Re: [lojban] Direction of Rotation

[Escape Landsome <escaaape@gmail.com>]

.

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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