From sentto-44114-23378-1099615616-lojban-in=lojban.org@returns.groups.yahoo.com Thu Nov 04 16:47:37 2004 Received: with ECARTIS (v1.0.0; list lojban-list); Thu, 04 Nov 2004 16:47:38 -0800 (PST) Received: from n18a.bulk.scd.yahoo.com ([66.94.237.47]) by chain.digitalkingdom.org with smtp (Exim 4.34) id 1CPsGF-00031g-3i for lojban-in@lojban.org; Thu, 04 Nov 2004 16:47:27 -0800 Received: from [66.218.69.4] by n18.bulk.scd.yahoo.com with NNFMP; 05 Nov 2004 00:46:56 -0000 Received: from [66.218.66.27] by mailer4.bulk.scd.yahoo.com with NNFMP; 05 Nov 2004 00:46:56 -0000 X-Yahoo-Newman-Property: groups-email X-Sender: xah@xahlee.org X-Apparently-To: lojban@yahoogroups.com Received: (qmail 67670 invoked from network); 5 Nov 2004 00:46:55 -0000 Received: from unknown (66.218.66.166) by m21.grp.scd.yahoo.com with QMQP; 5 Nov 2004 00:46:55 -0000 Received: from unknown (HELO xahlee.org) (206.130.99.40) by mta5.grp.scd.yahoo.com with SMTP; 5 Nov 2004 00:46:55 -0000 Received: from [192.168.40.41] ([63.197.243.251]) (authenticated) by xahlee.org (8.11.6/8.11.6) with ESMTP id iA50ks322651 for ; Thu, 4 Nov 2004 17:46:54 -0700 In-Reply-To: <20041104031326.44792.qmail@web51604.mail.yahoo.com> References: <20041104031326.44792.qmail@web51604.mail.yahoo.com> Message-Id: <72DB34BB-2E96-11D9-8713-000A95C58224@xahlee.org> To: lojban@yahoogroups.com X-Mailer: Apple Mail (2.619) X-eGroups-Remote-IP: 206.130.99.40 From: xah lee X-Yahoo-Profile: p0lyglut MIME-Version: 1.0 Mailing-List: list lojban@yahoogroups.com; contact lojban-owner@yahoogroups.com Delivered-To: mailing list lojban@yahoogroups.com Precedence: bulk Date: Thu, 4 Nov 2004 11:19:29 -0800 Subject: [lojban] Re: how to say manifold Content-Type: text/plain; charset=ISO-2022-JP X-archive-position: 8950 X-ecartis-version: Ecartis v1.0.0 Sender: lojban-list-bounce@lojban.org Errors-to: lojban-list-bounce@lojban.org X-original-sender: xah@xahlee.org Precedence: bulk Reply-to: lojban-list@lojban.org X-list: lojban-list the "manifold" in its bare essence means a shaped space, so to speak. Curves for example, are 1-dimensional entities, which differs from what one normally thinks of 1-D space (straights lines) because it has a "shape" associated to it. Likewise, surfaces are 2-dimensional "skins" that is a plane with a shape. Similarly, there can be 3-dimensional entities that differs from our "straight" 3-space we live in. And so on for n-dimensions. in math　technicality, manifold has more specific meaning. i.e. that it is everywhere differentiable etc. Or the similar notion of term "variety" in algebraic geometry, which essentially also means n-dimensional curve/surface entity like manifold, but with nuances or technicalities that suits algebraic geometry. all considered, there is the basic need for a word to specify curve/surface entities of more than 2/3 dimensions. And i think their essential meaning is "shaped-space". Thus i think lojban word of shaped-space would be a good candidate. i was surprised it wasn't a core word in lojban or one haven't already been devised and settled. At first i thought sefta was it. sefta @ x1 is surface/face [bounded shape/form] of [higher-dimension] object x2, on side x3, edges x4 but as someone pointed out in previous post, sefta means a particular face/side/part of an n-dimensional object. (and this object has sides and edges, apparently referring to higher-dimensional polygons (i.e. polytopes)). i thought a manifold word would have a structure like this: x1 is a manifold of dimension x2 embedded in dimension x3 with properties x4 How do lojban say curves and surfaces? Xah xah@xahlee.org http://xahlee.org/PageTwo_dir/more.html ------------------------ Yahoo! Groups Sponsor --------------------~--> Make a clean sweep of pop-up ads. Yahoo! Companion Toolbar. Now with Pop-Up Blocker. Get it for free! http://us.click.yahoo.com/L5YrjA/eSIIAA/yQLSAA/GSaulB/TM --------------------------------------------------------------------~-> To unsubscribe, send mail to lojban-unsubscribe@onelist.com Yahoo! Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/lojban/ <*> To unsubscribe from this group, send an email to: lojban-unsubscribe@yahoogroups.com <*> Your use of Yahoo! Groups is subject to: http://docs.yahoo.com/info/terms/