alternative conception - Science-Education-Research

Sleep can give us energy

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

Keith S. Taber

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

And earlier in the year, you were doing about dissolving sugar. Do you remember that?
Erm, yeah.
Do you think that's got anything to do with the human body?
Erm, we eat sugar.
Mm. True.
Gives us energy…It powers us.
Ah. And why do we need power do you think?
So we can move.

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

Ah what if you were a lazy person, say you were a very lazy rich person? And you were able to lie in bed all day, watch telly, whatever you like, didn't have to move, didn't have to budge an eyelid, … you're rich, your servants do everything for you? Would you till need energy?
Yes.
Why?
I dunno, 'cause being in bed's tired, tiring.
Is it?
When I'm ill, I stay off for a day, I just feel tired, and like at the end of the day, even more tired than I do when I come to school some times.

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

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

So maybe when you are ill, you should come to school, and then you would feel better?
No.
No, it doesn't work like that?
No.
Okay, so why do you think we get tired, when we are just lying, doing absolutely nothing?
Because, it's using a lot of our energy, doing something.
Hm, so even when we are lying at home ill, not doing anything, somehow we are using energy doing something, are we?
Yes.
What might that be, what might we use energy for?
Thinking.

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

Do you think it uses energy to think?
(Pause, c.3s)
Probably.
Why do you think that?
Well cause, like, when you haven't got any energy, you can't think, like the same as TV, when it hasn't got any energy, it can't work. So it's a bit like our brains, when we have not got enough energy we feel really tired, and we just want to go to sleep, which can give us more energy, a bit like food.

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

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

So sleeping can give us energy?
Yeah.
How does that work?
Er, it's like putting a battery onto charge, probably, you go to sleep, and then you don't have to do anything, for a little while, and you, then you wake up and you feel – less tired.
Okay so, you think you might need energy to think, because if you have not got any energy, you are very tired, you can't think very well, but somehow if you have a sleep, that might somehow bring the energy back?
Yeah.
So where does that energy come from?
(Pause c.2s)
Erm – dunno.

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

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

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

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

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

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

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

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

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

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

Sodium and chlorine don't actually overlap or anything

Keith S. Taber

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?
No.

Although the image included the standard '+' and '-' symbols to signify that ions were shown, Annie referred to "atoms". It transpired that Annie had an idiosyncratic understanding of what was meant by charge. (Read: Na+ has an extra electron in its outer shell and Cl- is minus an electron and K-plus represents a potassium atom that has an extra electron.)

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.

When Annie was asked if what was shown in the figure would would fall apart or hold together, Annie suggested that If you heated it, or reacted it in some way, it would hold together, and it would probably get held together by just forces. However, she did not consider that (i.e., even after reacting) amounted to chemical bonding. (Read: Sodium has one extra electron in its outer shell, and chlorine is minus an electron, so by force pulls they would hold together.)

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.

Some particles are softer than others

Keith S. Taber

Bill was a participant in the Understanding Science Project. Bill was a Year 7 student when he told me that previously, when he had been in primary school, "we did a lot about plants, and – inside them, how they produce their own food". As he had been talking to me about learning about particles (e.g. Gas particles try to spread out and move apart), I asked if there was any link between these two topics.

Okay. What about particles, we were just talking about particles, do you think that's got anything to do with particles?
Well in the plant, there is particles.
Are there?
'cause it's a solid.
Ah. So there'll be particles in that then?
Yeah.
Is it all solid, do you think?
Inside the stem is, 'cause going up the stem there would be water, so that's a liquid. And, it also uses oxygen, which is a gas, to make its food, so. I think so.
So it would be solids, liquids and gases?
Mm, I think some.
But they've all got some particle in them, they are all made up of particles.
Yeah.
Okay.

