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*To*: "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu>*Subject*: Re: [xmca] a minus times a plus*From*: Ed Wall <ewall@umich.edu>*Date*: Tue, 28 Apr 2009 19:56:35 -0400*Delivered-to*: xmca@weber.ucsd.edu*Domainkey-signature*: a=rsa-sha1; s=2007001; d=ucsd.edu; c=simple; q=dns; b=ZxApMx1uXfTAauGi8Nt0ZseI+Gw4g9Kc9kNx47K2kt7NCEZSZnIyat5e2k/wNZA2R AAfa2hHPoPTUFCkswRqbQ==*In-reply-to*: <14a6419f0904281618w18a893bl6ba547d8a54038ae@mail.gmail.com>*List-archive*: <http://dss.ucsd.edu/mailman/private/xmca>*List-help*: <mailto:xmca-request@weber.ucsd.edu?subject=help>*List-id*: "eXtended Mind, Culture, Activity" <xmca.weber.ucsd.edu>*List-post*: <mailto:xmca@weber.ucsd.edu>*List-subscribe*: <http://dss.ucsd.edu/mailman/listinfo/xmca>, <mailto:xmca-request@weber.ucsd.edu?subject=subscribe>*List-unsubscribe*: <http://dss.ucsd.edu/mailman/listinfo/xmca>, <mailto:xmca-request@weber.ucsd.edu?subject=unsubscribe>*References*: <30364f990904271547o5b4df21eifca69bf8318483f2@mail.gmail.com> <2C46D7A7-AD94-441C-AABD-269045835E3D@umich.edu> <0193A85F-03A7-4811-B912-217722A5770B@uvic.ca> <C23F99F4-D4AC-463B-AF11-30585E74F7CF@me.com> <30364f990904271949r3cfef116m89d39ea419d112b2@mail.gmail.com> <p06240805c61c2a15a97a@192.168.1.65> <49F68AEE.40502@mira.net> <3B19033D3E2EC34C97DF364119A79A61C90CDD@EXVS1.its.uidaho.edu> <49F70BF8.6050904@unm.edu> <3B19033D3E2EC34C97DF364119A79A61C90D8A@EXVS1.its.uidaho.edu> <14a6419f0904281618w18a893bl6ba547d8a54038ae@mail.gmail.com>*Reply-to*: "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu>*Sender*: xmca-bounces@weber.ucsd.edu

Ng Foo Keong

Ed Wall On Apr 28, 2009, at 7:18 PM, Ng Foo Keong wrote:

regarding sand and multiplication:- another crazy analogy i was toying with. i imagine Mr Sand-man piling up sand (+) and taking away sand (-). i imagine his counter-part Mr Hole-man living upside down in the ground, who treats holes as "real stuff" and sand as absence of holes. When Mr Sand-man digs a hole say 6 feet below ground (-6), he's piling up something "real" for Mr Hole-man. If Mr Hole-man living upside-down below ground uses his magic spade to dig away one feet of hole "-(-3)", he's in fact filling up one feet of sand (+3). If Mr Hole-man does this twice, then it is (-2 × -3), same as filling up the hole (2 × 3). it seems we got to tweak our ontologies to get this to work. regarding discs:- i was part of a Singapore team that did the AlgeTools software that included AlgeDisc, an electronic version of "number discs". You can do this just as well with coins (heads vs tails) or coloured discs. There are 2 types of discs e.g. blue (positive) and red (negative). a blue and a red disc forms a zero-pair, so a blue and a red disc annihilate each other. you can also put in pairs of blue and red discs at will with impunity. so put in say 6 such zero-pairs. -2 × -3 means two times _removing_ sets of 3 red discs. that leaves the 6 blue discs i.e. the operation has the same effect as adding two sets of blue discs (2 × 3). regarding structure and agency, arbitrariness:- i think now it's time for me to pop this question that has been bugging me for some time. i am convinced that mathematics is socially constructured, but i am not so convinced that mathematics is _merely_ socially constructured. if we vary across cultures and different human activities, we might find different ways in which patterns and structure can be expressed and yet we might find commonalities / analogies. the question i am asking is: is maths just a ball game determined by some group of nerds who happen to be in power and dominate the discourse, or is there some invariant, something deeper in maths that can transcend and unite language, culture, activity .... ? Foo Keong, NIE, Singapore 2

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**References**:**[xmca] a minus times a plus***From:*Mike Cole <lchcmike@gmail.com>

**Re: [xmca] a minus times a plus***From:*Ed Wall <ewall@umich.edu>

**Re: [xmca] a minus times a plus***From:*Wolff-Michael Roth <mroth@uvic.ca>

**Re: [xmca] a minus times a plus***From:*Steve Gabosch <stevegabosch@me.com>

**Re: [xmca] a minus times a plus***From:*Mike Cole <lchcmike@gmail.com>

**Re: [xmca] a minus times a plus***From:*Andy Blunden <ablunden@mira.net>

**RE: [xmca] a minus times a plus***From:*"Duvall, Emily" <emily@uidaho.edu>

**Re: [xmca] a minus times a plus***From:*David Atencio <atencio1@unm.edu>

**RE: [xmca] a minus times a plus***From:*"Duvall, Emily" <emily@uidaho.edu>

**Re: [xmca] a minus times a plus***From:*Ng Foo Keong <lefouque@gmail.com>

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