Date: Dec 4, 2012 10:58 AM
Author: Joe Niederberger
Subject: Re: In "square root of -1", should we say "minus 1" or "negative<br> 1"?

>I mean, by the time you figure out the cars or un-losing poker hands, you have probably developed the elements (habits of mind) behind formal thinking. 

Another answer (sorry):

Really "formal thinking" leads one down the "Martinez" road where one realizes that the rule could be different, but the usual rule as is preserves other nice properties like distributivity, identity. That seems about where Peter Duveen ended up but long time after formal schooling.

Simply working through the logic of some time-reversal scenario or other way of illustrating the sign rule, may in fact stand in the way of deeper understanding, because the person may think that somehow "proves" the matter.
It good, but its not enough by itself.

Nor do I think "virtuous circles" (Manzur) prove it.

Cheers,
Joe N