[RascalPuff]

It is frequently said in conversation on and off the net that there are 10, 11, 26, 37, and/or an infinite number of 'dimensions'.

Perhaps there are.

It seems to be a matter of what context the various interpretations of dimensions are applied to...

Whereas, the following column is a list of the (at least) 17 formally recognized types of geometric and/or mathematical dimension(s).
.......................

Euclidean,
Pythagorean,
Plane,
Solid,
Non-Euclidean,
Spatially Functional:
metric,
Cartesian,
Analytic,
Riemannean,
Algebraic,
Spatially:
non- metric,
Descriptive,
Differential,
linear transformable affine collineations,
or Projective.
(17 definitions for dimensions)...

The generally affine geometry...
(which I do not and never have pretended to understand, along with higher mathematics - has always been perplexing to me, though I comprehend metric mathematics - as opposed to non metric mathematics, where two correct equations can mutually contradict each other - and have some understanding of calculus, algebra, plane and solid geometry)...proving the translation of right angle motion from preceding dimensions, is the geometry upon which the 4th, 5th & 6th dimensions of gravity, electricity and magnetism, is based...

(The unprecedented work of Truly yours, arranged and authenticated by the - previously unrecognized, 'unrelated' works of many others)

Based: in metric, functionally spatial, solid geometry:
although neither geometric point A, nor geometric 1-D Straight Line ( A--->B ), nor the geometric 2-D Plane generated by the right angle motion (B----->C ), occurs in or generates functional, metric (real, existential), space:
whereas, when Plane B-----> C moves at right angles to itself, C--D, it generates a three dimensional,. existentially manifest, functional - metric (measurable) space.

Respectfully reminding any challenge to the viability of my statement (which is not 'my statement' at all) - that when a geometric point moves, no matter which way: it moves at right angles to itself - commencing a series of right angle extrapolations, progressively generating dimensions - at right angles/ 90o out of what ever preceding dimension.

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. (Refer, the half dozen mistaken quotes from authorities, at the progression of this book.)
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..
Image-11.gif Picture by Txpoet 800 x 336 (135 kb) ShowHide Exif Data

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?'
_____________________________

REVIEW OF THE ABOVE (W'out illustrations)

At the locus of the ongoing, characteristically harlequin controversy:
Metric, functionally spatial, solid geometry:
begins with a non-existent Geometric Point A:
that is (also, furthermore) circular
(- morphologically: round - O - of shape... It does not exist, other than to convenience human innovated means by which locations in space may be precisely established - the geometric intersection of two or more - likewise non-existent - One Dimensional Straight Lines).

No matter which way Geometric Point A may move, at whatever speed, for whatever distance, it moves at right angles from it's self (A----> B) generating a (non existent) geometric Straight Line.

When non existent One Dimensional Straight Line (A ----> B), moves at right angles to itself, B---> C), it generates a (non-existent) Two Dimensional Plane.

In metric, solid, spatially functional geometry, when the 2-D plane moves at right angles to itself (C--->D), it generates existential, 3-D spatial reality, occupied or unoccupied by matter.

When any 3-Dimensionally manifest entity moves at right angles to itself - all three of it's established coordinates (D---->E) - it is 4- Dimensional.

Einstein proved everything is 4 Dimensional, and, that the 4th dimension, previously unknown and inherent within 3-Dimensionally manifest entities, is closely related to time & motion (are synonymous).

The afore-reviewed, qualified laws of geometry demand therefore, of all three dimensional entitites, a sequential, progressively ongoing (perforce moving) right angle motion of all three manifestly recognized dimensions:

...recently proven and 'acknowledged' as inherent to and with the three recognized dimensions of space, having to do with time and motion: causing any and all such 4-Dimensional entities to be, either constantly contracting - fulfilling it's assigned obligation be conform to Einstein's 4th D.

Or:

...to be constantly expanding, fulfilling Einstein's (allegedly 'acknowledged') 4-D space-time continuum.

Since test objects released near and above the earth's surface do not 'fall up', continuous contraction is ruled out as a functional 4-D vector.

Whereas, test objects released near and above the earth's surface do 'fall down', establishing - in the two possibilities of what this author calls 'the 4-D ultimatum' - that the 4-D quality of time and motion (space-time; space-time curvature) Einstein proved applicable to universal 3-D matter, is one of continuous enlargement, accelerating expansion.

Densities of 4-D accelerating entities remain uniform at any given moment, while continuously distributing themselves, omnidirectionally, in the law of the inverse square.

There is no infringement on the Law of Conservation of MassEnergy - it's the same amount of energy, distributed over an increasing volume of space, via the Law of the Inverse Square: squared.

