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These files are maintained strictly for historical reference, research, and recordkeeping purposes,
and the content has not been altered or updated since archiving.
Content on this site may not meet current digital accessibility standards.
If you require an alternative, accessible format of any information found on this site,
please contact Bruce Jones, bjones@ucsd.edu to request an accommodation.
WHERE ARE U!!?? We miss you mike 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 > > > _______________________________________________ > xmca mailing list > xmca@weber.ucsd.edu > http://dss.ucsd.edu/mailman/listinfo/xmca > _______________________________________________ xmca mailing list xmca@weber.ucsd.edu http://dss.ucsd.edu/mailman/listinfo/xmca