# Re: cardinal directions

• From: Marc Ruehlaender <[email protected]>
• Subject: Re: cardinal directions
• Date: Wed, 01 Dec 1999 16:11:43 CST

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In message <[email protected]> Ben Gibson writes:
[snip]
> My [..] objection [..] is that when translating from a polar
> coordinate system to such an isonormal system, to uniquely
> identify a point requires one extra coordinate.
why?

> [..] in polar notation, one can say “‘ev chan ‘ev,
> chuq cha’maH qelI'qam”.
this is as the word "chuq" clearly indicates, obviously
not a point on the surface.

it seems that by "polar notation" you mean something like
a set of directions? this is of course quite different
from a coordinate system!

> But to identify the map coordinates
> of the same point, you would have to give a set of 3 vectors
no.

> The intersection of two rows in such a map
?? what do you mean by "rows of a map"
are you using "map" in the mathematical sense, as
in a "map from the space of points on the surface of a sphere
to the space of coordinate vectors"?
are you then referring to the "rows" of a matrix representation
of such a map?

and in any case, what do you mean by the "intersection"
of such or any "rows"?

> gives not one triangle, but two.
ah... maybe I'm beginning to understand.

by "rows" you mean the area of points with the values of one
coordinate in some finite value, while the second runs through
all allowed values?

if so, then I think you are mistaken. remember that such
"rows" in 'ev or tIng directions will be spirals ending at the
two poles, thus intersecting any given "row" in chan direction
only once. any "row" in 'ev direction may however have several
"intersections" with a "row" in tIng direction.

[snip]
> Now you may argue that such an objection can be overcome by
> more precisely defining the length of the basis vectors. And
> Klingons are an exact culture. That would be a good argument
>
now you lost me again. what do you think would change
with the length of the basis vectors?

[snip]
> triangles than using Cartesian squares. You get far less
> geometric distortion in mapping a globe to a flat surface
> using the isonormal system, than in using the system we
> presently use. (For an example, take a look at
> http://www.bfi.org/map.htm and compare it to a Mercator
> projection.
>
this map doesn't show any coordinate system.
and again, I think you are forgetting that "rows" in
'ev or tIng direction are spiraling towards the poles
and thus creating the same discontinuity as orthogonal
coordinates. (instead of rectangles Klingons have
ahm... "diamonds", sorry I forgot the english word for
the shape of a tetragon with equal opposite sides
but angles different from right ones)

[snip]
> You make a comment about how it appears “that Klingons do
> not have any special sense of orientation to the poles.”
> That I think would be detrimental to the culture, and
> unrealistic. (Yes, I know we are talking about a fictional
> culture. I am not that loony. However, I am the type of guy
> who can’t help but nit-pick such things. It is a sickness.)

I'm not sure how relevant this point is for your argument,
but some native american cultures used the point of sunset
and sunrise at the winter and summer turning points as
cardinal directions, roughly NE (sunrise in summer),
SE (sunrise in winter), SW (sunset in winter) and NW
(sunset in summer).

they still had a pretty good way of figuring out when
to plant and harvest crops.

[snip]
>
> For information, including means of building your own Klin
> Zha set, goto http://www.fyi.net/~kordite/klinzha.htm. On
> the page http://www.fyi.net/~kordite/takzh/variant.htm it
> discusses the means by which one identifies a specific
> position on the triangular board. (I found it a rather fun
> game, until my son got to the point he could quickly beat me
> every time.:) )
>
and finally I know what you mean by the "two triangles in each
intersection" above... might have helped to cite that page earlier :)

note however, that each _point_ is uniquely identified by
two coordinates. for the sake of simplicity replace the letters
I..A with numbers 1..9 and assume that they label not the
"row" but its upper borderline, and assume that the original
numbers label the "left" borderline. the midpoint of E-38
is at (4.67;3.33), the midpoint of E-37 is at (4.33;3.67).

coordinates do not label areas, they label points.

of course we don't know how Klingons do coordinates, as
has been pointed out already. but certainly the use of
chan and either or both of 'ev and tIng is not so far out.

Marc Ruehlaender
aka HomDoq
[email protected]
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