Re: All you (n)ever wanted to know about the Ferochromon

On Thu, Apr 21, 2005 at 09:02:30PM +0100, Simon Clarkstone wrote:
> On 4/21/05, H. S. Teoh <hsteoh@...> wrote:
> > For the sake of keeping it to a sane length, I decided to omit the
> > history of the Ebisédi, which incidentally is already covered by
> > another document, and stick only to the large-scale physical structure
> > of the Ferochromon. Anyway, you may read it here:
> >
> > http://conlang.eusebeia.dyndns.org/ferochromon/cosmohist.html
> One slight problem: I was totally confused until I realised that by
> "function", you don't mean mathematical function, but purpose or use.
Yeah, that's the problem with the polysemy of the English word
"function". I don't know what other term to use, though. I guess it
gets doubly bad when I start talking about differentiation, which
isn't referring to the calculus operation, but rather a specialization
in function.

The basic idea is that high energy FE is akin to a ball sitting at the
top of a hill, which can decide which valley (function/mode) it wants
to fall into, whereas a low energy FE is a ball that has fallen into
the valley and doesn't have enough energy to climb the sides of the
valley (can't change function/mode anymore).


> Also, I make the dimensionality of the Hyperether to be 3 that the
> lattices correspond to (each is a spacial dimension of the
> corresponding realm) + 2 that all three realms have (the other two
> dimensions of space for the realms) + (at least) 1 along the line
> between the two poles = (at least) 6.
>
> AFAICT, the realms have dimensions u-v-x, u-v-y, and u-v-z, where x,
> y, and z correspond to the three lattices, so the realms are (flat)
> 3-manifolds embedded in a 5(or higher)-manifold.
Yeah, in my conception of it, the realms are essentially 3-manifolds
embedded in higher-dimensional space.

Although, in my mind lattice "orientation" is more the "shape" of the
lattices themselves, such that only compatible shapes can tile
together.  To use a 2D example, one "orientation" might be squares,
and another might be hexagons. Squares produce a regular tiling that
covers (2D) space as do hexagons, but a mixture of squares and
hexagons can't form a gapless tiling.

In this analysis, the undifferentiated state would correspond with a
higher dimensional space such that the shapes become compatible. What
I have in mind here is something like this: the "squares" and
"hexagons" that tile the 2D plane are actually 3D cubes confined in a
2D plane in different orientations. Cubes that got embedded in the
plane perpendicular to their axis occupy a square area in the plane
(because the perpendicular intersection of the cube with the plane is
a square), whereas cubes that got embedded in a tilted orientation
occupy a hexagonal area (the maximal intersection of the cube with the
plane is a hexagon). Because they are now stuck to the 2D plane, they
can no longer rotate in 3D, so the "hexagons" and the "squares" can no
longer interconvert. So even though the same cubes could tile 3D space
seamlessly, they behave as though they were different shapes in 2D,
because they are oriented differently when they got stuck on the 2D
plane.

In other words, the lattices are higher-dimensional space-tiling
polytopes that got entrapped in a lower-dimensional manifold, so that
they form different space-tiling shapes depending on their orientation
at the time they got entrapped.


BTW, out of curiosity, what do you have in mind w.r.t. how to approach
creating equations that describe the Ferochromon? I've attempted this
a few times but gave up because it just got way too complicated. The
bit that requires constant force to remain in motion is easy, but I
have a hard time coming up with precise equations that would predict
such things as approaching objects spiralling inwards rather than
collide head-on, or how objects in curved motion would be drawn
inwards in the direction of the curve, etc..


T

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