Date: Nov 28, 2012 5:28 AM
Author: GS Chandy
Subject: Re: Some important demonstrations on negative numbers

Robert Hansen (RH) posted  Nov 28, 2012 7:26 AM  (GSC's remarks interspersed):
> On Nov 27, 2012, at 5:51 PM, Joe Niederberger
> <> wrote:

> > Your war against common sense though,...
> I have no war against common sense. That would be
> like having a war against taste or smell. My claim is
> simple. Common sense just isn't synonymous with
> mathematics, or more precisely, with reasoned thought
> and analysis. In fact, the two domains share nothing
> in common, no pun intended. Regardless of the fact
> that reasoned thought can explain common sense and
> fathom its examples, it acts entirely in spite of
> common sense. And "commonplace" is certainly not
> synonymous with "common sense". That has a different
> meaning altogether.

As so often, RH's claims arise out of a total misunderstanding of just what he is writing about, in this case, about what 'common sense' may be; and just what its derivates, such as 'reasoned thought and analysis' (and 'synthesis'; and, for that matter, 'mathematics') are. Reasoned thought and analysis (and synthesis' and for that matter, mathematics) in fact all *grow out* of 'common sense'. It is true enough that one person's 'common sense' may be another's 'nonsense' - the great human adventure, in which 'language' has played a crucial role, has always been to try and arrive at an adequate mutual understanding of each others' 'common sense'.

A little reasoned thought and analysis will show that the above is inescapably true in all circumstances. It is a fact that reasoned thought and analysis (and synthesis) can often lead us to results that may seem counter-intuitive (i.e. against 'common sense') - but that does not negate their origins.
> Common sense is the perception of the concrete world
> that we all share.

True enough.
> Common sense is devoid of reasoned
> thought and analysis.

> That is my definition and in
> the context of this discussion, neither unfair nor
> unwarranted.

It's a 'definition' arising out of a ridiculous misunderstanding.
> Mathematics on the other hand is
> analysis. It is a reasoned and imagined theory about
> abstract and imagined entities, most significantly,
> the real numbers. When we attempt to teach this
> imagined theory and its imagined elements to the
> unaware student, we use concrete examples (common
> sense) as an aid in that task but not as a substitute
> for that task and not as a substitute for the goal of
> the task, reasoned analysis and thought.

See all of above.

("Still Shoveling Away!" - with apologies if due to Barry Garelick for any tedium caused; and with the observation that there is a SIMPLE way to avoid such tedium)