anthropomorphism: where narratives are offered such that non human entities are treated as if sentient actors, with goals, that behave deliberately;
  • analogies where an explicit comparison is made to map a familiar concept onto the target concept being introduced; 5
  • similes and metaphors: that present the technical material as being similar to something familiar and everyday.

Simplification

Simplification means ignoring some of the details, and offering a gloss on things. The details may be important, but in order to get across some key idea it is introduced as a simplification. Progress in understanding would involve subsequently filling in some details to develop a more nuanced understanding later.

In teaching there are dangers in simplification, as if the simplified idea is readily latched onto (e.g., there are two types of chemical bonds: ionic and covalent) it may be difficult later to shift learners on in their thinking. This may mean that there is a subtle balance to be judged between

giving learners enough time to become comfortable with the novel idea as introduced in a simplified form,andseeking to develop it out into a more sophisticated account before it become dogma.

In a one-shot input, such as a public lecture or appearance in the media, the best a scientist may be able to do is to present an account which is simple enough to understand, but which offers a sense of the science.

Simplification: all elements/atoms are formed in stars

When introducing the 'In Our Time' episode, Lord Bragg suggested that

"…every element in our bodies, every planet, was made in one of those stars, either as they burned, or as they exploded".

Clearly Melvyn cannot be an expert on the very wide range of topics featured on 'In our time' but relies on briefing notes provided by his guests. Later, in the programme he asks Professor Rees (what would clearly be considered a leading question in a research context!) "Is the sun recycled from previous dead stars?"

"Yes it is because we believe that all pristine material in the universe was mainly just hydrogen and helium, and all the atoms we are made of were not there soon after the big bang. They were all made in stars which lived and died before our solar system formed. And this leads to the problem of trying to understand more massive stars which have more complicated lives and give rise to supernovae…

The cloud from which our solar system formed was already contaminated by the debris, from earlier generations of massive stars which had lived and died more than say five billion years ago so we're literally the ashes of those long dead stars or if you are less romantic we're the nuclear waste from the fuel that kept those old stars shining."

Prof. Martin Rees

There is a potential for confusion here.

"all the atoms we are made of were not there soon after the big bang. They were all made in stars which lived and died before our solar system formed"seems to be meant to convey something likenot all the atoms we are made of were there soon after the big bang.
[Some were, but the rest/others] were all made in stars which lived and died before our solar system formed

A different interpretation (i.e., that all atoms/elements are formed in stars) might well be taken, given Lord Bragg's introductory comments.

Professor Rees referred to how "…the idea that the elements, the atoms we are made of, were all synthesised in stars…" first entered scientific discourse in 1946, due to Fred Hoyle, and to

"this remarkable discovery that we are literally made of the ashes of long dead stars"

Prof. Martin Rees

Before the first star formation, the only elements present in the universe were hydrogen and helium (and some lithium) and the others have been produced in subsequent high energy nuclear processes. Nuclear fusion releases energy when heavier nuclei are formed from fusing together lighter ones, up to iron (element 56).

Forming even heavier elements requires an input of energy from another source. It was once considered that exploding stars, supernovae, gave rise to the conditions for this, but recently other mechanisms have been considered: and Prof. Sullivan described one of these:"we think these combining neutron stars are the main sites where heavy elements like strontium or plutonium, perhaps even gold or silver, these kinds of elements are made in the universe in these neutron stars combining with each other".

A human body includes many different elements, though most of these in relatively small amounts. Well represented are oxygen, carbon, calcium, and nitrogen. These elements exist because of the processes that occur in stars. However, hydrogen is also found in 'organic' substances such as the carbohydrates, proteins, and fats found in the human body. Typically the molecules of these substances contain more hydrogen atoms than atoms of carbon or any other element.


substanceformula
glucose (sugar)C6H12O6
leucine (amino aid)C6H13NO2
leukotriene B4 (inflammatory mediator)C20H32O4
thymine (nucleobase)C5H6N2O2
adreneline (hormone)C9H13NO3
insulin (hormone)C257H383N65O77S6
cholesterol (lipid)C27H46O
cobalamin (vitamin B12)C63H88CoN14O14P
formulae of some compounds found in human bodies

The body is also said to be about 60% water, and water has a triatomic molecule: two hydrogen atoms to one of oxygen (H2O). That is, surely MOST of "the atoms we are made of" are hydrogen, which were present in the universe before any stars were 'born'.

So, it seems here we have a simplification ("every element in our bodies…was made in one of those stars, either as they burned, or as they exploded"; "atoms we are made of … were all made in stars") which is contradicted later in the programme. (In teaching, it is likely the teacher would feel the need to draw the learner's attention to how the more detailed information was actually developing an earlier simplification, and not leave a learner to work this out for themselves.)

Simplification: mass is changed into energy

Explaining nuclear fusion, Prof. Crawford suggested that

"Nuclear fusion is when you combine nuclei of elements to form heavier elements, and when you do this there is a loss of mass, which is converted to energy which provides the thermal pressure and that is what counteracts the gravity and stalls the gravitational collapse."

Prof. Carolin Crawford

This seems to reflect a common alternative conception ('misconception') that, in nuclear processes, mass is converted to energy. This is often linked to Albert Einstein's famous equation E = mc2.

Actually, as discussed before here, this is contrary to the scientific account. The equation presents an equivalence between mass and energy, but does not suggest they can be inter-converted. In nuclear fusion, the masses of the new nuclei are very slightly less than the masses of the nuclei which react to form them (the difference is known as the mass defect), but this is because this omits some details of the full description of the process. If the complete process is considered then there is no loss of mass, just a reconfiguration of where the mass can be located.


The formation of helium from hydrogen in a star

(Image source: Wikamedia Commons)

Although the 4He formed has slightly less mass than four 1H; the positrons, neutrinos and gamma rays produced all have associated (energy and) mass, so that overall there is conservation of mass.


This is a bit like cooking some rice, and finding that when the rice is cooked the contents of the saucepan had slightly less weight than when we started – as some of the water we began with has evaporated and is no longer registering on our balance. In a similar way, if we consider everything that is produced in the nuclear process, then the mass overall is conserved.

As E = mc2 can be understood to tell us that mass follows the energy (or vice versa) we should expect mass changes (albeit very, very small ones) whenever work is done: when we climb the stairs, or make a cup of tea, or run down a mobile 'phone 'battery' (usually a cell?) – but mass is always conserved when we consider everything involved in any process (such as how the 'phone very, very slightly warms -and so very marginally increases the mass of – the environment).

Read 'How much damage can eight neutrons do?'

Despite the scientific principles of conservation of energy and conservation of mass always applying when we make sure we consider everything involved in a process, I have mentioned on this site another example of an astrophysicist suggesting mass can be converted into energy: "an electron and the positron, and you put them together, they would annihilate…they would annihilate into energy" (on a different episode of 'In Our Time': come on Melvyn…we always conserve mass).

Read 'The missing mass of the electron'

Perhaps this is an alternative conception shared by some professional scientists, but I wonder if it sometimes seems preferably to tell the "mass into energy" narrative because it is simpler than having to explain the full details of a process – which is inevitably a more complex story and so will be more difficult for a novice to take in. After all, the "mass into energy" story is likely to seem to fit with a listener's interpretive resources, as E=mc2 is such a famous equation that it can be assumed that it will be familiar to most listeners, even if only a minority will have a deep appreciation of how the equivalence works.

Anthropomorphic narratives

In science learning, anthropomorphism is (to borrow a much used metaphor) a double edged sword that can cut both ways. Teachers often find that using narratives that present inanimate entities which are foci of science lessons as if they are sentient beings with social lives and motivations engages learners and triggers mental images that a student can readily remember. So, students may recall learning about what happens at a junction in a circuit in terms of a story about an electron that had to make a decision about which way to go – perhaps she took one branch while her friend tried another? They recall that covalent bonds are the 'sharing' of electrons between atoms, and indeed that atoms want, perhaps even need, to fill their electron shells, and if they manage this they will be happy.

Read about anthropomorphism

The danger here is that for many students such narratives are not simply useful ways to get them thinking about the science concepts (weak anthropomorphism) but seem quite sufficient as the basis of explanations (strong anthropomorphism) – and so it may become difficult to shift them towards more canonical accounts. They will then write in tests that chemical reactions occur because the atoms want full shells, or that only one electron can be removed from a sodium atom because it then has a full shell. (That is, a force applied to an electron in an electric field is seen as irrelevant compared with the atom's desires. These are genuine examples reflecting what students have said.)

However, there is no doubt that framing scientific accounts within narratives which have elements of human experience as social agent does seem to help make these ideas engaging and accessible. Some such anthropomorphism is explicit, such as when gas molecules (are said to) like to move further apart, and some is more subtle by applying terms which would normally be used in relation to human experiences (not being bothered; chomping; escaping…).

