More along the lines of multidimensional mapping: Okay! I'm
thinking this way: EXPRESSING 2 DIMENSIONS IN 1 DIMENSION. Start
with a line. ______ If you had to express 2 dimensions in 1
dimension, how would you do it? You'd use two lines, and just
remember that the 2nd line is going in a dimension you cannot
directly manipulate. ________ ________ EXPRESSING 3 DIMENSIONS
IN 2 DIMENSIONS. Okay - you have two dimensions. | | |
|_________ You want to express 3 dimensions in 2 dimensions? | |
| |_________ | | | |_________ You would just have to remember
that the 2nd |_ is representing the 3rd dimension - going "up"
in a direction you can't directly manipulate [but since we're in
3 dimensions, we could simply pick up the 2nd |_ and flip it
around into a 3 dimensional shape). But as a 2 dimensional
being, you wouldn't be able to use the parlor trick of making a
3D-looking box in 2 dimensions, because you can only think 3
dimensionally in theory - perhaps even mathematically.
EXPRESSING 4 DIMENSIONS IN 3 DIMENSIONS Okay - we're getting
limited already, because e-mail is 2 dimensions. You have a 3D
cube. You want to express a 4D cube. How to do it? Same way! You
have another cube. Two cubes. But the two cubes are really 1
cube, just stretching upwards in a direction that we cannot
perceive. Notice what's happening here!!! Each dimension is
STILL being expressed by a 1 dimensional thing: The ___________.
For 2 dimensions, you have a GROUP of 2 or more __________ for 3
dimensions you have a GROUP of 3 or more ___________ For 4
dimensions, you have a group of 4 or more ___________ OR: You
have two dimensions: | |___ To get three dimensions, you need
TWO of these: | |___ | |___ always remembering that the 2nd one
is flipped 'up', towards you. Now, same logic: You have 3
dimensions. A cube. To get 4 dimensions, you need 2 CUBES. or 3
2D |_'s or 4 ______ (lines). To get FIVE dimensions, you need 2
4D cubes at minimum. *BUT* - since we are limited in expressing
ourselves in 3 dimensions, we have other options!! 3 3D cubes
will express 5 dimensions minimally. 4 2D |_'s will express 5
dimensions minimally as well... 5 ______'S will also express 5
dimensions. [to see 5 dimensions in a common computer
application, see Microsoft Excel. You have Row: 1 [one
dimension) You have Column A (2nd dimension) You have Worksheet
named: REPORT_1 (3rd dimension) You have Filename named:
NOV_REPORTS.XLS (4th dimension) You have Directory named:
C:\REPORTS\ (5th dimension) etc. It seems to get "flat" after
you have the 4th dimension - but it's not! NOTICE THIS! A
DIRECTORY (5) can have a collection of Excel FILES (4). An Excel
FILE (4) can have a collection of WORKSHEETS (3). A WORKSHEET
(3) can have a collection of COLUMNS (2) A COLUMN (2) can have a
collection of ROWS (1). [and one single cell, which is in a row
that is in a column, that is in a worksheet, that is in a file,
that is in a directory, can reference ANY OTHER cell in any
other DIRECTORY, or FILE, or WORKSHEET, or COLUMN, or even ROW!]
] A box inside of boxes is a way often used to express
multidimensionality. Even time! -- Look at Russian nesting
dolls. They express, in one small package, 4 dimensions. It is
the same person, at different stages in time. The Russian
nesting doll is a 4 dimensional object. Pretty neat stuff.
Thanks for listening - thoughts? Kenneth