As Bill had talked to me earlier about there being particles in a gas when ice was melted, and then boiled, I wanted to see if he though the particles in different substances were the same:

Erm. Do you think that the particles in the – oxygen's a gas isn't it?
Yeah.
Do you think the particles in the oxygen gas, are the same as the particles in the steam that you said was a gas, in your experiment you did earlier?
Erm, I don't think so, no.
You think they'd be different sort of particles?
Yeah, they're different gases.
Okay. And in the solid part of the plant, do you think the particles that make up the solid part of the plant, are the same as the particles that make up this table, that's a solid?
Well, the particles, plants are soft, some plants are soft, and you, when you squeeze them they're, they feel soft and erm, but the table is hard so I think that the particles would be slightly different, but they would have, because they hold this different shape, and they would, they would be {pause} erm {pause} then they would, ob¬, then they would be softer as well.
So the softer, the plant which is softer, > > would have softer particles?
< Yeah. < I think so yeah
And the harder wood, made of harder particles?
I think so.

Here Bill offered evidence of a very common alternative conception about the particle theory. A key feature of particle theory is that chemists use particle models to explain the properties of substances macroscopically (what can be observed directly) in terms of the very different nature and properties of conjectured 'particles' (quanticles) at a submicroscopic level.

Yet after learning about these 'particles', students commonly 'explain' macroscopic properties of substances and materials by suggesting that the particles of which they are made up themselves have the property to be explained – being hard, sharp, colourless, conducting, etc.

Single bonds are different to covalent bonds

Single bonds are different to covalent bonds or ionic bonds

Keith S. Taber

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 commonl y used in chemistry teaching. She was shown a representation of the resonance between three canonical forms of BF3, sometimes used as away of reflection polar bonding. She had just seen another image representing resonance in the ethanoate ion, and had suggested that it contained a double bond. She had earlier in the interview referred to covalent bonding and ionic bonding, and after introducing the ideas of double bond, suggested that a double bond is different to a covalent bond.

What about diagram 14?…
Oh.
(pause, c.13s)
Seems to be different arrangements. Of the three, or two elements.
Uh hm.
(pause, c.3s)
Which are joined by single bonds.
What, where, what single, what sorry are joined by single bonds?
All the F to the B to the F. Are single bonds they are not double like before. [i.e., a figure discussed earlier in the interview]
So are they covalent bonds? Or ionic bonds, or? Or are single bonds something different again?
Single bonds are different.

This reflected her earlier comment to the effect that a double bond is different to a covalent bond, suggesting that she did not appreciate how covalent bonds are considered to be singular or multiple.

However, as I checked what she was telling me, Annie's account seemed to shift.

They're different to double bonds?
Yeah.
And are they different to covalent bonds?
No 'cause you probably get covalent bonds which are single bonds.

So single bonds, just moments before said to different to covalent bonds, were now 'probably' capable of being covalent. As she continued to answer questions, Annie decided these were 'probably' just alternative terms.

So covalent bonds and single bonds, is that another word for the same thing?
Yeah, probably. But they can probably occur in different, things like in organic you talk about single bonds more than you talk about covalent, and then like in inorganic you talk about covalent bond, more than you talk about single bonding or double bonding.
So you think that maybe inorganic things, like sort of, >> copper iodide or something like that, that would tend to be more concerned with covalent bonds?
< Yeah. < Yeah.
But if you were doing organic things like, I don't know, erm, ethane, >> that's more likely to have single bonds in.
< Yeah. < Yeah.
So single bonds are more likely to occur in carbon compounds.
Yeah.
And covalent bonds are more likely to occur in some other type of compound?
Yeah. Sort of you've got different terminology, like you could probably use single bonds to refer to something in inorganic, but when you are talking about the structures and that, it's easier to talk about single bonds and double bonds, rather than saying that's got a covalent bond or that's got an ionic bond.

Annie's explanation did not seem to be a fully thought-out position. It was not consistent with the way she had earlier reported there being five covalent bonds and one double bond in an ethanoate ion.

It seems likely that in the context of the research interview, where being asked directly about these points, Annie was forced to make explicit the reasons she tended to label particular bonds in specific ways. The interview questions may have acted like Socratic questioning, a kind of scaffolding, leading to new insights. Only in this context did she realise that the single and double bonds her organic chemistry lecturer talked about might actually be referring to the same entities as the covalent bonds her inorganic chemistry lecturer talked about.