What gravity did next

Consider this statement:

"All stars have the problem of supporting themselves against gravitational collapse, whether that is a star like our sun which is burning hydrogen into helium, and thus providing lots of thermal pressure to stop collapse, or whether it is a white dwarf star, but it does not have any hydrogen to burn, because it is an old dead star, fading away, so it has another method to stop itself collapsing and that is called degeneracy pressure. So, although a white dwarf is very dense, gravity is still trying to pull that white dwarf to be even denser and even denser."

Prof. Mark Sullivan

There is an explicit anthropomorphism here: from the scientific perspective gravity is not trying to pull the white dwarf to be even denser. Gravity does not try to do anything. Gravity is not a conscious agent with goals that it 'tries' to achieve.

However, there is also a more subtle narrative thread at work – that a star has the problem of supporting itself, and it seems that when its first approach to solving this problem fails, it has a fallback method "to stop itself collapsing". But the star is just a complex system where various forces act and so processes occur. A star is not the kind of entity that can have a problem or enact strategies to achieve goals. Yet, this kind of language seems to naturally communicate abstract ideas though embedding them within an accessible narrative.

Star as moral agents

In the same way, a star is not the type of entity which can carry out immoral acts, but

"A star like our sun will never grow in mass, because it lives by itself in space. But most stars in the universe don't live by themselves, they live in what are called binary systems where you have two stars orbiting each other, rather than just the single star that we have as the sun. They are probably born with different masses, and so they evolve at different speeds and one will become a white dwarf. Now the physics is a bit complicated, but what can happen, is that that white dwarf can steal material from its companion star."

Prof. Mark Sullivan

The meaning here seems very clear, but again there are elements of using an anthropomorphic narrative. For one star to steal material from another star, that material would have to first belong to that other star, and its binary 'partner' would have to deliberately misappropriate that material knowing it belongs to its 'neighbour' (indeed, "companion").

Such a narrative breaks down on analysis. If we were to accept that the matter initially belongs to the first star (leaving aside for the moment what kind of entities can be considered to own property) then given that the material in a star got to be there through mutual gravitational attraction, the only obvious basis for ownership is that that matter has become gravitationally bound as part of that star.

If we have no other justification than that (as in the common aphorism, possession is nine points of the law), then when the material is transferred to another star because its gravitational field gives rise to a net force causing the matter to become gravitationally bound to a different star, then we should simply consider ownership to have changed. There is no theft in a context where ownership simply depends on pulling with the greater force. Despite this, we readily accept an analogy from our more familiar human social context and understand that (in a metaphorical sense) one star has stolen from another!

Actually, theft can only be carried out by moral agents – those who have capacity to intend to deprive others of their property

"A person [sic] is guilty of theft if he dishonestly appropriates property belonging to another with the intention of permanently depriving the other of it; and "thief" and "steal" shall be construed accordingly"

U.K. Theft Act 1968

Generally, these days (though this was not always so), even non-human animals are seldom considered capable of being responsible for such crimes. Admittedly, the news agency Reuters reported that as recently as 2008 "A Macedonian court convicted a bear of theft and damage for stealing honey from a beekeeper", but this seems to have been less a judgement on the ability of the bear (convicted it its absence) to engage in ethical deliberation, and more a pragmatic move that allowed the bee-keeper to be awarded criminal damages for his losses.

But, according to astronomers, stars are not only involved in the petty larceny of illicitly acquiring gas, but observations of exoplanets suggests some stars may even commit more daring, large-scale, heists,

"fairly small rocky planets two or three times the mass of the earth, in quite tight orbits around their star and you can speculate that they were once giant planets like Jupiter that have had the outer gassy layers blasted off and you are left with the rocky core, or maybe those planets were stolen from another star that got too close"

Prof. Carolin Crawford
A ménage à trois?

And there were other suggestions of anthropomorphism. It is not only stars that "don't live by themselves" in this universe,

"Nickel-56 [56Ni] is what's called an iron peak element, so it lives with iron and cobalt on the periodic table…"

Prof. Mark Sullivan

And, it is not only gravity which seems to have preferences:

"And like Mark has described with electrons not wanting to be squeezed, you have neutron degeneracy pressure. Neutrons don't like to be compressed, at some point they resist it."

Prof. Carolin Crawford

Neither electrons nor neutrons actually have any preferences: but this is an anthropomorphic metaphor that efficiently communicates a sense of the natural phenomena. 'Resist' originally had an active sense as in taking a stand, but today would not necessarily be understood that way. Wanting and liking (or not wanting and not liking), however, strictly only refer to entities that can have desires and preferences.

Navigating photons

Professor Rees explained why some imploding stars are not seen as very bright stars that fade over years, but rather observed through extremely intense bursts of high energy radiation that fade quickly,

"The energy in the form of ordinary photons, ordinary light, that's arisen in the centre of a supernova, diffuses out and takes weeks to escape, okay, but if the star is spinning, then it will be an oblate spheroid, it will have a minor axis along the spin axis, and so the easy way out is for the radiation not to diffuse through but to find the shortest escape route, which is along the spin axis, and I mention this because gamma ray bursts are … when a supernova occurs but because the original star was sort of flattened there is an easy escape route and all the energy escapes in jets along the spin axis and so instead of it diffusing out over a period of weeks, as it does in a supernova, it comes out in a few seconds."

Prof. Martin Rees

Again, the language used is suggestive. Radiation is not just emitted by the star, but 'escapes' (surely a metaphor?). The phrasing "an easy way out" implies something not being difficult. Inanimate entities like photons do not actually (literally) find anything difficult or easy. Moreover, the radiation might "find the shortest escape route": language that does not reflect a playing out of physical forces but an active search – only a being able to seek can find. Yet, again, the language supports an engaging narrative, 'softening' the rather technical story by subtly reflecting a human quest.

Professor Rees also referred to how,

"when those big stars face a crisis they blow off their outer layers"

Prof. Martin Rees

again using phrasing which seems to present the stars as deliberate actors – they actively "blow off" material when they "face a crisis". A crisis is (or at least was originally) a point where a decision needs to be made. A star does not reach the critical point where it reluctantly decides it needs to shed some material – but rather is subject to changing net forces as the rate of heat generation from nuclear processes starts to decrease.

A sense of anthropomorphic narrative also attaches to Professor Crawford's explanation of how more massive stars process material faster,

"…more massive stars … actually have shorter lifetimesthey have to chomp through their fuel supply so furiously that they exhaust it more rapidly

Prof. Carolin Crawford

'Chomping', a term for vigorous eating (biting, chewing, munching), is here a metaphor, as a star does not eat – as pointed out in the companion piece, nutrition is a characteristics feature of living things, but does not map across to stars even if they are described as being born, living, dying and so forth. To be furious is a human emotional response: stars may process their remaining hydrogen quickly, but there is no fury involved. Again, though, the narrative, perhaps inviting associated mental imagery, communicates a sense of the science.

Laid-back gas

Another example of anthropomorphism was

"…if you have a gas cloud that's been sitting out in space for billions of years and has not bothered to contract because it's been too hot or it's too sparse…"

Prof. Carolin Crawford

This is an interesting example, as Prof. Crawford explicitly explains here that the gas cloud has not contracted because of the low density of material (so weak gravitational forces acting on the particles) and/or the high temperature (so the gas comprises of energetic, so fast moving, particles), so the suggestion that the material cannot be bothered (implication: that the 'cloud' operates as a single entity, and is sentient if perhaps a little lazy) does not stand in place of a scientific explanation, but rather simply seems to be intended to 'soften' (so to speak) the technical nature of the language used.

Analogy

An analogy goes beyond a simile or metaphor because there is some kind of structural mapping to make it explicit in what way or ways the analogue is considered to be like the target concept. 5 (Such as when explaining mass defect in relation to the material lost from the saucepan when cooking rice!)


A potential teaching analogy to avoid alternative conceptions about mass defect in nuclear processes

Read about science analogies

So, Prof. Rees suggests that scientists can test their theories about star 'life cycles' by observation, even though an individual star only moves through the process over billions of years, and uses an analogy to a more familiar everyday context:

"We can test our theories, not only because we understand the physics, but because we can look at lots of stars. It is rather like if you had never seen a tree before, and you wandered around in a forest for a day, you can infer the life cycles of trees, you'd see saplings and big trees, etcetera. And so even though our lifetime is minuscule compared to the lifetime of a stable star, we can infer the population and life cycles of stars observationally and the theory does corroborate that fairly well."

Prof. Martin Rees

This would seem to make the basis of a good teaching analogy that could be discussed with students and would likely link well with their own experiences.

