art theory 101~ The LUFE Matrix: Infinite Dimensions 

The LUFE Matrix: Infinite Dimensions
(A room with a view within a room with a view within a room with a view)
A new, speculative journey to account for the multiple dimensions that have informed The LUFE Matrix since its introduction in 1985.
Copyright © 2004, Reginald Brooks. All rights reserved
NOTE: The Frequently Asked Questions (FAQ) format presented below presupposes that the reader has prepared her/himself by reviewing the earlier works upon which this work is based. Including:
"Naughty Physics (a.k.a. The LUFE Matrix )"
"The LUFE Matrix Supplement: Examples and Proofs"
"The LUFE Matrix Supplement: References"
I. General: the short answer (click for elaboration)
II. General: elaboration (click # to return to short answer above)
III. Details
Picture all the possible rooms with a view that are smaller and larger than the room you are occupying. Each of these possible rooms has its own 3D space + 1D time orientation, randomly pointing in various directions. Now those other rooms whose orientation, by happenstance, lines up with...and therefore resonates with...your room's orientation, form a consistent and seemingly unique view of the entire universe...from the very small to the very large...with just 1 set of 3D space + 1D time dimensions. Still, all the other rooms with a view with differing orientations, nevertheless, exist with full vigor...only you can not track them so easily.
An example by analogy: You have a very large panorama of flat, disc mirrors...from very small to very large...randomly orientated in every possible direction in dark space. You turn on a single, but powerful, light source and observe what you see.
Discounting secondary reflections, every disc mirror...and only those disc mirrors...that reflect back your light appear to exist. The vast majority of disc mirrors does not reflect directly back to you and thus do not appear to exist. Your observations and measurements would be limited to those that do.
The other disc mirrors still exist. If we say that the reflected light is the same as our sense of dimensions...3D space + 1D time...the we appear to have confirmed our own personal experience that there only exists 3D space + 1D time dimensions, and, they are no different from our own...when in fact, we have only confirmed the tyranny of a single, biased view. Our room with a view is not absolute, but relative.
Yes, of course. Each light source would reveal and resonate with a new grouping of mirror reflections...confirming 3D space + 1D time dimensions from each of their perspectives.
Yes.
Because they are there and they explain the part of the universe that we can not see or experience directly.
Both we as sentient beings, and the tools that we use to describe and measure our universe, are contained within a given room with a view perspective. All rooms with a view are constructed of and can only "see" 3D space + 1D time dimensions and therefore they will all agree that there are only 3D space + 1D time dimensions. Einstein showed us that under conditions of very high velocity and/or very high mass...in other words conditions of very high energy...that our initial perceptions (and conceptions) of the world perspective as being composed of only three absolute dimensions of space (3D space) were in error. 3D space was relative to the 1D of time...and the interrelationship of space to time as spacetime was born.
The "Twins Paradox"...in which one twin journeys out to a distant locale and back traveling at nearly lightspeed only to return home to find his/her twin, and everything else, to have aged in advance...illustrates the slowing of the clock (time dilation) with increased velocity relative to the home reference system.
Within The LUFE Matrix, time (or frequency) is treated as a dimension interactively with, but separate from, space. Graphically, it is placed perpendicular to space.
Within the The LUFE Matrix, time and space are not measured or quantified in the usual sense...but time and space are quantified as to the number of dimensions of each interacting with their perpendicular "other" dimension(s) informing the SpaceTime Interactional Dimension (STID) areas.
As mentioned earlier, The LUFE Matrix treats each change in time set, or subset(s), as a new time dimension. A set being a Space Or Time Area (SOTA) or a SpaceTime Interaction Dimension (STID) area. A set becomes a subset when it is embedded in a larger set. Each set has some number of time dimensions from zero on up (T_{0}...T_{n}). Adding another time dimension to a set embeds that original set into a larger set and makes it a subset that now is presented at the new frequency of time (cycles/second) of the larger set. Time dimensions grow as new subsets of frequency are formed. Thus acceleration, which is a change in velocity over time (m/s^{2}), actually invokes a second dimension of time as the first dimension of time is embedded in the subset of velocity (m/s).
