Umar was a participant in the Understanding Chemical Bonding project. When I spoke to him in the first term of his course he was unsure whether tetrachloromethane (CCl4) would have ionic or covalent bonding.
When I spoke to him near the start of his second term, I asked him again about this. Umar then thought this compound would have polar bonding, however he seemed to have difficulty explaining what this meant ⚗︎ . Given his apparently confused notion about the C-Cl bond I decided to turn the conversation to a covalent bond which I knew, well certainly believed, was more familiar to him.
Is it possible for chlorine to form a bond with another chlorine?
[Pause, c.2s]
Yeah.
What substance would you get if two chlorine atoms formed a bond?
[Pause, c.2s]
You get, it still, you get, if you had like two chlorines it depends what groups are attached to it, to see how electronegative or electropositive they are.
What about if you just had two chlorine atoms joined together and nothing else, is that possible?
[Pause, c.3s]
No.
No?
On their own.
Not on their own?
No.
Umar's response here rather surprised me, as I was pretty confident that Umar had met chlorine as an element, and would know it was comprised of diatomic molecules: Cl2.
So you couldn’t have sort of Cl2, a molecule of Cl2?
[Pause, c.1s]
Yeah, you could do.
Could you?
[Pause, c.2s]
They might be just, they might be like, be covalently bonded.
Perhaps the earlier context of talking about polar bonds and the trichloroethane molecule somehow acted as a kind of impediment to Umar remembering about the chlorine molecule. It seemed that my explicit reference to the formula, Cl2, (eventually) activated his knowledge of the molecule bringing to mind something he had forgotten. Although he suggested the bond was (actually "might be") covalent, this seemed less something that he confidently recalled, than something he was inferring from what he could remember – or perhaps even guessing at what seemed reasonable: "they might be just, they might be like, be covalently bonded".
As often happens in talking to learners in depth about their ideas it becomes clear that thinking of students 'knowing' or 'not knowing' particular things is a fairly inadequate way of conceptualising their cognition, which is often nuanced and context-dependent. This suggests that what students respond in written tests should be considered only as what they were triggered to write on that day in response to those particular questions, and may not fully reflect their knowledge and understanding of science topics. Other slightly different questions may well have cued the elicitation of different knowledge. Now Umar had recalled that chlorine comprises of covalent molecules, I asked him about the nature of the bond:
So what would that be, covalently bonded?
They share the electrons.
So how many electrons would they have then?
They’ll have
[Pause, c.7s – n.b., quite a long pause]
like the one on it, the one of the chlorines shares electrons with the other chlorine to fill in its shell on the other one, and the same does it with the other.
In thinking about covalent bonding, Umar (in common with many students) drew upon the full shells explanatory principle that considered bonding to be driven by the needs of atoms to 'fill' their outer electron shells. (The outer shell of chlorine would only actually be 'full' with 18 electrons, but that complication is seldom recognised, as octets and full shells are usually considered synonymous by students).
So how many electrons does each chlorine have to start with?
In the outer shell, seven.
And how many have they got after this?
They’ve got seven, but they share one.
[Pause, c.1s]
Maybe.
So that’s a covalent bond, is it?
Yeah.
So how many electrons are involved in a covalent bond?
[Pause, c.3s]
Erm,
[Pause, c.3s]
Two.
Two electrons.
So where do those two electrons come from?
They like, one that fills up the gap, fills up the – last electron needed in one of the chlorine shells, and the other chlorine shell fills it up in the other one.
So where do they come from?
Each chlorine. Outer shell.
One from each chlorine?
Yeah.
Okay, and that’d be a covalent bond?
Yeah.
Here, again, Umar is using the full shells explanatory principle as the basis for explaining the bond in terms of electrons 'filling up the gaps' in the electron shells, rather than considering how electrical interactions can hold the structure together. Umar's suggestion that the sharing of electrons "fills up the – last electron needed in one of the chlorine shells" demonstrates the anthropomorphic language (e.g., what an atom wants or needs) commonly used when learners have acquired aspects of the common octet rule framework that is developed from the full shells explanatory principle and used by many learners to explain bonding reactions, chemical reactions, patterns in ionisation energy, and chemical stability.
Annie was a participant in the Understanding Chemical Bonding project. She was interviewed near the start of her college 'A level' course (equivalent to Y12 of the English school system). Annie was shown, and asked about, a sequence of images representing atoms, molecules and other sub-microscopic structures of the kinds commonly used in chemistry teaching. She was shown a representation of part of a lattice in sodium chloride.
Focal figure (Fig. 5) presented to Annie
Any idea what that's meant to be?