The other explicit analogy introduced by Prof. Rees is one well-known to physics teachers (sometimes in an ice-skater variant),

"If a contracting cloud has even a tiny little bit of spin, if it is rotating a bit, then as it contracts, then just like the ballerina who pulls in her arms and spins faster, then the contracting cloud will start to spin faster…"

Prof. Martin Rees

Stellar similes

I take the difference between a simile and a metaphor as the presence of an explicit marker (such as '…as…',…like…') to tell the listener/reader that a comparison is being made – so 'the genome is the blueprint for the body' would be a metaphor, where 'the genome is like a blueprint for the body' would be a simile.

As if a black hole cuts itself off

So, when Professor Rees describes how a massive black hole forms, he uses simile (i.e., "…as if were…"),

"So, if a neutron star gets above that mass, then it will compress even further, and will become a black hole – it will go on contracting until it, as it were, cuts itself off from the rest of the universe, leaving a gravitational imprint frozen in the space that's left. It becomes a black hole that things can fall into but not come out."

Prof. Martin Rees

There is an element of anthropomorphic narrative (see above) again here, if we consider the choice of active, rather than passive, phrasing

  • …as it were, cuts itself off from the rest of the universe, compared with
  • …as it were, becomes cut off from the rest of the universe

This is presented as something the neutron star itself does ("it will compress…become a black hole – it will go on contracting until it, as it were, cuts itself off…") rather than a process occurring in/to the matter of which it is comprised.

As if galaxies drop over the horizon

Prof. Rees uses another simile, when talking of how the expansion of space means that in time most galaxies will disappear from view,

"All the more distant universe which astronomers like Mark [Sullivan] study, galaxies far away, they will all have expanded their distance from us and in effect disappeared over a sort of horizon and so we just wouldn't see them at all. They'd be too faint, rather like …an inside-out black hole as it were, but in this case they moved so far away that we can't see them any more …"

Prof. Martin Rees

The term horizon, originally referring to the extent of what is in sight as we look across the curved Earth, has become widely used in astronomical contexts where objects cease to be in sight (i.e., the event horizon of a black hole beyond which any light being emitted by an object will not be able to leave {'escape!'} the black hole because of the intense gravitation field), but here Prof. Rees clearly marks out for listeners ("…in effecta sort of…") that he is making a comparison with the familiar notion of a horizon that we experience here on Earth.

There is another simile here, the reference to the expansion of space leading to an effect "rather like…an inside-out black hole as it were" – but perhaps that comparison would be less useful to a listener new to the topic as it uses a scientific idea rather than an everyday phenomenon as the analogue.

Through a glass onion darkly?

Another simile used by Professor Rees was a references to a "sort of onion skin structure". Now 'onion skin' sometimes refers to the hard, dry, outer material (the 'tunic') usually discarded when preparing the onion for a dish. To a science teacher, however, this is more likely to mean the thin layer of epithelial tissue that can be peeled from the scales inside the bulb. These scales, which are potentially the bases of leaves that can grow if the bulb is planted, are layered in the bulb.

The skin is useful in science lessons as it is a single layer of cells, that is suitable for students to dissect from the onion, and mount for microscopic examination – allowing them to observe the individual cells. There is something at least superficially analogous to this in stars. Observations of the Sun show that convection processes gives rise to structures referred to as convection 'cells'.



Yet, when Professor Rees' simile is heard in context, it seems that this is not the focus of the comparison:

"…all the nuclear processes which would occur at different stages in the heavy stars…which have this sort of onion skin structure with the hotter inner layers"

Prof. Martin Rees

Very large stars that have processed much of their hydrogen into helium can be considered to have a layered structure where under different conditions a whole sequence of processes are occurring leading to the formation of successively heavier and heavier elements, and ultimately to a build-up of iron near the centre.


The onion model of the structure of a large star (original image by Taken from Pixabay)

When I heard the reference to the onion, this immediately suggested the layered nature of the onion bulb being like the structure of a star that was carrying out the sequence of processes where the products of one fusion reaction become the raw material for the next. Presumably, my familiarity with the layered model of a star led me to automatically make an association with onions which disregarded the reference to the skin. That is, I had existing 'interpretive resources' to understand why the onion reference was relevant, even though the explicit mention of the skin might make the comparison obscure to someone new to the science.

Metaphors – all the way back up?

Some metaphors can easily be spotted (if someone suggests mitochondria are the power stations of the cell, or a lion is King of the jungle), but if our conceptual systems, and our language, are built by layers of metaphor upon metaphor then actually most metaphors are dead metaphors.

That is, an original metaphor is a creative attempt to make a comparison with something familiar, but once the metaphor is widely taken up, and in time becomes common usage and so a part of standard language, it ceases to act as a metaphor and becomes a literal meaning.

This presumably is what has happened with the adoption of the idea that stars are born, live out their lives, and then die: originally it was a poetic use of language, but now among astronomers it reflects an expanded standard use of terms that were once more restricted (born, live, lifetime, die etc.).


"…Stars dived in blinding skies / Stars die / Blinding skies…"
Stars die, but only due to artistic license
(Artwork from 'Star's die' by Porcupine Tree, photographer: Chris Kissadjekian)

If you see a standard candle…

When Professor Sullivan refers to a "standard candle", this is now a widely used astronomical notion (in relation to how we estimate distances to distant stars and galaxies that are much too far away to triangulate from parallax as the earth changes its position in the solar system) – but at one time this was used as a figure of speech.

Some figures of speech are created in the moment, but never widely copied and adopted. The astronomical community adopted the 'standard candle' such that it is now an accepted term, even though most young people meeting astronomical ideas for the first time probably have very little direct experience of candles. What might once have seemed a blatantly obvious allusion may now need explaining to the novice.

When Sir Arthur Eddington (famous for collecting observations during an eclipse consistent with predictions from relativity theory about the gravitational 'bending' of starlight) gave a public lecture in 1932, he seems to have assumed that his audience would understand the analogy between an astronomer's 'standard candles' (Cepheid variables) and standard candles they might themselves use!

"If you see a standard candle anywhere and note how bright it appears to you, you can calculate how far off it is; in the same way an astronomer observes his [or her] 'standard candle' in the midst of a nebula, notes its apparent brightness or magnitude, and deduces the distance of the nebula"

Eddington, 1933/1987, pp.7-8

This ongoing development in language means that it may not always be entirely clear which terms are still engaged with as if metaphors and which have now become understood as literal. That is, in considering whether some phrase is a metaphor we can ask two questions:

  • did the author/speaker intend this as a comparison, or do they consider the term has direct literal meaning?
  • does the reader/listener understand the term to have a literal meaning, or is it experienced as some novel kind of comparison with another context which has to be related back to the focus?

In the latter case we might also think it is important to distinguish between cases where the audience member can decode the intention of the comparison 'automatically' as part of normal language processing – and cases where they would have to consciously deliberate on the meaning. (In the latter case, the interpretation is likely to disrupt the flow of reading, and when listening could perhaps even require the listener to disengage from the communication such that subsequent speech is missed.)

(Metaphorical?) hosts

So, when Prof. Crawford suggests that

"The supernovae, particularly, are of fundamental importance for the host galaxy…"

Prof. Carolin Crawford

her use of the term 'host' is surely metaphorical (at least for a listener – this term is widely used in the literature of academic astronomy 6). A host offers hospitality for a guest. That does not seem to obviously reflect the relationship between a supernova and the galaxy it is found in and is part of. It is not a guest: rather, in Prof. Sullivan's terms we might suggest that star has 'lived its entire life' in that galaxy – it is its galactic 'home'. Despite this comparison not standing up to much formal analysis, I suspect the metaphor can be automatically processed by anyone with strong familiarity with the concept of a host. Precise alignment may not be a strong criterion for effective metaphors.

Another meaning of host refers to a sacrificial victim (as in the host in the Christian Eucharist) which seems unlikely to be the derivation here, but perhaps fits rather well with Prof. Crawford's point. A supernova too close to earth could potentially destroy the biosphere – an unlikely but not impossible event.

(Metaphorical?) bubbles

Professor Crawford described some of the changes during a supernova,

"You have got your iron core, it collapses down under gravity in less than a second, that kind of leaves the outer layers of the star a little behind, they crash down, bounce on the surface of the core, and then there's a shockwave, that propels all this stellar debris, out into space. So, this is part of the supernova explosion we have been talking about, and it carves out a bubble within the interstellar medium."

Prof. Carolin Crawford

There are a number of places here where everyday terms are applied in an unfamiliar context such as 'core', 'bouncing', 'layers' and 'debris'. But the idea of carving a bubble certainly seems metaphorical, if only because a familiar bubble would have a physical surface, where surely, here, there is no strict interface between discrete regions of gases. But, again, the term offers an accessible image to communicate the process. (And anyone looking at the NASA image above of convection cells in the Sun might well feel that these can be perceived as if bubbles.)