Within The LUFE Matrix, the space dimensions are perpendicular to the time dimensions. As described in more detail below, they are added in series as one proceeds from 1D as a line (xaxis), adding a second space dimension invokes the yaxis and a 2D area is formed. Adding yet another 1D space dimension along the zaxis sums up to a 3D space and forms "a room with a view" spatial set alluded to before. The cycle of 1D, 1D + 1D =2D, and 1D + 1D + 1D = 3D, repeats for each room with a view set, only the origin of the newer room is always the full 3D subset of the smaller room with a view set. In this way each room with a view maintains its distinct 3D space dimensional view.
And now, as viewed within The LUFE Matrix, we see that multiple time dimensions are contained within any given room with a view...so that all previous references to a room with a view having 3D space + 1D time dimensions should have the "1" of 1D replaced with "M" for MultiDimensions...and so should be designated as 3D space + MD time dimensions hereafter. (Yes Dr.Time can fix your time.)
First the latter. Yes, the biased view towards seeing, and only seeing, 3D space + time dimension is being pointed out and emphasized precisely because it is also the limiting factor to our experience of the other dimensions. We are locked in just like the light source in #1. above.
Earlier it was alluded to how The LUFE Matrix sees time. Conceptionally, we have to deconstruct time into the various time dimensions that composed the STID area that we are concerned with. In the past the various time dimensions were all rolled into one relativitybased time dimension. Thus the new designation: MD time.
As to the extra dimensions of space as one generates larger and larger rooms with a view...many of which, just like the flat disc mirrors above, seem only to validate a single set of 3D space + 1D time dimensions...there are three important concepts to keep in mind.
First, spatial extension creates time and spatial contraction dilates (slows) time.
Second, all ST pulses into and out of existence...that is all that is spatial extended, at the level of ST interaction, is created and extinguished, created and extinguished, created and extinguished, as a pulse generation...a cyclic frequency of spatial extension per unit of time...over and over. It is the basis of all matter and fields formed (see the DarkDarkLight reference above).
Third, and this is the hook that reveals the source of the additional spatial dimensions as a series of telescoping rooms with a view unfolds, when the 3D space dimensions of a smaller subset room with a view become embedded, and thus become that subset origin of a larger room with a view set, that origin becomes the point that spatially extends along the x, y, or zaxis of the new, larger room with a view, which is itself undergoing a pulse generation to form its x, y, or zaxial extension. Thus while the 3D space dimensions are pulse generating in their own smaller subset room with a view, at the same time, they are forming a new space dimension(s) in the larger set room.
In the simplest case, the xaxis of the subset room matches the orientation of the xaxis of the larger set room...and like the flat disc mirror analogy, it appears all is well in the 3D, and only 3D, world view. In any number of other orientations, however, the axes do not line up and the other dimensions are not revealed.
If you were in the smaller subset room you would not see this 4th dimension that your very own movement is creating. If you are in the larger room...well first of all you will have to wait until two more dimensions have been added to actually exist and function in that room with a view. If you were in still a larger room...now having a subset room with a view embedded in a subset room with a view...you still will only be able to perceive and measure those with similar orientations throughout all three rooms with a view which functions in, and thereby limited to, 3D space + MD time dimensions. It is a real catch22 situation. You have to conceptionally see the extra dimensions to account for them.
The LUFE Matrix is a language, and thus a tool, for the conceptual visualization of multiple dimensions of space and time interactions that form...inform...our universe.
It shows how the mathematics of physics, when broken down to the basics of space and time dimensions, can be simplified into: a.) The addition (exponential multiplication) of dimensions; b.) The subtraction (exponential division) of dimensions; and, c.) Their net interactional ST combination.
