I was aware that research has suggested that children often do not appreciate how carbon obtained from the carbon dioxide in the air is a key source of matter for plants to build up tissue, so learners may assume that the mass increase during growth of a plant will be balanced by a mass reduction in the soil it is growing in.
"The extra [mass of a growing tree] comes from the things it eats and drinks from the ground. It's just like us eating and getting larger."
Response of 15 year old student in the National science survey carried out the Assessment of Performance Unit of the Department of Education and Science, as reported in Bell and Brook, 1984: 12.
During an interview in her first year of secondary education (Y7), Sophia reported that she had been studying plants in science, and that generally a plant was "a living thing, that takes up things from soil, to help it grow" (although some grew in ponds). Sophia was therefore asked a hypothetical question about weighing a pot of soil in which a seed was planted, with the intention of seeing if she thought that the gain in mas of the seed as it grew into a mature plant would be balanced by a loss of mass from the soil.
Sophia was asked about a pot of soil (mass 400g) in which was planted a seed (1g), and which was then watered (adding 49g of water).
A learner considers that the mass of pot, seed and water is collectively 450g, and assumes that as the mass of plant grows, the mass of soil decreases accordingly to conserve total mass at 450g.
A learner is aware that in photosynthesis carbon is 'captured' from carbon dioxide in the air, so the mass of the plant in the soil will exceed 450g once the plant grows.
Of course, a learner might also invoke other considerations – the evaporation of the water, or the acquisition of water due to condensation of water from cold air (e.g., dew); that soil is not inert, but contains micro-organisms that have their own metabolism, etc.
I first wanted to check that Sophia appreciated we had (400 + 1 + 49 =) 450g of material at the point the seed was first watered. That was indeed her initial thought, but she soon 'corrected' herself.
Any idea how much it would weigh now?
[Four] hundred and fifty, no, cause, no cause it will soak it up, wouldn't it, so just over four hundred (400).
So we had four hundred (400) grammes of soil plus pot, didn't we?
Uh hm.
…And we had one (1) gramme of erm, of plant seed. Just one little seed, one (1) gramme. And forty nine (49) grammes of water. But the water gets soaked up into the soil, does it? So when it's soaked up, you reckon it would be, what?
Erm, four hundred and twenty (420).
Sophia's best guess at the mass of the pot with soil (initially 400g) after planting a 1g seed and adding 49g of water was 420g, as the water gets soaked up.
So, Sophia suggests that although 49g of water has been added to a pot (with existing contents) of mass 401g , the new total mass will be less than 450g, as the water is soaking into the soil. Her logic seems to be that some of the water will have soaked into the soil, so it's mass is not registered by the balance.
If you poured the water in, quite quickly, not so quickly that it splashes everywhere, but quite quickly. Before it had a chance to soak up, if you could read what it said on the balance before it had a chance to soak up, do you think it would say four hundred and twenty (420) grammes straight away?
No, it would probably be just under, erm, four hundred and fifty (450).
And it would gradually drop down to about four twenty (420) say, would it?
Yeah.
Might be four hundred and fifteen? (415) Could be four hundred and twenty five (425)?
Yeah.
Not entirely sure,
No
but something like that?
Yeah.
It appears Sophia recognises that in principle there would be a potential mass of 450g when the water is added, but as it soaks up, less mass is registered.
Sophia recognises that mass is initially conserved, at least before the water soaks into the soil.
In other words Sophia in the context of water soaking into soil is not conserving mass.
This is a similar thought experiment to when students are asked about the mass registered during dissolving, where some learners suggest that as a solid dissolves the total mass of the beaker/flask plus its contents decreases, as if the mass of the dissolved material is not registered (Taber, 2002). In that case it has been mooted that ideas about buoyancy may be involved – at least when it is clear that the learners recognise the dissolved material is still present in the solution.
However, that would not explain why Sophia thinks the balance would not register the mass of water soaked into the soil in this case. Rather, it sees more a notion that 'out of sight' is out of mass. Sophia's understanding of what is happening to mass here would be considered an alternative conception or misconception, and is likely based on her intuition about the scenario (acting as a grounded learning impediment) rather than something she has been told.
Sources cited:
Bell, B., & Brook, A. (1984). Aspects of Secondary Students' Understanding of Plant Nutrition. Leeds: : Centre for Studies in Science and Mathematics Education, University of Leeds.
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.
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.
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.
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 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.
Focal figure (14) presented to Annie
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?
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.
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.
