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<201208102246.34877.jezuch@interia.pl> Date: Sat, 11 Aug 2012 10:33:41 +0200 Message-ID: Subject: Re: [lojban] Direction of Rotation From: Escape Landsome To: lojban@googlegroups.com X-Original-Sender: escaaape@gmail.com X-Original-Authentication-Results: gmr-mx.google.com; spf=pass (google.com: domain of escaaape@gmail.com designates 209.85.214.180 as permitted sender) smtp.mail=escaaape@gmail.com; dkim=pass header.i=@gmail.com Reply-To: lojban@googlegroups.com Precedence: list Mailing-list: list lojban@googlegroups.com; contact lojban+owners@googlegroups.com List-ID: X-Google-Group-Id: 1004133512417 List-Post: , List-Help: , List-Archive: Sender: lojban@googlegroups.com List-Subscribe: , List-Unsubscribe: , Content-Type: text/plain; charset=ISO-8859-1 X-Spam-Score: -0.7 (/) X-Spam_score: -0.7 X-Spam_score_int: -6 X-Spam_bar: / . To put it simply, you may say that CLOCKWISE and COUNTER-CLOCKWISE are defined is LEFT and RIGHT are, or if DIRECT and REVERSE FRAMES are. Let's say that X = (1,0,0), Y = (0,1,0) and Z = (0,0,1) are a direct frame (X,Y,Z). Then (X,Z,Y) (or any simple transposition of (X,Y,Z) is a reverse frame. (indirect frame) Det (X,Y,Z) = +1 Det(X,Z,Y) = -1 Two frames are oriented the same way if they have the same Det Two frames are oriented opposite ways if theirs Det are opposite Now, the STRANGE thing you learn in Tensor algebra is that there is no way to tell Det, outside a convention. One COULD decide that it is (X,Y,Z) that has Det = -1, after all ! Then it would be (X,Z,Y) that has Det = +1 The only thing that remains STABLE in all this is that their Dets are opposite ! (since there is a transposition of Y and Z between (X,Y,Z) and (X,Z,Y)) --- Now, human beings and physicists in particular need a way to compute Det. So they CREATE A WAY to compute some Det, by STATING that X, Y and Z are "normally" in those directions we know. But, --- hold on, this is the difficult point where most people can't follow the reasonning ---, there is no way to specify this out of a convention rooted in OUR EXPERIENCE OF OUR DAILY UNIVERSE, that is, in OUR BODY and OUR CULTURE. For, saying that X is defined as (1,0,0), Y as (0,1,0) and Z as (0,0,1) does not mean anything sensible in the absolute. It means somethings SENSIBLE only if we have SENSES that tell us, for instance, that X direction is the sense of my right hand thumb, Y my right hand index, and Z my right hand middle finger... THEN, it becomes sensible But, without that, it would be possible to trace the Z-axis in opposite direction, and Z would still be (0,0,1), --- but you would say "clockwise" and I would see "counterclockwise". --- So, to get the coordinate system sensible, you need to root them in an experience. Kant's experience of a right hand means that if you write down the set of all points pertaining to a right hand, R = { (x1,y1,z1), (x2,y2,z2), (x3,y3,z3), ... } you still have no clue whether R is a right hand or a left hand, until you have not decided to set an orientation to space --- which is what space does NOT have per se. ORIENTATION does NOT pertain to space, as all mathematicians and kantians know (and wittgenstenians too, and carrollians too). ORIENTATION comes only through convention. --- No, I'm in holiday, so I do not have books with me currently, so we'll have to wait a month or so till I can give you extracts of high maths books (or philosophy books) that speak of that, but all this is known for long by scholars. -- You received this message because you are subscribed to the Google Groups "lojban" group. To post to this group, send email to lojban@googlegroups.com. To unsubscribe from this group, send email to lojban+unsubscribe@googlegroups.com. For more options, visit this group at http://groups.google.com/group/lojban?hl=en.