very simple to join
all you have to understand is
Imagine all the optical data that exists at any observation point in three-dimensional planar space. Consider that observation can be made from any perspective at any one singular point of observation. That is, optical information flows onto that point from 360 degrees of 3-d space. For now, to make it easier to visualize, let’s assume that optical information comes in only from a constricted angular viewpoint, say, 180 degrees. Observing the 180 degrees of 3-d planar space as colors (optical information), now set this spectrum of observation on a 2-dimensional plane. Observation is made from this central point (in the case of 180 degrees) as a definite vector whose angular direction sets the control point of symmetry, while the planar dimension through which this vector of observation is made looses all value when we convert all 3-dimensional optical data onto a 2-dimensional plane. Although the set value is meaningless, lets say for the point of conceptualization that the angular vector of observation always describes the ‘z’ dimension. In true 3-dimensional space, absent of gravity, there is no meaning in applying terms such as “up”, ”down”; ”left”, or “right”. Thus, as we cast this moment of observation onto our 2-dimensional plane; definite direction in terms of the ‘z’ direction looses all true meaning. Consider again that the vector of observation forms the central point of geometric symmetry in our 2-dimensional plane, such as the center point of the circle above. We now reapply the 3rd dimension ‘z’.
While infinite smallness is true, there is some definite “bottoming out” of space for that spatial dimension-system. This “bottoming out” is set by that dimensional realm’s time frequency, and is indirectly described in our dimension by Planck’s constant [?]. Thus, we use the term “relative infinite”.
As in the circle above, consider a vertex point of x and y lines to be junction points where the z-dimension is formed. The empty space in between these lines form definite 2-dimensional space. The angle at which these lines intersect the z-junction remains constant in terms of x & y. However, when we reapply the 3rd dimension to our z-dimensional plane, we can change the value of these z-junction to any arbitrary value, though all of these z-junction points must remain relative to themselves in correlation with this arbitrary change. Any arbitrarily assigned value is true within 4th dimensional space – granted that all points within the system adhere to each other in their correlative, inter-related change of values. This forms the very basis by which 4th dimensional planar space is formed. For every set value of 3rd dimensional, there is relative infinite 4th dimensional space. For 5th dimensional spaces, every z-junction value may be variable, at independent, totally arbitrary values. This is contrary to 4th dimensional spaces (to reiterate), where all z-junction values are intrinsically inter-related to one another, and thus cannot behave independently of one another.
The 4th dimension is time dependant. The 5th dimension is not (at least, not in any linear manner in which we may understand “time” in this, the 3rd dimension).
Subatomic particles are comprised of smaller particles, which in turn are comprised of smaller particles, to infinity. However, (and that’s a big one!), this infinite smallness is relative, bound to a “bottoming out” value that is governed by dimensional limit in potential energy [the “speed of light”, or the absolute limit to the frequency of electromagnetic energy found within that system], which sets the frequency of time. These absolute values in the upper limits are directly related to setting the absolute values in the lower limits. At any given dimensional state, there exist absolutes in describing that energy state’s upper & lower limits. That is not to say that values outside those boundaries do not exist; they simply exist/are at different dimensional energy rates. The values that determine these constant values of dimensional energy phase separation – solid membranes of quantum & cosmic energy division – are rigid and definite. These values are determined by the cyclic number base and the periods of celestial time intervals determined using this number base in its application to cosmological observation – or, tentatively, subatomic particle orbital pathways and the time-dependant nature of quantum interactions.
In the 4th dimension, at any given point in time, T, any given point within a set 3rd dimensional space may rationally become any other point, relative to itself. So, in a sphere, the outermost point may become the inner-most point, for every value [x,y,z]. The inverse of this is also true. The addition of a 4th dimension to a 3rd dimensional volume allows for the spatial inversion of that field.
4th Dimensional “Volume”
In order to get the 4th dimensional “volume”, you must exclusively multiply just the radius value, r, by 6 [which doesn’t really exist in the traditional sense] :
Bear in mind that the above outlay is a 2-dimensional representation of 4th dimensional space; that these inversion reflections take place in volumetric space. Notice that ‘K’ is the diameter of the original 3-dimensional sphere.
While the above graph may help to visualize the effective “space” that is gained by adding another dimension to a 3-d object, bear in mind that the actual volumetric space remains absolutely constant. Rather than physically expanding in volumetric dimensional ‘girth’, t he 3-dimensional space remains constant, while with the addition of the 4th-dimension, objects are now able to freely move in manners that were otherwise wholly impossible. Notice that every dotted circle (and the infinity of others which lay between each one) represents the 4th dimensional movement – a reflected or partial inversion – over some z-junction point. All other points in that system remain reliant upon each other, with every z-junction point that is crossed. With the addition of yet anther dimension to the 4th, there exists quite literally an infinite amount of 3-dimensional space – volumetric or otherwise. In the 5th dimension, z-junction points may reflect off each other, independent of original 3-dimensional, time-dependant form. Thus a z-junction point (or, one of the dotted circles) may reflect off another, and that, off yet another; onto infinity [and beyond!].