(pause, c.6s)
Just sodium and chlorine atoms
That's sodium and chlorine atoms, erm would you say that there was any kind of bonding there?
Annie had already identified chemical bonding in representations of molecules of hydrogen , tetrachloromethane , and oxygen, so she was asked why she though there was no bonding in this example:
No bonding. Why do you say that? What is the difference between that and the ones we've seen before?
Well the other ones electrons were shown, and these no electrons are shown and they don't actually overlap or anything they just go in rows.
They go in rows. Okay. … but unlike (the images) we've seen previously they've had bonds in,
Yeah.
chemical bonds, whereas this, we don't have chemical bonds?
No.
So Annie did not interpret the representation of NaCl as portraying bonding. However, on further probing she did recognise that the structure could get held together by forces.
The canonical interpretation of the figure is that it is a slice through a three dimensions structure of ions, where the attractive forces between cations pull the ions into a bound structure (to the point where attraction and repulsions are in equilibrium), and that this kind of binding is called ionic bonding.
Annie did not see ions, but atoms. She thought there was no bonding because no overlap was shown. In chemistry a wide range of different types of representation are used to show structures at the submicroscopic level – bonds may sometimes be shown by lines or sometimes by overlap or (in the case of ionic structures) neither. This is a potential source of confusion for learners who may not appreciate why different conventions may be used to represent different, or even the same, structures.
Does our whole system of physics forbid us from believing someone has been on the moon?
Keith S. Taber
Image by WikiImages from Pixabay (with Emoji superimposed)
I never had the chance to interview Ludwig for my research, but was intrigued when I found out about his outright dismissal of the possibility of manned missions to the moon.
There are of course people who are strongly committed to ideas at odds with current scientific consensus – suggesting the earth is flat; that evolution does not occur; that COVID-19 was deliberately produced in a laboratory; that governments have physical evidence of alien visitors, but deny it and keep all relevant documentation classified; and so forth.
Moon landing deniers
Even in the United States of America, the home of the Apollo missions, surveys regularly show that a substantial minority of people doubt that people ever actually went to the moon, and think the Apollo moon landings were faked. Why would NASA have gone to such trouble with the collusion of the US Government machinery and the support of Hollywood studios?
As President Kennedy had put such weight on (American) people getting to the moon before the end of the 1960s, then – the argument goes – once it became clear this was technically impossible, it became important to convince the population that JFK's challenge had been met by a massive initiative to forge and disseminate evidence. There has been something of an industry in explaining how the photographs released by NASA can be seen to have been clearly faked if one looks carefully enough and knows a little science.
Unreasonable doubt?
I try to be someone who is always somewhat sceptical (as any scientist should be) of any claims, no matter how widely believed, as in time some canonical ideas are found to be flawed – even in science. But I tend to give little credence to such conspiracy theories.
Sometimes there are good reasons why science is doubted by sections of the public when it seems to conflict with well established world-view beliefs deriving from religious traditions or traditional ecological knowledge which has sustained a culture for a great many generations. So, even when the science is well supported, we can sometimes understand why some people find it difficult to accept. But the Apollo missions being faked in a film studio: surely that is just the kind of nonsense that only ignorant cranks like to believe – isn't it?
Ludwig on the sure belief that no one has been to the moon
Thus my interest in Ludwig, who was certainly not an ignorant person. Indeed he was highly intelligent, and something of an intellectual – a deep thinker who was very interested in the nature of knowledge and considered issues of how we could ground our beliefs, given that the evidence was never sufficient to be absolutely sure.
He thought that individual ideas were convincing when they were embedded in a 'nest' of related ideas – what we might call a conceptual framework. One example he discussed was his accepting that people always had parents: he thought this "sure belief" was based "not only on the fact that I have known the parents of certain people but on everything that I have learnt about the sexual life of human beings and their anatomy and physiology: also on what I have heard and seen of animals". Ludwig thought that although this could not be considered definite proof, it was robust grounds for someone to accept the belief.
Another example of such a sure belief was that a person could be confident that they had never been on the moon,
A principal ground for [a person] to assume that he was never on the moon is that no one ever was on the moon or could come [i.e., get] there; and this we believe on grounds of what we learn.
¶171
Physics forbids moon landings
Ludwig seemed to consider the impossibility of people getting to be on the moon was something he could be pretty sure of,
"But is there no objective truth? Isn't it true, or false, that someone has been on the moon?" If we are thinking within our system, then it is certain that no one has ever been on the moon. Not merely is nothing of the sort ever seriously reported to us by reasonable people, but our whole system of physics forbids us to believe it. For this demands answers to the questions "How did he overcome the force of gravity?" "How could he live without an atmosphere?" and a thousand others which could not be answered…
The intellectual status of unreasonable people
So someone making such a claim would not be a 'reasonable' person in Ludwig's evaluation. So how would Ludwig feel about such an unreasonable person?