A case of justifying dubious medical ethics by treating epistemology as ontology
Keith S. Taber
Image by Mohamed Hassan from Pixabay
I was puzzled by something I heard a hospital doctor say regarding kidney functioning. The gist of his comments were that
once kidney function was below about 10% of normal functioning…
then protecting remaining kidney function was not important…
because estimates of function at that level are unreliable.
I thought this was an illogical argument as it confused ontology (the state of the kidneys and their functioning) and epistemology (how well we can measure kidney function).
The kidneys are essential organs that regulate hydration levels and eliminate toxic materials from the body. They are 'essential' in the sense that without kidney function someone soon dies. Typically healthy people have plenty of scope for contingency in the capacity of their kidneys. (Living kidneys donors give up one of their two kidneys for transplantation, so, after donation, they will only have, at best, 50%,of normal functioning.) So when people's kidneys start to deteriorate due to disease the patient can continue with normal life for some time. I am not an expert, but from what I understand, a person can manage a normal life with 20% of normal functioning.
Of course there reaches a point in progressive kidney disease when the remaining capacity is not enough to keep someone alive for an extended period. So if kidney function drops to something like an eighth of normal healthy functioning, the situation gets critical.
Kidney dialysis
These days people can have dialysis if their kidneys fail. Someone with 0% kidney function – someone who never excretes any urine at all – can be kept alive indefinitely by dialysis. However this is not ideal. The patient has to attend a clinic and have treatment for 3-4 hours at a time, usually three times a week. No time off – no holidays from dialysis if the patient wants to continue living (and some decide they would rather not continue living, although most 'tolerate' the treatment). Often patients feel unwell on, or after, dialysis – they may say they feel 'washed out', for example. Dialysis also costs the health service (or in some countries, the patient) a good deal of money.
Dialysis patients also have to be very careful about diet and avoid some foods (e.g., eating bananas can lead to dangerously high levels of potassium that can interfere with heart function and could lead to a heart attack), as sessions of dialysis (with no, or very little, blood filtration occurring in-between) is never as good as having constantly functioning kidneys.
Then there's the problem of fluid intake
Dialysis patients are asked to limit their intake of fluids. A healthy person who drinks a lot (whether tap water, tea, beer, etc.) simply produces more urine. Most dialysis patients, however, produce little, if any, urine, and the difference between what they 'should' excrete (to maintain homeostasis), and what they can actually excrete, needs to be removed during the dialysis process. So, whatever water a patient takes in drinks during the 45 or so hours between sessions (and is not lost through some other mechanism such as sweating or breathing), is all taken off during three or so hours on the machine. This brings about changes in the blood volume much more quickly than is comfortable. As the body cannot remove excess fluid via the kidneys, fluid intake means the fluid levels build up between dialysis sessions which can lead to various complications such as increases in blood pressure.
Dr McCoy is unimpressed by 20th Century medicine
(Star Trek IV: The Voyage Home, Paramount Pictures)
So, having kidney function of, say, 10% or less of normal is a real pain and requires reorganising your entire life around your dialysis sessions (or perhaps getting a transplant if you are strong enough for surgery and are lucky enough that a good match can be found).
That provides some background in considering whether, once kidneys have deteriorated below, say 10%, it really makes any difference in worrying about the actual level. If you have 8% of normal functioning and are on dialysis for life, why would it matter if that fell to 6%?
An actual case
The context of this question was a patient with kidney failure or end-stage renal disease (a haemodialysis* patient, who would only live a matter of days without regular treatment) who was given a CAT scan** using a contrast medium*** to show up features that would not be observable otherwise. Such media are widely considered to have some toxicity in relation to the kidneys (Ahmed, Williams & Stott, 2009), but in a healthy person they are eliminated through the kidneys quite quickly and any risk is considered small. A person with kidney failure does not eliminate toxins in this way, and so when a scan is indicated, it can be scheduled for just before their next dialysis session.
"In every study comparing patients with and without some degree of renal insufficiency [kindeys not functioning adequately], renal insufficiency increased the likelihood of RCIN [radiocontrast-medium-induced nephropathy, i.e., kidney damage due to the use of contrast media]"
"Both peritoneal and hemodialysis remove substantial amounts of the contrast medium (50% to 90% of the dose); hemodialysis is more effective."
Solomon, 1998: 230, 236.
This patient, however, was admitted to a hospital very ill. The emergency department doctor ordered an immediate scan – late at night, at a weekend – but told the patient that the on-call dialysis staff could be called in to give dialysis after the scan. At the X-ray department, the radiographer then said that this was not needed, as long as the patient had dialysis within 24 hours of the scan.