It would probably not have occurred to Annie's lecturers (of which, I was one) that she would not realise that single and double bonds were covalent bonds. It may well have been that if she had been taught by the same lecturer in both areas, the tendency to refer to single and multiple bonds in organic compounds (where most bonds were primarily covalent) and to focus on the covalent-ionic dissension in inorganic compounds (where degree of polarity in bonds was a main theme of teaching) would still have lead to the same confusion. Later in the interview, Annie commented that:

if I use ionic or covalent I'm talking about, sort of like a general, bond, but if I use double or single bonds, that's mainly organic, because sort of it represents, sort of the sharing, 'cause like you draw all the molecules out more.

This might be considered an example of fragmentation learning impediment, where a student does not make a link that the teacher is likely to assume is obvious.

Plants mainly respire at night

Plants mainly respire at night because they are photosynthesising during the day

Keith S. Taber

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. She suggested that "respiration produces energy, but photosynthesis produces glucose which produces energy". (See 'How plants get their food to grow and make energy'). She told me that she respired to get energy.

How do you get your energy then?
We respire.
Is that different then [from photosynthesis]?
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.
… What about plants? Do they respire all the time?
They mainly do it at night.
Why's that?
'cause they're photosynthesising during the day, cause they need the light.

I was not clear why Mandy thought that plants should respire less when they were photosynthesising.

So why do you need to respire all the time?
'cause you're making energy and you need energy to do everything.
So are you respiring at the same rate all the time, do you think?
No.
So sometimes more than others?
Yeah.
So when might you need to respire more?
When you are doing exercise. Running around a lot.
So are there time when you do not need to respire as much?
Yeah.
So when might you not need to respire very much?
When you 're sleeping or just sitting watching tele [television].
…Do you have to respire at all during the night – you are not doing anything are you?
You need a little bit of energy.
What for?
Erm, I don't [indistinct], well I suppose it's just to keep everything, cause if you did not have energy then your heart would not beat, and you need it to keep breathing, and your heart pumping.

Mandy recognised the need for people to respire continuously, although she associated this with functioning at the organism level (breathing, blood circulation) and did not seem to be thinking about cellular level metabolism.

Why do plants need to respire? What do they use it, the energy for?
Erm, to grow, and to fix cells that are – broken.
Oh right, like repair damage?
Yeah.
So, do you think they are like us then, that they sort of sleep sometimes and don't need to respire as much, or?
Not as much, I don't know. I don't know.
Do you think a plant sleeps, a tree has a good sleep?
No.
So when do you think plants need to respire the most, or do you think they respire the same all the time?
They respire more at night, because – they do it then instead of in the day because they do photosynthesis during the day, but they still respire a little bit.
So is it difficult to try and do both at the same time?
Probably.
Or just maybe they are too busy photosynthesising to do much respiration?
Yeah, erm, I don't know.
Not sure?
No.

Mandy was not offering any specific reason why a plant should need to respire less at night (and did not seem to have previously thought about this), but simply seemed to assume that when the plant was photosynthesising a lot it would only respire "a little bit". This seemed to be an intuition rather than a considered proposition. It was almost as if she implicitly assumed that the plant would be fully occupied photosynthesising, and so would put respiration 'on the back burner'.

It seemed Mandy's understanding of the roles of photosynthesis and respiration at that point in her learning was limited by not fully seeing how energy was involved in the two processes (i.e., respiration produces energy, but photosynthesis produces glucose which produces energy), and because she was not considering the need for respiration to support ongoing basic cell functions.

How plants get their food to grow and make energy

Respiration produces energy, but photosynthesis produces glucose which produces energy

Keith S. Taber

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.

The moon is a long way off and it is impossible to get there

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.

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

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

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

Two alternative conceptions

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

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

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

Linking qualitative understanding of relating concepts and the mathematical formula

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

Okay. Let’s say we had, erm, two circuits, and they both have resistance and you wanted to get one amp of current to flow through the circuits, and you had a variable power supply.
Okay.
And the first circuit in order to get one (amp) of current to flow through the circuit.
Yes.
You have to adjust the power supply, until you had 10 volts.
Okay.
So it took 10 volts to get one amp to flow through the circuit. And the second (unclear) the circuit, when you got up to 10 volts, (there is) still a lot less than one amp flowing. You can turn it up to 25 volts, and only when it got to 25 volts did you get one amp to flow through the circuit.
Yes, okay.

