[RascalPuff]

The Physical Dimensions, 1 thru 4 (Revisited):
The mathematical definition for the 4th Dimension is also the geometric definition. In order to consider the geometric definition for the 4th Dimension we will first review the singularly scientific and formal definition for the Three recognized Dimensions of Space. Then we will consider the 4th Dimension's relationship if any, to Einstein's General Principle of Relativity and/or Newton's Gravitational Alternative.
(Refer to Drawing 1 Illustrations 1 & 2)

The (only known; geometric; metrically spatial) definition for physical dimensions, begins with no dimensions whatsoever - specifically a geometric point. We will call it 'point zero ('0'). Any motion of point '0' will inevitably be at right angles from itself, and, any motion, at any speed, for any length of time, generates a One Dimensional Straight Line 'O' - 'A', of arbitrary length.

It cannot be a curved line yet, because it has no dimension(s) to curve into. It may become a longer or shorter One Dimensional Straight Line, but it cannot change its dimensional quality until it moves at right angles (90 degrees, perpendicular) from itself (again). Then it generates a Two Dimensional Plane 'A'- 'B'.

When a Two Dimensional Plane ('A'-'B') moves at right angles to itself (yet a third time), it generates a Space and/or Solid 'B'-'C' of Three Dimensions.

(Picture a line-drawn cube; progressively generated from 0 dimensions to 3-Dimensions: by the right angle extrapolation of the geometric point 0, to 0-A, generating a One Dimensional Straight Line <0------->A>.
The Straight Line 0- - - - >A then moving at right angles to itself, generating A-- - ->B Two Dimensional Plane. The Two Dimensional Plane A- - - ->B moving at right angles to itself B- - - - >C; generating a Three Dimensional Solid, occupied or occupiable-by 3-dimensional matter).

The rule here is the right angle/perpendicular projection of each dimension from out of the preceding dimension. This is how physical dimensions are generated, hence, this is their singular physical and philological definition.

That leaves us here and now with the conceptual-geometric credentials to contemplate the Three recognizable Dimensions of Space occupied - or occupiable - by matter. A familiar enough concept; by-way of its Universal physical-conditional manifestation in the entire reception of physical-sensory, instrumental and therefore psychological-conceptual human experience (at large).
Knowing; not speculating, that we are obliged by the laws of geometry, combined with Einstein's (allegedly 'acknowledged') proof that the entire physical Universe is 4-Dimensional: not merely to 'consider', but to find, observe and experience the physical as well as spatial Three Dimensions of Space moving at right angles from themselves. This is not a mere idea, or consideration, or project; it is an ultimatum.

THE 4-DIMENSIONAL ULTIMATUM.
Because, it demands without ambiguity or equivocation, that the entire recognized physical 3-Dimensional Universe of Space and Matter , must be and is moving at right angles from itself in one of two possible 4-Dimensional directions: that of overall 4-Dimensional contraction, where everything recognizable as 3-Dimensional, is constantly growing smaller (moving at right angles from all three of it's recognized dimensions)...

Or, the direction of overall 4-Dimensional expansion, where everything recognizable as 3-Dimensional, is constantly growing larger (moving at right angles, constantly, to all three of its recognized dimensional coordinates).

Do we see or measure - do we recognize -3-Dimensional reality as moving at right angles from itself; shrinking ever-smaller with 4-Dimensional contraction, or, growing ever-larger with 4-Dimensional expansion?

The unanimous and seemingly inevitable answer to this (apparently absurd and pointless) question, since Einstein required it, has uniformly been (as will be *documented, shortly), *“No, we do not observe or measure 3-Dimensional reality as 4-Dimensional. Obviously matter is not expanding. If the universe is made up of a number of disturbed areas, by now it would have spread indefinitely."

Furthermore, it is uniformly agreed, We cannot measure, comprehend, or even imagine the 4th Dimension; nor will we ever. The 4th Dimension is declared to be non-mathematically incomprehensible; descriptively inaccessible without a mathematically encrypted frame of reference.

The Three recognized Dimensions Of Space must move at right angles from themselves - that is to say, expand, or, contract, in order to fulfill the only definition there is for any geometric or mathematical consideration of - or address to - a physically prevailing 4th Dimension..


Of which, in the meantime, prevails ubiquitously: we are abundantly reassured that *Einstein left no doubt (*the dimensionless TIME magazine-appointed Man Of The Century).

Probably safe to presume that some of you who are not snoozing, already have more than a vague idea of what's next, and if so - you're quite right of course. The formula is exactly as simple as it is inescapable. Einstein's GENERAL PRINCIPLE OF RELATIVITY equates gravity with acceleration. Einstein's 4th Dimension demands overall right-angle motion of the Three recognized Dimensions Of Space: in one of two possible 4-Dimensional directions (Overall expansion or overall contraction). Since objects do not fall 'upward' and away from 3-D Matter, this rules out overall 4-Dimensional contraction.

Objects do fall 'downward' toward the center of 3-D Matter; therefore confirming by demonstration, in situ (as is): a physically (materially) expanding Universe. The unrecognized causal identity (the source) of the observed, measured, acknowledged, recognized spatially expanding universe.




The conclusion is without precedent - although it has many historically noted revolutionary counterparts and parallels, in the history of Western Science. Recognizing the four dimensional space time continuum as being gravity, and conversely, is and has been patently unavoidable since its remarkably progressive advent; for the reasons provided herein (Refer to Drawing 1 Illustrations 3 & 4)

The material as well as spatial Universe is 4-Dimensionally expanding; it is this 4-Dimensional accelerating expansion that generates the force experienced and recognized as gravity. Hence objects do not fall to earth; the earth - instead - accelerates upwardly and overtakes them (just as the floor does in Einstein's elevator). Gravity is the 4-D space-time Dimension.

If anyone asks or demands from this point onward, that this statement must or need be proven, they are reminded that this has already been accomplished. By Einstein. And Newton. And the laws of mathematics and geometry at - by definition - their most fundamental, physically definitive level. We have simply taken Einstein's renowned accomplishments and recommendations seriously enough to actually apply-them-to and recognize-them-within, the human Gravitational Experience.

The Question is no longer, 'What & Where is the 4th Dimension in my own experience?' Einstein proved that it is time and motion; applicable to: Everything; Everywhere. The Question regarding the 4th D. is:
'What & Where is it not?'

(To be continued)

Excerpted from http://forums.delphiforums.com/EinsteinGroupie
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