Each space dimension is in and of itself, identical to every other space dimension. On The LUFE Matrixthey are arranged sequentially in columns, starting from the origin and working outwards, increasing the dimensional count as 1, 1+1, 1+1+1... and designated S_{I}, S_{II}, S_{III}...and so on. At any occasion that you increase or decrease the space dimension count (by exponential multiplication or division), you simply move left or right across the graphic row. This is possible because the fundamental conception of the space dimension is similar whether you are adding or subtracting one or more space dimensions.
On The LUFE Matrix: Infinite Dimensions Chart (ID chart, for short), each space dimension is symbolically represented as a line (solid to segmented), along the x, y or zaxis, between two points from an origin to a surface of a circle/sphere. Each circle/sphere represents a room with a view. Yes, that means that there are always three dimensions of space within each of the telescoping rooms with a view...only the origin of the next larger room with a view always consists of the circle/sphere of the previous room. Diagrammatically, this is presented as a circle/sphere within a circle/sphere within a circle/sphere.
And in any given room with a view, a line along the xaxis from its origin to the edge of the circle represents 1 dimension (1D). Note that it is still 1D no matter what axis is taken (The 360 degree rotation of that radian line establishes all possible values of 1D and effective establishes the xplane as the reference to which all other axial planes refer.).
2D is diagrammatically represented as a second line, along the yaxis and perpendicular to the xaxis, from origin to edge. Note that 2D only requires that the second line is perpendicular to the first, not what axis is selected for presentation. Basically, 2D represents area... encompassing all forms of the length x width (or height) theme.
And of course, 3D is presented by a third line from the origin out to the edge or surface of that circle...now becoming a sphere. It is also perpendicular to both of the previous two lines (dimensions).
The 4D, 5D and 6D repeat this pattern, only now in a larger room with a view. And now the earlier 3D sphere becomes the new origin to a much larger circle/sphere. Again, the particular path the lines take in forming this larger dimensional room is independent of the previous room's axial choices...shown here for diagrammatical ease to always be along the common X, y and Zaxis convention.
The 7D, 8D and 9D repeat this pattern, only now in an even larger room with a view. And now the second, earlier 3D sphere becomes the new origin to a much larger circle/sphere. The dimensions are embedded...a room with a view within a room with a view within a room with view...and so on.
The first room with a view may be at the level of quarks and leptons, the second (or more) within the atomic orbitals, the third within molecular arrangements...and so on to galactic clusters out to the original light cone of the universe. Whatever rotates may indeed generate its own room with a view only to be dimensionally linked to other rooms with a view when a common point of origin is established. Each room establishes its own absolute 3D, yet each of the 3 dimensions forming its 3D is relative, not absolute, when accounting for dimensions in either a smaller room with a view contained within, or a larger room outward. Remember that spacetime pulses...as do the rooms with a view.
As you move from left to right across any row in the ID chart, you will see that the space dimensions always follow the same pattern...1 line=1D, 2 lines=2D and 3 lines=3D for each room with a view (circle/sphere). This corresponds on The LUFE Matrix to the adding (multiplying) of space dimensions, or conversely, when going from right to left, the subtraction (division) of space dimensions.
Much of what has been said above of the space dimensions applies here...only the time dimensions are arranged in rows perpendicular to the space dimensions, and, diagrammatically, the time dimensions are represented as the number of segments within each of the line segments of the space dimensions.
Each time dimension is, in and of itself, identical to every other time dimension. On The LUFE Matrixthey are arranged sequentially in rows, starting from the origin and working downwards, increasing the dimensional count as 1/1, 1/(1+1), 1/(1+1+1)... and designated 1/T_{I}, 1/T_{II}, 1/T_{III}...and so on. We are on the S/T quadrant in the matrix. Here we have space/time dimensions presented as this presently accounts for most of the activity.