All enlarging 4-D entities remain relatively (comparatively) the same size and density, at any given moment; while having been more dense and smaller in the Past - MOMENT 'A', relative to the Present - *MOMENT 'B', *always at the center of the representative geometry of expansion expressed in the convergence of two straight lines - V - the 'bottom' of which structure representing infinite Past in time and density (microcosmic infinity - 'strong nuclear binding forces')... The middle - what would be the cross bar of V if it was an upside down A - being the Present - 'eternal now', and the increasingly progressing forks of which represent 'the arrow of time', moving into the infinite Future.

While the two lines - 'the Arrow of Time' - moving upward and outward from their microcosmically inifinite confluence (which finitely 'ends', only in 3-Dimensions), proceeding as the same amount of energy, increasingly distributed over a greater amount of inverse squared structured macrocosomic space: squared.

End of review
___________________________________

An ever enlarging universe of space-time (4-dimensionally moving matter), Without beginning or ending.

Constituting: reinstatement of Bondi, Gold & Hoyle's presently abandoned Steady State Universe.

Reinstatement of Einstein's presently abandoned Unified Field Theory.

Many readers of this work have directly proclaimed or suggested it may result in non-violent world revolution and a metaphorical 'quantum leap' in generalized, mainstream human consciousness.

Evolved perceptions not only in all branches of Physical Science, but also of and within Philosophy, the Arts, Architecture and very significantly reassuring confirmation of the ability of the average person to comprehend - without mathematics - what was otherwise considered non-mathematically incomprehensible.

Adversaries are advised to take their argument to Martin Gardner's (exemplary) RELATIVITY FOR THE MILLION, and P. D. Ouspensky's Chapter On The 4th Dimension, in A NEW MODEL OF THE UNIVERSE, as well as every authority on General Relativity's 4th dimension of time & motion (material space-time. space-time curvature, the equivalence of inertial and gravitational mass, the <so called> 'universal rate of descent' - every applied example of the 4-D 'Super-Cube', on international record, in as many languages.

The 4th dimension of accelerating expansion of matter constitutes the 'impelling/'/attractive' effects of gravity on or near a major gravitational mass - the cause of which is actually the 'pushing' of the accelerating earth' upon all objects upon it's surface, and the earth's ever enlarging surface overtaking and striking apparently 'falling' objects; explaining the previously enigmatic fact that all objects, regardless of their mass value, when released from the same height, at the same time, invariably descend at the same rate of acceleration - 32' per" per", namely, because such 'falling' objects are not actually falling after all, but, rather, being overtaken and struck by the - unrecognized - ever accelerating expansion of the earth's surface.

Ergo:
Newton's gravity is Einstein's 4-D space-time continuum.

Whereas, the 5th & 6th Dimensions of Electricity & Magnetism invariably generated by, and constantly emitting from the 4th dimension of matter, re: Maxwell's discovery of the existence and spider-web shaped, inverse square law structure generated by matter: causing the impelling - quasi-magnetic -force of 'action-at-a-distance'...
(other than upon or near the surface of gravitational matter, where and when gravity is a pushing force; whereas, it is an electromagnetic pulling force at greater distances from it's material source)
...terrestrial, aquatic and atmospheric tidal effects, for example.

Gravity - the 4-D space-time continuum - at earlier, microcosmic moments, is the controversial, enigmatic and equivocationally 'identified': 'strong nuclear binding force' (within and beyond the bottom of the diagramatically proposed, afore described 'V'.

Gravity at larger, later moments (of chronologically sequential space-time - A, B, C acceleration from the convergent bottom 'ending') of the considered 'V' shape of expansion: structurally shaped as a so-called 'dimple' - in the rubber sheet (analogy) - of Riemannian Geometry, possibly generating what are presently and recently called (chrono-spatial) - space-time 'curls' and 'curlicues' - not unlike thin shavings of wood from a fine plane; constituting the same 'weaker' force, at a later, larger moment, relative to observers, who are always exactly in the middle of the V (apple or pizza pie slice) shaped representation of Past - smaller more dense space-time (re: 'black hole singularities, if they exist).

That is to say, the ('strong force' influenced) microcosms are as infinitely endless as the ('weak force' influenced) macrocosms.

If Dear Reader finds the points being made here, redundant, this record may only beg pardon, for the characteristically called upon 'adjustment' to these all time prevelant, but previously unrecognized, disconnected composites of reality at large.

There is no 'ending' of space at the small end of the diagrammatic V, representing the ever enlarging arrow of 4-D space-time.

Where, the V shape formed by two lines, intersect with each other at the 'beginning', represent the '3-Dimensional end' of space-time, whereas, in a 4-D universe - such as that within which we are proven to live and be part of, whether we recognize it or not - smallness (Moment A) - the microcosms - is just as endless and dense, as infinite largeness (Moment C); with 'us' always directly in the (Moment B) center of the eternally V shaped diagram of space-time.

