--- In BoundaryPoint@y..., "granthutchison" <granthutchison@b...> wrote:
> Michael:
> > has prompted me to focus
> > again even if still a bit prematurely on our whole phenomenal
> collection of
> > world class boundary crosses
> How can you tell if the boundaries cross? Is it by the numbering of
> the monuments?
> Because in general I find the notion of crossed boundaries a little
> odd. If I am walking clockwise around H1 in Baarle with Baarle-Hertog
> on my right, it seems strange to be suddenly walking around H2 in an
> anticlockwise direction with Baarle-Hertog on my left. I'd rather not
> reverse the intrinsic vector of my boundary, and would prefer to
> bounce off the shared point to circumnavigate H2 clockwise too,
> keeping Baarle-Hertog on the right.
> In fact, I'd rather ignore the monument numbers and accept a universal
> rule that:
> Widdershins (anticlockwise) = entity always on left
> Deasil (clockwise) = entity on always on right
> With this scheme, you can circumnavigate H1 with or without H2, and H2
> with or without H1. Without it, you end up doing sneaky
> figure-of-eights and shifting your entity from left to right.
>
> Grant
well you certainly may do all that & think all that & thus spare yourself the benefit &or deficit of the crosses
& i confess i really do think of crosses almost purely as plusses
so that is perhaps a little imbalanced of me right from the start
but to answer your questions from this odd perspective of mine
i can tell that the boundaries actually cross with me rather than turn with you in walking the baarle example & probably the bengal examples too simply because there is no demarcation of the quadripoint on the spot to turn at but at best only the intersecting sight lines from 4 neighbor marks to guide me thru the crossing for indeed there is no earthly nor heavenly reason to stop & complicate everything at that point just in order to pivot & point doggedly about the point
for to me that would really be sneaky & shifty
& i realize you may still choose not to believe or follow your eyes but only your feet even then too
now admittedly this is not the case at jungholz & indeed had it not been marked by a vertical cross it would actually have suggested even to a cross enthusiast such as me that the boundaries neither form a truly cruciform cross there nor could they nor should they be thought to actually cross
just as you choose to believe & establish by universal rule
& the numbering of the monuments may well be deemed to settle it in your favor in every case for i dont know about this
& whatever the plusses &or minuses may be of the crosses in europe we probably cant expect to find such extreme enthusiasm for them from the muslims & hindus in bengal so i would agree you are generally looking perfectly golden with pivoting & recovering if that is your choice
& yet i also wonder whether the pioneer topologist in you doesnt also thrill to behold possible evidence of moebius & escher realities & leftright alphaomega entities on the face of the earth
but i agree it is optional at best
m