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

Do you think those two circuits would have resistance?
Erm, (pause, three seconds) Probably yeah.

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

Same resistance?
No because they are not the same circuit, but – it would depend what components you had in your circuit, if you had different resistors in your circuit.
Yeah, I've got different resistors in these two circuits.
Then yes each would have a different resistance.
Can you tell me which one had the bigger resistance? Or can’t you tell me?
No, I can’t do that.
You can’t do it?
No I don’t think so. No.

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

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

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

Okay, let me, let me think of doing it a different way. For the same two circuits, erm, but you got one let's say for example it’s got 10 volts across it to get an amp to flow.
Yeah. So yes okay so the power supply is 10 volts.
Yeah. And the other one also set on 10 volts,
Okay.
but we don’t get an amp flow, we only get about point 4 [0.4] of an amp, something like that, to flow.
Yeah, yeah.
Any idea which has got the high resistance now?
The second would have the higher resistance.
Why do you say that?
Because less erm – There’s less current amps flowing around the circuit erm when you have the same voltage being put into each circuit.
Okay?
Yes.

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

You seem pretty sure about that, does that make sense to you?
Yes, it makes sense when you put it like that.
Right, but when I had it the other way, the same current through both, and one required 10 volts and one required 25 volts to get the same current.
Yes.
You did not seem to be too convinced about that way of looking at it.
No. I suppose I have just thought about it more.

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

Yes. So if I get you a different example like that then…let’s say we have two different circuits and they both had a tenth of an amp flowing,
Okay. Yes.
and one of them had 1.5 volt power supply
Okay yes.
and the other one had a two volt power supply
Yeah.
but they have both got point one [0.1] of an amp flowing. Which one has got the high resistance?
Currents the same, I would say they have got different voltages, yeah, so erm (pause, c.6s) probably the (pause, c.2s) the second one. Yeah.
Because?
Because there is more voltage being put in, if you like, to the circuit, and you are getting less current flowing in and therefore resistance must be more to stop the rest of that.
Yes?
I think so, yes.
Does that make sense to you?
Yeah.

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

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

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

and that

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

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

Okay and how does that relate to the formula you were just telling me before?
Erm, No idea.
No idea?
Erm (pause, c.2s) once you know the resistance of a circuit you can work out, or once you know any of the, two of the components you can work out, the other one, so.
Yeah, providing you know the equation, when you know which way round the equation is.
Yes providing you can remember the equation.
So can you relate the equation to the explanations you have just given me about which would have the higher resistance?
So if something has got a higher resistance, so (pause, c.2s) so the current flowing round it would be – the resistance times the voltage (pause, c.2s) Is that right? No?
Erm, so the current is resistance time voltage? Are you sure?
No.

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

Go back to thinking in terms of resistance.
Okay.
So you reckoned you can work out the resistance in terms of the current and the voltage?
Yes, I think.
Okay, now if we keep, if we keep the voltage the same and we get different currents,
Yes.
Which has, Which has got the higher resistance, the one with more current or the one with less current?
Erm (Pause, c.6s) So, so, if they keep the same voltage.
That’s the way we liked it the first time so.
Okay.
Let’s say we have got the same voltage across two circuits.
Yes.
Different amounts of current.
Yes.
Which one’s got the higher resistance? The one with more current or the one with less current?
The one with less current.
So less current means it must be more resistance?
Yes.
Ok, so if we had to have an equation R=.
Yes.
What’s it going to be, do you think?
Erm
(pause, c.7s)
R=
(pause, c.3s)
I don’t know. It's too hard.