The renal doctor's viewpoint
The next afternoon, the patient had still not gone for dialysis when the hospital renal doctor visited the patient. This doctor took the view that as the patient was due their regular dialysis the following day (i.e., about 38 hours after the scan), there was no point sending the patient for an additional dialysis session, as – after all – the kidneys had already failed sufficiently for the patient to be relying on dialysis for survival.
The patient's viewpoint
The counter-argument presented to the renal specialist (by the patient's spouse) was that even at this point further deterioration should be avoided if possible – that even if 8% of normal kidney function was not good, it was inherently better than 6% of normal kidney function.
After all, if for some reason a patient was further compromised (by an unrelated illness, or by delay in accessing normal dialysis due to some unexpected contingency) a few percentage points – making a small difference in how much the body could remove toxins and excess fluid from the blood by itself between dialysis sessions – could still be the critical factor in determining whether the person survived. (Those attending hospital dialysis notice the high frequency of fellow regular patients who, suddenly, are no longer attending for treatment.)
The renal doctor's justification
The doctor responded to this with the counter-argument that once kidney function was this low, there was no reason to be concerned about a change in measured kidney function from (say) 8% to 6% as the difference between such measurements was within the usual variations in measurements found in patients from time to time.
There are two issues here of interest.
Consent that is conditional is not consent if the conditions are broken
One issue relates to ethics (here, medical ethics). A patient consented to a diagnostic procedure with a possible risk of side effects on the understanding that a suitable counter measure would be taken immediately after the procedure to minimise any detrimental effect. The hospital undertook the procedure, but then decided (when it was too late for the patient to withdraw consent) not to follow through on the promised counter-measure. In effect, a procedure was carried out without consentas the consent was (as was made absolutely clear by the patient) conditional on the scan being followed by dialysis.
Reasons for refusing to provide treatment
The second issue relates to the justification given by the doctor as reported above.
The day after the explanation about measurement not clearly distinguishing between 8% and 6% functioning had been made, when dialysis was finally provided, another renal specialist offered a different justification entirely – that the potential risk to kidneys of the contract medium was just a myth. However, the earlier conversations
in the emergency department;
in the X-ray department; and
with the first renal doctor within 24 hours of the scan,
were all clearly undertaken on the basis that both patient and medical staff thought the contrast medium was potentially damaging to kidneys.
"These contrast media can occasionally cause kidney damage, especially in patients who already have kidney disease"
Ahmed, Williams & Stott, 2009
In the context of that discourse, the first renal specialist had argued that because (a) the precision of estimates of kidney function was not great enough to reliably measure a difference between 6% and 8% functionality, then (b) there was no need to be concerned about treatment which could potentially cause damage bringing about deterioration of this order.
Presumably,
at any one time, a person's kidney function will be at a certain level.
If the kidney is then further damaged by toxins then that functionality will drop.
A more damaged kidney is inherently less desirable than a less damaged (better functioning) kidney.
So further damage to an already damaged kidney is inherently undesirable,
and should be avoided if possible, if the costs of doing so are not too high.
The state of a diseased person's kidneys could vary slightly 'naturally' in response to various factors related to their general health, diet, environment, etcetera. This is an ontological consideration – the actual state of the kidneys changes. This may well mean that changes of a few percent between measurements could just be natural fluctuation.
It may therefore be difficult to tell if a person's kidneys have become more damaged due to a particular event, such as a diagnostic scan. That is an epistemological issue – the limitation on how well we can identify a specific change that is masked by noise.
Presumably, there are also various factors that limit the precision of such estimates – all measurements are subject to errors, and small (real) differences may be difficult to identify if they are at the level of the likely measurement error. That is also an epistemological issue.
But, just because an effect cannot be clinically measured (epistemology), that does not mean it is not real and will not have consequences (ontology). A drop from 8% kidney function to 6% kidney function is only a change of 2% compared with normal functioning, BUT it is a loss of 25% of the patient's actual kidney function.
A small deterioration in already severely compromised kidneys may seem insignificant to the renal doctor because he does not think he could reliably measure the change. One day it could be the difference between life and death to the kidneys' owner.
Sources cited:
Ahmed, A., Williams, G., & Stott, I. (2009). Patient information-What I tell my patients about contrast medium nephrotoxicity. British Journal of Renal Medicine, 14(3), 15-18.
* haemodialysis involves the patient having permanent 'plumbing' installed that allows their vascular system to be connected to a dialysis machine, so the blood can be diverted to the machine to be cleaned. This usually done using blood vessels in the arm. In the case discussed the surgeon cut into the neck and chest (with the patient fully conscious), and connected tubing to a vein in the neck. The tubing was run beneath the skin to exit in the chest below the neckline, where a fitting acted as a tap and connector for the external tubing to the machine. Very special care has to be taken to keep the area clean, and the dressing dry, as the plumbing provides a direct route into the bloodstream. (Baths, swimming, hot-tubs, etc. are not advisable.)