We should feel ourselves intellectually very distant from someone who said this.
¶108
But of course there are people who claim this has indeed happened, that we have been to the moon,and walked there and whilst there collected rocks and indeed played golf. (Had this been more recent, we would perhaps instead have danced the tango and baked cakes.) NASA astronauts have since often acted as ambassadors for space science, and told their stories across the world, including to the young – enthusing many of them about space and science.
How might Ludwig respond to a child who had met one of those Apollo astronauts who claimed to have walked on the moon?
Suppose some adult had told a child that he had been on the moon. The child tells me the story, and I say it was only a joke, the man hadn't been on the moon, no one has ever been on the moon, the moon is a long way off and it is impossible to climb up there or fly there.
Ludwig adds, rhetorically,
If now the child insists, saying perhaps there is a way of getting there which I don't know, etc. what reply could I make to him?
¶106
Believers in moon landings are ignorant and wrong
So how could Ludwig explain that there are many people, indeed a majority today, who do believe that people have visited the moon, and returned to earth to tell others about the experience?
What we believe depends on what we learn. We all believe that it isn't possible to get to the moon; but there might be people who believe that that is possible and that it sometimes happens. We say: these people do not know a lot that we know. And, let them be never so sure of their belief-they are wrong and we know it.
If we compare our system of knowledge with theirs then theirs is evidently the poorer one by far.
¶286
So, just as I might suspect the moonshot deniers are somewhat ignorant, for Ludwig it is the reverse: it is those who think people can get to the moon who have poor knowledge systems and are simply wrong.
Now I suggested above that Ludwig was an intelligent and reflective person – indeed he worked as a school teacher, both in primary and secondary education – so his views may seem incongruent. As some readers may have suspected, I am being a little unfair to Ludwig. I pointed out at the outset that I never had the chance to interview Ludwig – indeed I never met him, although he did spend part of his life in Cambridge where I now work.
We can all be wrong
Ludwig did not live to see the moon landings, as he died in 1951 almost a decade before I was born (of parents – he was right about that), shortly after he wrote the material that I have quoted above. That is a few years before Sputnik was launched by the Soviet Union and the 'space race' began. So, Ludwig was not a denier of the moon landings as such, refusing to accept the media accounts, but rather a denier of the possibility of there ever being moon landings at a time when no one was yet actively planning the feat.
Ludwig was wrong. But had he lived another 20 years I am pretty sure he would have changed his mind. That's because one of the things he was best known for was changing his mind.
Having written a highly influential book of philosophy that convinced many intellectuals he was one of the greatest thinkers of his time, if not all time (the Tractatus Logico-Philosophicus) he took a long sabbatical from Academia, only to later write an equally influential and profound book (that he did not live to see published – the Philosophical Investigations) that contradicted his earlier ideas. Had Ludwig seen the technological developments of the 'space race' in the 1960s, it seems certain – well, a sure belief – that he would have accepted the possibility of people going to the moon.
However, when I first read the comments I quote above I was struck by how such a highly intelligent and deep thinker could be so sure that getting people to the moon was not possible that he actually chose to use the idea of people on the moon as an exemplar of something that was impossible ("it is certain that no one has ever been on the moon"), and indeed contrary to the laws of physics.
Presumably at the time he was writing he could assume most intelligent people would fully accept his position (as "we all believe that it isn't possible to get to the moon") and see the suggestion of people going to the moon as absurd enough to stand as an example of an idea that could not be accepted by us reasonable people, only by someone "intellectually very distant" from us.
However, barely a decade later JFK was convinced enough of the possibility of getting people safely to the moon and back to commit his nation to achieving it – and a decade after that men being on the moon was already ceasing to be seen as anything out of the ordinary (until the near disaster of the Apollo 13 mission got the flights back into the popular imagination).
I do not present this example to ridicule Ludwig Wittgenstein. Far from it. But it does make me reflect on those things that we think we can treat as 'sure beliefs'. Even the most intelligent and reflective of us can be very wrong about things we may treat as certain knowledge. That's always worth keeping in mind.
Nothing is absolutely certain, except, perhaps, uncertainty itself!
All citations are from ¶ in Wittgenstein, L. (1975). On Certainty (D. Paul & G. E. M. Anscombe, Trans. G. E. M. Anscombe & G. H. v. Wright Eds. Corrected 1st ed.). Malden, Massachusetts: Blackwell Publishing.