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

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

Resistance is how much something is being slowed down

"Resistance is how much something is being slowed down or is stopped going round"

Adrian was a participant in the Understanding Science Project. When I interviewed him in Y12 when he was studying Advanced level physics he told me that "We have looked at resistance and conductance and the formulas that go with them". However, when asked about the formula, he suggested, without conviction, that "resistance is current over voltage". So, I asked him how he might go about explaining resistance to a younger student:

We will come back to the formula in a minute then, so let us say you had a younger brother or sister who hasn’t done much physics.
Yes.
And doesn’t do, doesn’t like maths, doesn’t like formulas.
Okay.
So what does it mean though? Why is it important? What’s resistance about?
Erm – I would say it was how much something is being slowed down, or erm how much it is being stopped going round. If it is in electric¬… electricity then it is in a circuit. If it’s in like the wide open range of things it's like erm how resistant is something if you push it? How much force does it give back?

So Adrian was aware of electrical resistance, and also aware of resistance in the context of mechanics.

Oh I see, so, erm if I asked you to push that table over there
Yes.
There might be resistance to that?
Yes.
And that’s different to if we were talking about meters and wires and things?
Yes.
Are they similar in some way?
They have got the same name. {laughs}
Got the same name, okay.
They probably are similar. I've never really thought about it.

So although Adrian associated electrical resistance with 'resistance' in mechanical situations, the similarity between the two types of resistance seemed primarily due to the use of the same linguistic label. This was despite him describing the two forms of resistance in similar terms – "how much something is being slowed down… how much it is being stopped going round" cf. "how resistant is something if you push it".

To a physicist, a property such as resistance should be defined precisely, and therefore preferably mathematically – and so operationally in the sense that there is no ambiguity in how it would be measured. However when students are learning, definitions and formulae may be abstract and have little meaning or connection to experience, so qualitative understanding is important. Students' initial suggestions of what technical terms mean when they first learn about them may be vague and flawed, but if this is linked to a feeling for the concept this may ultimately be a better starting point than a formula which cannot be interpreted meaningfully – as seemed to be the case with Adrian.

Arguably, understanding a relationship in qualitative terms can support later formalising the relationship in mathematical terms, whereas trying to learn a formulae by rote may lead to misremembering and algorithmic application (and so, for example, not noticing when non-feasible results are calculated).

Adrian's suggestion that resistance might be"how resistant is something if you push it? How much force does it give back?" presumably linked to his own experiences of pushing and pulling objects around. However, it seemed to confuse notions of inertia and reaction force (as well as possibly frictional forces). If Adrian were to push with a force of 100N on the wall of a building, a puck on an ice rink, or on a sledge on gravel the reaction force would be 100N in each case (cf. Newton's third law) – although the subjective experience of resistance would be very different in the different situations – as would the outcome on the object pushed.

In these situations it may be difficult for a teacher to know if a vague or confused description reflects conceptual confusion (and/)or limited expression. Yet, students need time and opportunities to be able to explore concepts in their own terms to link the abstract scientific ideas with the 'spontaneous conceptions' they have developed based on their own experiences of acting in the world.

The teacher should offer feedback, and model clear language, but needs to recognise that understanding abstract scientific ideas takes time. After all, Aristotle would be considered to have alternative conceptions of mechanics by comparison with today's science, but Aristotle was clearly highly intelligent and gave the matter a lot of thought!

After this there was extended discussion on the way resistance related to current and voltage, following Arian's comment that resistance is current over voltage. As part of this he was asked about ⚗︎ an example where different voltages were needed in different circuits to allow the same current to flow. ⚗︎ He suggested that the circuit with the higher resistance would be the one where "there is more voltage being put in, if you like, to the circuit, and you are getting less current flowing in, and therefore resistance must be more to stop the rest of that".

Adrian's way of talking about the current in the circuits did not seem to reflect a view of current as driven by a given p.d. across a circuit and limited by a certain resistance, but almost as a fixed potential flow, some of which would be permitted to pass, but some of which would be stopped by the resistance ("how much it is being stopped going round", "resistance … to stop the rest of that"). Yet, as suggested above, it can take time, and opportunities for exploration and discussion, for students' concepts and ways of talking about them to mature towards canonical science.

That Adrian could talk of "more voltage…less current…therefore resistance must be more" seemed promising, although ⚗︎ Adrian could not relate his qualitative description to the mathematical representation of the formula. ⚗︎

When is V=IR the formula for Ohm's law?

