04Z9WhatDim

Adapted for the Internet from:

Why God Doesn't Exist

What really is a
dimension?

The following points synthesize some of the differences between dimensions, coordinates, vectors, and

number lines:

•

From a conceptual point of view, a dimension and a coordinate are drawn with a solid line.

They

represent

static concepts. A vector and a number line, on the other hand, consist of

segmented lines

•

A dimension and a coordinate are static concepts. They are photographs, still images. A

vector and

number line are dynamic concepts. They are movies, a series of frames.

•

A dimension, a coordinate and a vector have direction. A number line does not.

•

A dimension and a coordinate are continuous (made of a single piece). A vector and a

number line

are

necessarily made of parts.

•

The three dimensions are length, width, and height; the three coordinates are known

as longitude,

latitude,

and altitude; the three vectors are known as depth, breadth,

and elevation. The names of the

three number

lines are parallel, meridian, and either

radius or diameter (in the case of circular and

spherical objects). We

have no name for

the third leg of straight edge solids. We can just as well call it

radius or diameter to

distinguish it from qualitative height, altitude, and elevation.

•

Number lines are a measure of distance traveled, of how many steps we need to get

somewhere, or

how

many frames a film has. An ordered pair symbolically depicts two

number lines.

•

Dimensions, coordinates, and vectors have two properties: direction and orthogonality.

Length

runs

at 90

to width and to height. Number lines don't run at 90

to anything.

We can place number

lines in

any direction.

Direction is not a feature of number lines.

It can't be because, for the purposes

of a

scientific discussion, a

moving object cannot

have direction. Direction is a static concept.

Direction has

to do with orientation and tilt

and not with displacement. It may apply only for a given

location of an

object. For example,

we can say that

the Moon is moving in the direction the

Andromeda Galaxy. But

this

statement belongs squarely within

ordinary speech. The next frame of

the film of the

Moons orbit

shows the Moon moving to the side of

Andromeda and so on down the

line.

The Moon can be said to be

moving along a line of direction leading to

Andromeda only if

assume that for the next few frames it

continues traveling parallel to a straight line

leading to

Andromeda. We trace an imaginary straight line

from the Moon to Andromeda

and assume that the

Moon will travel along this route.

For the purposes of Physics, the term three-dimensional

(3-D)

means that three hypothetical

mutually-

perpendicular planes of an object can be brought together to form a

corner

while their edges meet to

form

vertex

. We call these

edges

– which are typically regarded as

lines

–

dimensions.

hree-dimensional

(adj.): A word used to qualify an object that contains a vertex or corner.

We see objects in 2-D. In order to see in 3-D, we would have to have another eye or set of eyes to see

the

same object from a lateral perspective. With holography we are able to perceive an object in 3-D,

but

what is

really in front of us is a 2-D image with different shades, tones,

and

colors

of light

. Nevertheless, an

object is

not 3-D

because the observer visualizes it as such (proof). An object is 3-D if it points or

faces in three

mutually

perpendicular directions

on its own

(

i.e.,

by definition).

hologram

is not a standalone

physical

object, but

rather the projection of images much like what you see on a movie screen.

Hence,

a hologram is

not 3-D

because

it is not a physical object. A hologram

is entirely dependent on

observers.

A hologram is nothing

but a 3D

shadow

Note that the definition of the term

three-dimensional

precedes that of

dimension

. One reason for this

historical. Our ancestors started out with real objects and only later developed

abstract

concepts such as

plane

and

line

. Since all objects are three-dimensional, this seems like a natural starting point. An

even more

important

reason is that dimensions have two properties,

facing

and

orthogonality

, both of

which are

qualitative. Facing

stands alone, but not orthogonality. This attribute requires either implicit

or explicit

referencing to another

dimension. All by itself, a dimension is just a line that has direction

(one end

compared

to the other). A

direction graduates to a dimension only when it lies perpendicular

to at least

one

of her sisters.

Each of the

dimensions faces orthogonally away from the other two.

Width is naught without

length or height!

This

converts

the right angle into a sine qua non

feature of the definition.

Edge

-land

is not

even a figment

of the

imagination:

you cannot conceived of a

standalone

1-D

When we use the word

width

to label

conceptually

one-dimensional edge we are tacitly

referencing this width to either the length

or the

height of the object the

edge forms a part of. As a standalone

concept, width has no meaning, and

any

object we are capable of

visualizing is at least 2-D: width and height.

Like its

sine qua non properties --

facing

and

orthogonal

dimensions are

qualitative

relations that belong exclusively to Physics.

Mathematics has no business using

length, width, and height.