(Metaphorical?) pepper

Similarly, the idea of heavy elements from exploding suns being added to the original hydrogen and helium in the interstellar medium as like adding pepper also offers a strong image,

"…this is the idea of enrichment, you start off with much more primordial hydrogen and helium gas that gets steadily peppered with all these heavy elements…"

Prof. Carolin Crawford

Perhaps 'peppered' is now a dead metaphor, as it is widely used in various contexts unrelated to flavouring food.

(Metaphorical?) imprints

When Professor Rees referred to a neutron star that has become a black hole leaving a "gravitational imprint frozen in the space that's left" this makes good sense as the black hole will not be visible, but its gravitational field will have effects well beyond its event horizon. Yet, one cannot actually make an imprint in space, one needs a suitable material substrate (snow, plater, mud…) to imprint into; and nor has anything been 'frozen' in a literal sense. Indeed, the gravitational field will change as the black hole acquires more material through gravitational capture (and in the very long term loses mass though evaporates Hawking radiation – which is said to cause the black hole to 'evaporate'). So, this is a kind of double metaphor.

(Metaphorical?) blasts and blows

I report above both the idea that rocky planet close to large stars might have derived from 'giant' planets "that have had the outer gassy layers blasted off" and how "big stars…blow off their outer layers". Can stars really blow, or is this based on a metaphor. Blasts usually imply explosions, sudden events, so perhaps these are metaphorical blasts? And it is not just larger stars that engage in blowing off,

"[The sun] will blow off its outer layers and become a red giant, expanding so it will engulf the inner planets, but then the core will settle down to what's called a white dwarf, this is a dead, dense star, about a million times denser than normal stuff…."

Prof. Martin Rees

Metaphors galore!

Perhaps those last examples are not especially convincing – but this reflects a point I made earlier. Language changes over time: it is (metaphorically-speaking) fluid. If language started from giving names to things we can directly point at, then anything we cannot directly point at needs to be labelled in terms of existing words. Most of the terms we use were metaphors at some point, but became literal as the language norms changed.

But society is not a completely homogeneous language community. The requirements of professional discourse in astronomy (or any other specialised field of human activity) drive language modifications in particular regards ahead of general language use. It is not just people in Britain and the United States who are divided by a common language – we all are to some extent. What has become literal meaning for for one person (perhaps a science teacher) may well only be a metaphor to another (a student, say).

After all, when I look up what it is to blow off, I find that the most common contemporary meaning relates to a failure to meet a social obligation or arrangement – I am pretty sure (from the context) that that is not what Professor Rees was suggesting ("…when those big stars face a crisis they [let down] their outer layers".) Once we start looking at texts closely, they seem to be 'loaded' with figures of speech. A planet is not materially constrained in space, yet we understand why an orbit might be considered 'tight'.

In the proceeding quote, the core of a star seems to need no explanation although it presumably derives by analogy with the core of an apple or similar fruit, which itself seems to derive metaphorically form an original meaning of the heart. Again, what is meant by engulf is clear enough although originally it referred to the context of water and the meaning has been metaphorically (or analogously) extended.

The terms red giant and white dwarf clearly derive from metaphor. (Sure, a red giant is gigantic, but then, on any normal scale of human experience, so is a white dwarf.) These terms might mystify someone meeting them for the first time so not already aware they are used to refer to classes of star. This might suggest the value of a completely objective language for discussing science where all terms are tightly (hm, too metaphorical…closely? rigidly? well-) defined, but that would be a project reminiscent of the logical positivist programme in early twentieth century that ultimately proved non-viable. We can only define words with more words, and there are limits to the precision possible with a usable, 'living', language.

Take the "discovery that we are literally made of the ashes of long dead stars". Perhaps, but the term ashes normally refers to the remains of burnt organic material, especially wood, so perhaps we are not literally, but only metaphorically made of the ashes of long dead stars. Just as when when Professor Sullivan noted,

"the white dwarf is made of carbon, it's made of oxygen, and the temperature and the pressure in the centre of that white dwarf star can become so extreme, that carbon detonation can occur in the centre of the white dwarf, and that is a runaway thermonuclear reaction – that carbon burns in astronomer speak into more massive elements…"

Prof. Mark Sullivan
Are we stardust, ashes or just waste?

Burning is usually seen in scientific terms as another word for combustion. So, the nuclear fusion, 'burning' "in astronomer speak" of its nuclear 'fuel' in a star represents an extension of the original meaning by analogy with combustion. 9 Material that is deliberately used to maintain a fire is fuel. A furnace is an artefact deliberately built to maintain a high temperature – the nuclear furnace in a star is not an artefact but a naturally occurring system (gravity holds the material in place), but is metaphorically a furnace. A runaway is a fugitive who has absconded – so to describe a thermonuclear reaction (which is not going anywhere in spatial terms) as 'runaway' adopts what was a metaphor. (Astronomers also use the term 'runaway' to label a class of star that seem to be moving especially fast compared with the interstellar medium – a somewhat more direct borrowing of the usual meaning of 'runaway'.)

To consider us to be made from 'nuclear waste' relies on seeing the star-as-nuclear-furnace as analogous to a nuclear pile in a power station. In nuclear power stations we deliberately process fissile material to allow us to generate electrical power: and material is produced as a by-product of this process (that is, it is a direct product of the natural nuclear processes, but a by-product of our purposeful scheme to generate electricity). To consider something waste means making a value judgement.

If the purpose of a star is to shine (a teleological claim) and the fusion of hydrogen is the means to achieve that end, then the material produced in that process which is no longer suitable as 'fuel' can be considered 'waste'. If the universe does not have any purpose(s) for stars then there is no more basis for seeing this material as waste than there is for seeing stars themselves as the waste products of a process that causes diffuse matter to come together into local clumps. That is, this is an anthropocentric perspective that values stars as of more value than either the primordial matter from which they formed, or the 'dead' matter they will evolve into when they no longer shine 'for us'. Nature may not have such favourites! If it has a purpose, then stars seem to only be intermediate steps towards its ultimate end.


What does support the turtle? Surely, it's metaphors all the way down.
(Source: Pintrest)


Sources cited:

Notes:

1 It may seem fanciful that we give a specific individual tree a proper name but should a child inherently appreciate that we commonly name individual hamsters (say, or ships, or roads), but not individual trees? 'Major Oak' is a particular named Oak tree in Sherwood Forest, so the idea is not ridiculous. (It is very large, but apparently the name derives from it being described by an author with the army rank of major. Of course, this term for a soldier leading others derives metaphorically from a Latin word meaning bigger, so…)


2 "So how do we bridge between dogs and trees on one hand and electrons and the strong nuclear force on the other (so to speak!)? The answer is we build using analogy and we talk about those constructions using a great deal of metaphor."

  • We understand what is meant by bridge here in relation to an actual bridge that physically links two places – such as locations on opposite sides of a river or railway line.
  • There is no actual building up of materials, but we understand how we can 'build' in the abstract by analogy.
  • These things are not actually at hand, but we make a metaphorical comparison in terms of distinguishing items held in 'opposite' hands. We understand what is meant by a great deal of something abstract by analogy with a great deal of something we can directly experience, e.g., sand, water, etcetera.

Justice personified, on the one hand weighing up the evidence and on the other imposing sanctions

(Image by Sang Hyun Cho from Pixabay)


We construct scientific concepts and models and theories by analogy with how we construct material buildings – we put down foundations then build up brick by brick so that the top of the structure is only very indirectly supported by the ground.

(Image by joffi from Pixabay)


3 A point is a hypothetical, infinitesimally small, location in space, which is not something a person could actually make. The 'point' of an argument is metaphorically like the point of a pencil or spear which is metaphorically an approximation to an actual point. Of course, we (adult members of the English language community) all know what is meant by the point of an argument – but people new to a language (such as young children) have to find this out, without someone holding up the point of an argument for them to learn to recognise.


4 In part, this means linguistic resources. Each individual person has a unique vocabulary, and even though sharing most words with others, often has somewhat unique ranges of application of those words. But it also refers to personal experiences that can be drawn upon (e.g., having cared for an ill relative, having owned a pet, having undertaken part-time work in a hospital pharmacy, having been taken to work by a parent…) and the cultural referents that are commonly discussed in discourse (cultural icons like the Mona Lisa or Beethoven's fifth symphony; familiarity with some popular television show or film; appreciating that Romeo and Juliet were tragic lovers, or that Gandhi is widely considered a moral role model, and so forth.)


"Penny, I'm a physicist. I have a working knowledge of the entire universe and everything it contains."

"Who's Radiohead?"

"I have a working knowledge of the important things in the universe."