(Likewise represented by the characteristic shape of Riemannian Geometry, where the transient structure approximately curves back toward itself - refer the north and south polarities of a given electron, planet or sun, where the electromagnetic field is generated by and projected from the 'upper' - north - pole, to curve back around the physical structure - electron, planet, sun or star - and return to and within the south pole of such electromagnetic field-generating elements, all the while growing ever larger, squared, ad infinitum:
... wherein such a bi-polar system may sustain, maintain and enlarge itself: the larger the faster the faster the larger: etceteras)

Orbiting satellites, natural and artificial, do not actually describe circular or elliptical orbits O 0, but rather, spirals - @ .

Citing the example of a person running around an apparently 3-D circular track, likewise actually describing a 4-D - @ - spiral with each completion of whatever round or ecliptic track being jogged upon or raced over...

The planet Mercury is astrophysically observed to 'inexplicably' lose 46 seconds of arc per century. Whereas, this 'unexplainable' loss is probably due to the exclusion of calculating it's orbit to be 4 - Diimensionally spiral @ shaped, instead of 3- dimensionally circular or elliptical.

All the other planets likewise, 'inexplicably' lose lesser but measurable amounts of seconds of arc per century; apparently for the same reason...

Apparently, with regard to Moments *A, *B and *C, constituting the *'beginning', *'middle' and *'end' of conventionally perceived, expanding 3-D space: in Einstein's 4-D universe, the 'ending' convergence of space at the bottom of the proposed, diagrammatic V, is in fact without end, the microcosms of 4-D space being just as endless as the macrocosms - the ever distancing forks progressing 'upward' (re: 'the arrow of time') at the top of the V, with the 'eternal present' always between the top and the bottom of the diagramatically proposed - pizza or apple pie slice-shaped - V.

THE EXPLANATION FOR 'TIME DILATION' and NON-ABSOLUTE TIME.

In such a universally prevailing 4-D dynamic, there is no 'beginning' of space, and, there is no 'ending' of space.

The unification of Newton's Classical Mechanical 'space and time', in to Einstein's realization of 'space-time, resulting from the functional inseparability of the only recently recognized, ominidirectionally moving 4th dimension (from the center of any point mass, or collective systems of mass points), prevailing in the 3 recognized, apparently 'static and non-expanding' - uniform expansion of what is now recognizable as '4-D space-time', and the reason for that term and its conceptual unification of what was formerly called, 'space and time'; as though they were seperable and independent considerations, which they are not.

Newton contemplated a 4-D space and time continuum, but his consideration was one of a linear, non expanding line of time (the interval between two or more events in space), within which space (matter and the interval between material points) occurred in a 'static' continuum of non-expansion...

That is, Newton realized, wrote and spoke of a continuum of time, past, present and future, but, perceived that the value of past, present and future time was comparatively the same, which, in a 4-Dimensionally acclerating physical universe, it is not.

(Incidentally and very notably, Galileo and Kepler inspired Newton to contemplate the incomplete - non-expanding, linearly restricted - 4-D space time continuum, as previously described, which eventually evolved into Einstein's advanced modifications of Newton's unarguably magnanimous work.)

THE 4-D, PHYSICALLY & OMNIDIRECTIONALLY ACCELERATING UNIVERSAL EXPANSION OF SPACE-TIME, consequences, continued:

Refer: The presently abandoned, now reinstated, Steady State Universe, and, Einstein's likewise abandoned, now reinstated Unified Field (Cosmological Constant) Theory (the cardinal objective of which is to find electromagnetism and gravity, two apparently unrelated 'forces', actually having the same causal identity).

THE CAUSE OF EINSTEIN'S NON-ABSOLUTE SPACE (SPACE-TIME):
In Einstein's 4-D space-time universe, yesterday's square mile, is comparatively much smaller than today's. Tomorrow's square mile is exponentially larger.

Yesterday's 60 mph, is comparatively much slower than today's. Tomorrow's 60 mph is exponentially faster than today's.

Yesterday's (24,000 mile circumferenced) earth was comparatively much smaller, yesterday's hour was comparatively much shorter.

WHY THE VELOCITY OF LIGHT (Celertitas C) IS CONSTANT, REGARDLESS OF THE VELOCITY OF IT'S SOURCE:

In Einstein's 4-D Space-Time Universe, yesterday's velocity of light, is comparatively slower than today's. Tomorrows velocity of light is exponentially faster than today's.

This is why the velocity of light is constant, regardless of the velocity of it's source. The (accelerating) inconstancy of light's velocity is - at any given moment - what sustains its apparent constancy.

(For further details and information on these issues, please honor this record with a study of the condensed content and import of the theoretical physics file, on the multi-topic menu at http://forums.delphiforums.com/EinsteinGroupie )

Regards

- RP