[Peritoneal dialysis is an alternative treatment that involves a catheter being implanted in the abdomen, and being used to allow a solution into the abdominal cavity, which is later removed after it has absorbed waste materials. The patient can manage the process at home, but needs to change the solution in the abdomen a number of times each day.]
** computerised tomography: a process that uses a series of X-ray bursts to collect data that can be compiled into a 3-D image.
*** a substance that shows up on X-ray scans, and which when injected into the blood helps detect vascular structures. (The term is generic – it also applies to substances swallowed before scans of the alimentary canal.)
Note: this post was originally prepared in October 2015, but was not published at the time when the patient was alive and attending for treatment.
I was checking some proofs for something I had written today* [Taber, 2017], and was struck by an ironic parallel between one of the challenges for teaching about the scientific theory of evolution by natural selection and one of the arguments put forward by those who deny the theory. The issue concerns the value of having only part of an integrated system.
The challenge of evolutionary change
One of the arguments that has long been made about the feasibility of evolution is that if it occurs by many small random events, it could not lead to progressive increases in complexity – unless it was guided by some sense of design to drive the many small changes towards some substantive new feature of ability. So, for example, birds have adaptations such as feathers that allow them to fly, even though they are thought to have evolved from creatures that could not fly. The argument goes that for a land animal to evolve into a bird there need to be a great many coordinated changes. Feathers would not appear due to a single mutation, but rather must be the result of a long series of small changes. Moreover, simply growing features would not allow an animal to fly without other coordinated changes such as evolving very light bones and changes in anatomy to support the musculature needed to power the wings.
The same argument can be made about something like the mammalian eye, which can hardly be one random mutation away from an eyeless creature. The eye requires retinal cells, linked to the optic nerve, a lens, the iris, and so on. The eye is an impressive piece of equipment which is as likely to be the result of a handful of random events, as would be – say, a pocket watch found walking on the heath (to use a famous example). A person finding a watch would not assume its mechanism was the result of a chance accumulation of parts that had somehow fallen together. Rather, the precise mechanism surely implies a designer who planned the constructions of the overall object. In 'Intelligent Design' similar arguments are made at the biochemical level, about the complex systems of proteins which only function after they have independently come into existence and become coordinated into a 'machine' such as a flagellum.
The challenge of conceptual change
The parallel concerns the nature of conceptual changes between different conceptual frameworks. Paul Thagard (e.g., 1992) has looked at historical cases and argued that such shifts depend upon judgements of 'explanatory coherence'. For example, the phlogiston theory explained a good many phenomena in chemistry, but also had well-recognised problems.
The very different conceptual framework developed by Lavoisier [the Lavoisiers? **] (before he was introduced to Madame Guillotine) saw combustion as a chemical reaction with oxygen (rather than a release of phlogiston), and with the merits of hindsight clearly makes sense of chemistry much more systematically and thoroughly. It seems hard now to understand why all other contemporary chemists did not readily switch their conceptual frameworks immediately. Thagard's argument was that those who were very familiar with phlogiston theory and had spent many years working with it genuinely found it had more explanatory coherence than the new unfamiliar oxygen theory that they had had less opportunity to work with across a wide range of examples. So chemists who history suggests were reactionary in rejecting the progressive new theory were actually acting perfectly rationally in terms of their own understanding at the time. ***
Evolution is counter-intuitive
Evolution is not an obvious idea. Our experience of the world is of very distinct types of creatures that seldom offer intermediate uncertain individuals. (That may not be true for expert naturalists, but is the common experience.) Types give rise to more of their own: young children know that pups come from dogs and grow to be adult dogs that will have pups, and not kittens, of their own. The fossil record may offer clues, but the extant biological world that children grow up in only offers a single static frame from the on-going movie of evolving life-forms. [That is, everyday 'lifeworld' knowledge can act as substantial learning impediment – we think we already know how things are.]
Natural selection is an exceptionally powerful and insightful theory – but it is not easy to grasp. Those who have become so familiar with it may forget that – but even Darwin took many years to be convinced about his theory.
Understanding natural selection means coordinating a range of different ideas about inheritance, and fitness, and random mutations, and environmental change, and geographical separation of populations, and so forth. Put it all together and the conceptual system seems elegant – perhaps even simple, and perhaps with the advantage of hindsight even obvious. It is said that when Huxley read the Origin of Species his response was "How extremely stupid not to have thought of that!" That perhaps owes as much to the pedagogic and rhetorical qualities of Darwin's writing in his "one long argument". However, Huxley had not thought of it. Alfred Russel Wallace had independently arrived at much the same scheme and it may be no coincidence that Darwin and Wallace had both spent years immersing themselves in the natural history of several continents.