Z-junction points are able to reflect off themselves in any direction in the 5th dimension, in manners that defy – and pretty much completely obliterate – any measure of common sense. The 5th dimension allows for a potentially infinite amount of vectors to project in infinite directions, all reflecting time-independent permutations of one definite 3-dimensional planar space. As far as solving for volume goes, in 5th dimensional space volume is solved by:
V = whatever the hell you want it to be!
Rather, we may be able to calculate some value that may vaguely resemble a “volume” by determining how much space-time our 5th dimensional cookie monster may have consumed. In the 5th dimension, our 3rd dimensional linear-time serves as an abstract form of planar “space”. There surely exists some manner in which to precisely calculate the “volume” of a 5h dimensional object – first, by calculating the amount of space-time it “consumes”, and then, by calculating the volumetric equivalency of this initially derived value. Either way, any such “volumetric” calculation would serve as more of a rational equivalency; a means by which to compare the ratio of ‘volumetric potential’ between systems of different dimensional states. I think this could be done using complex matrices[?]…
For flat space-time you basically have the metric (a metric bascially shows how far an object is from a choosen origin):
ds^2 = x^2 + y^2 + z^2 - (ct)^2
As you would expect there are only four variables used to describe the positon of an object: x, y, z and ct.
for a curved spacetime you use a different metric, for example the Schwarzchild metric describes the spacetime around a spherically symmetric object like a star, planet, black hole, etc:
ds^2 = (1- \frac{2GM}{c^2r})d(ct)^2 - \frac{1}{1 - \frac{2GM}{c^2r}}dr^2 - r^2(d\theta^2 + \sin^2{\theta}d\phi^2)
This uses polar co-ordinates, so the variables used to describe the postion of an object are r, \theta, \phi and ct. So you can see there are still only four dimensions in this equation even though spacetime here is curved
the important thing is that the curvature of spacetime doesn't represent an extra degree of freedom for objects in spacetime.
Originally posted by hh?
very simple to joinall you have to understand is
Imagine all the optical data that exists at any observation point in three-dimensional planar space. Consider that observation can be made from any perspective at any one singular point of observation. That is, optical information flows onto that point from 360 degrees of 3-d space. For now, to make it easier to visualize, let’s assume that optical information comes in only from a constricted angular viewpoint, say, 180 degrees. Observing the 180 degrees of 3-d planar space as colors (optical information), now set this spectrum of observation on a 2-dimensional plane. Observation is made from this central point (in the case of 180 degrees) as a definite vector whose angular direction sets the control point of symmetry, while the planar dimension through which this vector of observation is made looses all value when we convert all 3-dimensional optical data onto a 2-dimensional plane. Although the set value is meaningless, lets say for the point of conceptualization that the angular vector of observation always describes the ‘z’ dimension. In true 3-dimensional space, absent of gravity, there is no meaning in applying terms such as “up”, ”down”; ”left”, or “right”. Thus, as we cast this moment of observation onto our 2-dimensional plane; definite direction in terms of the ‘z’ direction looses all true meaning. Consider again that the vector of observation forms the central point of geometric symmetry in our 2-dimensional plane, such as the center point of the circle above. We now reapply the 3rd dimension ‘z’.
While infinite smallness is true, there is some definite “bottoming out” of space for that spatial dimension-system. This “bottoming out” is set by that dimensional realm’s time frequency, and is indirectly described in our dimension by Planck’s constant [?]. Thus, we use the term “relative infinite”.
As in the circle above, consider a vertex point of x and y lines to be junction points where the z-dimension is formed. The empty space in between these lines form definite 2-dimensional space. The angle at which these lines intersect the z-junction remains constant in terms of x & y. However, when we reapply the 3rd dimension to our z-dimensional plane, we can change the value of these z-junction to any arbitrary value, though all of these z-junction points must remain relative to themselves in correlation with this arbitrary change. Any arbitrarily assigned value is true within 4th dimensional space – granted that all points within the system adhere to each other in their correlative, inter-related change of values. This forms the very basis by which 4th dimensional planar space is formed. For every set value of 3rd dimensional, there is relative infinite 4th dimensional space. For 5th dimensional spaces, every z-junction value may be variable, at independent, totally arbitrary values. This is contrary to 4th dimensional spaces (to reiterate), where all z-junction values are intrinsically inter-related to one another, and thus cannot behave independently of one another.
