[lojban] carna, my turn.

[Robin Lee Powell <rlpowell@digitalkingdom.org>]

(Jesus fuck this is long; it's *really* not as bad as it looks.
It's certainly nowhere near as complicated as, say, the tense
system.)

This is my attempt to synthesize the thinking so far into an
alternate definition for {carna} that shouldn't invalidate any
current usage.

Note that between this and the problem we've had with {farna}, I'm
inclined to write up a full tutorial on directions, distances,
locations, vectors, and so on, add it to the CLL, and have these
words just have the basic definition and say "See chapter N".  But
here it is anyway.

The basic mechanism here, in programming terms, is polymorphism in
the x2 and x4 places.

Since this *looks* crazy complicated, I'm going to start with
examples, to show that what comes out is quite reasonable.

  {mi carna fi lo pritu}
  I turn towards something to my right.  The distance is
  unspecified and left up to context; it could mean you spin in
  place many times, or that you turn just enough to face the house
  on your right, or anything in between.

  {mi carna fi lo berti}
  I turn towards the north [again, distance unspecified].

  {mi carna (mi/zo'e) lo pritu (li pi re mu/lo julra'o be li so
  no/lo radno be li pi mu pi'i pai)}
  I turn a quarter turn to the right.

  {do carna do lo pritu li pi re mu}
  You turned a quarter turn to your right.

  {mi carna fo lo pritu}
  I turn in some direction unspecified such that I end up facing
  something to my right (i.e. that was on my right before I started
  turning).  Since minimal distance is assumed, this is the shortest
  way to say "I turn right" with almost no risk of being
  misunderstood.

  {mi carna fi lo pritu lo pritu}
  I turn to the right.  This is the same as the previous example,
  just being extra clear.

  {do carna mi lo pritu}
  From my point of view, you rotated clockwise [which, assuming two
  standing humans facing each other, implies a cartwheel or similar]

  {do carna do lo pritu be mi}
  You turned towards something on my right.

  {do carna le zunle tupyjanco be fi do ce'o le pritu tupyjanco be
  fi do le zunle be mi li pi mu}
  You rotated over your hips towards something to my left, one half
  a turn, i.e. you are now standing on your hands or something.  A
  situation that would make this perfectly reasonable is if you're
  doing a flip into a handstand, and I'm your spotter, and I'm
  standing to your right.  Note that in this case, because the thing
  being turned towards isn't relative to the x1, the direction of
  the x2 vector isn't important.  For the same reason, we don't know
  if the gymnast did a front or back flip.

  {do carna le zunle tupyjanco be fi do ce'o le pritu tupyjanco be
  fi do lo zunle li pi mu}
  Same thing, but now we know for certain that it was a back flip.
  If you were willing to argue that the line through a person's hips
  has a natural front, you could say {lo gapru} instead of {lo
  zunle}, because if you imagine a person pointing an arm out of the
  middle of their crotch, a back flip is equivalent to that arm
  moving upwards.

  {do carna mi lo zunle li pi mu}
  If I'm your spotter and I'm on your right and you are sideways to
  me facing to my right, this means exactly the same thing as the
  previous sentence, and is what would be used in almost every case.

  {le selkei cu carna fo so'i da}
  The toy is spinning.

  {le selkei cu carna mi lo pritu so'i da}
  The toy is spinning clockwise from my point of view.

  {le selkei cu carna (lo gapru/le drudi) lo pritu so'i da}
  The toy is spinning clockwise if viewed from above.

  {le selkei cu carna le loldi ce'o le drudi lo pritu so'i da}
  The toy is spinning clockwise if viewed from above.

  {le selkei cu carna le drudi ce'o le loldi lo pritu so'i da}
  The toy is spinning clockwise if viewed from below.

And here's the actual definition plus notes/tutorial.  This really
is *fundamentally* complex, as we've discovered in this discussion.
My previous version, which relied on the right hand rule, was very
easy to define, but led to *horrendous* sentences that were
extremely counter-intuitive.  In this version, I've sacrificed some
initial learning curve for very easy use once you get used to it.

  x1 turns about vector x2 towards direction x3, turning angular
  distance / to face point x4

  Notes: When reading these notes please give allowances for the
  fact that facing in three dimensions is inherently complicated,
  but note that the defaults make this actually very easy to use.
  Each subsequent section gets more general and less likely to be
  needed in practice.

  Let's start with an x1 object that has both a top and a front,
  i.e. you yourself.  Your default x2 is a vector running along your
  body from the bottom to point out of the top of their head.
  Imagine that you start pointing your hand in some direction, and
  then move your pointing hand towards the x3.  The movement
  describes a circle around you, perpendicular to the x2 vector;
  we'll reference that later.  For this case in the x2 you could use
  {zo'e}, or {mi}, or just skip it entirely; all of those options
  are shorthand for "the vector running through me pointing out the
  top of my head".  The x3 is anything you can point at.  We'll
  cover x4 seperately.

  This holds for any object with a top and a front; by default, if
  the x2 is {zo'e} or the object itself, the x2 vector is from the
  bottom pointing topwards, and the turning is from the front of the
  object as though the object was a person describing eir own
  movement.

  If the object has a top but not the front, it's basically the
  same, you just can't specify anything but {lo pritu} or {lo zunle}
  for the x3.  If it has a front you could talk about the front
  turning "towards the north" or whatever, but with no natural front
  you can only talk about the direction of rotation in general
  terms.

  Note that in all such cases, which is things like "x1 carna x1 lo
  pritu", these are equivalent to "x1 rotates clockwise if viewed
  from above", and similarily for "lo zunle" and
  "counter-clockwise".

  If the x2 is a single object or place other than the x1, then draw
  the vector from the x1 to the x2.  This leads to very natural ways
  to talk about something you're looking at moving clockwise or
  whatever; {le junla grana cu carna mi lo pritu} means "if the clock was
  a person, with its head pointing towards me and its clock hand
  sticking out in front of it, it would say that it is moving its
  clock hand to the right", which happens to be what "clockwise"
  is, as with viewing a person from above in the {do carna do lo
  pritu} case.

  Similarily, {le selkei cu carna lo gapru lo zunle} is "the toy
  [perhaps a top] is spinning counter-clockwise when viewed from
  above", because that's what it would look like if a human was in
  place of that top, and standing up (i.e. head pointing to {lo
  gapru}) and turning to what they called {lo zunle}.

  For maximum specificity, you can specify the vector exactly, by
  using "ce'o"; the vector points from the first element of the
  "ce'o" to the last.  This is unlikely to be useful very often.

  The x4 is one of a number, in which case it is the (possibly
  fractional) number of complete turns made; an exact specification
  of radians or degrees or whatever (i.e. {lo julra'o li so no}), in
  which case that's how far the turn went; or an object or place, in
  which case the turn was the minimum distance required to end with
  the x1 facing that object or place.  That last is not OK if the x1
  has no natural front.

  Unless clearly specified otherwise, the x3 and the x4 from the point of
  view of the circle of movement perpendicular to the x2 vector, as
  everything was positioned before the movement started.  This is
  almost always the same as saying that the x3 and x4 are from the
  point of view of the x1 before the movement started.

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