Multiple (physical) Dimensions for dummies (by Ken Udut- simplify3@aol.com)

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

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