* for a one click look up of words you don't understand click the link   

 

quick index

index page

 

 

 

 

 

DIMENSION AND DIMENSIONS

DIMENSION

anything one dimensional can only be imagined although reality does appear to be using the straight line as the foundation of being

a point represents a position in space

to imagine a line one metre long that stretches out from a point is an example of a finite line 

 


DIMENSIONS

to make a square from a line... multiply the distance of the line by 2 which is called 4 squared metres )

( 2 dimensions )

to make a cube multiply the length of the line by 2 and then by 2 again which is called 8 cubic metres

( 3 dimensions )

to make a 4 dimensional cube multiply the line by 2 and then by 2 again and then by 2 again which is called 16 hypercubic meters

( which is called a four dimensional hypercube )

and so on for as many dimensions as you want

entry composed by buck McHugh and the writer

 

 

 

 

 

 

 

 

 

 

 

 

see summary and the straight line (the absolute of being)

 

this a 4 dimensional cube performing a double rotation about two orthogonal planes

 

 

 

 

NOTES

DIMENSIONS

anaximander and dirac both had a similar vision of the underlying fabric of reality...

 

 

NOTES

0 a point is a hypercube of dimension zero
1 if one moves this point one unit length, it will sweep out a line segment, which is a unit hypercube of dimension one
2 if one moves this line segment its length in a perpendicular direction from itself; it sweeps out a 2-dimensional square
3 if one moves the square one unit length in the direction perpendicular to the plane it lies on, it will generate a 3-dimensional cube
4 if one moves the cube one unit length into the fourth dimension, it generates a 4-dimensional unit hypercube which is called a tesseract

 

 

 

NOTES

 

 

 

NOTES

this process of sweeping out volumes can be formalized mathematically as a minkowski sum: the d-dimensional hypercube is the Minkowski sum of d mutually perpendicular unit-length line segments, and is therefore an example of a zonotope

the 1-skeleton of a hypercube is a hypercube graph

 

 

 

NOTES

there aren't any simple explantions that the writer could find  which explain space

let's see if making a few assumptions helps

space can only ever be flat

that the straight line connects all of reality

it does so in 1 planck time

the consideration here is that reality is infinite and how can anything be endless and exist in less than a second... point starts the square

2 centimetres x 2 = 1 cube x 2 = hypercube

then times 2 for a 4d cube

135 degrees is 50% larger than 90 degrees

square... an edge times an edge equals a square

~~~~

 "every point in our space is part of a perpendicular line

although all the lines forming the fourth dimension are perpendicular to every point in the third dimension they're not necessarily parallel to us

 if enough of the lnes are parallel in both dimensions in a given area they might create an opening or access to it"

 (quote from "liitle girl lost"; an episode from the original series of "the twilight zone"