The 4th dimension is time dependant. The 5th dimension is not (at least, not in any linear manner in which we may understand “time” in this, the 3rd dimension).
Subatomic particles are comprised of smaller particles, which in turn are comprised of smaller particles, to infinity. However, (and that’s a big one!), this infinite smallness is relative, bound to a “bottoming out” value that is governed by dimensional limit in potential energy [the “speed of light”, or the absolute limit to the frequency of electromagnetic energy found within that system], which sets the frequency of time. These absolute values in the upper limits are directly related to setting the absolute values in the lower limits. At any given dimensional state, there exist absolutes in describing that energy state’s upper & lower limits. That is not to say that values outside those boundaries do not exist; they simply exist/are at different dimensional energy rates. The values that determine these constant values of dimensional energy phase separation – solid membranes of quantum & cosmic energy division – are rigid and definite. These values are determined by the cyclic number base and the periods of celestial time intervals determined using this number base in its application to cosmological observation – or, tentatively, subatomic particle orbital pathways and the time-dependant nature of quantum interactions.
In the 4th dimension, at any given point in time, T, any given point within a set 3rd dimensional space may rationally become any other point, relative to itself. So, in a sphere, the outermost point may become the inner-most point, for every value [x,y,z]. The inverse of this is also true. The addition of a 4th dimension to a 3rd dimensional volume allows for the spatial inversion of that field.
4th Dimensional “Volume”
In order to get the 4th dimensional “volume”, you must exclusively multiply just the radius value, r, by 6 [which doesn’t really exist in the traditional sense] :
Bear in mind that the above outlay is a 2-dimensional representation of 4th dimensional space; that these inversion reflections take place in volumetric space. Notice that ‘K’ is the diameter of the original 3-dimensional sphere.
While the above graph may help to visualize the effective “space” that is gained by adding another dimension to a 3-d object, bear in mind that the actual volumetric space remains absolutely constant. Rather than physically expanding in volumetric dimensional ‘girth’, t he 3-dimensional space remains constant, while with the addition of the 4th-dimension, objects are now able to freely move in manners that were otherwise wholly impossible. Notice that every dotted circle (and the infinity of others which lay between each one) represents the 4th dimensional movement – a reflected or partial inversion – over some z-junction point. All other points in that system remain reliant upon each other, with every z-junction point that is crossed. With the addition of yet anther dimension to the 4th, there exists quite literally an infinite amount of 3-dimensional space – volumetric or otherwise. In the 5th dimension, z-junction points may reflect off each other, independent of original 3-dimensional, time-dependant form. Thus a z-junction point (or, one of the dotted circles) may reflect off another, and that, off yet another; onto infinity [and beyond!].
Z-junction points are able to reflect off themselves in any direction in the 5th dimension, in manners that defy – and pretty much completely obliterate – any measure of common sense. The 5th dimension allows for a potentially infinite amount of vectors to project in infinite directions, all reflecting time-independent permutations of one definite 3-dimensional planar space. As far as solving for volume goes, in 5th dimensional space volume is solved by:
V = whatever the hell you want it to be!
Rather, we may be able to calculate some value that may vaguely resemble a “volume” by determining how much space-time our 5th dimensional cookie monster may have consumed. In the 5th dimension, our 3rd dimensional linear-time serves as an abstract form of planar “space”. There surely exists some manner in which to precisely calculate the “volume” of a 5h dimensional object – first, by calculating the amount of space-time it “consumes”, and then, by calculating the volumetric equivalency of this initially derived value. Either way, any such “volumetric” calculation would serve as more of a rational equivalency; a means by which to compare the ratio of ‘volumetric potential’ between systems of different dimensional states. I think this could be done using complex matrices[?]…
For flat space-time you basically have the metric (a metric bascially shows how far an object is from a choosen origin):ds^2 = x^2 + y^2 + z^2 - (ct)^2
As you would expect there are only four variables used to describe the positon of an object: x, y, z and ct.
for a curved spacetime you use a different metric, for example the Schwarzchild metric describes the spacetime around a spherically symmetric object like a star, planet, black hole, etc:
ds^2 = (1- \frac{2GM}{c^2r})d(ct)^2 - \frac{1}{1 - \frac{2GM}{c^2r}}dr^2 - r^2(d\theta^2 + \sin^2{\theta}d\phi^2)
This uses polar co-ordinates, so the variables used to describe the postion of an object are r, \theta, \phi and ct. So you can see there are still only four dimensions in this equation even though spacetime here is curved
the important thing is that the curvature of spacetime doesn't represent an extra degree of freedom for objects in spacetime.
shock I think I really truly found religion now notworthy