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Joshua Lawrence

Empirically Modelling Self Balancing Binary Trees

You have done some good background research on this theme. To my mind, the area of modelling data structures has been ripe for exploration for some time, and may have interesting connections with other topics of current interest. It may be that modelling an abacus can be construed as "modelling a data structure" for example (albeit a data structure for supporting arithmetic that might appear to be of peripheral interest in computer science contexts where we treat arithmetic as what the computer routinely does). It's also possible that we should pay more attention to 'structural' rather than 'object-like' organisation in EM - this is certainly in line with Nick Pope's recent thinking (though he emphasises the idea of structure as a primitive characteristic rather than something to be modelled using definitive scripts).

Your abstract makes a number of claims that I consider quite plausible, but for which I don't know of empirical evidence. It would be good to cite references that attest to "a perceived inaccessibility of understanding data structures for those with less technical experience" for instance. It is even more difficult to provide the kind of explicit evidence that would satisfy an educational research specialist that after making a construal "understanding of the traditional, formal representations becomes less difficult", since no empirical studies of EM of this nature have yet been carried out. So it's important be careful as to how you present your ideas - perhaps stating hypotheses rather than claims, and giving informal reasons why they might be plausible. It may be worth consulting sources such as EM paper 090: "Learning about and through Empirical Modelling", which ventures some kind of justification. Of course, some discussion of how you might corroborate your claims about benefit to the learner in principle (especially in the light of your modelling exercise) would be excellent material for your paper.

Your reference to "currently unforeseen applications of the model" is most welcome and underlines the qualities of the exercise you have chosen. Generally the orientation in your submission is just right for EM. In your description of the model, there is some ambiguity - in the writing at least - about the extent to which you have automation in mind as the primary objective: "this will require the model to check ...". I'm assuming that you realise that - from an EM perspective - the process of arriving at these automated activities involves first engineering them as manual procedures in the same way that this has been done in the heapsort construal. One thing that is worth stressing is the way in which the distinction between a heap and a balanced tree can be expressed in terms of how it is being observed - the 'same' tree might actually be interpretable as being either a heap or a balanced tree. It would be good to bring this out in your written account, and perhaps even to demonstrate it using your model. If you attempt to make a practical model that supports this ambiguity in interpretation, be aware of the importance of avoiding overlapping namespaces by choosing distinctive names for the observables in your construal.

Empirically Modelling ...

With reference to your title, the term "Empirically Modelling" is not one I'm entirely comfortable with (cf. my comment on the term "Empirical Model"). It is unfortunate that we have to use capitalisation to distinguish EM from what is otherwise understood by 'empirical modelling', and I would prefer not to extend the convention in this way.

empirical modelling →  Empirical Modelling

different than →  different from