Evolution is counter-intuitive, and only makes sense once we can construct a coherent theoretical structure that coordinates a range of different components. Natural selection is something like a shed that will act as a perfectly stable building once we have put it together, but which it is very difficult to hold in place whilst still under construction. Good scaffolding may be needed.
Incremental change
The response to those arguments about design in evolution is that the many generations between the land animal and the bird, or the blind animal and the mammal, get benefits from the individual mutations that will collectively, ultimately lead to the wing or mammalian eye. So a simple eye is better than no eye, and even a simple light sensitive spot may give its owner some advantage. Wings that are good enough to glide are useful even if their owners cannot actually fly. Nature is not too proud to make use of available materials that may have previously had different functions (whether at the level of proteins or anatomical structures). So perhaps features started out as useful insulation, before they were made use of for a new function. From the human scale it is hard not to see purpose – but the movie of life has an enormous number of frames and, like some art house movies, the observer might have to watch for some time to see any substantive changes.
A pedagogical suggestion – incremental teaching?
So there is the irony. Scientists counter the arguments about design by showing how parts of (what will later be recognised as) an adaptation actually function as smaller or different advantageous adaptations in their own right. Learning about natural selection presents a situation where the theory is only likely to offer greater explanatory coherence than a student's intuitive ideas about the absolute nature of species after the edifice has been fully constructed and regularly applied to a range of examples.
Perhaps we might take the parallel further. It might be worth exploring if we can scaffold learning about natural selection by finding ways to show students that each component of the theory offers some individual conceptual advantages in thinking about aspects of the natural world. That might be an idea worth exploring.
(Note. 'Representing evolution in science education: The challenge of teaching about natural selection' is published in B. Akpan (Ed.), Science Education: A Global Perspective. The International Edition is due to be published by Springer at the end of June 2016.)
Notes:
* First published 30th April 2016 at http://people.ds.cam.ac.uk/kst24/
** "as Madame Lavoisier, Marie-Anne Pierrette Paulze, was his coworker as well as his wife, and it is not clear how much credit she deserves for 'his' ideas" (Taber, 2019: 90). Due to the times in which they works it was for a long time generally assumed that Mme Lavoisier 'assisted' Antoine Lavoisier in his work, but that he was 'the' scientist. The extent of her role and contribution was very likely under-estimated and there has been some of a re-evaluation. It is known that Paulze contributed original diagrams of scientific apparatus, translated original scientific works, and after Antoine was executed by the French State she did much to ensure his work would be disseminated. It will likely never be know how much she contributed to the conceptualisation of Lavoisier's theories.
*** It has also been argued (in the work of Hasok Chang, for example) both that when the chemical revolution is considered, little weight is usually given to the less successful aspects of Lavoisier's theory, and that phlogiston theory had much greater merits and coherence than is usually now suggested.
Sources cited:
Taber, K. S. (2017). Representing evolution in science education: The challenge of teaching about natural selection. In B. Akpan (Ed.), Science Education: A Global Perspective (pp. 71-96). Switzerland: Springer International Publishing
Plants mainly respire at night because they are photosynthesising during the day
Keith S. Taber
Image by Konevi from Pixabay
Mandy was a participant in the Understanding Science Project. When I spoke to her in Y10 (i.e. when she was c.14 year old) she told me that photosynthesis was one of the topics she was studying in science. So I asked her about photosynthesis. 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.
Respiration produces energy, but photosynthesis produces glucose which produces energy
Keith S. Taber
Image by Frauke Riether from Pixabay
Mandy was a participant in the Understanding Science Project. When I spoke to her in Y10 (i.e. when she was c.14 year old) she told me that photosynthesis was one of the topics she was studying in science. So I asked her about photosynthesis:
So, photosynthesis. If I knew nothing at all about photosynthesis, how would you explain that to me?
It's how plants get their food to grow and – stuff, and make energy
So how do they make their energy, then?
Well, they make glucose, which has energy in it.
How does the energy get in the glucose?
Erm, I don't know.
It's just there is it?
Yeah, it's just stored energy
I was particularly interested to see if Mandy understood about the role of photosynthesis in plant nutrition and energy metabolism.
Why do you think it is called photosynthesis, because that's a kind of complicated name?
Isn't photo, something to do with light, and they use light to – get the energy.
So how do they do that then?
In the plant they've got chlorophyll which absorbs the light, hm, that sort of thing.