"Resistance is current over voltage, I think"

So what exactly is resistance?
Resistance is, erm (pause, c.3s) Resistance is current over, voltage, I think. (Pause, c.3s) Yeah. No.
Not sure?
I can’t remember formulas.

So Adrian's first impulse was to define resistance using a formula, although he did not feel he was able to remember formulae. He correctly knew that the formula involved resistance, current and voltage, but could not recall the relationship. Of course if he understood qualitatively how these influenced each other, then he should have been able to work out which way the formula had to go, as the formula represents the relationship between resistance, voltage and current.

And what about this resistance in electricity then, do you measure that in some kind of unit?
Yes, in, erm, (pause, c.2s) In ohms.
So what is an ohm?
Erm, an ohm is, the unit that resistance is measured in.
Fair enough.
It comes from ohm's law which is the, erm, formula that gives you resistance.

V=IR is the formula that gives you resistance, but it is a common misconception, that Ohm's law is V=IR.

Actually, Ohm's law suggests that the current through a metallic conductor (kept at constant conditions, e.g., temperature) is directly proportional to the potential difference across its ends.

So, in such a case (a metal that is not changing temperature, etc.)

I ∝ V

which is equivalent to

V ∝ I

which is equivalent to

V = kI

where k is a constant of proportionality. If we use the symbol R for the constant in this case then

V= RI

which is equivalent to

V = IR

So, it may seem I have just contradicted myself, as I denied that V=IR was a representation of Ohm's law, yet seem to have derived V=IR from the law.

There is no contradiction as long as we keep in mind what the symbols are representing in the equation. I represented the current flowing through a metallic conductor being held at constant conditions (temperature, tension etc.), and V represented the potential difference across the ends of that metallic conductor. If we restrict V and I to this meaning then the formula could be seen as a way of representing Ohm's law.

Over-generalising

However, that is not how we usually understand these symbols in electrical work: V generally represents the potential difference across some resistive component or other, and I represents the current flowing through that component: a resistor, a graphite rod, a salt bridge, a diode, a tungsten filament in a lamp…

In this general case

V = IR

R = V/I

is the defining equation for resistance. If R is defined as V/I then it will always be the case, not because there is a physical law that suggests this, but simply because that is the meaning we have given to R.

This is a bit like bachelors being unmarried men (an example that seems to be a favourite of some philosophers): bachelors are not unmarried men because there is some rule or law decreeing that bachelors are not able to get married, but simply because of our definition. A bachelor who gets married and so becomes a married man ceases to be a bachelor at the moment they become a married man – in a similar way to how a butterfly is no longer a caterpillar. Not because of some law of nature, but by our conventions regarding how words are used. If V and I are going to be used as general symbols (and not restricted to our carefully controlled metallic conductor) then V = IR simply because R is defined as V/I and the formula, used in the general case, should not be confused with Ohm's law.

In Ohm's law, V=IR where R will be constant.

In general, V=IR and R will vary, as Ohm's law does not generally apply.

It would perhaps be better for helping students see this had there been a convention that the p.d. across, and the current through, a piece of metal being kept in constant conditions were represented by, say V_ⓜ and I_ⓜ, so Ohm's law could be represented as, say

V_ⓜ = k I_ⓜ

but, as this is not the usual convention, students need to keep in mind when they are dealing with the special case to which Ohm's law refers.

A flawed teaching model?

The interesting question is whether:

teachers are being very careful to make this distinction, but students still get confused;
teachers are using language carefully, but not making the discrimination explicit for students, so they miss the distinction;
some teachers are actually teaching that V=IR is Ohm's law.

If the latter option is the case , then it would be good to know if the teachers teaching this:

have the alternative conception themselves;
appreciate the distinction, but think it does not matter;
consider identifying the general formula V=IR with Ohm's law is a suitable simplification, a kind of teaching model, suitable for students who are not ready to have the distinction explained.

It would be useful to know the answers to these questions, not to blame teachers, but because we need to diagnose a problem to suggest the best cure.

