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Re: [xmca] a minus times a plus


We miss you

On Tue, Apr 28, 2009 at 7:28 AM, Jerry Balzano <gjbalzano@ucsd.edu> wrote:

> On Apr 27, 2009, at 9:49 PM, Andy Blunden wrote:
>> Why is a number line easier to understand than the
>> symmetries of topological or rhetorical transformations? I
>> don't know, but intuitively I think it is. But different
>> people think differently. Maybe the Linda's rhetorical
>> explanation is easier for a verbal thinker than a spatial
>> thinker? (is this mumbo-jumbo?)
> Andy, although I do think the Mirror is the most powerful and generalizable
> way to introduce the idea, one that is probably more "ready-to-hand" would
> use a coin or a card.  Now the transformations are "leave it alone"/"turn it
> over", and there is nothing esoteric or even particularly "geometric" about
> them (the pattern is pre-numerical AND pre-geometric).   Turn-it-over twice
> in succession has same result as leave-it-alone.  Not done with mirrors, or
> numbers.  ;)
> But the importance of the pattern is its ubiquity!  Even within the realm
> of numbers, before the child tackles the "less than zero" stuff, it's
> customary to learn the "Evens" and the "Odds".  Well, consider how the Evens
> and Odds behave under addition:  E+E = E;  E+O = O;  O+E = O;  O+O = E.
>  Adding an odd number "flips" (reflects) what (some of) us grownups would
> call the "parity" of the number, whereas adding an even number "leaves it
> alone".  Kind of like what multiplying pos & neg numbers do to the sign of
> their product.
> Jerry
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