If you can’t say it and you can’t show it then you don’t know it

This was one of the two stock phrases that I used in teaching (the other one was ‘No one ever looked good making someone else look bad’, used in behaviour management). The point of ‘If you can’t say it and you can’t show it then you don’t know it’, was that I encountered a fair few learners who insisted that they knew one thing or another, despite being unable to answer questions or perform actions that demonstrated that knowledge. The knowledge that they had was some sort of private revelation that was not amenable to external scrutiny.

I have chanced to learn some intriguing things since my time in the classroom that make me think that there could after all be some truth to learners’ claims of private knowledge (although I think that the claim of such knowledge is generally an empty one). 

As an educator, my specialism is physics. Physics offers a variety of interesting ways to think about things, including about thinking.

The particular example of this that I am discussing here is quantum cognition.

Quantum cognition is the phenomenon of human decision making that is inconsistent with classical logic but is consistent with quantum mechanics. A well known example of this phenomenon involved asking students whether they would buy a ticket for a Hawaiian holiday, depending on whether

  • they had passed a big test.
  • they had failed the test.
  • they didn’t yet know whether they had passed or failed.

More than half said they would buy the ticket if they had passed. Even more than that said they would buy the ticket if they failed. Strangely though, 30 percent said they wouldn’t buy a ticket until they found out whether they had passed or failed.

This defies classical logic because if you would have some preference P if some condition C is true, and you have the same preference if C is false, then you should have the preference P whether C is true or false, whatever your current knowledge about the truth value of C. In quantum mechanics this does not lead to a contradiction however as quantum mechanics is based around operators that are non-commutative, meaning (A X B) ≠ (B X A); the order of these operations must be taken into account to find the result of them, so it is possible to have a situation where a preference can fail to exist because a question has not yet been asked where that preference would exist whatever the answer to the question was.

Quantum mechanics has been used to analyse the results of surveys where the order of pairs of ‘yes/no’ questions is reversed to see how switching the order of  the questions affects survey respondents’ answers to these questions. QM predicts not only that switching the order of question pairs should change what answers respondents give for them, but that the number of respondents who switch from answering both questions with ‘yes’ to answering both questions with ‘no’ when the order is switched should balance the number of respondents who do the opposite (switch from answering ‘no’ to both questions to answering ‘yes’ to both questions when the question order is reversed). Weirdly enough, this balancing is observed in survey results. No one yet understands why this is so.

What this implies (but falls far short of concluding) is that preferences are produced by the act of being asked questions about those preferences. The preferences apparently did not really exist before they were asked about. If we consider that preferences ought to be at least partly based on memories (we base our future expectations on our memories of the past) then the implication arises that memories are at least partially generated by the act of remembering!

To conjecture a bit further; preferences have dependencies with other preferences (the same is true of memories). Being asked a question that sets a preference/memory into a certain state therefore has knock on effects on other preferences/memories. If these dependencies also happen to work similarly to how QM does then some sets of preferences/memories could have complementary relationships with each other, meaning that determining the state of one of the complementary items would result in the state of the other complementary items becoming undetermined; knowing one thing clearly would mean that there would be something else that you couldn’t simultaneously know clearly.  

It seems to me that a complementarity principle of some sort (or something quantum-like at any rate) can be discerned in the process of learning. This phenomenon arises (I think) around the issue of the relationship between some knowledge (referred to for convenience as ‘k‘) that someone (referred to for convenience as ‘p‘) knows  and how it is known (by p or by someone else) that p knows whether or not they know k.

The basic idea is that whether or not p knows k is affected by asking p whether or not they know k. More specifically, asking p if they know k may reduce the extent to which they do know k. This may sound strange and far-fetched but I am arguing for this on the basis that asking p whether or not they knows k involves some sort of assessment process that the act of participation in alters how p perceives k. This argument rests on the principle (which I invoke here!) that just about any example of learning that a human can possess is decomposable in a variety of ways.

There are (in general) lots of different ways of knowing any particular thing, and the way that a learner knows a thing may be different to the way that someone assessing that learner’s knowledge knows that same thing (let’s call the knowledge again). If an assessor asks a learner questions (even indirectly) concerning k then those questions cannot help but influence the learner’s state of determination of some memories/preferences related to that k. If the assessor learned k in a different way than the learner did then the assessor’s questions could disrupt the learner’s state of determination of k.

QM terminology could be useful in explaining this situation. In QM, any measurement of the state of a system results in what is called the projection of the state of the measuring system onto the state of the measured system (this is a more technical way of stating the oft-repeated principle of QM that the act of observing a system changes that system). Using this sort of terminology, it would no longer be valid to speak of in itself but only of the projection of the assessor or learner on k. These projections can be denoted kassesor and klearner. When an assessor attempts to measure a learners knowledge of k, this results in a projection of kassesor onto klearner, which can be denoted kassesorklearner. This projection is different to klearner and may represent a less determined state of knowledge than klearner does.

Thinking in this sort of way, I speculate that two entities exist (they could be called variables, but that doesn’t do justice to how abstract and complex they are) that can have a complementary relationship to each other. These entities are ‘Whether learner knows k‘ and ‘What is’. Strange as it may sound, I am suggesting that it might be possible to say clearly whether a learner knew something but not be able to say clearly what it was they knew. Conversely, it might be possible to say clearly what a learner knew but not be able to say clearly whether or not they knew it. 

In practical terms, I would argue that these two entities need to be measured in distinctly different ways to try and minimise how complementary they are.

‘Whether learner knows k‘ should be measured in terms of some sort of minimally ambiguous outcome (perhaps a rather artificial one), and is more accurately expressed as ‘Whether learner can produce some outcome that has been assumed to be connected with knowledge of k‘. Only the outcome would be measured, the process by which the outcome was achieved would be a black-box to the assessor. Assessors could of course observe the process but their observations could not influence the determination of whether the outcome was or was not achieved.

‘What is’ would be measured not in terms of some outcome brought about by the learner but by how consistently successfully such outcomes were achieved by people other than that learner who were instructed by that learner in how to achieve the outcome. If a learner can consistently induce outcome achieving actions in others then some sort of shared construct must exist common to that learner and those whom they have instructed. Scrutinising different interpretations of this construct would go some way to establishing the characteristics of  k, especially in terms of how those constructs correlated with individuals’ ability to achieve outcomes. 

My speculations on this are, well, speculative. Intuitively I think that I am onto something and that learning will one day be understood to be more quantum than classical, and that what we learn is not our learning, but our learning exposed to our way of asking questions about what our learning is.



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