Weird spaces

[Skalt711]

We know how dimensional space works, but Jonathan Bowers has descripted super dimensions, trimensions (sic!) and etc. Here's the description (find it under Extending Array Notation): "Yet one can keep going into higher spaces, higher than dimensional space - consider the tetrational spaces (which includes super dimensions, trimensions, quadramensions, etc.) - what is this exactly - dimensional spaces can be represented as X^n where X represents a line, X^2 would then be a plane, X^100 would be 100 dimensional. Super dimensions are of this order - X^(X^n), trimensions, quadramensions, etc are as follows: X^(X^(X^n)), X^(X^(X^(X^n))), etc. - these kind of arrays are possible - so array notation can be addapted to these arrays, but the rules get trickier. Using Bird's inline technique we can represent super dimensional space as follows: {# (a,b,c,....,k) #} which represents going to the next a'th dimension of the b'th second level of dimensions of the c'th third level of dimensions .... of the k'th n'th level of dimensions - notice this is only super dimensions, it gets crazier in trimensions on up.

But Arrays can go even further - there are also pentational arrays such as an X^^^6 array which would be an X^^(X^^(X^^(X^^(X^^X)))) array where X^^X alone would be an X^(X^(X^(....^(X^X))....)))) array. Bird has attempted to write rules for extending past dimensional arrays and appears to have captured rules that fit tetration and possibly pentation - but they get quite tedious." and here (find the Higher Superdimensional Group): "Higher Superdimensional Group - includes trimentri, trongulus, quadrongulus, and goplexulus. Trimentri = {3,3 (0,0,0,1) 2} which is a size 3 - x^(x^3) array of 3's - it is also a 1 trimensional array = {3,3 ((0,1)1) 2} - in otherwords a size 3 x^x^x array of 3's, a 3 tetrated to 3 array of 3's - a trimension is a dimension of dimension of dimensions. To help see this, let R represent a line (R for real numbers which is graphed like a line) - R^3 = 3 dimensions, R^R = R^R^1 - is 1 super dimension, R^R^4 = 4 super dimensions. R^R^R = R^R^R^1 = 1 trimension. R^R^R = R tetrated to 3 = {R,3,2}. Even though trimentri is defined with trimensions, it's array is of the higher superdimensional sizes. Trongulus = {10,100 (0,0,0,1) 2}, and quadrongulus = {10,100 (0,0,0,0,1) 2} = size 100 - x^x^4 array of 10's. Goplexulus = {10,100 (0,0,0,.......,0,0,1) 2} - where there are 100 0's - this is a size 100 - x^x^100 array of 10's.".

How we should interpret such spaces in our Tiering System? They can have their tier for sure (ex. 1-B)...

 

[RRTheEndMan]

I understood 10% of that and I don't think that I'm copletely the right person to answer this question, but (don't quote me on that) I think it's somewhere in between High 1-B (infinite conventional dimentions) and 1-A (Beyond dimensions). Is this just theoretical?

 

[Skalt711]

@RRTheEndMan Maybe. Maybe not. Who knows?

 

[Andytrenom]

Brain...melting...help...

I have a feeling this won't reach 1-A, but how high exactly this will be in tier 1 I have no absolutely no clue.

 

[Skalt711]

This is what I found (find the Colossol Group) that may help resolve my question:
"Colossol Group - includes dimentri, colossol, colossolplex, terossol, terossolplex, petossol, petossolplex, ectossol, ectossolplex, zettossol, zettosolplex, yottossol, yottossolplex, xennossol, xennossolplex, and dimendecal. We are now going full force into the dimensional arrays. Dimentri = 3^3 & 3 = 3 x 3 x 3 array of 3's = {3,3,3 (1) 3,3,3 (1) 3,3,3 (2) 3,3,3 (1) 3,3,3 (1) 3,3,3 (2) 3,3,3 (1) 3,3,3 (1) 3,3,3} - think of a cube of 3's with 3 3's to the edge - that's the array. Colossol = 10^3 & 10 = {10,10 (3) 2} - here imagine a 10x10x10 cube of 10's. Colossolplex = colossol^3 & 10 = {10,colossol (3) 2} - here imagine a cube of tens that is so huge, there isn't enough universes to hold even a tiny fraction of it - it is a colossol by colossol by colossol cube of tens. Terossol = 10^4 & 10 = {10,10 (4) 2} - which is a 10 by 10 by 10 by 10 tesseract of tens. Terossolplex = terossol^4 & 10. Petossol is a size 10 penteract of tens - a 10^5 array of tens that is. Petossolplex is a size petossol penteract of tens. Ectossol is the value of a size 10 hexeract (six dimensional cube) of tens. Ectossolplex is an ectossol size hexeract of tens. Zettossol, yottossol, and xennossol are 7,8, and 9 dimensional size ten arrays of tens - in otherwords: 10^n & 10 = {10,10 2} where n=7,8,and 9 respectively. Dimendecal = 10^10 & 10's - which is a 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 array of 10's.