Many generations later it's just naturally always having fur

Keith S. Taber

Bert was a participant in the Understanding Science Project. In Y11 he reported that he had been studying about the environment in biology, and done some work on adaptation. he gave a number of examples of how animals were adapted to their environment. One of these examples was the polar bear.

…our homework we did about adapting, like how polar bears adapt to their environments, and camels….
And so a polar bear has adapted to the environment?
Yeah.
So how has a polar bear adapted to the environment?
Erm, things like it has white fur for camouflage so the prey don't see it coming up. Large feet to spread out its weight when it's going over like ice. Yeah, thick fur to keep the body heat insulated.

Bert gave a number of other examples, including dogs that were bred with particular characteristics, although he explained this in terms of inheritance of acquired characteristics: suggesting that dogs that have been taught over and over to retrieve have puppies that automatically have already got that sense. Bert realised that his example was due to the work of human breeders, and took the polar bear as an example of a creature that had adapted to its environment.

Yeah, so how does adaption take place then? …
I don't know. It may have something to do with negative feedback.…Like you have like, you always get like, you always get feedback, like in the body to release less insulin and stuff like that. So in time … organisms, learn to adapt to that. Because if it happens a lot that makes a feedback then it comes, yeah then they just learn to do that.
Okay. Give me an example of that. I'm trying to link it up in my head.
Okay, like the polar bear, like I don't know. It may have started off just like every other bear, but because it was put in that environment, like all the time the body was telling it to grow more fur and things like that, because it was so cold. So after a while it just adapted to, you know, always having fur instead of, you know, like dogs shed hair in the summer and stuff. But like if it was always then they'd just learn to keep shedding that hair.
So if it was an ordinary bear, not a polar bear, and you stuck it in the Arctic, it would get cold?
Yeah.
But you say the body tells it to grow more fur?
Erm, yeah.
How does that work?
I'm not sure, it just … I don't know. Like, erm, like the body senses that it's cold, it goes to the brain, and the brain thinks, well how is it going to go against that, you know, make the body warmer. And so it kind of, you know, it gives these things.

So Bert seemed to have notion of (it not the term) homoeostasis, that allowed control of such things as levels of insulin. He recognised thus was based on negative feedback – when some problematic condition was recognised (e.g. being too cold) this would trigger a response (e.g., more insulation) to bring about a countering change.

However, in Bert's model, the mechanism was not initially automatic. Bert thought that this process which initially was based on deliberation became automatic over many generations…

I see. So the bear has already got a mechanism which would enable it to have more fur, but it's turned on to some extent by being put into the cold?
Yeah.
And then over a period of time, what happens then?
Erm I guess it just it doesn't really need that impulse of being cold, it's just naturally there now, to tell it to do it more.
So how does that happen? Is this the same bear or is this many generations later?
I would probably think many generations later.
Right, so if it was just one particular bear, it wouldn't eventually just produce more hair automatically itself, but its offspring eventually might?
Yeah.
So how does that happen then?
I don't know. Probably from DNA or something. We haven't gone over that yet.

So for Bert, the individual bear could change its characteristics through activating a potential mechanism (in this case for keeping year-round thick fur) through a process of sensing and responding to environmental conditions. Over many generations this changed characteristic could become an automatic response by eventually being coded into the genetic material. As with his explanation of selective breeding, Bert invoked a model of evolution through the inheritance of acquired characteristics, rather than the operation of natural selection on the natural range of characteristics within a breeding population.

Like many students learning about evolution, Darwin's model of variation offering the basis for natural selection was not as intuitively appealing as a more Lamarckian idea that individuals managed to change their characteristics during their lives and pass on the changes to their offspring. This is an example of where student thinking reflects a historical scientific theory that has been discarded rather than the currently canonical scientific ideas taught in schools.

The brain thinks: grow more fur

The body senses that it's cold, and the brain thinks how is it going to make the body warmer?

Keith S. Taber

…our homework we did about adapting, like how polar bears adapt to their environments, and camels….
And so a polar bear has adapted to the environment?
Yeah.
So how has a polar bear adapted to the environment?
Erm, things like it has white fur for camouflage so the prey don't see it coming up. Large feet to spread out its weight when it's going over like ice. Yeah, thick fur to keep the body heat insulated.

