Softpedia
 

NEWS CATEGORIES:



NEWS ARCHIVE >>
SOFTPEDIA REVIEWS >>
MEET THE EDITORS >>
Home > News > Science > Space

January 17th, 2006, 12:06 GMT · By Vlad Tarko

What Are the Spatial Dimensions?

SHARE:

Adjust text size:


We live in a three dimensional space. The theory of relativity added another one. However, various miss-conceptions persist regarding the meaning of spatial dimensions. Surprisingly or not, the most common explanation of what spatial dimensions are is at least miss-leading, if not flat wrong.

Why is the computer screen bi-dimensional, while the world is three-dimensional (or forth-dimensional)?

The common explanation is that you need two numbers to express the position of some pixel on the computer screen (one number is not enough, while more than two are superfluous), while you need three numbers to express a position is space.

Truth is you certainly don't need two numbers to express the position of a pixel on a computer screen. A computer screen has a limited number
of pixels, you could simply label each one of them with a different number. However, you won't find any computer programmer in the game industry abolishing the two-dimensional system. But why don't they?

Interestingly, even if the computer screen would have had an infinite number of pixels infinitely small and it would have been infinitely wide, you could still have used only one single number to label all the pixels. This had been demonstrated in the late 19th century by the famous mathematician Georg Cantor. (He was as surprised as you are now, if not even more, that he managed to prove such a thing!)

Intuitively, you can imagine covering an entire infinite bi-dimensional plane with the help of only one number by using a spiral.

What is true for the bi-dimensional plane is true for any kind of space no matter how many dimensions it has. The three-dimensional space could also be covered with the help of a single number.

Thus, in what sense are the computer screen bi-dimensional and the world three-dimensional?

The key point is to think dynamically and not about static things. You have to think about the motion of objects in space (on the computer screen or in the real world).

Suppose one would use a spiral for covering a 2D space. Then, when an object would move in a straight line it would pass through the spiral - from the point of view of the numbers used to express the positions, the object would seem to jump from number to number, skipping a whole bunch of intermediary steps. However, when one uses a bi-dimensional system the motion over a small distance is reflected by small changes in each of the coordinates. A continuous motion is described by a continuous change in the values of the coordinates.

Thus, the fundamental reason why space is three-dimensional (or forth-dimensional as the theory of relativity asserts) has to do with motion and not just with the static description of positions. It is the only way a continuous motion can be represented mathematically by a continuous change of coordinates. If one would use a single number or more than three (or four) one would necessarily represent some continuous motions as discontinuous in the mathematical realm.

TELL US WHAT YOU THINK:

15,673 hits · 4 comments · Link to this article · Print article · Send to friend · Subscribe to news

MUST-READ RELATED ARTICLES:


The Science of Snowflakes

READER COMMENTS:


Comment #1 by: Rick Tresnak on 14 Dec 2009, 18:33 UTC reply to this comment

I have often pondered this when I relate it to my Christian religion. It is possible that the basic geometric boundaries for the differences in our human realm and the heavenly realm may share a fliud line vs. a solid line. I like the idea of a spiral point. It seems to explain how if two dimensions have a moving fluid for a boundary line have multiple intersecting points, these two dimesions can create possible transition points to travel through.

Ok in the bible the cross was a substantial point where two realms came together. It was the way to open heaven for those unable to enter before.

It would also explain why angelic beings have multiple eyes, each to view through multiple facets or through multiple dimesions. Perhaps these spiral points have a central apex, and if in that apex angels exsist this would make their added eyes very useful.

It would also beg to expose the possibility of alternate universes all in line with a central spiritual realm.

Thanks for the explanation. It makes me ponder.