On The LUFE Matrix: Infinite Dimensions Chart (ID chart, for short), each time dimension is symbolically represented as a line (solid to segmented), along the x, y or zaxis, between two points from an origin to a surface of a circle/sphere. Each circle/sphere represents a room with a view. Yes, that means that there are always three dimensions of space within each of the telescoping rooms with a view...only the origin of the next larger room with a view always consists of the circle/sphere of the previous room. Diagrammatically, this is presented as a circle/sphere within a circle/sphere within a circle/sphere.
Following the symbolic representation of space dimensions above, the time dimensions within any space dimension line(s) is simply represented as the number of segments forming that line(s). A solid line=1D, a 2segment line=2D and a 3segment line=3D...and so on as you progress down any given column.
The next three questions are crucial...so hang on!
On The LUFE Matrix not much happens because almost all of the actual physics occurs down and to either side of the diagonal from the origin to the power STID where there is symmetry or close to symmetry in space and time dimension interactions. Nevertheless, on the extreme borders we have a theoretical area of high space and low time dimensions along the top upper 1D time dimension row, and, a low space and high time dimension scenario down the far left 1D space dimension column. On the ID chart we can still represent them as before...as a series of increasing rooms with a view for the space dimensions and as increasing line segmentation in the time dimensions. Until actual meaningful physical parameters are found to occupy these farout ST dimensions we will not presently overconcern ourselves with their asymmetry. On the other hand, they do force the next question for clarity.
While it is easy enough to assign the time dimensions as a group to the space dimensions of a given room with a view, it becomes much more difficult to assign a particular time dimension to a particular x, y or zaxial space extension...and perhaps resistance is futile.
Within a given room with a view set, we may have 1, 2, 3 or more time dimensions interacting with the 3D space dimensions. It may be that each x, y and zspatial axis is equally segmented (divided by the number of time dimensions present) or not. It may be, though it seems highly unlikely, that one axis has one time dimension, another axis another time dimension and a third axis with a third time dimension.
Because of the interchangeability of each space or each time dimension, the graphical presentation of the second scenario above would look the same...a single unsegmented line for each axial dimension and its associated, but different, time dimension present.
Other possibilities would look different. A scenario in which the pulse generation of the 3D space dimension occurred at different changing rates of time might have one axis as a solid line, another as a 2segmented line and the third as a 3segmented line. This possibility is not likely within a given room with a view set, but is certainly possible when the rooms become embedded as subsets to larger room sets. The pulse generation frequency (and spatial orientation) of the smaller subset may well be different form that of the larger room with a view set. Only time will tell.
Actually, neither. A vector represents a parameter that has both magnitude (amount) and direction. That is, its payload of magnitude is only delivered along a certain direction...a direction that can be manipulated, for example, like velocity.
Scalars are parameters with magnitude alone...no directional orientation or requirements...like temperature.
The space (and time) dimensions have no magnitude values on The LUFE Matrix, other than the net number of dimensions of each being considered. They also inherently have no absolute direction, only a relative direction to the other dimensions, but never relevant to the actual STID parameters they graphically represent. Therefore, they are not vectors or scalars, but we like to refer to them as virtual pointers to aid in the graphical and conceptual visualization of their activity.
On The LUFE Matrix proper, each space dimension is represented side by side in columns as S_{I}, S_{II}, S_{III},...and so on. When a space dimension is activated, it acts like a laser light that is turned on and points vertically down its column. When a time dimension, perpendicularly arranged as rows, is activated, its laser light is activated and its entire horizontal row is lit up. Wherever a space and a time light interact on the matrix by crossing over each other's lightpath, they form a defining STID area. When divided out, the subsequent subtraction of the space and/or time dimensional light is extinguished and the STID area is, consequently, reduced to a smaller area and a new identity. In this sense the graphical direction of the pointers aids in presenting the language of ST dimensions.
