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 3Dlooking 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 email 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