types of 4-space

Higher-dimensional geometry (previously "Polyshapes").

Postby wendy » Fri Feb 10, 2006 8:05 am

CE3 is complex euclidean 3d: ie 3 complex axies + euclidean distance.

One measures the norms of distance.

In this space there are eight platonics and two infinites: the five usuals, along with 3{3}3{3}3, 3{3}3{4}2, 2{4}3{3}3, and the two infinite families p{4}2{3}2 and 2{3}2{4}p.

W
The dream you dream alone is only a dream
the dream we dream together is reality.

\ ( \(\LaTeX\ \) \ ) [no spaces] at https://greasyfork.org/en/users/188714-wendy-krieger
User avatar
wendy
Pentonian
 
Posts: 2014
Joined: Tue Jan 18, 2005 12:42 pm
Location: Brisbane, Australia

Postby thigle » Fri Feb 10, 2006 4:47 pm

what is a complex axis ?

3{3}3{3}3, 3{3}3{4}2, 2{4}3{3}3

sorry wendy, but though i read your pg twice back to front, i still can't decipher this. how come 3 more pop up ?
thigle
Tetronian
 
Posts: 390
Joined: Fri Jul 29, 2005 5:00 pm

Postby wendy » Sat Feb 11, 2006 8:00 am

Polygloss does not handle complex polytopes. Instead, use Coxeter's "regular complex polytopes".
The dream you dream alone is only a dream
the dream we dream together is reality.

\ ( \(\LaTeX\ \) \ ) [no spaces] at https://greasyfork.org/en/users/188714-wendy-krieger
User avatar
wendy
Pentonian
 
Posts: 2014
Joined: Tue Jan 18, 2005 12:42 pm
Location: Brisbane, Australia

Postby thigle » Sun Feb 26, 2006 2:46 pm

back to the counterspace kind of space, that falls within this thread and was mentioned few times, another answer i just got from Nick Thomas that i find interesting follows my following question (btw, ondrej is my real name, so in the following ondrej=thigle):
...is there anything like "counter(counterspace)" or double counterspace ? i mean, if the counterspace is the space of etheric processes, is there a precise structure of experiential space that corresponds to the space of
processes one meta -level up (emotional, astral, whathaveyou) ? in other
words can the construction leading from E3 to counterspace be generalised and (re-)applied to space/counterspace duality, leading to 4-fold projective i-don't-know-what ? (i am an artist not a geometer )

also, what is between 'space' (E3 ?) and countespace (= ?) ? some kind of
inversion mechanism ? a projective hinge ?

these questions might be silly from a mathematician's point of view, but i am just a hobbyist, so please bear with me. ;)
...


Dear ondrej,

Thank you for your questions, which are by no means silly.

I have not explored spaces "above" CS (counterspace), but I think they will have reduced dimensionality: astral 1-dimensional, ego 0-dimensional.
I don't think it will be arrived the way CS is.

Between space and CS there are _linkages_ of various kinds:

points where CS is at infinity for the elements;
bi-vectors (like cones) for light;
tri-vectors for chemistry;
tensors for life.

In each case the entity determines how space and CS interact. Inversion is involved from the start.

Re other logics, interesting. I am greatly interested in Spencer-Brown's approach (being an engineer myself) which goes beyond Boole but in a practical rather than an academic way.
...
All the best, Nick


*
In all mathematics it becomes apparent, at some stage, that we have for some time been following a rule without being consciously aware of the fact. This might be described as the use of a covert convention.
A recognisable aspect of the advancement of mathematics consists of the advancement of the consciousness of what we are doing, whereby the covert becomes overt.
Mathematics is in this respect psychedelic.
G.Spencer-Brown_Laws of Form
thigle
Tetronian
 
Posts: 390
Joined: Fri Jul 29, 2005 5:00 pm

Previous

Return to Other Geometry

Who is online

Users browsing this forum: Google [Bot] and 10 guests