What does it do once it absorbs the light?
Erm.
Does that mean it shines brightly?
No, I , erm – I don't know
Mandy explained that the chlorophyll was in the cells, especially in the plant's leaves. But I was not very clear on whether she had a good understanding of photosynthesis in terms of energy.
Do you make your food?
Not the way plants do.
…
So where does the energy come from in your food then?
It's stored energy.
How did it get in to the food? How was it stored there?
Erm.
[c. 2s pause]
I don't know.
At this point it seemed Mandy was not connecting the energy 'in' food either directly or indirectly with photosynthesis.
Okay. What kind of thing do you like to eat?
Erm, pasta.
Do you think there is any energy value in pasta? Any energy stored in the pasta?
Has lots of carbohydrates, which is energy.
…
So do you think there is energy within the carbohydrate then?
Yeah.
Stored energy.
Yeah.
So how do you think that got there, who stored it?
(laughs) I don't know.
Again, the impression was that Mandy was not linking the energy value of food with photosynthesis. The reference to carbohydrates being energy seemed (given the wider context of the interview) to be imprecise use of language, rather than a genuine alternative conception.
So do you go to like the Co-op and buy a packet of pasta. Or mum does I expect?
Yeah.
Yeah. So do you think, sort of, the Co-op are sort of putting energy in the other end, before they send it down to the shop?
No, it comes from 'cause pasta's made from like flour, and that comes from wheat, and then that uses photosynthesis.
Now it seemed that it was quite clear to Mandy that photosynthesis was responsible for the energy stored in the pasta. It was not clear why she had not suggested this before, but it seemed she could make the connection between the food people eat and photosynthesis. Perhaps (it seems quite likely) she had previously been aware of this and it initially did not 'come to mind', and then at some point during this sequences of questions there was a 'bringing to mind' of the link. Alternatively, it may have been a new insight reached when challenged to respond to the interview questions.
So you don't need to photosynthesise to get energy?
No.
No, how do you get your energy then?
We respire.
Is that different then?
Yeah.
So what's respire then, what do you do when you respire?
We use oxygen to, and glucose to release energy.
Do plants respire?
Yes.
So when do you respire, when you are going to go for a run or something, is that when you respire, when you need the energy?
No, you are respiring all the time.
Mandy suggested that plants mainly respire at night because they are photosynthesising during the day. (Read 'Plants mainly respire at night'.)
So is there any relationship do you think between photosynthesis and respiration?
Erm respiration uses oxygen – and glucose and it produces er carbon dioxide and water, whereas photosynthesis uses carbon dioxide and water, and produces oxygen and glucose.
So it's quite a, quite a strong relationship then?
Yeah.
Yeah, and did you say that energy was involved in that somewhere?
Yeah, in respiration, they produce energy.
What about in photosynthesis, does that produce energy?
That produces glucose, which produces the energy.
I see, so there is no energy involved in the photosynthesis equation, but there is in the glucose?
Yeah.
Respiration does not 'produce' energy of course, but if it had the question about whether photosynthesis also produced energy might have been expected to elicit a response about photosynthesis 'using' energy or something similar, to give the kind of symmetry that would be consistent with conservation of energy (a process and its reverse can not both 'produce' energy). 'Produce' energy might have meant 'release' energy in which case it might be expected the reverse process should 'capture' or 'store' it.
Mandy appreciated the relationship between photosynthetic and respiration in terms of substances, but had an asymmetric notion of how energy was involved.
Mandy appeared to be having difficult appreciating the symmetrical arrangement between photosynthesis and respiration because she was not clear how energy was transformed in photosynthesis and respiration. Although she seemed to have the components of the scientific narrative, she did not seem to fully appreciate how the absorption of light was in effect 'capturing' energy that could be 'stored' in glucose till needed. At this stage in her learning she seemed to have grasped quite a lot of the relevant ideas, but not quite integrated them all coherently.
Cause and effect?: People go to different places because of what they are wearing
Keith S. Taber
Image by anwo00 from Pixabay
Annie was a participant in the Understanding Chemical Bonding project. She was a second year 'A level' student (c.18 years of age) when she was talking to me about atoms and electrons, but I was struck with the way she used the word 'because'.
Technically this conjunction is linked with causality, something of importance in science. To say that X occurred because of Y is to claim that Y was a cause of X.
I wanted to clarify if Annie's use of 'because' in that chemical context actually implied that she was describing what she considered a cause, or whether she was using the word more loosely. To probe this I presented what I considered an obviously inappropriate use of 'because': that football fans following different teams in the same city would go to different matches BECAUSE of the colour of the clothes they wore (i.e., hats and scarves traditionally worn to show support to a particular team).