Still from 'The Big Bang Theory' (Chuck Lorre Productions / Warner Bros. Television)


The interpretive resources are whatever mental resources are available to help make sense of communication.


5 I am using the term concept in an 'inclusive' sense (Taber, 2019), in that whenever a person can offer a discrimination about whether something is an example of some category, then they hold a concept (vague or detailed; simple or complex; canonical or alternative).

That is, if someone can (beyond straight guesswork) try to answer one of the questions "what is X? ", "is this an example of X?" or "can you suggests an example of X?", then they have a relevant concept – where X could be…

  • a beaker
  • a force
  • a bacterium
  • opaque
  • a transition metal
  • an isomer
  • distillation
  • neutralisation
  • a representation of the ideal gas law
  • and so forth

Read more about concepts


6 The earliest reference to 'host galaxies' I found in a quick search of the scientific literature was from 1972 in a paper which used the term 'host galaxy' 8 times, including,

"We estimated the distances [of observed supernovae]…by four different methods:

  • (1) Estimating the absolute luminosity of the host galaxy.
  • (2) Estimating the absolute luminosity of the supernova.
  • (3) Using the measured redshift of the host galaxy and assuming the Hubble constant H = 75 km (s Mpc)-1
  • (4) Identifying the host galaxy with a cluster of galaxies for which the distance from Earth had already been estimated.
Ulmer, Grace, Hudson & Schwartz, 1972, p.209

The term 'host galaxy' was not introduced or defined in the paper, suggesting that either it was already in common use as a scientific term (and so a dead metaphor within the astronomical community) in 1972 or Ulmer and colleagues assumed it was obvious enough not to need explanation.


7 It should be pointed out that 'In Our Time' is not presented as succession of mini-lectures, or as a tightly scripted programme, but as a conversation between Melvyn as his guests. Of course, there is some level of preparation by those involved, but in adopting a conversational style, avoiding the sense of prepared statements, it is inevitable that a guest's language will sometimes lack the precision of a drafted and much revised account.


8 A supernova may appear as a new star in the sky if it is so far away that the star was not previously detectable, or as a known star quick;y becoming very much brighter.


9 One should be careful in making such equivalences, as in that although we may equate burning with combustion, burning is an everyday ('life world') phenomenon, and combustion is a scientific concept: often our scientific concepts are more precisely defined than the related everyday terms. (Which is why melting has a broader meaning in everyday life {the sugar melts in the hot tea; the stranger melted away into the mist} than it does in science.) But although we might say, as suggested earlier in the text, we have been burned by exposure to the sun's ultraviolet rays, or by contact with a caustic substance, in those contexts we are unlikely to consider our skin as 'fuel' for the process.


The missing mass of the electron

Annihilating mass in communicating science


Keith S. Taber


An episode of 'In Our Time' about the electron

The BBC radio programme 'In Our Time' today tackled the electron. As part of the exploration there was the introduction of the positron, and the notion of matter-antimatter annihilation. These are quite brave topics to introduce in a programme with a diverse general audience (last week Melvyn Bragg and his guests discussed Plato's Atlantis and next week the programme theme is the Knights Templar).

Prof. Victoria Martin of the School of Physics and Astronomy at the University of Edinburgh explained:

If we take a pair of matter and antimatter, so, since we are talking about the electron today, if we take an electron and the positron, and you put them together, they would annihilate.

And they would annihilate not into nothingness, because they both had mass, so they both had energy from E=mc2 that tells us if you have mass you have energy. So, they would annihilate into energy, but it would not just be any kind of energy: the particular kind of energy you get when you annihilate an electron and a positron is a photon, a particle of light. And it will have a very specific amount of energy. Its energy will be equal to the sum of the energy of electron and the positron that they had initially when they collided together.

Prof. Victoria Martin on 'In Our Time'

"An electron and the positron, and you put them together, they would annihilate…they would annihilate into energy" – but this could be misleading.

Now, I am sure that is somewhat different from how Prof. Martin would treat this topic with university physics students – of course, science in the media has to be pitched at the largely non-specialist audience.

Read about science in the media

It struck me that this presentation had the potential to reinforce a common alternative conception ('misconception') that mass is converted into energy in certain processes. Although I am aware now that this is an alternative conception, I seem to recall that is pretty much what I had once understood from things I had read and heard.

It was only when I came to prepare to teach the topic that I realised that I had a misunderstanding. That, I think, is quite common for teachers – when we have to prepare a topic well enough to explain it to others, we may spot flaws in our own understanding (Taber, 2009)

So, for example, I had thought that in nuclear processes, such as in a fission reactor or fusion in stars, the mass defect (the apparent loss of mass as the resulting nuclear fragments have less mass than those present before the process) was due to that amount of mass being converted to energy. This is sometimes said to explain why nuclear explosions are so much more violent than chemical explosions, as (given E=mc2): a tiny amount of mass can be changed into a great deal of energy.

Prof. Martin's explanation seemed to support this way of thinking: "they would annihilate into energy".


An alternative conception of particle annihilation: This scheme seems to be implied by Prof. Martin's comments

What is conserved?

It is sometimes suggested that, classically, mass and energy were considered to be separately conserved in processes, but since Einstein's theories of relativity have been adopted, now it is considered that mass can be considered as if a form of energy such that what is conserved is a kind of hybrid conglomerate. That is, energy is still considered conserved, but only when we account for mass that may have been inter-converted with energy. (Please note, this is not quite right – see below.)

So, according to this (mis)conception: in the case of an electron-positron annihilation, the mass of the two particles is converted to an equivalent energy – the mass of the electron and the mass of the positron disappear from the universe and an equivalent quantity of energy is created. Although energy is created, energy is still conserved if we allow for the mass that was converted into this new energy. Each time an electron and positron annihilate, their masses of about 2 ✕ 10-30 kg disappear from the universe and in its place something like 2 ✕ 10-13 J appears instead – but that's okay as we can consider 2 ✕ 10-30 kg as a potential form of energy worth 2 ✕ 10-13 J.

However, this is contrary to what Einstein (1917/2004) actually suggested.


Einstein did not suggest that matter could be changed to energy

Equivalence, not interconversion

What Einstein actually suggested was not that mass could be considered as if another kind/form of energy (alongside kinetic energy and gravitational potential, etc.) that needed to be taken into account in considering energy conservation, but rather that inertial mass can be considered as an (independent) measure of energy.

That is, we think energy is always conserved. And we think that mass is always conserved. And in a sense they are two measures of the same thing. We might see these two statements as having redundancy:

  • In a isolated system we will always have the same total quantity of energy before and after any process.
  • In a isolated system we will always have the same total quantity of mass before and after any process.

As mass is always associated with energy, and so vice versa, either of these statements implies the other. 1


Two conceptions of the shift from a Newtonian to a relativistic view of the conservation of energy (move the slider to change the image)

No interconversion?

So, mass cannot be changed into energy, nor vice versa. The sense in which we can 'interconvert' is that we can always calculate the energy equivalence of a certain mass (E=mc2) or mass equivalence of some quantity of energy (m=E/c2).

So, the 'interconversion' is more like a change of units than a change of entity.


Although we might think of kinetic energy being converted to potential energy reflects a natural process (something changes), we know that changing joules to electron-volts is merely use of a different unit (nothing changes).

If we think of a simple pendulum under ideal conditions 2 it could oscillate for ever, with the total energy unchanged, but with the kinetic energy being converted to potential energy – which is then converted back to kinetic energy – and so on, ad infinitum. The total energy would be fixed although the amount of kinetic energy and the amount of potential energy would be constantly changing. We could calculate the energy in joules or some other unit such as eV or ergs (or calories or kWh or…). We could convert from one unit to another, but this would not change anything about the physical system. (So, this is less like converting pounds to dollars, and more like converting an amount reported in pounds {e.g., £24.83} into an amount reported in pence {e.g., 2483p}.)

Using this analogy, the electron and positron being converted to a photon is somewhat like kinetic energy changing to potential energy in a swinging pendulum (something changes), but it is not the case that mass is changed into energy. Rather we can do our calculations in terms of energy or mass and will get (effectively, given E=mc2) the same answer (just as we can add up a shopping list in pounds or pence, and get the same outcome given the conversion factor, 1.00£ = 100p).

So, where does the mass go?

If mass is conserved, then where does the mass defect – the amount by which the sum of masses of daughter particles is less than the mass of the parent particle(s) – in nuclear processes go? And, more pertinent to the present example, what happens to the mass of the electron and positron when they mutually annihilate?

To understand this, it might help to bear in mind that in principle these process are like any other natural processes – such as the swinging pendulum, or a weight being lifted with pulley, or methane being combusted in a Bunsen burner, or heating water in a kettle, or photosynthesis, or a braking cycle coming to a halt with the aid of friction.

