Further my response (dt. Mar 10, 2013 1:42 AM http://mathforum.org/kb/message.jspa?messageID=8582530 ) to Robert Hansen's 'strategy question', namely, > > That is a solution. What was the strategy. > > Bob Hansen), > I try and provide some insights below about 'strategy'. What I consider to be the most useful part of the response was NOT the 'solution' to the '12-coin problem', but the passage below:
QUOTE The real issue is that we ALL do have these powers. After all, we all learn how to recognize our parents, sit up, stand up, walk, talk - ANY of these skills is INFINITELY more complex than anything taught at MIT or Harvard. Our conventional systems (of thought and work) severely constrain us from accessing these powers in a natural way.
I claim the OPMS can quite significantly help us:
a) recognise that we all do possess these powers;
b) access them quite often; understand them a bit better;
c) not get frustrated because of the barriers and disappointments we all do encounter from time to time. Frustration is the danger - because then the mind stops working in that crucial 'question-asking frame of mind';
d) keep going to try and discover the way to overcome barriers;
e) do MANY other things essential in problem-solving situations (in particular, to retain the 'question-asking frame of mind' which I believe is the heart of the matter). UNQUOTE
Leave the suggestion about OPMS out of it - and you do have 'a general strategy for problem solving'.
(I believe Robert Hansen has failed to recognise or understand this as constituting a 'strategy' - the only kind of strategy that can be replicated (see below for thoughts on 'strategy for the specific 12-coin problem' which I believe is what RH might have been seeking).
The crucial parts of this 'general strategy' are:
i) to recognise the problem solving powers that we all do possess; and then
ii) to become convinced that 'frustration' may be the greatest danger of losing these powers (because it prevents or severely hinders the free flow of ideas in our minds).
The OPMS is merely a useful means to help record and organise the ideas that we all do have.
Without a tool like the OPMS, it is sometimes quite difficult to record and then organise our ideas.
- -- Ideas that are not recorded are often lost.
- -- Ideas that are not 'organised' in appropriate fashion are often unusable.
That's about it for a 'general strategy for problem solving'.
Because the mind 'works in mysterious ways' (*which science has nowadays barely begun to understand*) it is usually very difficult (perhaps impossible) to write down the specific 'strategy' that one might have used (or might use) to resolve a particular problem.
Remarkably enough, the 'general strategy for problem solving' is much easier to do than to discover the specific strategy for any specific problem or issue; as noted, the 'mind works in mysterious ways'.
*As confirmation of this claim, check out (for instance) any issue of Scientific American that discusses anything about the 'mind', or Scientific American Mind (which ostensibly discusses 'mind' but is actually hung up on the 'brain'). You will soon find that science in general is seeking to explore the 'brain' and is not seeking much to understand the 'mind'. There are a great many such remarkable oddities in the 'scientific endeavor'. Please note that I am NOT in the least gainsaying the scientific utility of researches to explore the 'brain'.