The names of the

only

three dimensions

known to rational humans

are

length

width

, and

height

The

onvention

that

height

aligned parallel to the direction of gravity of the celestial body used as reference

and

width

with the observer’

s horizon. The word

dimension

(singular) refers to one of these straight lines

and

should not be confused

with the words

coordinate

vector

. A dimension is an attribute of a single

physical

object. A

coordinate

used to qualitatively determine the location of our test object with

respect to

extrinsic

reference points. A

vector

is used to represent the displacement of a

single object. Hence, each of

these terms

has radically different meanings and

connotations

in Physics.

The

athematic

ians routinely

confuse

all three

and take

them

for synonyms:

magnitude and

direction.

The relativist may comment now that, colloquially, we qualify the width of a box as being or having

meters'.

How can I then say that a dimension is exclusively qualitative?

The vernacular treats

width

as a noun because the word momentarily happens to be the subject of

the

sentence. Hence, in the expression '5 meter width',

is an

adverb

meter

is an

adjective

, and

width

acts

noun

. In Physics, however, width is always an adjective: an attribute of an

object

. The

qualitative,

directional

concept

width

is implicitly referenced to the length and/or height of the box.

Width cannot

just point in any

arbitrary direction, but implies a definitional relation with at least one of

the other two

dimensions. The

quantity

5 meters

, instea

d, is gauged against an extrinsic, pre-

established standard

the meter

. If the box

and

you are the

sole objects in the Universe, the box is

immediately identified as

dimensional, but you

could say

nothing yet

of the

magnitude

of 'the width'

of the box until you establish

standard

and then

compare this

specific side of

the box with the

standard.

Moreover,

width

conceptually

continuous

whereas

numbers

are

conceptually discrete.

By using the

magnitude

and

the unit

meter

, we are in effect chopping up an

indivisible direction

called

width

into little

pieces. The

mathematician

is not talking about a continuous

dimension, but

about a segmented number

line,

axis which he unwittingly places parallel to a particular

side of the

box and which he mistakenly

calls

width

This again shows that the vernacular of Mathematics is

unsatisfactory as a substitute language

for Physics.

The devil's advocate may now step in and say that under these circumstances we can nevertheless

tell

that

the

height of the box is twice that of the width, an apparently quantitative relation inherent in

the

box.

However, in order to determine this he inadvertently converted

width

into a standard and imagined

this

now

extrinsic standard parallel to

height

. Comparisons involve observers and motion, and

magnitudes

such as

'twice' invoke extrinsic objects. A cube is structurally different than a rectangular

box in the

absence of

observers or Math. The

right angle

, on the other hand, is not quantitative

because we are not

asked to

compare

it against the direction of another dimension to verify whether it

is indeed 90°. Width

by definition

perpendicular to the height and length of the test object under

study. To qualify an

object as 3-D implies that

for

the remainder of the presentation the object will be

deemed to have at least

one vertex.

As a final note, an object that contains a 3-D object is itself a

3-D object

. This need not be proven by

theorem

either. It follows from the definition. Hence,

sphere is 3-D because it contains a 3-

cube

( a vertex) and not

because we can locate a point on its surface with a given number of coordinates

SCIENCE versus RELIGION

You take me for a fool?
Longitude is not the same as
width. It says so right here in my
elementary textbook of Physics.

Fig. 3

Dimensions, coordinates, and vectors of Physics

Fig. 4

Dimensions, coordinates, and vectors of
Mathematical Physics

The dimensions, coordinates, and vectors of
Mathematics cannot be used consistently.
They belong exclusively to religion.

The dimensions, coordinates, and vectors of
Physics can be used consistently in a scientific
presentation.

Fig. 1

Fig. 2

In Physics, a dimension is conceptually
made of a single piece (direction) and is
nothing without the other two
(orthogonality is a requirement). We
tentatively draw a solid line to reflect this

In Math, they have no use for dimensions.
They use number lines which the idiots of
Mathematics call dimensions and later
attempt to relate to physical dimensions
in their dissertations. The number line of
Math has no direction (it is a segmented
concept). It only has magnitude. Thus, we
tentatively illustrate a number line with a
dashed arrow. the arrowhead does not
indicate direction. It indicates that numbers
increase.

odule

home page

The mathematical definition of

imension

is unscientific

Pages in this module:

The mathematical definition of

dimension

is not the one used by sane human beings

In Mathematics,

it is

space

and not the geometric figure

which

has dimensions

The 'number of numbers'

dimension

of Math

is not a definition

but a proof

The

multi-dimensional

'number of numbers'

definition of Math

is unscientific

The 'number of numbers'

definition of

dimension

cannot be used consistently

The

mathematical

dimension of

length

has zero size

And then t

he mathematicians

invented fractions of a

dimension

Conclusions (dimensions)

This page:

What really is a dimension?

A dimension differs from a coordinate in
that the arrowhead points or faces away
from the object. The arrowhead of a
coordinate points toward the object.

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