In any natural process (we currently believe)

  • the total mass of the universe is unchanged…
    • but mass may be reconfigured
  • the total energy of the universe is unchanged…
    • but energy may be reconfigured; and
  • as mass and energy are associated, any reconfigurations of mass and energy are directly correlated.

So, in any change that involves energy transfers, there is an associated mass transfer (albeit usually one too small to notice or easily measure). We can, for example, calculate the (tiny) increase in mass due to water being heated in a kettle – and know just as the energy involved in heating the water came from somewhere else, there is an equivalent (tiny) decrease of mass somewhere else in the wider system (perhaps due to falling of water powering a hydroelectric power station). If we are boiling water to make a cup of tea, we may well be talking about a change in mass of the order of only 0.000 000 001 g according to my calculations for another posting.

Read 'How much damage can eight neutrons do? Scientific literacy and desk accessories in science fiction.'

The annihilation of the electron and positron is no different: there may be reconfigurations in the arrangement of mass and energy in the universe, but mass (and so energy) is conserved.

So, the question is, if the electron and positron, both massive particles (in the physics sense, that they have some mass) are annihilated, then where does their mass go if it is conserved? The answer is reflected in Prof. Martin's statement that "the particular kind of energy you get when you annihilate an electron and a positron is a photon, a particle of light". The mass is carried away by the photon.

The mass of a massless particle?

This may seem odd to those who have learnt that, unlike the electron and positron, the photon is massless. Strictly the photon has no rest mass, whereas the electron and positron do have rest mass – that is, they have inertial mass even when judged by an observer at rest in relation to them.

So, the photon only has 'no mass' when it is observed to be stationary – which nicely brings us back to Einstein who noted that electromagnetic radiation such as light could never appear to be at rest compared to the observer, as its very nature as a progressive electromagnetic wave would cease if one could travel alongside it at the same velocity. This led Einstein to conclude that the speed of light in any given medium was invariant (always the same for any observer), leading to his theory of special relativity.

So, a photon (despite having no 'rest' mass) not only carries energy, but also the associated mass.

Although we might think in terms of two particles being converted to a certain amount of energy as Prof. Martin suggests, this is slightly distorted thinking: the particles are converted to a different particle which now 'has' the mass from both, and so will also 'have' the energy associated with that amount of mass.


Mass is conserved during the electron-positron annihilation

A slight complication is that the electron and position are in relative motion when they annihilate, so there is some kinetic energy involved as well as the energy associated with their rest masses. But this does not change the logic of the general scheme. Just as there is an energy associated with the particles' rest masses, there is a mass component associated with their kinetic energy.

The total mass-energy equivalence before the annihilation has to include both the particle rest masses and their kinetic energy. The mass-energy equivalence afterwards (being conserved in any process) also reflects this. The energy of the photon (and the frequency of the radiation) reflects both the particle masses and their kinetic energies at the moment of the annihilation. The mass (being perfectly correlated with energy) carried away by the photon also reflects both the particle masses and their kinetic energies.

How could 'In Our Time' have improved the presentation?

It is easy to be critical of people doing their best to simplify complex topics. Any teacher knows that well-planned explanations can fail to get across key ideas as one is always reliant on what the audience already understands and thinks. Learners interpret what they hear and read in terms of their current 'interpretive resources' and habits of thinking.

Read about constructivism

A physicist or physics student hearing the episode would likely interpret Prof. Martin's statement within a canonical conceptual framework. However, someone holding the 'misconception' that mass is converted to energy in nuclear processes would likely interpret "they would annihilate into energy" as fitting, and reinforcing, that alternative conception.

I think a key issue here is a slippage that apparently refers to energy being formed in the annihilation, rather than radiation: (i.e., Prof. Martin could have said "they would annihilate into [radiation]"). When the positron and electron 'become' a photon, matter is changed to radiation – but it is not changed to energy, as matter has mass, and (as mass and energy have an equivalence) the energy is already there in the system.


Energy is reconfigured, but is not formed, in the annihilation process.

So, this whole essay is simply suggesting that a change of one word – from energy to radiation – could potentially avoid the formation of, or the reinforcing of, the alternative conception that mass is changed into energy in processes studied in particle physics. As experienced science teachers will know, sometimes such small shifts can make a good deal of difference to how we are interpreted and, so, what comes to be understood.


Addenda:

Reply from Prof. Victoria Martin on twitter (@MamaPhysikerin), September 30:

"E2 = p2c2 + m2c4 is a better way to relate energy, mass and momentum. Works for both massive and massless states."

@MamaPhysikerin

Work cited:

Notes

1 In what is often called a closed system there is no mass entering or leaving the system. However, energy can transfer to, or from, the system from its surroundings. Classically it might be assumed that the mass of a closed system is constant as the amount of matter is fixed, but Einstein realised that if there is a net energy influx to, or outflow from, the system, than some mass would also be transferred – even though no matter enters or leaves.


2 Perhaps in a uniform gravitational field, not subject to to any frictional forces, with an inextensible string supporting the bob, and in thermal equilibrium with its environment.

A hundred percent conclusive science

Estimation and certainty in Maisie's galaxy


Keith S. Taber


An image from the James Webb Space Telescope
(released images are available at https://webbtelescope.org/resource-gallery/images)

NASA's James Webb Space Telescope is now operational, and offering new images of 'deep space'. This has led to claims of finding images of objects from further away in the Universe, and so from further back in time, than previously seen. This should support a lot of new scientific work and will surely lead to some very interesting findings. Indeed, it seems to have had an almost immediate impact.

Maisie's galaxy

One of these new images is of an object known as:

CEERSJ141946.35-525632.8

or less officially (but more memorably) as

Masie's galaxy.

A red smudge on one of the new images has been provisionally identified as evidence of a galaxy as it was less than 300 000 000 years after the conjectured 'big bang' event understood as the origin of the universe. The galaxy is so far away that its light has taken since then to reach us.

Three hundred million years seems a very long time in everyday terms, but it a small fraction of the current age of the universe, believed to be around fourteen billion years. 1

300 000 000 years

≪ 14 000 000 000 years

The age estimate is based on the colour of the object, reflecting its 'redshift':

"Scientists with the CEERS Collaboration have identified an object–dubbed Maisie's galaxy in honor of project head Steven Finkelstein's daughter–that may be one of the earliest galaxies ever observed. If its estimated redshift of 14 is confirmed with future observations, that would mean we're seeing it as it was just 290 million years after the Big Bang."

University of Texas at Austin, UT News, August 04, 2022

(CEERS is the Cosmic Evolution Early Release Science Survey.)

This finding is important in understanding the evolution of the universe – for example, observing the earliest galaxies puts a limit on how long the universe existed before star formation started. (Although the episode was called 'The first galaxies at the universe's dawn' Masie's galaxy is thought to contain heavier elements that were produced in even earlier stars.)

Uncertainty in science (and certainty in reporting science)

So, the claim is provisional. It is an estimate awaiting confirmation.

Strictly, science is concerned with provisional knowledge claims. This is not simply because scientists can make mistakes. All measurements are subject to limits in precision (measurement 'errors'). More fundamentally, all measurements depend on a theory of the instrumentation used, and theoretical knowledge is always open to being revisited on the basis of new ways of understanding.

We may not expect the theory behind the metre rule to change any time soon (although even there, our understanding shifted somewhat with Einstein's theories) but many scientific observations depend on highly complex apparatus, both for data collection and analysis. Despite this, science is often represented in the media, both by commentators and sometimes scientists themselves, as if it produced absolute certainty.

Read about science in public discourse and the media

Read about scientific certainty in the media

A rough estimate?

In the case of Maisie's galaxy, the theoretical apparatus seems to be somewhat more sophisticated than the analytical method used to provisionally age the object. This was explained by Associate Professor Steve Finkelstein when he was interviewed on the BBC's Science in Action episode 'The first galaxies at the universe's dawn'.


Masie's galaxy – it's quite red.
The first galaxies at the universe's dawn. An episode of 'Science in Action'

Professor Finkelstein explained:

"We can look deep into out past by taking these deep images, and we can find the sort of faintest red smudges and that tells us that they are extremely far away, and from exactly how red they are we can estimate that distance."

Associate Professor Steve Finkelstein

So, the figure of 290 000 000 years after the big bang is an estimate. Fair enough, but what 'caught my ear', so to speak, was the contrast between the acknowledged uncertainty of the current estimate, and the claimed possibility of moving from this to absolute knowledge,

"If this distance we have measured for Masie's galaxy, of a red shift of 14, holds true, and I can't stress enough that we need spectroscopic confirmation to precisely measure that distance. [*] Where you take a telescope, could be James Webb, could be a different telescope, you observe it [the galaxy] and you split the light into its component colours, and you can actually precisely measure – measure the red shift, measure the distance – a hundred percent conclusively."