Gongulus Group - includes gongulus, gongulusplex, gongulusduplex, gongulustriplex, and gongulusquadraplex. Now the dimensional arrays are breaking at the seams. Gongulus is utterly unspeakably enormous - it is the result of solving a size ten 100 dimensional array of 10's (10^100 & 10 that is) = {10,10 (100) 2} - there will be a googol tens in the form of a hundred dimensional cube, which seems to never come to an end when trying to solve. Just to shake you up a bit, the much much much smaller number {10,10,3 (99) 2} can best be described as follows: 1) start with 10, 2) next get a size ten 99-D array, 3) now get a size X 99-D array where X is the result of stage 2, 4) now get a size Y 99-D array where Y is the result of stage 3,....go to stage ten, call that number T2, keep going - all the way to stage T2 - call that number T3, now keep going to stage T3 - call this number T4 - keep this trend up until you get to stage T10 - that will be {10,10,3 (99) 2} - notice how the 10,10,3 works like linear arrays but acting on expanding a 99-D array's size. Now consider {10^99 & 10 (99) 2} - MUCH larger now, but still NO where near a gongulus which is {10,10 (100) 2} = {10^99 & 10 (99) 10^99 & 10 (99) 10^99 & 10 (99) 10^99 & 10 (99) 10^99 & 10 (99) 10^99 & 10 (99) 10^99 & 10 (99) 10^99 & 10 (99) 10^99 & 10 (99) 10^99 & 10}. A gongulusplex is {10,10 (gongulus) 2} which is a size 10 - gongulus dimensional array of 10's! Gongulusduplex is {10,10 (gongulusplex) 2}, continue this trend for gongulustriplex and quadraplex.

Dulatri Group - includes dulatri, gingulus, trilatri, gangulus, geengulus, gowngulus, and gungulus. This is the beginning of tetrational arrays, actually the beginning of superdimensional arrays. Dulatri = {3,3 (0,2) 2} = {3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (2,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (2,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3}. the (0,1) separates dimensional groups, the same way separates n-D structures. (0,1) can be thought of as (0+1*x) = (x) - which represents x^x structures being separated. (1,1) separates rows of dimensional groups, (n,1) separates n-D regions of dimensional groups. (0,2) separates groups of groups - so in the dulatri array {3,3 (0,2) 2} - the 2 is in the second group of groups, and the 3,3 is in the first group of groups. Dulatri then is a size 3 - x^2x array of 3's. {3,3 (0,1) 2} = 3^3 & 3 by the way. Dulatri

Gingulus = {10,100 (0,2) 2} = 100^100 array of D's where D is a 100^100 array of 10's. - so the gingulus array is a 100 dimensional array of 100-D dimensional groups, which is a size 100 - x^2x array of 10's. Trilatri = {3,3 (0,3) 2} = {A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (2,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (2,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A} where A represents "3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (2,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (2,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3" - this is a size 3 - x^3x array of 3's. Gangulus = {10,100 (0,3) 2}, geengulus = {10,100 (0,4) 2}, gowngulus = {10,100 (0,5) 2}, and gungulus = {10,100 (0,6) 2} - which is a size 100 - x^6x array of 10's."

 

[Skalt711]

It seems that it (find the Tetrational type of arrays) explains my question well. Here's the text:
"Tetrational:

These arrays go way beyond dimensional arrays, and take on structures that require tetrational spaces. They consist not only of rows, planes, realms, etc, but also dimensional groups, rows of groups, planes of groups, groups of groups, groups of groups of groups of groups, gangs, rows of gangs, groups of gangs, gangs of gangs, realms of groups of groups of gangs of gangs of gangs, etc, etc, etc, superdimensional groups, trimensional groups, etc,etc. These are the third smallest arrays (and the largest type that I have fully grasped how they work). Tetrational arrays consist of super dimensional arrays, trimensional, quadramensional, etc in the same way dimensional arrays consists of planar, realmic, flunic, etc arrays.

Positions of superdimensional arrays can be described by a dimensional array, i.e. (5,6,3 (1) 3, 5 (1) 6,7 (2) 5) represents the 5th entry of the 6th row of the 3rd plane of the 3rd dimensional group, of the 5th row of groups, of the 6th group of groups, of the 7th row of group of groups of the 5th dimensional gang. To represent a 3^(3^2) array, let A represent the 3^3 dimensional group {3,3,3 (1) 3,3,3 (1) 3,3,3 (2) 3,3,3 (1) 3,3,3 (1) 3,3,3 (2) 3,3,3 (1) 3,3,3 (1) 3,3,3}, now a 3^(3^2) array of 3's would be {A,A,A (1,1) A,A,A (1,1) A,A,A (2,1) A,A,A (1,1) A,A,A (1,1) A,A,A (2,1) A,A,A (1,1) A,A,A (1,1) A,A,A} To get a 3^(3^3) array let A be equal to the group of groups mentioned above (the 3^(3^2) array that is) and let (1,1) and (2,1) change into (1,2) and (2,2) respectively.

Positions of trimensional arrays can be described by a superdimensional array, positions of a quadramensional array can be described by a trimensional array, etc."

 

[Skalt711]

And this as well from the same article:
"Dimensional:

Dimensional arrays have a multidimensional structure - these are the second smallest arrays. These arrays consists of rows, planes, realms, flunes (4-spaces), and various n-spaces. The rules above can easily handle dimensional arrays - although the results seem to nearly reach infinity. The positions in the array can be described with a linear array, i.e. (4,5,3,1,2) represents the 4th entry on 5th row on 3rd plane on 1st realm on 2nd flune. Dimensional arrays can be represented as follows: {4,2,5,7 (2) 5,6,1,2 (2) 5,4 (1) 6 (3)(3)(2) 2,5,6 (1) 1,1,1,7 (2) 6,8,5,2 (5) 7,5,6,8}. Here (2) represents going to next second dimension (or going to next plane), (3) is next realm, (5) is next 5-space."

 

[RRTheEndMan]

what I understood


sdtghndghmutiuoidimensionsuzydfgvbisebglbutetrationsfhndfnbdfnnspacesdghdghh

However I have a feeling that if this involves higher level hyperoperations it's OP by default

 

[Skalt711]

One thing is sure: adding more lines to a superdimensional being involves adding much, much more points than adding more lines to a dimensional being.

 

[Crimson_Azoth]

 

[Elizhaa]

Up to super high 1-B at best