Because the sky is blue, it makes me cry
I expected Annie to point out that this was not the reason, and so 'because' should not be used – which would have then allowed me to return to her earlier use of 'because' in the context of atoms. However, Annie seemed quite happy with my supposedly 'straw-man' or 'Aunt Sally' example:
So we're talking about what you might call cause and effect, that something is caused by something else. We do a lot of talking about cause and effect in science – "this causes that to happen."
If you think about people in Liverpool, only because this is the first analogy that comes to mind, if you actually go to Liverpool on Saturday [*] and wander round, you'll probably find quite a few people wandering around wearing red, and quite a few people wandering around wearing blue, and sometime after lunch you'll find that all the people wearing red, a lot of the people wearing red, tend to move off to one particular place.[**] And the people wearing blue tend to move to a different sort of place, as though they are repelled, you know, similar colours attracted together.
Uh hm.
Agreed?
Yes.
And we could say therefore, that the reason that some people go towards the Liverpool ground, is because they're wearing red, and the reason some people go towards the Everton ground, is because they're wearing blue. Now would that be a fair description?
Yeah.
And do you agree with the sense of cause and effect there – that people go to watch Liverpool because they're wearing red hats and red scarves? And people go to look at Everton because they're wearing blue hats and blue scarves?
Yes.
So would you say the cause of which football team you go to see, the cause of that, is what clothes you happen to be wearing?
(Pause, c.4s)
Unless you're a rambler. {Laughs}…
No, no, well yes, if you're wearing, you're obviously supporting that colour, so, that team, so so you'd assume, that they were going to watch, the team they favoured.
Right, okay, erm, I'll think of a different example, I think.
Because the world is round, it turns me on
Annie did not seem to 'get' what I had thought would be an obvious flaw in the argument. Fans wear the colours of their team to show support and affiliation; and go to the place where their team is playing: but they do not go to the particular stadium because they happen to be wearing red or blue.
This is linked to the difference between causation and correlation. Often two correlated variables do not have a direct causal relationship, but have a relationship mediated by some other factor.
Height of children in a primary school will be correlated with their grade number (on average, the children in the first year are shorter than those in the second year, who are shorter than…). But children are not organised into grades according to height, and height is not caused by grade. Both are independently related to the child's age.
Colour of football scarves is correlated with destination on match day, but one does not cause the other – rather both colour choice and destination are actually due to something else: affiliation to a club. [***]
I switched to a another example I hoped would be familiar, based on a swimming pool. I though the idea that changing rooms are (usually) designated by gender would make it obvious that where people went to change on leaving the pool correlated to, but was not because of, what they were wearing. Again, however, Annie did not seem to consider it inappropriate to describe this in terms of the the different types of swimming costume causing the behaviour.
If you go to the swimming pool, and watch people swimming, you'll find out that some people when they're swimming at a swimming pool, tend to wear a swimming costume that only covers, the hips basically, and other people either a swimming costume that covers most of the trunk, or two separate parts to it. And if you observe them very closely, which is always a bit suspicious at a swimming pool, you'll notice that when they get out of the pool, they're attracted towards different rooms, these changing rooms…
But all the people who just have the one part of the costume, are attracted towards one room, and the others are attracted towards the other room, the ones with sort of either very long costumes or two part costumes. So is it fair to say that it's caused by what clothes they are wearing, that determines which room they go and get changed in?
Yes.
It is?
(Pause, c.4s)
Yes.
That's the cause of it?
(Pause, c5s)
Yeah. It's also conventional as well.
So in both cases Annie was happy to talk in terms of the clothing causing behaviour. After some further discussion Annie seemed to appreciate the distinction I was making, but even if she did not have a flawed notion of causality, it certainly appeared she have developed non-canonical ways of talking about cause and effect.
Because the wind is high, it blows my mind
Annie was a clever person, and I am sure that the issue here was primarily about use of language rather than an inability to understand causation. However, even if our thinking is not entirely verbal, the major role of verbal language in human thought means that when one does not have the language, one may not have the related explicit concepts.
It is very easy to assume that students, especially those we recognise as capable and having been academically successful, share common 'non-technical' language – but there is plenty of research that suggests that many students do not have a clear appreciation of how such terms are canonically used. These are terms we might think people generally would know, such as adjacent, efficient, maximum, initial, omit, abundant, proportion… (Johnstone & Selepeng, 2001). As always, a useful guide to the teacher is 'never assume'.
* At the time of the interview, it was general practice for most English football league matches to be played at 15.00 on a Saturday.