Associate Professor Steve Finke
[* To my ear, there might well be an edit at this point – the quote is based on what was broadcast which might omit or re-sequence parts of the interview.]

Spectroscopic analysis allows us to compare the pattern of redshifted spectral lines due to the presence of elements absorbing or emitting radiation, with the position of those lines as they are found without any shift. Each element has its own pattern of lines – providing a metaphorical fingerprint. A redshift (or blueshift) moves these lines to different parts of the spectrum, but does not change their collective profile as all the lines are moved to the same extent.


Spectral lines can be used like fingerprints to identify substances.
(Image by No-longer-here from Pixabay)

Some of these lines are fine, allowing precise measurements of wavenumber/frequency, and there are enough of them to be able to make very confident assignments of the 'fingerprints', and use this to estimate the shift. We might extend our analogy to a fingerprint on a rubber balloon which had been stretched since a fingerprint was made. In absolute terms, the print would no longer (or 'no wider' for that matter) fit the finger that made it, but the distortion is systematic allowing a match to be made – and the degree of stretching to be calculated.


If a pattern is distorted in a systematic way, we may still be able to match it to an undistorted version
(Original images by Clker-Free-Vector-Images (balloon), OpenClipart-Vectors (print) and Alexander (notepad) from Pixabay)

Yet, even though this is a method that is considered well-understood, reliable, and potentially very accurate and precise 2, I am not sure you can "precisely measure, measure the redshift, measure the distance. A hundred percent conclusively". Science, at least as I understand it, always has to maintain some small level of humility.

Scientists may be able to confirm and hone the estimate of 290 000 000 years after the big bang for the age of Maisie's galaxy. Over time, further observations, new measurements, refinement in technique, or even theory, may lead to successive improvements in that age measurement and both greater accuracy and greater precision.2 But any claim of a conclusive measurement to a precision of 100% has a finality that sounds like something other than science to me.


Notes

1 Oddly, most webages I've seen that cite values for the age of the universe do not make it explicit whether these are American (109) or English (1012) billions! It seems to be assumed that, as with sulfur [i.e., sulphur], and perhaps soon aluminum and fosforus, we are all using American conventions.


2 Precision and accuracy are different. Consider an ammeter.


An ammeter (Image by Gerd Altmann from Pixabay)

Due to the method of reading a needle position against a scale there is a limit to precision (perhaps assumed to the nearest calibration, so to ±0.5 calibrations). This measurement error of ±0.5 units is, in effect, a limit in detail or resolution, but not an 'error' in the everyday sense of getting something wrong. However, if the meter had been miscalibrated, or over time has shifted from calibration, so the needle is misaligned (so perhaps the meter reads +0.15 A when it is not connected into a circuit) then that is inaccuracy. There is always some level of imprecision (some limit on how precise we can be), even when we have an accurate reading.


In science, a measurement normally offers a best estimate of a true value, with an error range acknowledging how far the real value might be from that best estimate. See the example below: Measurement B claims the most precision, but is actually inaccurate. Measurement A is the most accurate (but least precise).

If we imagine that a galaxy was being seen as it was

275 000 000 years after the big bang

and three measurements of its age were given as:

A: 280 000 000 ± 30 000 000 years after the big bang

(i.e., 250 000 000 – 310 000 000)

B: 290 000 000 ± 10 000 000 years after the big bang

(i.e., 280 000 000 – 300 000 000)

C: 260 000 000 ± 20 000 000 years after the big bang

(i.e., 240 000 000 – 280 000 000)

then measurement B is more precise (it narrows down the possible range the most) but is inaccurate (as the actual age falls outside the range of this measurement). Of course, unlike in such a hypothetical example, in a real case we would not know the actual age to allow us to decide which of the measurements is more accurate.


A corny teaching analogy

Pop goes the comparison


Keith S. Taber


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


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

Teaching analogies

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

Read about analogies in science


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

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

Richard Gill describes how

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

Gill, 2022

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



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

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

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

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

Gill, 2022

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

Modelling the popcorn decay curve

The Australian Earth Science Education blog suggests

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

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

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

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

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

Feedback cycles

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

This pattern is characteristic of simple systems where

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

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

So,

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

and so forth.


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

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

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

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

Read about the classroom activity

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


A negative feedback cycle

Mapping the analogy

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


Mapping an analogy between making pop-corn and radioactive decay

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


Most analogies only map to a limited extent

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

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

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

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

Read about scaffolding learning

However, it is important to be careful to make sure

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

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

…unstable atoms/nuclei need to become stable…

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

Anthropomorphism

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

Read about anthropomorphism

The 'negative' analogy

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

Where does the energy come from?

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

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

When is random, random?

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

Read 'Nothing random about a proper scientific evaluation?'

Read about the randomisation criterion

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

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

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

On the recoil

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

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

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

Will this be on the exam?

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

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

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

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

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

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

Classes of radioactivity

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

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

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

Another corny analogy

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

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

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

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

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

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


Sources:

Notes

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

Read about metaphors in science


2 Here are some examples I found:

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

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

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

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

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

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

Lydia: Random?

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

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

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

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


3 Here are some examples I found:

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

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

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

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

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

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

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

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

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

Read off the graph, not the data table."

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


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


Climate change – either it is certain OR it is science

Is there a place for absolute certainty in science communication?

Keith S. Taber

I just got around to listening to the podcast of the 10th October episode of Science in Action. This was an episode entitled 'Youngest rock samples from the moon' which led with a story about rock samples collected on the moon and brought to earth by a Chinese mission (Chang'e-5). However, what caused me to, metaphorically at least, prick up my ears was a reference to "absolute certainty".

Now the tag line for Science in Action is "The BBC brings you all the week's science news". I think that phrase reveals something important about science journalism – it may be about science, but it is journalism, not science.

That is not meant as some kind of insult. But science in the media is not intended as science communication between scientists (they have journals and conferences and so forth), but science communicated to the public – which means it has to be represented in a form suitable for a general, non-specialist audience.

Read about science in public discourse and the media

Scientific and journalistic language games

For, surely, "all the week's science news" cannot be covered in one half-hour broadcast/podcast. 1

My point is that "The BBC brings you all the week's science news" is not intended to be understood and treated as a scientific claim, but as something rathere different. As Wittgenstein (1953/2009) famously pointed out, language has to be understood in specific contexts, and there are different 'language games'. So, in the genre of the scientific report there are particular standards and norms that apply to the claims made. Occasionally these norms are deliberately broken – perhaps a claim is made that is supported by fabricated evidence, or for which there is no supporting evidence – but this would be judged as malpractice, academic misconduct or at least incompetence. It is not within the rules of that game

However, the BBC's claim is part of a different 'language game' – no one is going to be accused of professional misconduct because, objectively, Science in Action does not brings a listener all the week's science news. The statement is not intended to be understood as an objective knowledge claim, but more a kind of motto or slogan; it is not to be considered 'false' because it not objectively correct. Rather, it is to be understood in a fuzzy, vague, impressionistic way.

To ask whether "The BBC brings you all the week's science news" through Science in Action is a true or false claim would be a kind of category error. The same kind of category error that occurs if we ask whether or not a scientist believes in the ideal gas law, the periodic table or models of climate change.

Who invented gravity?

This then raises the question of how we understand what professional academic scientists say on a science news programme that is part of the broadcast media in conversation with professional journalists. Are they, as scientists, engaged in 'science speak', or are they as guests on a news show engaged in 'media speak'?

What provoked this thought with was comments by Dr Fredi Otto who appeared on the programme "to discuss the 2021 Nobel Prizes for Science". In particular, I was struck by two specific comments. The second was:

"…you can't believe in climate change or not, that would just be, you believe in gravity, or not…"

Dr Friederike Otto speaking on Science in Action

Which I took to mean that gravity is so much part of our everyday experience that it is taken-for-granted, and it would be bizarre to have a debate on whether it exists. There are phenomena we all experience all the time that we explain in terms of gravity, and although there may be scope for debate about gravity's nature or its mode of action or even its universality, there is little sense in denying gravity. 2

Newton's notion of gravity predominated for a couple of centuries, but when Einstein proposed a completely different understanding, this did not in any sense undermine the common ('life-world' 2) experience labelled as gravity – what happens when we trip over, or drop something, or the tiring experience of climbing too many steps. And, of course, the common misconception that Newton somehow 'discovered' gravity is completely ahistorical as people had been dropping things and tripping over and noticing that fruit falls from trees for a very long time before Newton posited that the moon was in freefall around the earth in a way analogous to a falling apple!

