Hi All

I tried to reply before but I wasn't a member of the list so apparently it didn't get through. Thanks to Chris Douce for adding me, so this reply should work.

On 28/11/2009, at 7:43 AM, Raymond Lister wrote:

On Fri, 27 Nov 2009, Richard O'Keefe wrote:
Anthony Robins
recently noticed

Thanks to Richard for mentioning my paper on this. But there are some minor revisions to be made before it is published, so please don't quote the version on my web page quite yet. I'll put the final version up next week some time.

And G'day Ray, long time no see!

Third, I regard Anthony's model as a good counter argument to the
conventional "geek gene" argument, but if I ignore the "geek gene"
argument and merely examine Anthony's model in isolation, then I
suspect that the number of free parameters in his model means that
you can get any distribution you want, by a suitable choice of
parameter values.

I don't think it has an overabundance of free parameters. Given some pretty minimal assumptions that generate a normal distribution (M0), it requires exactly one additional parameter (an offset, M1) to turn the normal distribution into an anti-normal / bimodal one. This basic model can only vary the "flatness" of the distribution on a continuum from sharply peaked at the centre to normal to flat to bimodal to sharply peaked at the extremes (and, of less interest from my point of view, it can move the centre of the distribution). After that one further parameter shapes the curve at the top or bottom end, but I still don't think that you can quite get "any distribution you want" out if it!

I presented one particular version in the paper, but the actual effect is very robust. As Richard described it: "Roughly speaking: a series of topics where failure at any point makes later failure more likely, success makes later success more likely" - almost any reasonable interpretation and implementation of this concept can turn a normal distribution into an anti-normal / bimodal one.

As to what, if anything, the model means in educational terms, I make the case in the paper. But Ray's certainly right that there's plenty more to do - I welcome his suggestions as to where to look next, and all other suggestions too...


Anthony Robins =======================================================
Computer Science                                anth...@cs.otago.ac.nz
University of Otago                             ph:    +64 3 4798314
Dunedin                                                 fax:   +64 3 4798529
NEW ZEALAND                             

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