** One constraint on the scheduling of football matches is that, as far as possible, two local rival ('paired') teams should not play home matches on the same day, to avoid potential clashes between large crowds of rival fans. However, such 'paired clashes', as they are technically called (Kendall et al., 2013), are not always avoided.
*** Of course, this is not a direct cause. A person could support one team, yet choose to wear the colours of another for some reason, but their support for a team usually motivates the choice. Social patterns are messier than natural laws.
Sources cited:
Johnstone, A. H., & Selepeng, D. (2001). A language problem revisited. Chemistry Education: Research & Practice in Europe, 2(1), 19-29.
Kendall G., McCollum B., Cruz F.R.B., McMullan P., While L. (2013) Scheduling English Football Fixtures: Consideration of Two Conflicting Objectives. In: Talbi EG. (eds) Hybrid Metaheuristics. Studies in Computational Intelligence, vol 434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30671-6_14
I found a very kind invitation from an organisation calling itself "Peak Performance International" in my email Inbox this morning * ('Parents Workshop on 12th September 2015')), inviting me to a 'free' 2 hour workshop (in Nairobi) – free as long as I booked before a certain date.
The organisation claims to be run by two parents who had been concerned at their daughter's lack of progress at school and so (as one does) had travelled to various countries including "the US, Singapore, Indonesia, Malaysia" to learn about programmes of "Accelerated Learning and Brain Development". They claim that what they found was "mind blowing":
We saw children who would flip through a 200 page book of completely new material, at high speed for just a few minutes and then give an accurate account of what the book was about. Others would mentally calculate long mathematical equations and give the correct answers instantly while Professors took so long and still [did] not get the correct answer.
During our tour we attended several trainings. I learnt more about the brain than I had ever done in my whole life. I understood how easy it was to assist children tap into their genius realm and experience quantum leaps in IQ and EQ (Emotional Intelligence) by synchronizing the two brain hemispheres.
It seems Peak Performance International are now keen to share their findings with other parents, thus the invitation to their workshop. How I would have liked to think this is a genuine (even if misguided) and kind gesture. There may be the odd savant who can complete complex calculations faster than professors – but I doubt there is much that can be learnt from those to advise others. As for such extreme speed reading and retention of information: this can be understood two ways. It is either just a complete fabrication (the human brain works slowly with 'completely new material' which has to be understood in terms of familiar material, and engaged with through modest learning quanta) – or is trivial. Any good reader could actually 'flip through a 200 page book of completely new material, at high speed for just a few minutes and then give an accurate account of what the book was about' – by focusing on the blurb or an introduction. However, there would be very little knowledge of the book's detailed contents.
I am not sure whether I should be upset or pleased about this invitation. It is always annoying that some people want to cheat, mislead and swindle others. Often the widows of dictators, dying philanthropists, senior bankers or lawyers, or american military personnel seem to have a problem moving vast amounts of money out of some national jurisdiction and offer to make me rich if I help them. They clearly feel I am especially deserving or suitably skilled to undertake such projects. It is hard to have too much sympathy for anyone who is so stupid and greedy that they respond to such approaches.
Here, however, the scammers are playing upon parents who do not want to get rich quick, but just want to help their children learn more effectively and do better in school. I wonder how much money they will be asked to part with to share in the Peak Performance Programme with its surely fraudulent claims? Shame on the scammers. The only positive aspect of this sorry tale is that people consider education and learning important enough for scammers to think they can make a 'fast buck' out of the selling the pedagogic equivalent of snake oil. Perhaps this is not so different form the companies in countries like the UK where so much of professional development in the education sector has become commercialised, with 'providers' selling programmes in 'learning styles' which often have very little evidential support. (There is good research into some models of learning styles – but where popular ideas like VAK work this is likely either placebo, or the focus on multi-model teaching, rather than the underlying model which is more a distortion of multiple intelligence theory than based on the research on student learning styles.)
When I first saw the email I seriously wondered if this was a genuine but misguided or exaggerated attempt to apply genuinely effective learning/study techniques. I was persuaded otherwise by a link in the email that directed me to "one of our students". Actually this was a 'youtube' video of a young boy on a television programme who allegedly could read whilst blindfolded. He struggled to read an autocue whilst blindfolded – although to be fair he struggled equally to read the same autocue before the blindfold was put on. Looking at the video, and in particular how the boy angled his head, I very much suspect he was looking through the fabric of the black eyeshades (in the section of the programme I watched it did not seem to have occurred to the presenter to provide his own blindfold). Even if this was a genuine sensory skill and not the trick it seemed to be, it appeared to have nothing to do with "Accelerated Learning and Brain Development" or Peak Performance International.
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.