On The LUFE Matrix: Infinite Dimensions Chart, the same idea is present, only the graphic is different. Here the emphasis is on the overtly diagrammatic display of each space and/or time dimension as a symbol. Here the space virtual pointer dimensions are drawn out to emphasize the 3D spatial axis idea being repeated as a scaled up clone of itself as the number of dimensions increases. The time virtual pointer dimensions are simply represented as segmentation of the space dimension lines. Again, these are pointers, not vectors.
The LUFE Matrix: Infinite Dimensions Chart
(click for slide show)
© 2004, Reginald Brooks. All rights reserved.
This paper and all its contents © 2004, Reginald Brooks. All rights reserved. Permission is hereby granted for single copies to be made for personal, noncommercial use for students and teachers of schools, colleges and universities provided that: either the entire paper, including figures and tables, is kept intact; or, any extracts of the text, or figures or tables (in part or whole), be properly and visibly cited as to authorship and source.
Copyright©2004 Reginald Brooks, BROOKS DESIGN. All Rights Reserved.
The LUFE Matrix Operational Rules (See the graphic below.)This is part of The LUFE Matrix: IntroductionGeometryLayoutRules of engagement extracted from the original paper for easy reference here. It is not the full introduction, just a handy reference. In some cases it may be preferable to open the original paper from the links at the top or bottom of this page in a separate window. (Just click on the links and it will do it for you.)
The LUFE Matrix Graphic Dynamics
Digital version for the computer: graysinactive , coloractive
Axis
In the following graphics, hover your cursor over the text and the graphic will change to reflect that text. (You must allow the computer to load the images for the first time, thereafter it will respond more quickly.)
We start with the horizontal xaxis, graded in grays, to represent the pure "space" axis. Then we add the vertical yaxis for the "time" axis. Although we will in general keep all inactive areas in grayscale, we do find the "space", "time" axes in simple blues and greens so much more appealing.
In #4, we add the grid and in #5 the simple ST text. Note the origin, 0, is in red. This matrix graphic represents the null, net 0 state when there are no net SOTA or STID areas.
Geometry: Layout of The LUFE Matrix Axes
~hover your cursor over the text on the right for images~ ~click image for full matrix blowup~ ~if needed, click and hold while you scroll~ 



Quadrants
Quadrants are where most of the action is. Here is where a horizontal space dimension perpendicularly interacts, by crossing over, a vertical time dimension forming a STID area.
Graphics #610 take us on a tour of each of the separate quadrants ending with all four quadrants lit up in color.
Geometry: Layout of The LUFE Matrix Quadrants
~hover your cursor over the text on the right for images~ ~click image for full matrix blowup~ ~if needed, click and hold while you scroll~ 



Working Color Template
To make the color work for us a little better, we tried adding the bluegreen axes in #11, yet found it more workable to brake the quadrants into more discreet colors, as in #12. The text was added in #13 to complete our working color template.
Geometry: Layout of The LUFE Matrix Working Color Template
~hover your cursor over the text on the right for images~ ~click image for full matrix blowup~ ~if needed, click and hold while you scroll~ 



NEXT: On to Page 6a GeometryLayoutRules
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Page 5a DarkDarkLight: Dark Matter = Dark Energy
Page 5b The History of the Universe in Scalar Graphics
Page 5c The History of the Universe_update: The Big Void
Page 6a Geometry Layout
Page 6b Geometry Space Or Time Area (SOTA)
Page 6c Geometry SpaceTime Interactional Dimensions(STID)
Page 6d Distillation of SI units into ST dimensions
Page 6e Distillation of SI quantities into ST dimensions
Page 7 The LUFE Matrix Supplement: Examples and Proofs: IntroductionLayout & Rules
Page 7c The LUFE Matrix Supplement: References
Page 8a The LUFE Matrix: Infinite Dimensions
Page 9 The LUFE Matrix:E=mc^{2}
Page 10 Quantum Gravity ...by the book
Page 11Conservation of SpaceTime
Page 12LUFE: The Layman's Unified Field Expose`