Believing in gravity

Even if, in scientific terms, believing in a Newtonian conceptualisation of gravity as a force acting at a distance would be to believe something that was no longer considered the best scientific account (in a sense the 'force' of gravity becomes a kind of epiphenomenon in a relativistic account of gravity); in everyday day terms, believing in the phenomenon of gravity (as a way of describing a common pattern in experience of being in the world) is just plain common sense.

Dr Otto seemed to be suggesting that just as gravity is a phenomenon that we all take for granted (regardless of how it is operationalised or explained scientifically), so should climate change be. That might be something of a stretch as the phenomena we associate with gravity (e.g., dense objects falling when dropped, ending up on the floor when we fall) are more uniform than those associated with climate change – which is of course why one tends to come across more climate change deniers than gravity deniers. To the best of my knowledge, not even Donald Trump has claimed there is no gravity.

But the first comment that gave me pause for thought was:

"…we now can attribute, with absolute certainty, the increase in global mean temperature to the increase in greenhouse gases because our burning of fossil fuels…"

Dr Friederike Otto speaking on Science in Action
Dr Fredi Otto has a profile page at the The Environmental Change Unit,
University of Oxford

Absolute certainty?

That did not seem to me like a scientific statement – more like the kind of commitment associated with belief in a religious doctrine. Science produces conjectural, theoretical knowledge, but not absolute knowledge?

Surely, absolute certainty is limited to deductive logic, where proofs are possible (as in mathematics, where conclusions can be shown to inevitably follow from statements taken as axioms – as long as one accepts the axioms, then the conclusions must follow). Science deals with evidence, but not proof, and is always open to being revisited in the light of new evidence or new ways of thinking about things.

Read about the nature of scientific knowledge

Science is not about belief

For example, at one time many scientists would have said that the presence of an ether 3 was beyond question (as for example waves of light travelled from the sun to earth, and waves motion requires a medium). Its scientific characterisation -e.g., the precise nature of the ether, its motion relative to the earth – were open to investigation, but its existence seemed pretty secure.

It seemed inconceivable to many that the ether might not exist. We might say it was beyond reasonable doubt. 4 But now the ether has gone the way of caloric and phlogiston and N-rays and cold fusion and the four humours… It may have once been beyond reasonable doubt to some (given the state of the evidence and the available theoretical perspectives), but it can never have been 'absolutely certain'.

To suggest something is certain may open us to look foolish later: as when Wittgenstein himself suggested that we could be certain that "our whole system of physics forbids us to believe" that people could go to the moon.

Science is the best!

Science is the most reliable and trustworthy approach to understanding the natural world, but a large part of that strength comes from it never completely closing a case for good – from never suggesting to have provided absolute certainty. Science can be self-correcting because no scientific idea is 'beyond question'. That is not to say that we abandon, say, conversation of energy at the suggestion of the first eccentric thinker with designs for a perpetual motion machine – but in principle even the principle of conservation of energy should not be considered as absolutely certain. That would be religious faith, not scientific judgement.

So, we should not believe. It should not be considered absolutely certain that "the increase in global mean temperature [is due to] the increase in greenhouse gases because [of] our burning of fossil fuels", as that suggests we should believe it as a doctrine or dogma, rather than believe that the case is strong enough to make acting accordingly sensible. That is, if science is always provisional, technically open to review, then we can never wait for absolute certainty before we act, especially when something seems beyond reasonable doubt.

You should not believe scientific ideas

The point is that certainty and belief are not really the right concepts in science, and we should avoid them in teaching science:

"In brief, the argument to be made is that science education should aim for understanding of scientific ideas, but not for belief in those ideas. To be clear, the argument is not just that science education should not intend to bring about belief in scientific ideas, but rather that good science teaching discourages belief in the scientific ideas being taught."

Taber, 2017: 82

To be clear – to say that we do not want learners to believe in scientific ideas is NOT to say we want them to disbelieve them! Rather, belief/disbelief should be orthogonal to the focus on understanding ideas and their evidence base.

I suggested above that to ask whether "The BBC brings you all the week's science news" through Science in Action is a true or false claim would be a kind of category error. I would suggest it is a category error in the same sense as asking whether or not people should believe in the ideal gas law, the periodic table, or models of climate change.

"If science is not about belief, then having learners come out of science lessons believing in evolution, or for that matter believing that magnetic field lines are more concentrated near the poles of a magnet, or believing that energy is always conserved, or believing that acidic solutions contain solvated hydrogen ions,[5] misses the point. Science education should help students understand scientific ideas, and appreciate why these ideas are found useful, and something of their status (for example when they have a limited range of application). Once students can understand the scientific ideas then they become available as possible ways of thinking about the world, and perhaps as notions under current consideration as useful (but not final) accounts of how the world is."

Taber, 2017: 90

But how do scientists cross the borders from science to science communication?

Of course many scientists who have studied the topic are very convinced that climate change is occurring and that anthropogenic inputs into the atmosphere are a major or the major cause. In an everyday sense, they believe this (and as they have persuaded me, so do I). But in a strictly logical sense they cannot be absolutely certain. And they can never be absolutely certain. And therefore we need to act now, and not wait for certainty.

I do not know if Dr Otto would refer to 'absolute certainty' in a scientific context such as a research paper of a conference presentation. But a radio programme for a general audience – all ages, all levels of technical background, all degrees of sophistication in appreciating the nature of science – is not a professional scientific context, so perhaps a different language game applies. Perhaps scientists have to translate their message into a different kind of discourse to get their ideas across to the wider public?

The double bind

My reaction to Dr Otto's comments derived from a concern with public understanding of the nature of science. Too often learners think scientific models and theories are meant to be realistic absolute descriptions of nature. Too often they think science readily refutes false ideas and proves the true ones. Scientists talking in public about belief and absolute certainty can reinforce these misconceptions.

On the other hand, there is probably nothing more important that science can achieve today than persuade people to act to limit climate change before we might bring about shifts that are (for humanity if not for the planet) devastating. If most people think that science is about producing absolute certain knowledge, then any suggestion that there is uncertainty over whether human activity is causing climate change is likely to offer the deniers grist, and encourage a dangerous 'well let's wait till we know for sure' posture. Even when it is too late and the damage has been done, if there are any scientists left alive, they still will not know absolutely certainly what caused the changes.

"…Lord, here comes the flood
We'll say goodbye to flesh and blood
If again the seas are silent
In any still alive
It'll be those who gave their island to survive
…"

(Peter Gabriel performing on the Kate Bush TV special, 1979: BBC Birmingham)

So, perhaps climate scientists are in a double bind – they can represent the nature of science authentically, and have their scientific claims misunderstood; or they can do what they can to get across the critical significance of their science, but in doing so reinforce misconceptions of the nature of scientific knowledge.

Coda

I started drafting this yesterday: Thursday. By coincidence, this morning, I heard an excellent example of how a heavyweight broadcast journalist tried to downplay a scientific claim because it was couched as not being absolutely certain!

Works cited:

Notes

1 An alternative almost tautological interpretation might be that the BBC decides what is 'science news', and it is what is included in Science in Action, might fit some critics complaints that the BBC can be a very arrogant and self-important organisation – if only because there are stories not covered in Science in Action that do get covered in the BBC's other programmes such as BBC Inside Science.

2 This might be seen as equivalent to saying that the life-world claim that gravity (as is commonly understood and experienced) exists is taken-for-granted Schutz & Luckmann, 1973). A scientific claim would be different as gravity would need to be operationally defined in terms that were considered objective, rather that just assuming that everyone in the same language community shares a meaning for 'gravity'.

3 The 'luminiferous' aether or ether. The ether was the name given to the fifth element in the classical system where sublunary matter was composed of four elements (earth, water, air, fire) and the perfect heavens from a fifth.

(Film  director Luc Besson's sci-fi/fantasy movie 'The Fifth Element' {1997, Gaumont Film Company} borrows from this idea very loosely: Milla Jovovich was cast in the title role as a perfect being who is brought to earth to be reunited with the other four elements in order to save the world.)

4 Arguably the difference between forming an opinion on which to base everyday action (everyday as in whether to wear a rain coat, or to have marmalade on breakfast toast, not as in whether to close down the global fossil fuel industry), and proposing formal research conclusions can be compared to the difference between civil legal proceedings (decided on the balance of probabilities – what seems most likely given the available evidence) and criminal proceedings – where a conviction is supposed to depend upon guilt being judged beyond reasonable doubt given the available evidence (Taber, 2013).

Read about writing-up research

5 Whether acids do contain hydrated hydrogen ions may seem something that can reasonably be determined, at least beyond reasonable doubt, by empirical investigation. But actually not, as what counts as an acid has changed over time as chemists have redefined the concept according to what seemed most useful. (Taber, 2019, Chapter 6: Conceptualising acids: Reimagining a class of substances).