Amy was a participant in the Understanding Science Project. The first time I talked to Amy, near the start of her GCSE 'triple science' course in Y10 she told me that "in normal chemistry (i.e., the chemistry part of 'double science', as opposed to the optional additional chemistry lesson as part of 'triple science' that Amy also attended) we're doing about ionic bonding" which was "atoms which have either lost or gained electrons so they are either positively or negatively charged" and
"how the outer electron's transferred…to complete the outer shell of the erm chlorine, thing, ion…and the sodium atom loses erm, one electron is it, yeah one electron, erm, which the chlorine atom gains, and that yeah that completes its outer shell and makes the sodium positively charged and the chlorine negatively charged".
Amy told me that "in ionic bonding it's the electrons that are transferred, I think."
So Amy had acquired a common alternative conception, i.e. that ionic bonding involved electron transfer, and that this occurs to atoms to complete their electron shells.
Ionic bonding refers to the forces between ions that hold the structure of an ionic substance together, rather than a mechanism by which such ions might hypothetically be formed – yet often learners come away form learning about ionic bonding identifying it with a process of electron transfer between atoms instead of interactions between ions which can be used to explain the properties of ionic substances.
Moreover, the hypothetical electron transfer is a fiction. In the case of NaCl such an electron transfer between isolated Na and Cl atoms would be energetically unfavourable, even if reactants containing discrete atoms were available (which is unrealistic).
Whether students are taught that ionic bonding is electron transfer is a moot point, but often introductory teaching of the topic focuses not on the nature of the bonding, but on presenting a (flawed) teaching model of how the ions in the ionic structure could form by electron transfer between atoms. As this mechanism is non-viable, and so not an authentic scientific account, it may seem odd that teachers commonly offer it.
One explanation may simply be custom or tradition has made this an insidious alternative conception. Science teachers and textbooks have 'always' offered the image of electron transfer as representing ionic bonding. So, this is what new teachers had themselves been taught at school, is what they often see in textbooks, and so what they learn to teach.
Another possible explanation is in terms of what what is known as the atomic ontology. This is the idea that the starting pint for thinking about chemistry at the submicroscopic level is atoms. Atoms do not need to be explained (as if in nature matter always starts as atoms – which is not the case) and other entities such as ions and molecules do need to be explained in terms of atoms. So, the atomic ontology is a kind of misleading alternative conceptual framework for thinking about chemistry at the submicroscopic level.
Lovesh was a participant in the Understanding Chemical Bonding Project, studying 'A level' chemistry in a further education college. He was interviewed in his second year of the two year A level course, and was presented with focal figure 1 (below). He recognised figure 1 as showing a "sodium, atom", and was asked about its stability:
Is that a stable species, do you think?
Erm (pause, c.3s) No, because it hasn't got a, a full outer – electron shell, outer electron shell hasn't got eight electrons in.
Lovesh shared the common notion that an atom without a full outer shell / octet of electrons would be unstable compared with the corresponding ion with a full outer shell / octet of electrons. When comparing isolated atoms with the corresponding ions this is seldom the case, yet this is a common alternative conception about chemical stability. A sodium ion can be considered stable in an ionic lattice, or when hydrated in solution, but does not spontaneously ionise as the outer shell electron is attracted to the atom's positive core. Ionisation only occurs when sufficient work is done to overcome this attraction.
Lovesh was demonstrating the common full shells explanatory principle alternative conception which is central to the common octet rule framework – an alternative conceptual framework reflecting very common 'misconceptions' found among learners studying chemistry.
Lovesh was asked what would happen to the atom that he considered unstable:
So if it's not stable, what would tend to happen to that, do you think?
It will wanna donate the electron to another atom.
Right, when you say 'it wants to donate' it?
Erm. (pause, c.3s) Well because that outer electron is less attracted to the nucleus, erm it is, it can easily be transferred, attracted by another atom.
Lovesh's first response here used the term 'wanna' (want to) which if take literally suggests the atom has desires and preferences. This is an example of anthropomorphism, imbuing objects with human-like traits. Using anthropomorphic explanations is a common feature of the octet rule framework which often leads to students talking as if atoms deliberately act to get full outer electron shells.
It has been suggested that such anthropomorphism may be either 'strong'- where the learner is offering an explanation they find convincing – or 'weak' if they are using language metaphorically, just as a figure of speech.
In this case, when Lovesh's use of the notion of 'wants' was queried he was able to shift to a different language register in terms of the action of physics forces – the electron being attracted elsewhere. Lovesh had clearly acquired an appropriate way of thinking about the interactions between atoms, but his spontaneous explanation was couched in anthropomorphic terms. Although in this case the anthropomorphism was of a weak form, the habitual use of this kind of language may come to stand in place of offering a scientifically acceptable account.
