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Re: [lojban] Direction of Rotation
Escape, you are being needlessly confrontational (and somewhat
condescending), and it is not helping to make your point.
To contrast your point, in high school and university in the US, we
are taught basic calculus and basic physics, and it is made clear that
some arbitrary sign convention is necessary, and positive is chosen to
denote counterclockwise angles. This is a thoroughly shared
cross-cultural framework, and it's useful.
Also, you seem to be arguing a point that no-one is disputing. We are
trying to find a good (arbitrary) convention, which is present across
(or at least apparent to) various cultures; we are not trying to find
an absolute frame of reference.
On Sat, Aug 11, 2012 at 4:33 AM, Escape Landsome <escaaape@gmail.com> wrote:
> .
>
> 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.
>
> --
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--
mu'o mi'e .arpis.
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