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DIMENSIONS

of things of substance there is nothing less than one dimension

it does not have time or motion or mass or...

it is the absolute of being

see summary and the straight line

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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

a point represents a position in space

imagine a line from the point, say 2 metres

( 1 dimension )


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

 

 

 

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-dimesional 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

 

 

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