Further my last (dt. May 23, 2014 11:51 AM, http://mathforum.org/kb/thread.jspa?threadID=2633379), I observe that I had omitted several points that I should have made there. Herewith brief notes, next to the paragraphs where the discussion was inadequate in the earlier posting: > <snip> > > [This concept of *intricate involvement* is something > that only recently came to mind. I shall try and > make it clearer in what follows, but full clarity > will probably take somewhat longer to appear - even > in my own mind! It's a bit different from > *inextricable involvement* (though there surely is a > bit of each in the other)]. > I've not managed to make clear the distinction I am seeing between *intricate involvement* and *inextricable involvement*. Probably this can be done only with the aid of some 'prose + structural graphics' (p+sg) - this is my feeling anyway.
Possibly we'd need some discussion of the "IMPLICATIONS" involved in the structure of the 'thought systems' I am attempting to explore.
Here, I find myself at a bit of a loss because of the non-availability of a practical modeling tool for the "IMPLICATIONS" relationship in complex systems - something that could do for the "IMPLICATIONS" relationship what 'Interpretive Structural Modeling' (ISM) has done for the "CONTRIBUTION" and other such '1st order transitive relationships in complex systems'.
Possibly someone who has profoundly explored and thoroughly understood "IMPLICATIONS", like Robert Hansen, may be able to come to my aid? > > Anyway, there is clearly considerable *creativity* in > 'learning something new' (in math, or in any other > discipline); there is also great creativity in > ideating and then developing those new ideas (in > math, or in any other discipline). > I don't know if empirical studies have been done relating to these aspects of *creativity* - the creativity involved in learning something new, exploring new knowledge. I suspect that any such studies performed using the 'conventional systems' of thought are likely to be 'inadequate' (to put it mildly). > <snip> > > In his generally sound introductory remarks to the > excerpt he's provided to the book "The Philosophy of > Creativity", Scott Barry Kaufman makes clear his > appreciation of the importance of the issue for us as > humans: > <snip> I've snipped Scott Barry Kaufman's introductory remarks that I had quoted, and point out that they provide a useful '1st order appreciation' of *creativity*: we obviously do need to go somewhat deeper, which, in my view, is very difficult - perhaps even impossible - to do in the 'pure prose' mode. > <snip> > > However, I suggest another, further, proposition: > > There is considerable *real creativity* involved in > the 'learning of math' (at any level) - from the > most elementary to the most advanced. There is *real > creativity* (of probably a different order) involved > in the *creation* of 'new math'. > > There is both 'knowledge' and 'art' (in Robert > Hansen's sense) *intricately involved* in the > *creation* of 'new math'. In fact, there is, I > claim, both 'knowledge' and 'art' intricately > involved in the *creation* of 'new knowledge' in ANY > discipline! > > There are, for instance, VERY advanced levels of both > 'knowledge' and 'art' in the creation of one of > George Hart's 'geometrical sculptures'. > I'd like to emphasise all of the above. I'd also like to explore all of the above much more deeply (via the OPMS), as well as the many useful (along with several useless) ideas that have been expressed. Unfortunately, we lack the needed facilities for the interactive exploration of ideas. Maybe when such a facility becomes readily available, I shall be able to do some of that... <snip>