Category: associating ideas

Balding black holes – a shaggy dog story

Resurrecting an analogy from a dead metaphor?

Keith S. Taber

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

I was intrigued by an analogy in a tweet

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

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

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

(Read about peer review)

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

(Read about research writing)

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

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

The news article told me

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

Conover, 2013

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

just as

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

so, too, do

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

(Read about making the unfamiliar familiar)

But hair?

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

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

(Read about science analogies)

Why talk of black holes having 'hair'?

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

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

Bransgrove, Ripperda & Philippov, 2021

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

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

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

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

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

Spoiler alert

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

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

As the news item explained matters:

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

Conover, 2013

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

Balding is to hair, as…

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

hair = magnetic field

balding = shedding the magnetic field

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

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

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

A dead metaphor?

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

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

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

(Read adbout science metaphors)

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

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

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

Work cited:

The nucleus is the brain of the cell

Keith S. Taber

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

…but is it the same as an atomic nucleus?

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

Do you think there are any links with Biology?

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

Ah, that's interesting, so

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

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

So what's the nucleus then?

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

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

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

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

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

(Read about 'Concepts')

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

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

(Read about 'metaphor in science')

…

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

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

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

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

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

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

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

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

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

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

Source cited:

How plants get their food to grow and make energy

Respiration produces energy, but photosynthesis produces glucose which produces energy

Keith S. Taber

Image by Frauke Riether from Pixabay 

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

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

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

So how do they make their energy, then?

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

How does the energy get in the glucose?

Erm, I don't know.

It's just there is it?

Yeah, it's just stored energy

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

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

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

So how do they do that then?

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

What does it do once it absorbs the light?

Erm.

Does that mean it shines brightly?

No, I , erm – I don't know

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

Do you make your food?

Not the way plants do.

…

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

It's stored energy.

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

Erm.

[c. 2s pause]

I don't know.

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

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

Erm, pasta.

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

Has lots of carbohydrates, which is energy.

…

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

Yeah.

Stored energy.

Yeah.

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

(laughs) I don't know.

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

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

Yeah.

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

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

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

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

No.

No, how do you get your energy then?

We respire.

Is that different then?

Yeah.

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

We use oxygen to, and glucose to release energy.

Do plants respire?

Yes.

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

No, you are respiring all the time.

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

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

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

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

Yeah.

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

Yeah, in respiration, they produce energy.

What about in photosynthesis, does that produce energy?

That produces glucose, which produces the energy.

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

Yeah.

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

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

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