Bert gave a number of other examples, including dogs that were bred with particular characteristics, although he explained this in terms of inheritance of acquired characteristics: suggesting that dogs that have been taught over and over to retrieve have puppies that automatically have already got that sense. Bert realised that this example was due to the work of human breeders, and took the polar bear as an example of a creature that had adapted to its environment.

Yeah, so how does adaption take place then? You've got a number of examples there, bears and dogs and camels and people. So how does adaption take place?
I don't know. It may have something to do with negative feedback.
That's impressive.
Like you have like, you always get like, you always get feedback, like in the body to release less insulin and stuff like that. So in time people like or whatever, organisms, learn to adapt to that. Because if it happens a lot that makes a feedback then it comes, yeah then they just learn to do that.
Okay. Give me an example of that. I'm trying to link it up in my head.
Okay, like the polar bear, like I don't know. It may have started off just like every other bear, but because it was put in that environment, like all the time the body was telling it to grow more fur and things like that, because it was so cold. So after a while it just adapted to, you know, always having fur instead of, you know, like dogs shed hair in the summer and stuff. But like if it was always then they'd just learn to keep shedding that hair.
So if it was an ordinary bear, not a polar bear, and you stuck it in the Arctic, it would get cold?
Yeah.
But you say the body tells it to grow more fur?
Erm, yeah.
How does that work?
I'm not sure, it just … I don't know. Like, erm, like the body senses that it's cold, it goes to the brain, and the brain thinks, well how is it going to go against that, you know, make the body warmer. And so it kind of, you know, it gives these things.
Is that an example of feedback?
Yes.

However, in Bert's model, the mechanism was not automatic. Rather it depended upon conscious deliberation: "the brain thinks, well how is it going to …make the body warmer". Bert thought that this process which initially was based on deliberation then became automatic over many generations.

This seems to assume that bears think in similar terms to humans, that they identify a problem and reason a way through. This might be considered an example of anthropomorphism, something that is very common in student (indeed human) thinking. To what extent it may be reasonable to assign this kind of conscious reasoning to bears is an open question.

However there was a flaws in the process described by Bert that he might have spotted himself. This model suggested that once the bear had become aware of the issue, and the needs to address, it would be able to grow its fur accordingly. That is, as a matter of will. Bert would have been aware that he is able to control some aspects of his body voluntarily (e.g., to raise his arm), but he cannot will his hair to grow at a different rate.

Of course, it may be countered that I am guilty of a kind of anthropomorphism-in-reverse: Bert is not a bear, but rather a human who does not need to control hair growth according to environment. So, just because Bert cannot consciously control his own hair growth, this need not imply the same is true for a bear. However, Bert also used the example of insulin levels, very relevant to humans, and he would presumably be aware that insulin release is controlled in his own body without his conscious intervention.

As often happens in interviewing students (or human conversations more generally) time to reflect on the exchange raises ideas one did not consider at the time, that one would like to be able to to text out by asking further questions. If things that were once deliberate become instinctive over time, then it is not unreasonable in principle to suggest things that are automatic now (adjusting insulin levels to control blood glucose levels) may have once been deliberate.

After all, people can control insulin levels to some extent by choosing to eat a different diet. And indeed people can learn biofeedback relaxation techniques that can have an effect on such variables as blood pressure, and some diabetics have used such techniques to reduce their need for medical insulin. So, did Bert think that people had once consciously controlled insulin levels, but over generations this has become automatic?

In some ways this does not seem a very likely or promising idea – but that is a judgement made from a reasonably high level of science knowledge. It is important to encourage students to use their imaginations and suggest ideas as that is an important aspect of how science woks. Most scientific conjectures are ultimately wrong, but they may still be useful tools for moving science on. In the same way, learners' flawed ideas, if explored carefully, may often be useful tools for learning. At the time of the interview, I felt Bert had not really thought his scheme through. That may well have been so, but there may have been more coherence and reflection behind his comments than I realised at the time.