Comment #2 by: hddfhd on 24 Jan 2011, 15:06 UTC reply to this comment

wowza

Comment #2.1 by: measureman on 27 Jul 2011, 18:11 GMT

The initiation of questions about “space” cannot be initiated
until a language system establishes a dictionary of terms. The form of the
answer will use the dictionary of terms.
Necessarily, the form of the space would be that which can be described as
a Volume. Of course, in order to have a volume, there must be some THING
in the space, thus, an “object”. Since “empty” space cannot be an
“object”, we must therefore define a “substance”.
A one inch cube filled with water, will then be available to “weigh”
the volume of the substance in the cube form.
It is necessary to initiate the measure of “weight” from (first
Principle) acceleration as the factor of our experience “to weigh”. The
dictionary term for a measure of weight, derived from the period of a
pendulum, as the time, can be taken from the length of the major diagonal
of the cube.
The length of the major diagonal is, in inches 1.732050809 inches.
Since this is the cotangent of the angle 35.26438968, it is therefore
possible to link the idea of time with a length and if the period of a
1.732050809 inches pendulum as a number multiply 35.26438968 =
61.07971463 which as a number is interesting since the weight of a cubic
foot of water is approximately 61.09 lbs. Avoir. This would be about
977.1441472 ounces.
Also, the number of the measure of the angle of the major diagonal
furnishes a value of the number of grams weight to an ounce, thus 1 /
35.26438968 = .0283572184, this as 28.3572184 to be “seen” as the
standard of a measure of grams to an ounce in the Avoirdupois system. The
number here is (slightly) different.
The number 977.1441472 divided by 1000, and taken to its reciprocal =
1.023390462 The very number for the ratio of the acceleration of
“Gravity”.

Note, ALL values and numbers applying to functions as physical
demonstrations are inherently false because of the factor of acceleration.
But the “Falseness”, or lack of agreement with the “expected” need
only be a very small measure. Thus the term measure, inherently (first
principle) includes the universal expansion and acceleration as in the
number.
There is not nor can there be any simple and final definition of the
“state” of rest.

Since the election of one cubic inch as the geometric form of the volume
of a measure of water as one cubic inch of water is 1 / 1728 of the volume
of a cubic foot of water, the measure in grams weight of a cubic foot of
water would be 977.1441472 X
Therefore 977.1441472 X 28.3572184 = 27709.089 grams of water in a
cubic foot of space.
Now then the definition of a space is defined by the measure of the
volume of substance within that space.
Therefore, the number of grams of water in a cubic inch of volume would be
(conservatively)
27709.089 / 1728 = 16.035353 grams of water in one cubic inch.
It is important to take note that the reciprocal number 1 /
16.035353 = .0623622068.
It is also to be noticed that the number 16.035353 as 1.6035353 develops
the ratio of the transitional temperature of centigrade boiling point
to 1 / 1.6035353
The factor is 212 / 100 = 2.12 Reciprocal number = .4716981132
which is the natural logarithm of 1.602713373.
Ceratrinly a
“reflection” of the number for the grams to a cubic inch of water.
1.6035353 as opposed to 1.602713373.

There is also to be considered the measure of the temperature of the
substance within the 1cubic foot volume.
From a first principle connection with physical measurable temperature,
the necessity is to see that there does actualize a transition point, as
water boiling at a temperature (sea level) of (conservatively) 212 degrees
Fahrenheit, = to 100 degrees centigrade .

A form, such as a cube defines itself as 12 identical units of edge. The
major diagonal of the cube as an angle of 35.26438968 degrees. If the
edge of this form as a cube, (geometry), is a length of 1, and the 1 is,
actually a length of 1 “inch” then the “inch” ought to define
itself from and because of FIRST PRINCIPLES , then the length, as a
pendulum will express a “period” of .3199047448 of one second.
The first and primary definition of a length is in the expression of its
length as a functioning pendulum as time.
It is at the juncture of the number 1.228068554 that the function of a
pendulum one foot 2.736822+inches = as a pendulum a period of its own
number as 1.228068554 seconds of time

Bernard Pietsch
bernard@sonic.net


Comment #3 by: me on 11 Oct 2011, 17:55 UTC reply to this comment

u talk 2 much

Copyright © 2001-2012 Softpedia. Contact/Tip us at

WindowsGamesDriversMacLinuxScriptsMobileHandheldNews

SUBMIT PROGRAM   |   ADVERTISE   |   GET HELP   |   SEND US FEEDBACK   |   RSS FEEDS   |   UPDATE YOUR SOFTWARE   |   ROMANIAN FORUM